AN EXPERIMENTAL AND THEORETICAL ANALYSIS OF COLD WORKING AND
RIVETING IN FIBER METAL LAMINATE MATERIALS
By
David S. Backman

A DISSERTATION

Submitted to
Michigan State University
In partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Mechanical Engineering
2011

ABSTRACT
AN EXPERIMENTAL AND THEORETICAL ANALYSIS OF COLD WORKING AND
RIVETING IN FIBER METAL LAMINATE MATERIALS
By
David S. Backman
This research describes the results of an investigation into the behaviour of fiber metal
laminate (FML) materials after cold expansion and riveting, using both experimental and
theoretical methods with an overall aim of producing a new FML variant optimized for
these manufacturing processes. To achieve this aim three primary research objectives
have been identified including: 1. Experimentally measure the strains in fiber metal
laminates due to both hole cold expansion and riveting. 2. Develop a theoretical model
that could be used to analytically predict the strains resulting from hole cold expansion
and riveting. 3. Develop and test new variants of FML optimized with regards to cold
expansion and riveting.

Using digital image correlation techniques, full-field strains were measured on various
grades of FML after both hole cold expansion and riveting. The cold expansion results,
showed how the residual strain field was dependent on the split sleeve direction with
respect to the material orientation and that by changing the orientation of the split
sleeve one could significantly reduce the magnitude of the residual strains. The effects
of material orthotropy were also evident in the riveted coupons, but less pronounced
due to the driven and manufactured heads of the rivet obscuring the region closest to
the rivet hole. The results from this static testing suggested that designing a more

isotropic fiber metal laminate material could improve performance after cold expansion
and riveting.

Two different analytical approaches were used in this research. In the first, a closed
form solution for the strains resulting from cold expansion and riveting was put forward
and corroborated against experimental results. In the second, a classical laminated
plate approach was used to develop an analytical tool that could predict the material
properties of fiber metal laminates based on the glass fiber orientation and the number
of aluminum and of fiber layers. This approach was validated against experimental data
and used as a design tool to predict the material properties of a variety of new fiber
metal laminate (FML) variants.

Static tensile testing of the various FML variants confirmed that FML 4 with a
quasi-isotropic layup had a constant elastic modulus of approximately 50 GPa,
regardless of material direction. Strain measurements made after cold expansion and
riveting showed that this quasi-isotropic FML 4 variant had a more uniform residual
strain field, which was a significant improvement in this regard over standard FML 4 or
FML 3. Fatigue testing showed that overall, cold expansion was effective in extending
fatigue life. Such testing with the FML 4 variant showed that although it had a lower
fatigue life than standard FML 4 in one material orientation, its overall fatigue life was
fairly constant, regardless of material orientation. The results suggest that this FML 4
variant may prove to be a valuable addition to the standard grades of FML currently in
use today.

This thesis is dedicated to my wife Chantal and our children.

iv

ACKNOWLEDGEMENTS
Just as it takes a village to raise a child, it takes a talented and dedicated support staff
to complete a research program. Over the course of this research I have been fortunate
enough to have worked with some very talented researchers and technicians. I hope a
mention in this list will serve to express my appreciation for those that have contributed
their expertise to making this research program a success. I would also like to
acknowledge the contribution from the NRC-IAR New Initiative Fund who sponsored
this work and without whom this research program could not have been completed.

Nick Bellinger
Tom Benak
Richard Bos
Kyle Chisholm
Stephan Cloutier
Caleb Cowal
Larry Crichlow
Richard Desnoyers
Thomas Sears

v

PREFACE
This thesis is based upon research conducted from April 2006 to December 2010 at the
National Research Council Canada’s Institute for Aerospace Research, Ottawa, Ontario
Canada.

I would like to express my sincere gratitude to my supervisor Eann Patterson. Without
his advice and support this thesis would never had become a reality. I would also like to
thank my supervising committee, Professor Dahsin Liu, Professor Gary Cloud,
Professor Gary Burgess and Mr. Jerzy Komorowski for their guidance and advice.

I would also like to express my gratitude and appreciation to my wife Chantal, who
supported me and looked after our young son Noah, during my many weekends spent
in the lab poring over data and writing up the results.

David S. Backman, December 2010.

vi

TABLE OF CONTENTS
LIST OF TABLES ........................................................................................................... x
LIST OF FIGURES......................................................................................................... xi
LIST OF ABBREVIATIONS....................................................................................... xxiii
1.0
Introduction......................................................................................................... 1
1.1
Research Objectives......................................................................................... 2
2.0
Background......................................................................................................... 5
2.1
Fiber Metal Laminates ...................................................................................... 5
2.2
Fatigue of Fiber Metal Laminate Materials...................................................... 14
2.2.1
Crack Bridging and the Fatigue Crack Growth Mechanism ..................... 15
2.2.2
Fatigue Crack Growth in FML .................................................................. 17
2.3
Cold Expansion Process ................................................................................. 19
2.4
Riveting Process ............................................................................................. 21
2.5
Experimental Strain Measurement Techniques .............................................. 23
2.5.1
Thermoelastic Stress Analysis................................................................. 23
2.5.2
Digital Image Correlation (DIC)................................................................ 28
3.0
Literature Review.............................................................................................. 33
3.1
Cold Expansion of Aluminum Alloys ............................................................... 33
3.1.1
Fatigue of Aluminum Alloys as a Result of Cold Expansion..................... 33
3.1.2
Strain measurements of the Cold Expansion Process ............................. 36
3.2
Riveting of Aluminium Alloys........................................................................... 41
3.3
Riveting of Fiber Metal Laminate Materials ..................................................... 45
3.4
Cold Expansion of Fiber Metal Laminate Materials......................................... 47
3.5
Discussion: Identification of Knowledge Gaps ................................................ 48
4.0
Rational decision making process.................................................................. 51
4.1
Technology Selection for Measuring Strains During Cold Expansion ............. 51
4.2
Technology Selection for Measuring Strains During Riveting ......................... 55
4.3
Discussion....................................................................................................... 58
5.0
Experimental Methods ..................................................................................... 60
5.1
Static Test Setup............................................................................................. 60
5.1.1
Hole Cold Expansion Procedure.............................................................. 61
5.1.2
Riveting procedure................................................................................... 63
5.2
Fatigue test setup ........................................................................................... 65
5.3
Production of FML and 2024-T3 Aluminum Coupons ..................................... 67
5.4
Design of FML and 2024-T3 Aluminum Coupons ........................................... 68
5.5
Residual Stress Measurement of FML Panels ................................................ 73
6.0
Static Test Results ........................................................................................... 77
6.1
Process Variability .......................................................................................... 78
6.2
Material Orientation......................................................................................... 83
vii

6.3
Comparison Between FML 3 and FML 4 ........................................................ 87
6.4
FML 45º Orientation ........................................................................................ 89
6.5
Mandrel Entry and Exit Face Results (2024-T3 and FML) .............................. 92
6.5.1
Effect of Increased Edge Distance........................................................... 99
6.6
Static Riveting Results .................................................................................. 105
6.6.1
Process Variability Rivet Results ........................................................... 105
6.6.2
Comparison Between FML 3 and FML 4 Rivet Results ......................... 108
7.0
Theoretical Analysis and Comparison to Static Results ............................ 110
7.1
Discussion of Yield Criterion ......................................................................... 110
7.1.1
Distortion Energy Yield Criteria.............................................................. 111
7.2
Failure Criteria for Fiber Metal Laminates..................................................... 115
7.2.1
Tsai-Hill Failure Criteria ......................................................................... 116
7.2.2
Tsai-Wu Failure Criteria ......................................................................... 119
7.3
Elastic-Plastic Material Models ..................................................................... 121
7.4
Review of Closed Form Solution for Cold Expansion.................................... 123
7.4.1
Stresses Due to Loading of Plate by Mandrel........................................ 128
7.4.2
Closed Form Solution for Elastic-Plastic Unloading............................... 137
7.4.3
Calculation of Radial and Tangential Strains ......................................... 140
7.5
Development of Closed Form Model for Riveting.......................................... 141
7.6
Closed Form Modelling of FML Properties.................................................... 143
7.6.1
Micromechanics Approach to Modeling Prepreg Properties .................. 143
7.6.2
Classical Laminated Plate Approach to Laminate Properties ................ 150
7.7
Comparison of Closed Form Results to Experimental Measurements.......... 156
7.7.1
Comparison to Cold Expansion Strains: 2024-T3 Coupons................... 156
7.7.2
Comparison to Cold Expansion Strains: FML 3 Coupons ...................... 158
7.7.3
Comparison to Riveting Strains: 2024-T3 Coupons............................... 161
7.7.4
Comparison to Riveting Strains: FML 3 Coupon.................................... 163
8.0
Baseline Fatigue behaviour ........................................................................... 166
8.1
Fatigue Behaviour After Cold Expansion ...................................................... 166
8.1.1
Aluminum: Cold Expansion Strain and Fatigue Results......................... 167
8.1.2
FML: Cold Expansion Strain and Fatigue Results ................................. 179
8.2
Fatigue Results After Riveting....................................................................... 196
8.2.1
Aluminum: Rivet Fatigue Results........................................................... 198
8.2.2
FML: Rivet Fatigue Results.................................................................... 202
9.0
Design and Testing of a new FML variant .................................................... 206
9.1
Theoretical Design of New FML 4 Variants................................................... 206
9.1.1
Baseline Mechanical Testing of New FML 4 Variants............................ 209
9.2
Validation of New Prepreg Batch .................................................................. 219
9.2.1
Manufacture of a New FML 4 Variant .................................................... 223
9.3
Static Strength of FML 4 Variant ................................................................... 224
10.0 Fatigue Testing and Residual Strength of FML 4 [-60/0/60] ........................ 227
10.1 FML 4 and FML 4 Variant Overall Fatigue Results ....................................... 228
10.2 Residual Strength Results ............................................................................ 231
viii

10.3 FML 4: DIC and TSA Measurements ............................................................ 234
10.3.1 FML 4: Unexpanded Coupons ............................................................... 234
10.3.2 FML 4: Cold Expanded Coupons........................................................... 238
10.4 FML 4 Variant: DIC and TSA Measurements................................................ 241
10.4.1 FML 4 Variant: Unexpanded Coupons................................................... 241
10.4.2 FML 4 Variant: Cold Expanded Coupons............................................... 245
10.4.3 FML 4 Variant: Riveted Coupons........................................................... 248
10.5 Ultrasonic Inspection of FML 4 and FML 4 Variant Coupons........................ 249
10.6 Discussion..................................................................................................... 253
11.0 Discussion ...................................................................................................... 263
11.1 Cold Expansion of FML................................................................................. 264
11.1.1 Influence of Mandrel Geometry.............................................................. 268
11.2 Fatigue Testing of Cold Expanded Coupons................................................. 272
11.3 Fatigue Testing of Riveted Coupons............................................................. 273
Table 14: Coefficients for determining pressure from pixel intensity values ...... 278
11.4 Effectiveness of New FML 4 [-60/0/60] variant.............................................. 288
11.5 Error Analysis................................................................................................ 290
11.5.1 Static Testing and Measurements ......................................................... 290
11.5.2 Closed Form Solution ............................................................................ 291
11.5.3 Fatigue Testing ...................................................................................... 292
11.6 Innovation and Contribution to Scientific Knowledge .................................... 293
11.6.1 Scientific publications and conference proceedings .............................. 293
12.0 Recommendations and Future Work ............................................................ 296
12.1 Cold Expansion Process Changes................................................................ 296
12.2 FML Process Changes ................................................................................. 299
12.3 Future work ................................................................................................... 300
13.0 Conclusions .................................................................................................... 302
13.1 Experimental Measurements ........................................................................ 302
13.2 Development of a Theoretical Model ............................................................ 303
13.3 Development and Testing of New FML Variants........................................... 304
13.3.1 Fatigue Testing ...................................................................................... 304
13.3.2 Effectiveness of Quasi-Isotropic FML 4 [60/0/-60] ................................. 305
13.4 Summary....................................................................................................... 305
REFERENCES............................................................................................................ 308

ix

LIST OF TABLES
Table 1: Standard FML grades and material properties .................................................. 8
Table 2: Longitudinal (L) and longitudinal transverse (LT) tensile and compressive
13
properties of FML and 2024-T3 aluminum ................................................................. 13
Table 3: Camera calibration parameters ....................................................................... 32
Table 4: Viability of various experimental mechanics techniques for measuring strains
during cold expansion ................................................................................................... 52
Table 5: Techniques excluded from decision making and reason for exclusion............ 52
Table 6: List of non-essential attributes for the techniques that met the essential
requirements ................................................................................................................. 53
Table 7: Viability of various experimental mechanics techniques for measuring strains
during riveting................................................................................................................ 57
Table 8: Techniques excluded from decision making and reason for exclusion............ 57
Table 9: Summary residual stress results for various types of FML panels................... 76
Table 10: Disbond area for cold expanded and unexpanded coupon ......................... 193
Table 11: Summary failure locations from fractography of aluminum coupons ........... 202
Table 12: Summary of crack nucleation locations for aluminum and FML riveted
coupons....................................................................................................................... 205
Table 13: Summary material information regarding Cytec FM-94 ............................... 220
Table 14: Coefficients for determining pressure from pixel intensity values ................ 278
Table 15: Comparison between cold expansion and riveting stress values during fatigue
loading......................................................................................................................... 285

x

LIST OF FIGURES
Figure 1: Exploded view of a typical layup for FML 4-3/2 ................................................ 9
Figure 2: Variation in elastic modulus with orientation for FML 3 and FML 4 from NRC
11
13
testing with comparison to published values .......................................................... 11
Figure 3: Variation in yield strength with orientation for FML 3 and FML 4 from NRC
11
13
testing with comparison to published values .......................................................... 12
Figure 4: Variation in ultimate strength with orientation for FML 3 and FML 4 from NRC
11
13
testing with comparison to published values .......................................................... 12
Figure 5: Crack bridging from the fiber layer and the resulting delamination from Vlot
9
and Gunnink ................................................................................................................ 16
Figure 6: Basic stages of the split sleeve hole cold expansion process ........................ 20
Figure 7: The four basic stages of the riveting process ................................................. 22
28

Figure 8: Simple signal processing model for the Deltatherm TSA system

............... 27

Figure 9: Residual stress measurements around a 4% cold expanded hole (a)
46
measured using x-ray diffraction from Stephanescu et al and (b) measured using a
modified Sach’s method from Odzemir and Edwards

61

................................................ 40
73

Figure 10: Radial and hoop strains due to the riveting process from Fox and Withers .
Vertical line denotes interface between rivet and coupon. Dashed lines are provided for
clarity only ..................................................................................................................... 43
Figure 11: Plot of importance versus performance for digital image correlation and inplane moiré ................................................................................................................... 54
Figure 12: Plot of importance versus performance for holographic interferometry and
reflection photoelasticity ................................................................................................ 54
Figure 13: Plot of importance versus performance for electronic speckle pattern
interferometry and strain gauges................................................................................... 54
Figure 14: Cumulative scores for each technique evaluated using the rational decision
making process ............................................................................................................. 55
Figure 15: Plot of importance versus performance for digital image correlation and strain
gauges .......................................................................................................................... 58

xi

Figure 16: a) Plot of importance versus performance for reflection photoelasticity b)
Cumulative scores for each technique evaluated using the rational decision making
process.......................................................................................................................... 58
Figure 17: Isometric diagram of coupon retention fixture .............................................. 61
Figure 18: Initial mandrel placement for hole cold expansion process .......................... 62
Figure 19: Mandrel displacement vs. tool rotation......................................................... 62
Figure 20: Manual riveting tool and coupon fixture........................................................ 64
Figure 21: Chosen area of interest for rivet processing. (a) area of interest showing
position of rivet and corresponding shadow and (b) actual reference image used........ 65
Figure 22: (a) Integral stop and support platen for the coupon during riveting with an (b)
instrumented arbor press with load cell ......................................................................... 67
Figure 23: Standard cure cycle used for FML 3 and FML 4 .......................................... 68
Figure 24: Layout for standard static test coupons (dimensions in inches) ................... 70
Figure 25: Layout for 45º static coupons (dimensions in inches)................................... 71
Figure 26: Dimensions of static test coupon after machining (dimensions in inches).... 71
Figure 27: Layout for standard fatigue test coupons (dimensions in inches)................. 72
Figure 28: Dimensions of fatigue test coupon after machining (dimensions in inches) . 72
Figure 29: Layout for multi directional fatigue coupons (dimensions in inches)............. 73
Figure 30: Experimental setup for FML panel residual strain measurement ................. 74
Figure 31: Sample strain results from DIC for (panel 35) FML 4 [-60/0/+60] (a) maximum
principal strain and (b) minimum principal strain ........................................................... 75
Figure 32: Radial co-ordinate system of the annular data extraction ............................ 78
Figure 33: Plot of maximum principal strains on the entry face for two FML 3 coupons
(a) specimen GAL1 and (b) specimen GAL3................................................................. 79
Figure 34: Plot of minimum principal strains on the entry face for two FML 3 coupons (a)
specimen GAL1 and (b) specimen GAL3 ...................................................................... 80
Figure 35: Plot of principal strains for two FML 3 coupons, specimen GAL1 and
specimen GAL3) (a) maximum principal strain and (b) minimum principal strain.......... 80

xii

Figure 36: Plot of maximum principal strains on the entry face for two 2024-T3
aluminum coupons (a) specimen AL1 and (b) specimen BL1 ....................................... 81
Figure 37: Plot of minimum principal strains on the entry face for 2024-T3 aluminum
coupon (a) specimen AL1 and (b) specimen BL1 ......................................................... 82
Figure 38: Plot of principal strains for two 2024-T3 aluminum coupons, specimen AL1
and specimen BL1 (a) maximum principal strain and (b) minimum principal strain....... 82
Figure 39: Maximum principal strain on the entry face for two FML 4 coupons (a)
specimen GBL1 (longitudinal orientation) and (b) specimen GBT1 (transverse
orientation) .................................................................................................................... 83
Figure 40: Minimum principal strain on the entry face for two FML 4 coupons (a)
specimen GBL1 (longitudinal orientation) and (b) specimen GBT1 (transverse
orientation) .................................................................................................................... 84
Figure 41: Plot of principal strains for two FML 4 coupons, specimen GBL1 and
specimen GBT1 (a) maximum principal strain and (b) minimum principal strain........... 85
Figure 42: Maximum principal strain on the entry face for 2024-T3 aluminum coupons
(a) specimen AL3 (longitudinal orientation) and (b) specimen AT3 (transverse
orientation) .................................................................................................................... 86
Figure 43: Minimum principal strain on the entry face for 2024-T3 aluminum coupons (a)
specimen AL3 (longitudinal orientation) and (b) specimen AT3 (transverse orientation)
...................................................................................................................................... 86
Figure 44: Plot of principal strains for 2024-T3 coupons, specimen AL6 (Longitudinal)
and Specimen AT6 (Transverse) for (a) maximum principal strain and (b) minimum
principal strain ............................................................................................................... 87
Figure 45: Maximum principal strains on the entry face for (a) FML 3 (specimen GAL2)
and (b) FML 4 (specimen GBL1)................................................................................... 88
Figure 46: Minimum principal strains on the entry face for (a) FML 3 (specimen GAL2)
and (b) FML 4 (specimen GBL1)................................................................................... 88
Figure 47: Plot of principal strains for FML 3 (specimen GAL2) and FML 4 (specimen
GBL1) for (a) maximum principal strain and (b) minimum principal strain ..................... 89
Figure 48: Maximum principal strains on entry face for FML 3 (a) specimen GAL2
(standard orientation) and (b) specimen GCF2 (45° orientation). Note: Dotted line
shows orientation of split sleeve.................................................................................... 90
Figure 49: Minimum principal strains on entry face for FML 3 (a) specimen GAL2
(standard orientation) and (b) specimen GCF2 (45° orientation). Note: Dotted line
shows orientation of split sleeve.................................................................................... 91

xiii

Figure 50: Plot of principal strains for FML 3 specimens GAL2 (longitudinal) and GCF2
(transverse) with (a) maximum principal strains and (b) minimum principal strains ...... 92
Figure 51: Maximum principal strains for (specimen 15-A-7) FML 3 coupon (a) mandrel
entry face and (b) mandrel exit face .............................................................................. 93
Figure 52: Minimum principal strains for (specimen 15-A-7) FML 3 coupon (a) mandrel
entry face and (b) mandrel exit face .............................................................................. 94
Figure 53: Plot of entry and exit face principal strains for (specimen 15-A-7) FML 3 (a)
maximum principal strains and (b) minimum principal strains ....................................... 95
Figure 54: Vertical line profile (180º) of entry and exit principal strains for FML 3 coupon
(specimen 15-A-7)......................................................................................................... 95
Figure 55: Maximum principal strains for (specimen AL-T-7) 2024-T3 aluminum (a)
mandrel entry face and (b) mandrel exit face ................................................................ 96
Figure 56: Minimum principal strains for (specimen AL-T-7) 2024-T3 aluminum (a)
mandrel entry face and (b) mandrel exit face ................................................................ 97
Figure 57: Plot of entry and exit face principal strains for (specimen AL-T-5) 2024-T3
aluminum (a) maximum principal strains and (b) minimum principal strains ................. 98
Figure 58: Plot of entry and exit principal strains for 2024-T3 aluminum coupon
(specimen AL-T-5)......................................................................................................... 98
Figure 59: Plot of maximum principal strain on entry face for a) high edge ratio coupon
(specimen CL3) and b) low edge ratio coupon (specimen AL1).................................. 100
Figure 60: Vertical line profile showing variation in maximum principal strain through
coupon center for both high edge ratio (specimen CL3) and low edge ratio (specimen
AL1) 2024-T3 aluminum coupons ............................................................................... 101
Figure 61: Vertical line profile showing variation in minimum principal strain through
coupon center for both high edge ratio (specimen CL3) and low edge ratio (specimen
AL1) 2024-T3 aluminum coupons ............................................................................... 102
Figure 62: Plot of maximum principal strain on the entry face for FML 3 a) high edge
ratio coupon (specimen GCL2) and b) low edge ratio coupon (specimen GAL1)........ 103
Figure 63: Vertical line profile showing variation in maximum principal strain through
coupon center for both high edge ratio (specimen GAL1) and low edge ratio (specimen
GCL2) FML 3 aluminum coupons ............................................................................... 103
Figure 64: Vertical line profile showing variation in minimum principal strain through
coupon center for both high edge ratio (specimen GAL1) and low edge ratio (specimen
GCL2) FML 3 aluminum coupons ............................................................................... 104

xiv

Figure 65: Maximum principal strains for 2024-T3 aluminum riveted coupons on driven
head side for (a) specimen BL17 and (b) specimen BL19........................................... 106
Figure 66: Minimum principal strains for 2024-T3 aluminum riveted coupon on driven
head side for (a) specimen BL17 and (b) specimen BL19........................................... 107
Figure 67: Plot of principal strains for riveted 2024-T3 coupon BL17 and BL19 (a)
maximum principal strain and (b) minimum principal strain......................................... 107
Figure 68: Maximum principal strains on the driven head side for (a) FML 3 (specimen
GAL4) and (b) FML 4 (specimen GBL5)...................................................................... 108
Figure 69: Minimum principal strains on the driven head side for (a) FML 3 (specimen
GAL4) and (b) FML 4 (specimen GBL5)...................................................................... 109
Figure 70: Plot of principal strains for riveted FML 3 (specimen GAL4) and FML 4
(specimen GBL5) for (a) maximum principal strain and (b) minimum principal strain . 109
Figure 71: Comparison of Maximum Shear and Maximum Distortion Energy yield criteria
.................................................................................................................................... 115
105

Figure 72: Effect of isotropic versus kinematic hardening on the yielding of a material
.................................................................................................................................... 123
Figure 73: Free body diagram of a finite plate with circular hole

124

............................ 125

Figure 74: Diagram of the variables associated with elastic-plastic deformation

124

... 130

Figure 75: Polished surface used for rivet measurement with rivet diameter highlighted
in red ........................................................................................................................... 142
Figure 76: Representative volume element (RVE) showing applied stress in the
direction of the fiber..................................................................................................... 144
Figure 77: Representative volume element (RVE) showing applied stress transverse to
the direction of the fiber............................................................................................... 145
Figure 78: Comparison between closed form and experimental measurements for
aluminum coupon in transverse direction (specimen AL1) .......................................... 157
Figure 79: Comparison between closed form and experimental measurements for
aluminum coupon in longitudinal direction (specimen AL1)......................................... 158
Figure 80: Comparison between closed form and experimental measurements for FML
3 coupon in transverse direction (specimen GAL1)..................................................... 159
Figure 81: Comparison between closed form and experimental measurements for FML
3 coupon in longitudinal direction (specimen GAL1) ................................................... 159
xv

Figure 82: Comparison between closed form and experimental measurements for FML
3 coupon in 45 degree direction (specimen GAL1) ..................................................... 161
Figure 83: Comparison between closed form and experimental measurements for
riveted aluminum 2024-T3 coupon in transverse direction (specimen AT8)................ 162
Figure 84: Comparison between closed form and experimental measurements for
riveted aluminum 2024-T3 coupon in longitudinal direction (specimen AT8) .............. 163
Figure 85: Comparison between closed form and experimental measurements for FML
coupon in transverse direction (specimen GAL4)........................................................ 164
Figure 86: Comparison between closed form and experimental measurements for FML
coupon in longitudinal direction (specimen GAL4) ...................................................... 164
Figure 87: Comparison between closed form and experimental measurements for FML
coupon in 45º degree direction (specimen GAL4) ....................................................... 165
Figure 88: Mean fatigue results for aluminum coupons both with and without coldexpansion of the hole .................................................................................................. 168
Figure 89: Crack growth curves for 2024-T3 aluminum coupons (a) Net Stress 165
MPa: Open Hole (specimen Al-L-20) and cold expanded (specimen Al-L-28) coupons
(b) Net Stress 176 MPa: Open Hole (specimen AL-L-26) and cold expanded (specimen
AL-L-29) coupons and (c) Net Stress 198 MPa: Open Hole (specimen AL-L-36) and
cold expanded (specimen AL-L-35) coupons .............................................................. 170
Figure 90: Variation in number of cycles to 1 mm crack length (columns) versus da/dN
(symbols) for 2024-T3 aluminum at various stress levels............................................ 171
Figure 91: Maximum principal strains obtained from digital image correlation from
aluminium coupons with both an unexpanded (left, specimen AL-L-25 ) and cold–
expanded (right, specimen AL-L-27 ) hole pre-crack and with crack lengths of 1, 2 and
3.7 mm ........................................................................................................................ 173
Figure 92: Full-field maps of the thermoelastic signal (A/D units) from the exit face for
unexpanded (left) and cold-expanded (right) holes. Date reflected about the loading
axis for ease of comparison vertical) axis for ease of comparison .............................. 174
Figure 93: Fracture surface of the coupon with cold-expanded hole orientated as in
Figure 92 with the exit face on the lower side and with increasing levels of magnification
from top to bottom ....................................................................................................... 178
Figure 94: Optical (top) and SEM (bottom) images of the fracture surfaces for the
coupon with the unexpanded hole at increasing levels of magnification from top to
bottom and orientated with the exit face on the lower side.......................................... 179

xvi

Figure 95: Mean fatigue results. (a) FML 3 [90/0] longitudinal coupons both with and
without cold-expansion of the hole and (b) FML 4 [0/90/0] longitudinal coupons both with
and without cold-expansion of the hole ....................................................................... 180
Figure 96: Crack growth curves for FML 3 coupons (a) Net Stress 165 MPa: Open Hole
(specimen 15-A-3) and cold-expanded (specimen 15-A-6) coupons (b) Net Stress 176
MPa: Open Hole (specimen 15-A-2) and cold-expanded (specimen 15-A-5) coupons
and (c) Net Stress 198 MPa: Open Hole (specimen 15-A-1) and cold-expanded
(specimen 15-A-4) coupons ........................................................................................ 182
Figure 97: Crack growth curves for FML 4 [0/90/0] longitudinal coupons (a) Net Stress
165 MPa: Open Hole (specimen 16-B-4) and cold expanded (specimen 13-B-3)
coupons (b) Net Stress 176 MPa: Open Hole (specimen 16-B-6) and cold expanded
(specimen 13-B-2) coupons and (c) Net Stress 198 MPa: Open Hole (specimen 16-B5) and cold expanded (specimen 13-B-1) coupons..................................................... 183
Figure 98: Variation in number of cycles to 1 mm crack length (columns) versus da/dN
(symbols) for FML 3 at various stress levels ............................................................... 184
Figure 99: Variation in number of cycles to 1 mm crack length (columns) versus da/dN
(symbols) for FML 4 [0/90/0], cut in the longitudinal direction, at various stress levels 184
Figure 100: Maximum principal strains obtained from digital image correlation
measurements on the entry face of FML 3 coupons with both an unexpanded (left,
specimen 12-A-1) and cold–expanded (right, specimen 12-A-4) hole with crack lengths
of 0, 1, 2 and 3.7mm ................................................................................................... 187
Figure 101: Full-field maps of the thermoelastic signal (A/D) units from the exit face for
both unexpanded (left, specimen 12-A-1) and cold-expanded (right, specimen 12-A-4)
FML 3 holes ................................................................................................................ 188
Figure 102: Maximum principal strains obtained from digital image correlation
measurements on the entry face of FML 4 coupons with both an unexpanded (left, 16B-5) and cold–expanded (right, specimen 13-B-1) hole with crack lengths of 0, 1, 2 and
3.7 mm ........................................................................................................................ 190
Figure 103: Full-field maps of the thermoelastic signal (A/D) units from the exit face for
both unexpanded (left, 16-B-5) and cold-expanded (right, specimen 13-B-1) FML 4
holes............................................................................................................................ 191
Figure 104: Pulse echo ultrasonic scans of FML 3 specimen 12-A-1 (open hole) and
specimen 12-A-4 (cold expanded). Image (a) unexpanded entry face (b) cold expanded
entry face (c) unexpanded exit face and (d) cold expanded exit face ......................... 193
Figure 105: Pulse echo ultrasonic scans of FML 4 specimen 16-B-5 (open hole) and
specimen 13-B-1 (cold expanded). Image (a) unexpanded entry face (b) cold expanded
entry face (c) unexpanded exit face and (d) cold expanded exit face ......................... 193

xvii

Figure 106: S-N curve for riveted aluminum 2024-T3 coupons at various stress levels
.................................................................................................................................... 198
Figure 107: S-N curve for open hole, cold expanded and riveted 2024-T3 aluminum
coupons....................................................................................................................... 199
Figure 108: a-b) Maximum principal strain from rivet driven face and c-d) TSA strain
information from rivet manufactured head face for the aluminum 2024-T3 coupon, at
pre-crack formation and at 75% of the number of cycles to failure (specimen Al-L-15).
Note: Net stress of 263 MPa ....................................................................................... 200
Figure 109: (a) Optical micrograph of failure surface of AL-L-14 (b) Scanning electron
micrographs of left hand specimen surface below manufactured head. (c) Right hand
side of specimen. Note: Crack nucleation origin highlighted in red ............................. 201
Figure 110: Fatigue results for FML 4 [0/90/0] riveted coupon, overlaid on S-N curve
data for FML 4 cold expanded coupon fatigue data .................................................... 203
Figure 111: a-b) Maximum principal strain information from rivet driven face and c-d)
TSA strain information from rivet manufactured head face for the FML 4 [0/90/0]
coupon, at pre-crack formation and at 75% of the number of cycles to failure (specimen
13-B-5). Note: Net stress of 263 MPa ......................................................................... 204
Figure 112: Pulse-echo ultrasonic images post test for: (a) FML 4 coupon (Specimen
13-B-5 driven face and (b) FML 4 manufactured face ................................................. 205
Figure 113: Theoretical modulus as a function of orientation for FML 4 [0/60/-60],
FML 4 [-45/90/45], FML 4 [30/0/-30], and standard FML 4-3/2 [0/90/0]....................... 209
Figure 114: Maximum principal strains for cold expanded FML 4 [-45/90/+45] (specimen
17-C-7) on the (a) entry face and (b) exit face ............................................................ 210
Figure 115: Minimum principal strains for cold expanded FML 4 [-45/90/+45] (specimen
17-C-7) on the (a) entry face and (b) exit face ............................................................ 211
Figure 116: Mean fatigue results for FML 4 [-45/90/45] coupons both with and without
cold-expansion of the hole .......................................................................................... 211
Figure 117: Maximum principal strains for cold expanded FML 4 [-30/0/+30] (specimen
18-D-7) on the (a) entry face and (b) exit face ............................................................ 212
Figure 118: Minimum principal strains for cold expanded FML 4 [-30/0/+30] (specimen
18-D-7) on the (a) entry face and (b) exit face ............................................................ 213
Figure 119: Mean fatigue results for FML 4 [-30/0/+30] coupons both with and without
cold-expansion of the hole .......................................................................................... 213

xviii

Figure 120: Maximum principal strains for cold expanded FML 4 [-60/0/+60] (specimen
26-D-1-T) on the (a) entry face and (b) exit face ......................................................... 214
Figure 121: Minimum principal strains for cold expanded FML 4 [-60/0/+60] (specimen
26-D-1-T) on the (a) entry face and (b) exit face ......................................................... 215
Figure 122: Plot of entry and exit face principal strains for (specimen 26-D-1-T)
FML 4 [-60/0/+60] (a) maximum principal strains and (b) minimum principal strains... 216
Figure 123: Baseline fatigue data for FML 4 [-60/0/+60]. Comparison between
unexpanded and cold expanded coupons................................................................... 217
Figure 124: Maximum principal strains due to riveting for FML 4 [-60/0/+60] (specimen
26-D-7-L) coupons (a) driven and (b) manufactured head face .................................. 218
Figure 125: Summary fatigue graph highlighting fatigue performance of all grades of
FML tested, both in the open hole and cold expanded configuration. Note: Dotted lines
are for visualization purposes only and FML 4 [-60/0/60] is highlighted with blue symbols
.................................................................................................................................... 219
Figure 126: Experimentally determined elastic modulus for current FML 4 [90/0/90] with
11
new prepreg and FML 4 [90/0/90] made from old prepreg with analytical results.
Note: Dotted line for visualization purposes only......................................................... 221
Figure 127: Disbond measurements for FML 4 made with old and new prepreg ........ 222
Figure 128: Comparison between old and new batches of prepreg (a) in FML 4
unexpanded coupons and (b) in FML 4 cold expanded coupons ................................ 223
Figure 129: Template tool for cutting precise 60º plies................................................ 224
Figure 130: Elastic modulus for FML 4 [90/0/90] and FML 4 [-60/0/60] measured from
static failure tests (columns) combined with results from elastic modulus calculated
using classical laminated plate theory (symbols). Note: Dotted line for visualization
purposes only.............................................................................................................. 225
Figure 131: Yield strength plotted against laminate direction for FML 4 [90/0/90] and
FML 4 variant [-60/0/60] .............................................................................................. 226
Figure 132: Fatigue results for unexpanded and cold expanded FML 4 and FML 4
variant tested at a net stress of 198 MPa .................................................................... 228
Figure 133: Comparison of fatigue results for FML 4 variant (longitudinal) showing
cycles to failure of open hole, cold expanded and riveted coupons tested at a net stress
of 198 MPa.................................................................................................................. 229
Figure 134: Variation in number of cycles to 1 mm crack length (columns) versus da/dN
(symbols) for FML 4 in various material orientations ................................................... 230
xix

Figure 135: Variation in number of cycles to 1 mm crack length (columns) versus da/dN
(symbols) for the FML 4 variant in various material orientations ................................. 231
Figure 136: Residual elastic modulus for FML 3, FML 4 [90/0/90] and FML 4 variant
coupons after fatigue failure. Note: Analytical results overlaid with dotted lines for
visualization purposes only ......................................................................................... 233
Figure 137: Residual peak load for FML 3, FML 4 [90/0/90] and FML 4 variant coupons
after fatigue failure....................................................................................................... 234
Figure 138: FML 4 [90/0/90] maximum principal strains from the entry face (a-d)
unexpanded longitudinal coupon (Specimen 30-B-3-L), (e-h) unexpanded transverse
coupon (Specimen 30-B-1-T) and (i-l) unexpanded 45º degree coupon (Specimen 27B-4-F) .......................................................................................................................... 236
Figure 139: FML 4 [90/0/90] TSA images from the exit face (a-d) unexpanded
Longitudinal coupon (Specimen 30-B-3-L), (e-h) unexpanded transverse coupon
(Specimen 30-B-1-T) and (i-l) unexpanded 45º degree coupon (Specimen 27-B-4-F) 237
Figure 140: FML 4 [90/0/90] maximum principal strains from the entry face (a-d) cold
expanded longitudinal coupon (Specimen 33-B-3-L), (e-h) cold expanded transverse
coupon (Specimen 30-B-2-T) and (i-l) cold expanded 45º degree coupon (Specimen 33B-6-F) .......................................................................................................................... 239
Figure 141: FML 4 [90/0/90] TSA images from the exit face (a-d) cold expanded
longitudinal coupon (Specimen 33-B-3-L), (e-h) cold expanded transverse coupon
(Specimen 30-B-2-T) and (i-l) cold expanded 45º degree coupon (Specimen 33-B-6-F)
.................................................................................................................................... 240
Figure 142: FML 4 variant maximum principal strains on entry face for (a-d) unexpanded
longitudinal coupon (Specimen 32-D-2-L), (e-h) unexpanded transverse coupon
(Specimen 32-D-4-T) and (i-l) unexpanded 45º degree coupon (Specimen 32-D-6-F)
.................................................................................................................................... 243
Figure 143: FML 4 variant TSA images on exit face for unexpanded (a-d) longitudinal
coupon (Specimen 32-D-2-L), (e-h) transverse coupon (Specimen 32-D-4-T) and (i-l)
45º degree coupon (Specimen 32-D-6-F) ................................................................... 244
Figure 144: FML 4 variant maximum principal strains for (a-d) cold expanded
longitudinal coupon (Specimen 29-D-2-L), (e-h) cold expanded transverse coupon
(Specimen 29-D-3-T) and (i-l) cold expanded 45º degree coupon (Specimen 35-D-3-F)
.................................................................................................................................... 246
Figure 145: FML 4 variant TSA images for (a-d) cold expanded longitudinal coupon
(Specimen 29-D-2-L), (e-h) cold expanded transverse coupon (Specimen 29-D-3-T) and
(i-l) cold expanded 45º degree coupon (Specimen 35-D-3-F) ..................................... 247

xx

Figure 146: a-b) Maximum principal strain information from rivet driven face and c-d)
TSA strain information from rivet manufactured head face for the FML 4 variant coupon,
at pre-crack formation and at 75% of the number of cycles to failure (specimen 35-D-2L). Note: Net stress of 198 MPa ................................................................................. 248
Figure 147: FML 4 open hole tested at a net stress of 198 MPa with cycles to failure (Nf)
provided. Longitudinal (specimen 30-B-3-L), transverse (specimen 30-B-1-T) and 45º
degree (specimen 27-B-4-F) ....................................................................................... 250
Figure 148: FML 4 cold expanded hole tested at a net stress of 198 MPa with cycles to
failure (Nf) provided. Longitudinal (specimen 33-B-3-L), transverse (specimen 30-B-2T) and 45º degree coupon (specimen 33-B-6-F) ......................................................... 250
Figure 149: FML 4 variant open hole tested at a net stress of 198 MPa with cycles to
failure (Nf) provided. Longitudinal (specimen 32-D-2-L), transverse (specimen 32-D-4T) and 45º degree coupon (specimen (32-D-6-F)........................................................ 252
Figure 150: FML 4 variant cold expanded hole tested at a net stress of 198 MPa with
cycles to failure (Nf) provided. Longitudinal (specimen 29-D-1-L), transverse (specimen
35-D-1-T) and 45º degree coupon (35-D-4-F) ............................................................. 252
Figure 151: Ultrasonic inspection of FML 4 Variant coupons post riveting tested at a net
stress of 198 MPa with cycles to failure (Nf) provided. Note: Only coupon 35-D-2-L
failed in grip................................................................................................................. 253
Figure 152: Cross-section of an unexpanded hole in FML 3 (a) x10 magnification and
(b) x20 magnification with area of possible disbond highlighted in red........................ 255
Figure 153: Cross-section of FML 3 coupon (exit side) after cold expansion but before
reaming at (a) x10 magnification and (b) x20 magnification with area of disbond
highlighted with arrows................................................................................................ 256
Figure 154: Cross-section of two FML 3 coupons (exit face) at x20 magnification (a)
specimen with 0.09 mm disbond length and (b) specimen with 0.05 mm disbond length
.................................................................................................................................... 257
Figure 155: Measured area of disbond from pulse echo ultrasound for FML 4 [90/0/90]
in both unexpanded and cold expanded conditions [combined entry and exit face
average of n=2 coupons]............................................................................................. 262
Figure 156: Measured area of disbond from pulse echo ultrasound for FML 4 variant in
both open hole and cold expanded conditions [combined entry and exit face average of
n=2 coupons]............................................................................................................... 262
Figure 157: Maximum principal strains in aluminum coupon (specimen AL1): (a)
mandrel fully inserted and (b) mandrel removed ......................................................... 265

xxi

Figure 158: Maximum principal strains in FML 3 coupon (specimen GAL1): (a) mandrel
fully inserted and (b) mandrel removed ....................................................................... 266
Figure 159: Mandrel profile used for cold expansion process with schematic of the full
mandrel overlaid.......................................................................................................... 271
Figure 160: Geometric constraint conditions for a nominal material element (a) at the
entrance face and (b) at the exit face .......................................................................... 272
Figure 161: Minimum principal strains for an aluminum coupon (specimen AL-L-64) on
both the driven and manufactured faces with shank ................................................... 277
Figure 162: Pressure film stains from (a) low (b) medium and (c) high grade films taken
from the manufactured head of a rivet......................................................................... 279
Figure 163: Pressure distribution for consolidated pressure film stains on manufactured
head of a riveted coupon. Regression line for visualization purposes only ................. 279
Figure 164: Hoop (e1), radial (e2) and through thickness strains (e3) for both a riveted
and cold expanded (cx) coupon. Note: dotted line denotes the elastic-plastic boundary
for the riveted coupon only .......................................................................................... 282
Figure 165: Comparison of maximum principal strains between (a) cold expanded
aluminum (specimen AL-L-27) and riveted aluminum (AL-L-9) ................................... 283
Figure 166: Cold expansion (specimen AL-L-27) and rivet strains (specimen AL-L-41) at
high load (10 kN) and at low load (1 kN). Note: Dotted line denotes elastic-plastic
boundary for cold expansion only................................................................................ 285
Figure 167: (a) Front view of riveted coupon highlighting pressure affected zone and (b)
side view of rivet showing line of action of frictional force ........................................... 287
Figure 168: (a) Overview of open hole at the end of the cold expansion process.
Location of the split sleeve highlighted in white box. (b) Close up view of split sleeve
region with arrows highlighting deformation caused by the sleeve.............................. 298

xxii

LIST OF ABBREVIATIONS
ARALL

ARamid ALuminum Laminate

CFRP

Carbon Fiber Reinforced Polymer

CX

Cold Expansion

DIC

Digital Image Correlation

FAA

Federal Aviation Administration

FAR

Federal Aviation Regulation

FTI

Fatigue Technologies Inc.

FML

Fiber Metal Laminate

GLARE™

GLAss REinforced

IAR

Institute for Aerospace Research

NRC

National Research Council Canada

OH

Open Hole

PAA

Phosphoric acid anodized

PE-UT

Pulse echo ultrasound

SEM

Scanning Electron Microscope

TSA

Thermoelastic Stress Analysis

UH

Unexpanded Hole

xxiii

1.0

INTRODUCTION

The use of fiber metal laminate materials in aerospace is increasing as large
manufacturers such as Airbus and smaller manufacturers such as Bombardier
investigate and integrate fiber metal laminates (FML) into aircraft structures. These
materials, especially variants based on a combination of aluminum and glass fibers, are
being promoted as potential replacements for monolithic aluminum based on their lower
weight and increased fatigue life.

Widespread adoption of fiber metal laminates in aerospace applications is contingent
upon the material adhering to the damage tolerant philosophy required by the Federal
Aviation Administration (FAA) regulations, specifically Federal Aviation Regulation
1

(FAR) 25. As Alderliesten and Homan pointed out, this requirement is currently met by
manufacturers of monolithic aluminum alloys by applying fatigue crack growth reduction
strategies, which translates to lowering the design allowable stress. Although the
elastic modulus of FML is lower than that of aluminum, ideally, the high ultimate
strength, low density and better fatigue resistance of FML-based materials should allow
for the overall weight of the structure to be reduced.

Manufacturing processes such as cold expansion and riveting are more critical in FML
owing to the inherent tensile residual stresses that are locked into the material during
the manufacturing process. Crack nucleation and growth to a detectable level tends to
occur more rapidly than is the case in monolithic aluminum alloys, but the overall

1

propagation of these cracks to failure is greatly curtailed by crack bridging from the fiber
reinforced laminate layers

1,2

.

Early crack nucleation in FML is a result of three factors. The first is the tensile residual
stresses in the aluminum layers arising during the heating/curing process due to the
difference in the coefficient of thermal expansion between the metal and the fiber
reinforced thermoset layers. The second factor is that crack bridging becomes effective
only when cracks have grown past the effective crack length. The effective crack length
at which fiber bridging becomes effective is dependent on the laminate and is typically
3

of the order of 0.5-1.5 mm . The third factor is the difference in stiffness between the
aluminum layer (75 GPa) and the glass layer (50 GPa) that results in a higher stress in
the aluminum layer.
1.1

Research Objectives

Although both experimental and theoretical research has been performed on the effect
of hole cold expansion and riveting in aluminum alloys, little research to date has
focused on FML materials, and much of this has relied on computational modeling. By
building on the current understanding of fatigue life in FML and combining this with
experimental data detailing the strain field resulting from cold expansion and riveting,
the aim of this thesis is the production of a new FML variant optimized for these
manufacturing processes. To achieve this aim three primary research objectives have
been identified:

2

1. Experimentally measure the strains in fiber metal laminates due to both the cold
expansion and riveting processes and establish the effect these processes have on
structural performance. Advanced full-field strain measurement techniques are used to
determine the residual strains that develop as a result of both cold expansion and
riveting. Standard grades of FML 3 and FML 4 are tested alongside aluminum 2024-T3
coupons. The information obtained from these experimental techniques will provide
insight into how current FML formulations can be improved and could lead to the
development of new FML variants that are optimized for cold expansion and riveting.

2. Develop a theoretical model that can be used to analytically predict the strains
resulting from the hole cold expansion and riveting processes. A survey of several
current closed-form solutions for cold expansion will be examined to determine whether
it is possible to modify them for use with FML materials and for use in describing the
riveting process. In addition, a classical laminate plate approach will be used to develop
an analytical design tool that is useful for modeling the material properties of any new
FML variants that are developed.

3. Based on the above results, develop and test new variants of FML optimized with
regards to standard manufacturing processes such as cold expansion and riveting. The
results garnered from the experimental measurements will be used as a starting point
for designing a new FML variant, optimized for manufacturing processes such as cold
expansion and riveting. A limited static and fatigue testing program will be used to

3

benchmark the performance of these new FML variants against currently accepted FML
types to determine if the new design(s) are successful.

4

2.0

BACKGROUND

This section is focused on providing background information in five critical areas. The
first subject area focuses on the history and the properties of fiber metal laminate (FML)
materials. The second focuses on fatigue in fiber metal laminates, while the third and
fourth subject areas focus on the process specifics and mechanics of hole cold
expansion and riveting respectively. The fifth and final subject area provides some
background on the experimental strain measurement techniques that will be used.
2.1

Fiber Metal Laminates

The theoretical basis for fiber metal laminate (FML) materials likely originated with
4

research done by Kaufman in 1967 on the fracture toughness of multi-layered,
adhesively bonded aluminum panels. Kaufman showed that the fracture toughness of
multi-layer, adhesively bonded panels was higher than that of either sheet or plate of
the same thickness. Kaufman’s hypothesis regarding this phenomenon was that the
bonding process used to adhere each layer of material served to retard fracture growth
due to an increase in the number of shear surfaces as each layer can crack
independently. Engineers at Fokker Aerospace first started to work on the concept of
combining thin sheets of aluminum with fiber reinforcement in the early 1970’s with the
5

goal of improving fatigue resistance and damage tolerance in airframes . At about the
same time, the department of Aerospace Engineering at the Technical University of
Delft became involved with fiber metal laminate materials and began a research
program to optimize these materials with respect to strength, weight and damage
tolerance

6,7

. The first commercial product produced by this research group was a

5

4

combination of aluminum 7075-T61 sheet and aramid fibers; a combination termed
ARALL (ARramid ALuminum Laminate). ARALL suffered from several intrinsic
deficiencies, including:
1) Poor interface strength between the aramid fibers and the adhesive, which effectively
limited the achievable fiber volume fractions to 50% (compared to current FML with
typical fiber volume fractions of 59%) in order to achieve acceptable peel and
interlaminar shear strength

6,8

.

2) Compressive failure of the aramid fibers when the material was put into compression.
When this occurred, the crack bridging mechanism that normally served to enhance
fatigue life could be compromised, which proved to be an issue in reversed fatigue
8

loading conditions .
3) Poor blunt notch behavior of ARALL compared to typical aluminum alloys, a likely
8

side effect of the low failure strain (~2.4%) of the aramid fibers .
4) An inability to produce crossed ply laminates, meaning that ARALL was more
8

anisotropic than current FML materials with biaxial layups .

The shortcomings with ARALL led researchers at the Technical University of Delft to
explore new ways to improve on the inherent design principles behind this new class of
composites, with the end result being a research program centered on replacing the
aramid fibers with high strength glass fibers. Researchers found that the adhesion
between the glass fibers and the resin was better than with the aramid fibers and that
the glass fibers were stronger when loaded in compression, improving the fatigue

6

resistance of the material and reducing the incidence of fiber failure during fatigue
8

loading . This new fiber metal laminate (FML) variant was termed GLARE™ (GLAss
REinforced) and overall it provided higher tensile and compressive strength, better
6,8

impact behavior, higher ultimate strain and higher residual strength than ARALL

. The

bonding properties and the higher tensile strength of the glass fibers also made it easier
to construct FML variants with multi-axial fiber layups making the material more
6,8

isotropic and thus better suited to applications where biaxial loads occur

. The

superior mechanical properties of FML have focused attention on how to incorporate
this material into the design and construction of new airplanes, specifically as
8

replacements for monolithic alloys used in the aircraft fuselage .

Production of this type of FML has become standardized with six grades being
commonly produced. All grades are produced using uni-directional S2-glass fibers
embedded in thermoset resin adhesive to produce a 0.127 mm (0.005 in) thick
glass/resin matrix with a nominal volume fraction of 59% and different layups depending
on the grade. The combination of the S2-glass pre-embedded in the thermoset resin
matrix is often referred to as a prepreg. Table 1 lists the various grades of FML,
showing the layup for each grade as well as providing some basic information regarding
9

each grade . For FML 1, FML 2, FML 4 and FML 5 the prepregs in the fiber layer are
symmetrically stacked. In the case of FML 3, the prepreg closest to the outer aluminum
layer is oriented along the rolling direction of the aluminum (0° degree). For FML 6, the
prepreg closest to the outer aluminum layers is oriented in the +45° degree direction for
7

FML 6A and in the -45° degree direction for FML 6B. A specific laminate coding system
also exists for FML and is used to precisely describe the constituent makeup of the FML
grades in question. The generalized nomenclature for FML takes the form FML A – B/C
– D where A represents the grade of FML (specifying the layup), B represents the
number of aluminum layers, C represents the number of fiber regions and D represents
the thickness of each aluminum sheet. Thus FML 3–3/2–0.3 represents an FML 3, with
3 aluminum layers, 2 fiber regions (with a fiber layup of [0/90] in each region) and
utilizing 0.3 mm thick aluminum sheet.
Table 1: Standard FML grades and material properties
FML
grade

Sub
Grade

Metal Thickness (mm)
and Alloy

Fiber
Layup

Main characteristics

0.3-0.4 7475-T761

[0/0]

Fatigue, strength,
yield stress

FML 2A

0.2-0.5 2024-T3

[0/0]

Fatigue, strength

FML 2B

0.2-0.5 2024-T3
0.2-0.5 2024-T3

[90/90]
[0/90]

FML 4A

0.2-0.5 2024-T3

FML 4B

0.2-0.5 2024-T3

FML 1
FML 2

0.2-0.5 2024-T3

FML 3
FML 4
FML 5
FML 6

FML 6A

Fatigue, strength
Fatigue, impact
Fatigue, strength
[0/90/0]
in 0° direction
Fatigue, strength in
[90/0/90]
90° direction
[0/90/90/0 Impact

0.2-0.5 2024-T3

[+45/-45]

Shear, off axis
properties

[-45/+45]

Shear, off axis
properties

FML 6B

The S2-glass fibers used in the construction of typical FML variants are approximately
10 m thick, with an ultimate strength of 4.0 GPa, an elastic modulus of 95 GPa and a
failure strain of approximately 4.45%. The mechanical properties of the matrix within
which the fibers are embedded are negligible by comparison (ultimate strength 50 MPa,

8

stiffness 1.7 GPa, failure strain 5-10%) however they make an important contribution to
the strength of this material by determining the bond strength between the aluminum
and fiber layers. The production of FML usually involves pre-treating the aluminum
layers with chromic or phosphoric acid anodizing and priming them with BR-127
corrosion inhibiting bond primer. The FML is then cured in an autoclave at 120°
C,
resulting in such high adhesive strength that bond lines typically remain intact until
cohesive adhesive failure occurs

9,10

. An exploded view of FML 4-3/2 is shown in

Figure 1. Although the exact layup structure for FML 4 can be denoted as
[2024-T3/90/0/90/2024-T3/0/90/0/2024-T3] the shorthand notation for the FML grades
used in this research will refer only to the orientation of the fiber layers (i.e FML 4
[0/90/0]) and will assume a symmetrical laminate with one aluminum layer in the interior
and two on the outside as shown in Figure 1.

Figure 1: Exploded view of a typical layup for FML 4-3/2

9

FML 1 and FML 2 with unidirectional fibers can be strongly anisotropic with respect to
10

yield strength, ultimate tensile strength and ultimate elongation . These behaviours
led to the development of FML 3 and FML 4 with cross-ply fibers which reduced the
degree of anisotropy and made these materials more suitable for aerospace
applications where loading is often biaxial. The unpublished results of tests performed
11

at the National Research Council

are shown in Figure 2 - Figure 4, which demonstrate

the variation of the elastic modulus, yield strength and ultimate strength with respect to
material direction. As with standard polymeric composites, the fibers in FML reinforce
the strength and modulus in the direction with which they are aligned. The ultimate
failure of FML in the longitudinal direction is typically characterized by the tensile failure
of the constituent fibers. Material failure occurs when the fibers reach their tensile
failure strain. Most FML variants have improved ultimate tensile strength compared to
monolithic aluminum sheet; however the yield strength of FML composite materials is
dependant on the residual stress in the metal layers, the mechanical properties of the
alloy used and the degree of strain imparted to the fibers during the curing process.
The metal volume fraction approach, using the rule of mixtures, defines the fraction of
load supported by the metal layer based on the proportions and modulus of the glass
prepreg and metal layer respectively and can be used to predict the material properties
12

in the principal orientations . The elastic modulus of FML composites tends to be
lower than that of monolithic 2024-T3 aluminum, due to the lower modulus of the glass
prepreg used for reinforcement. The elastic modulus in compression is nearly
equivalent to the tensile modulus since the glass fibers provide reinforcement during

10

compressive loading as well. Furthermore, while the compressive yield strength of FML
is slightly lower than the tensile yield strength, it is not limited to tension dominated
applications, as the S2 glass fibers are not as prone to suffering micro-buckling under
6

compression as are the aramid fibers in ARALL .
65

Elastic Modulus (GPa)

60

55

50

45

40
0

15

30

45

60

75

90

Angle (degrees)
FML 4

FML 3

FML 3 (Published)

FML 4 (Published)

Figure 2: Variation in elastic modulus with orientation for FML 3 and FML 4 from NRC
11
13
testing with comparison to published values

11

400

Yield Strength (MPa)

350

300

250

200

150
0

15

30

45

60

75

90

Angle (degrees)
FML 4

FML 3

FML 3 (Published)

FML 4 (Published)

Figure 3: Variation in yield strength with orientation for FML 3 and FML 4 from NRC
11
13
testing with comparison to published values

Ultimate Strength (MPa)

950

800

650

500

350
0

15

30

45

60

75

90

Angle (degrees)
FML 4

FML 3

FML 3 (Published)

FML 4 (Published)

Figure 4: Variation in ultimate strength with orientation for FML 3 and FML 4 from NRC
11
13
testing with comparison to published values

12

13

Wu and Yang

performed a large number of tests to determine the tensile and

compressive properties of the various standard grades of FML and a summary of some
of their tensile and compressive property data is shown in Table 2 (in addition to being
overlaid in the graphs of Figure 2 - Figure 4). The published data show a reasonable
11

correspondence to the test data from NRC testing

and also serve to highlight the

degree of anisotropy inherent in both FML 3 and FML 4.

Table 2: Longitudinal (L) and longitudinal transverse (LT) tensile and compressive
13
properties of FML and 2024-T3 aluminum
Property

FML 3-3/2

FML 4-3/2

2024-T3

Ultimate Strength, L (MPa)

717

1027

455

Ultimate Strength, LT (MPa)

716

607

448

Yield Strength, L (MPa)

305

352

359

Yield Strength, LT (MPa)

283

255

324

Elastic Modulus, Ex (GPa)

58.2

57.6

72

Elastic Modulus, Ey (GPa)

58.2

51.2

72

Compressive Yield Strength, L (MPa)

309

365

304

Compressive Yield Strength, LT (MPa)

306

285

345

Compressive Elastic Modulus, L (GPa)

60

60

74

Compressive Elastic Modulus, LT (GPa)

60

54

74

Poisson' Ratio (vxy)
s

0.288

0.289

0.33

Poisson' Ratio (vyx)
s

0.288

0.257

0.33

Shear Modulus (GPa)

23.3

23.3

28

2.5

2.42

2.78

3

Density (g/cm )

13

Although many advantages exist to using FML type material’s, the lower modulus
compared to monolithic aluminum can pose a problem in specific applications. For
aerospace use, FML materials are used in conjunction with new manufacturing
processes that bond internal reinforcing stringers and ribs to produce a resultant
structure that can support the same load as an aluminum fuselage with riveted
reinforcements. From a fatigue perspective, current FML materials must be oriented
carefully to ensure that the direction of the applied load is aligned with the materials
stiffest orientation, otherwise unexpectedly rapid fatigue crack growth could result.
2.2

Fatigue of Fiber Metal Laminate Materials

Although the static properties of a material are always important from an engineering
design perspective, for aerospace applications another critical factor is fatigue
performance. For a typical aerospace component, the number of flight loading cycles
required for a fatigue crack to grow from a detectable to a critical length typically drives
the required inspection interval, while the number of cycles to crack nucleation typically
drives the start of the inspection regime.

It was the early work on aramid based FML materials such as ARALL that showed how
the concept of adhesively combining monolithic alloy sheets with unidirectional prepregs
resulted in a material with fatigue properties superior to those of the monolithic
7,8,14

alloy

. This fatigue resistance was attributed to a phenomenon known as fiber or

crack bridging.

14

2.2.1 Crack Bridging and the Fatigue Crack Growth Mechanism
Crack bridging is the term used to describe the load redistribution that occurs when
cracks form in the aluminum layers of a fiber metal laminate. The fiber layers are
insensitive to fatigue loading, and can transfer load over the fatigue crack, effectively
9,15

restraining crack opening

. In conjunction with fiber bridging, delamination typically

occurs at the interface between the aluminum and fiber layers in the wake of the crack
(Figure 5). During the crack propagation phase, a large part of the applied stress is
transferred over the crack in the aluminum layer by the intact fiber layer immediately
adjacent to it. The mechanism for load transfer between the aluminum and the fiber are
the cyclic shear stresses in the composite layer. The cyclic shear stresses in the
composite layer are directly related to the fiber bridging stresses. These cyclic shear
stresses cause the delamination between the aluminum and the composite layer to
grow, meaning that the free length over which the fibers are elongated increases,
effectively decreasing the fiber strain. A balance exists between delamination growth
and the fiber bridging stress. Increasing the adhesion of the composite layer would
result in better crack bridging and thus slower crack growth, however, increasing
adhesion beyond a critical point would increase the fiber strain to the point where failure
15

would occur and crack growth would increase . At the beginning of the crack
propagation phase the crack opening is sufficiently small such that the fibers in the
prepreg layer are not fully loaded. A certain amount of crack length and crack opening
displacement are needed (approximately 1 mm) before fiber bridging becomes fully
9

effective . This may play a role in limiting the ability of techniques like cold expansion
to effectively retard the early onset of short cracks in FML.

15

Figure 5: Crack bridging from the fiber layer and the resulting delamination from Vlot
9
and Gunnink
During the crack propagation phase, a large portion of the fatigue stresses are
transferred over the cracks in the aluminum layer by the intact fiber layer (Figure 5).
Load is transferred to the aluminum layers through the adhesive resin matrix
surrounding the glass fibers in the prepreg, thereby inducing cyclic shear stresses in the
adhesive resin matrix and thus shear deformation. These cyclic shear stresses cause
delamination growth between the aluminum and the prepreg layer. The crack
propagation phase in FML is typically characterised by lower stress intensities at the
crack tip compared to monolithic materials which is a result of crack bridging. The lower
9

stress intensity at the crack tip results in close to constant crack growth rates in FML .
It is thought that the crack opening displacement which occurs during the crack
propagation phase is also due to the adhesive shear deformation and the delamination
between the aluminum substrate and the prepreg. This shear deformation serves to
constrain the crack opening, but cannot reduce it completely, thus resulting in a stress

16

intensity at the crack tip in the aluminum layer, albeit a smaller one than in monolithic
9

materials .
2.2.2 Fatigue Crack Growth in FML
According to the definition by Schijve

16

fatigue crack growth in monolithic materials can

be divided into two stages; the crack initiation period and the crack growth period. The
crack initiation period is comprised of crack nucleation and micro crack growth. Since
these are surface phenomena, linked to cyclic shear stresses on crystallographic slip
16

planes , these mechanisms are still at work in the aluminum layers of a fiber metal
laminate material.

The start of crack growth in FML materials can be treated in a similar manner as for
monolithic materials if a similarity approach is used. Similar stress states in the
aluminum layer of FML as in monolithic materials will produce the same result – crack
nucleation. The stresses in the aluminum layers consist of both the static residual
stresses and the applied stresses. Static residual stresses in FML are due to the
-

mismatch between the coefficient of thermal expansion of the aluminum (22x10 6/ºC)
-

and the glass (2.9x10 6/ºC) fiber layer during the curing process. Although the exact
magnitude of the residual stress varies depending on the layup and the cure cycle, the
autoclave curing process generally results in some degree of tensile residual stress in
17

the aluminum layers. This explains why Young et al

noticed that a significant

improvement (40-50%) in fatigue life was obtained by statically overloading FML
specimens to 200 MPa before fatigue testing began. This static overload induced

17

compressive residual stresses in the aluminum layer that mitigated the tensile residual
stresses from the autoclave curing process. This suggests that understanding and
controlling the residual stress state in FML may have important ramifications for fatigue
performance after hole cold expansion and riveting, as both processes can induce
compressive residual stresses.

18

Vasek et al

focused on examining the nucleation location for fatigue cracks in FML by

milling off individual layers of the laminate and examining each individual aluminum
layer. From the results of his investigation, he was able to determine that fatigue cracks
nucleated separately in the individual aluminum layers. Specifically, more cracks formed
in the inner layer while longer cracks were forming on the surface layers.

3

19

Homan and Bradshaw and Gutierrez

added to the work done on the fatigue

properties of FML by focusing on what they referred to as “fatigue crack initiation”. In
both cases “fatigue crack initiation” referred to the number of cycles required for a crack
3

of arbitrary length, in this case 1.0 mm, to propagate. Homan went into more detail in
his explanation of the terminology and defined the “initiation period” as including cyclic
slip, crack nucleation and micro crack growth. The key point in his discussion was that
“crack bridging” by the fiber layers does not come into play until the “macro crack
growth” period, meaning that during fatigue testing of FML, small cracks may grow more
3

quickly than in monolithic aluminum alloys. Homan was also able to show that

18

classical laminate plate analysis could be useful for calculating the internal stresses as
well as for estimating material properties of different FML variants.
2.3

Cold Expansion Process

Any technique that could improve the fatigue performance of fastener holes without
increasing weight, would be especially valuable in extending the fatigue life of new and
existing aircraft. In the 1960’s Boeing engineers developed just such a process, using a
split sleeve shim and an oversized mandrel that could be pulled through a fastener hole
of a specific size. The insertion of this tool plastically deformed the hole in both the
radial and tangential directions, and when the tool was removed the elastic material
surrounding the plastically deformed region would force it to spring back so that
compressive residual stresses formed in the vicinity of the hole edge. These
compressive residual stresses served to reduce crack growth rates by lowering the
20,21

stress intensity factor at the crack tip

. This technology is typically referred to as

“split sleeve” cold expansion and has become one of the most accepted methods for
performing hole cold expansion. This technique has been qualified for use in aerospace
applications and as a result was the method selected for this investigation. An
understanding of the cold expansion process, with an emphasis on the “split sleeve”
technique is critical to understanding the results presented in this report and further
details are described below.
The basic procedure for hole cold expansion begins with the drilling of a slightly
undersized hole. The actual diameter of this hole is a function of the amount of cold
expansion being applied, as well as the diameter of the fastener or rivet that would
eventually be inserted. A hardened steel mandrel with a slightly oversized head is

19

passed through this initial hole. On the shank of the mandrel is a split sleeve shim of a
specified thickness. Once the mandrel head (which is sized to pass through the pilot
hole) is inserted, the split sleeve is seated in the hole. The key to the operation of the
split sleeve cold expansion system, is that the diameter of the mandrel head and the
thickness of the split sleeve are such that when the mandrel head is pulled through the
sleeve, the combination of the two results in interference, which causes the pilot hole to
be enlarged by a specified amount as a result of plastic deformation. A cross-sectional
view of various stages of cold expansion are shown in Figure 6a to Figure 6d.

(a)

(c)

(b)

(d)

Figure 6: Basic stages of the split sleeve hole cold expansion process

The workpiece being cold expanded consists of two sides, the side with the puller unit is
called the exit side, since this is the side from which the mandrel exits the workpiece.
The opposite side is termed the entry side, as this is the side from which the mandrel
enters the workpiece. This distinction will be important later when the surface strain
fields on these two sides are compared and discussed. Another important point is that

20

the mandrel used in this investigation had a cylindrical segment portion of greater width
than the width of the coupons being cold expanded, meaning that at one point during
the process the entire width of the coupon has been expanded the maximum amount.

Another important feature of the cold expansion process is the use of a “split sleeve”
shim. From a conceptual design point of view, the split sleeve shim is crucial as it
allows for easy insertion onto the mandrel initially, and it allows the split sleeve shim to
be easily removed after the cold expansion process is completed. The orientation of the
split sleeve is given minimal mention in the manufacturers documentation (Fatigue
Technology Inc), except to say that in instances where one is cold expanding close to a
22

free edge, the split should be oriented away from the free edge . Using digital image
correlation methods to measure the principal strains surrounding a cold expanded hole
will hopefully provide additional information regarding what if any effect the orientation
of the split has on the resulting strain field.
2.4

Riveting Process

Although new methods for material joining are gaining in popularity, riveted structures
are still a mainstay in the aerospace industry. A basic understanding of how a rivet
works to create a tight and efficient joint is necessary for discussing the strain fields
measured during the riveting process.

The riveting process can be broken down into four key stages as illustrated in Figure 7.
The first stage of riveting involves drilling an oversized hole (approximately 0.1 mm
larger than the rivet shank) to allow the rivet head to seat correctly (Figure 7a). As an

21

axial compressive load is applied to the rivet, the rivet expands radially. The diameter
of the rivet shank increases with the increase in squeeze force until the rivet diameter is
equal to that of the pilot hole. The second phase in the riveting process is characterized
by increased stress in the surrounding sheet material caused by the expanding rivet’s
interference with the edge of the hole (Figure 7b). In addition, the unsupported portion
of the rivet shank begins to form the driven head. In the third stage, the area around the
rivet shank becomes plastically deformed. During this phase, the diameter of the driven
head and the hole enlargement increase until a preset protrusion height or squeeze
force is reached. The driven head typically takes on a barrel shape as a result of
contact with the sheet on one side and contact with the riveting gun on the other (Figure
7c). As the driven head makes contact with the sheet material less squeeze force is
transferred through the sheet, reducing the degree to which the rivet material is
squeezed into the hole. The final stage in the riveting process (Figure 7d) involves the
removal of the squeeze force. This stage is marked by the elastic relaxation of both the
23

rivet and the sheet material .

(a)

(b)

(c)

Figure 7: The four basic stages of the riveting process

22

(d)

2.5

Experimental Strain Measurement Techniques

Two main strain measurement techniques are used in this research program: digital
image correlation (DIC) and thermoelastic stress analysis (TSA). Digital image
correlation provides the more comprehensive results of the two, since it presents the
full-field strain tensors in the area of interest. The results from TSA can be more difficult
to interpret since it provides results proportional to the sum of the principal stresses.
2.5.1 Thermoelastic Stress Analysis
Thermoelastic stress analysis (TSA) is a non-contacting technique for measuring fullfield stresses over the surface of a cyclically loaded specimen. The technique is based
on the measurement of the minute temperature changes that are associated with stress
changes in a solid. An elastic solid subjected to a compressive stress will register a
small increase in temperature, while a tensile stress will cause a small decrease in
temperature. From a practical standpoint, TSA entails applying a cyclic load to a test
specimen, at a frequency high enough to ensure adiabatic conditions, while monitoring
the surface temperature changes. This allows the stress changes due to the cyclic
24,25

loading to be inferred

.

Until recently, the majority of all practical TSA work has involved the use of a system
called SPATE (Stress Pattern Analysis by Thermal Emission), which employed a
cadmium mercury telluride (CMT) infra-red detector, operating in a point by point
26

scanning mode to provide a stress contour map . A major advance in TSA work has
been the introduction of indium antimonide (InSb) detector arrays which obviate the

23

need for point by point scanning and significantly reduce the time required to perform
thermoelastic stress analysis.

The theoretical basis behind thermoelastic stress analysis was first put forward by Lord
27

Kelvin in 1853, with his work relating temperature change and elastic deformation .
Lord Kelvin put forward the most generalized form of the thermoelastic equation, which
relates the change in temperature of a component ( T) to the stress change in an
elastic solid. In practical thermoelastic stress analysis, specimens are cyclically loaded
at such a rate that virtually no heat conduction takes place, so one can ignore the heat
input to obtain the fundamental equation behind thermoelasticity:

∆T =

T
⋅
ρ CE

i

∂σ i
∆ε i for i,= 1,2...6
∂T

2.5.1

where T is the absolute temperature of the material, CE is the specific heat at constant
strain,

is the density, i is the contracted stress tensor, and i is the contracted strain

tensor.

Equation 2.5.1 is a very general form of the thermoelastic equation, useful for isotropic
or anisotropic materials provided that the conditions of adiabaticity are met. To derive
the more commonly used form of this equation one starts with the general relationship
between stress, strain and temperature for an orthotropic material:

σi =

6
j =1

(

Cij ⋅ ε j − α j ⋅ ∆T

)

with i,j = 1,2...6

24

2.5.2

26

where Cij is the stiffness matrix and j are the coefficients of thermal expansion . As
an aside, if one were to expand Equation 2.5.2, one would notice that the shear term
has no temperature term associated with it because shear deformations are volume
independent and do not result in temperature increases. Equation 2.5.2 can also be
inverted to provide an explicit expression for the strain:

εi =

6
i =1

Sij ⋅ σ i + αi ∆T

with i,j=1...6

2.5.3

If one assumes that both the modulus (E) and the Poisson’s ratio ( ) are constant, then
it is possible to evaluate the differential of stress with respect to temperature in Equation
2.5.1 to obtain:

6
∂σ i
Cij ⋅ α j
=−
∂T
j =1

for i,j=1...6

2.5.4

Equation 2.5.3 and Equation 2.5.4 can be substituted into Equation 2.5.1 along with the
established relationship between the specific heat at constant strain (CE) and the
26

specific heat at constant pressure (Cp) :

C p − CE =

T

ρ

⋅
i, j

Cij ⋅ α 2
j

with i,j=1....6

2.5.5

The final equation then reduces to the general form:

∆T = −

T
ρC p

i

αi ⋅ ∆σ i

with i=1....6

2.5.6

Equation 2.5.6 can then be applied to either isotropic materials:

∆T =

−T
⋅ α ⋅ ∆ (σ11 + σ 22 )
ρC p

25

2.5.7

Or it can be applied to orthotropic materials:

∆T =

−T
⋅ (α ∆σ + α ∆σ )
ρ C p 11 11 22 22

2.5.8

The key difference between Equation 2.5.7 and Equation 2.5.8 is that for an orthotropic
material the coefficients of thermal expansion in both principal directions must be
known.

For the results discussed in this research, the term TSA signal is often used

and it refers to the value of the temperature change T measured in camera analog to
digital (a/d) units.

Additional insight into TSA can be realized by examining the response from the infrared
cameras from a signal processing perspective. For the sake of simplicity it can be
assumed that the material being analyzed is isotropic so that Equation 2.5.7 is
applicable. The Deltatherm system is designed to measure small variations in
temperature ( T) caused by cyclic loading. The infrared camera produces thermal
images using an array of InSb (indium antimonide) detectors. Images are captured at a
rate of over 400 frames/sec and processed to produce an image of the temperature
variation over the entire field of view. A simple analog electronics model can be used to
explain the fundamental signal processing being used to produce stress images. Figure
8 shows this idealized electronic model of the Deltatherm system, where S represents
the IR signal from the camera, minus any noise. One of the purposes of signal
processing is to eliminate the noise in the system and measure the amplitude of this IR
signal (S). This is done by correlating the reference signal (r) coming from the load
frame to the IR signal (S) from the camera. In order for the correlation to work, the
reference signal must be at the same frequency as the applied load, meaning that either

26

the load or displacement signal can typically be used. The signal conditioner digitizes
the reference signal, converting it to a square wave that oscillates between +1 and -1 at
the same frequency as the reference signal (r). Two digital reference signals are
produced from this, the first labelled “F” in Figure 8, is a conditioned cosine reference
and the second signal labelled “G” is a conditioned sine reference. When the
conditioned sine reference (F) is at the same frequency and has the same zerocrossings as S, they are multiplied together resulting in a rectified sine wave that can
then be passed through a low pass filter to obtain a single value Ix. This operation can
be summarized mathematically with the following expression:

Ix =

(S ⋅ F )

2.5.8

28

Figure 8: Simple signal processing model for the Deltatherm TSA system

27

If the in-phase reference F is replaced with the sine reference (G) in Equation 2.5.8 then
the result is Iy. Since G is always 90° degrees out of phase from F, the Iy image is zero
when the Ix image is maximized. The magnitude (R) for both the Ix and Iy images is
defined as:

2
R = Ix + I 2
y

2.5.9

The value of R remains constant regardless of the phase differences between S and F.
The phase between the digitized reference signal F and the infrared signal S can be
adjusted in software after image capture. Ideally the phase should be adjusted so that
the Iy image is as close to zero as possible. However, there may not be a phase setting
that maximizes the Ix images due to phase lag in the structure. Phase lag can be
caused by high stress gradients in the part, low cycling frequencies, or even differences
in paint thickness (thicker paint increases the amount of time it takes for heat to be
28

conducted to the surface and be emitted, thereby causing a phase lag) .
2.5.2 Digital Image Correlation (DIC)
Image correlation equipment is typically broken down into two levels of complexity: twodimensional and three-dimensional image correlation. Two-dimensional image
correlation is accomplished using only a single camera image of a surface under test
and a software based algorithm to calculate the strain field. This procedure is adequate
for measuring in-plane strains in specimens as long as little or no out-of-plane motion
exists. Three-dimensional image correlation is accomplished by using stereo-camera
photogrammetry, as well as the same software based algorithm employed with two-

28

dimensional DIC. The addition of the second camera and a photogrammetry algorithm
allow a three-dimensional DIC system to measure surface topography as well as
surface strains.
2.5.2.1 Two Dimensional Digital Image Correlation
The image correlation algorithm employed with two-dimensional DIC is common to both
the two and three-dimensional versions of this technology. The hardware used with
two-dimensional DIC consists of a single digital video camera in conjunction with
appropriate lighting. One limitation of two-dimensional image correlation is its inability
to deal with significant out-of-plane displacement. Changes in magnification due to
small amounts of out-of-plane displacement, or changes in the depth of field, can result
in large errors in the surface strain measurement. However, this deficiency can be
overcome by using two cameras.

The basic concept behind the use of image correlation for strain measurement is that a
set of points on an undeformed object can be matched to the same set of points on the
deformed object

29-31

. For image correlation to work effectively, it is important that the

surface of the object examined has enough contrast to ensure that each subset of
points on the object is statistically different from every other subset of points. It is for
this reason that a black and white speckle pattern is often applied to the surface of the
object being tested.

The process of converting an image into digital form, represented by a matrix of pixels,
has important implications for the matching process. During the deformation of a

29

subset, it is entirely possible that the object centre in the undeformed image will be
mapped to a location between pixels on the deformed image. In order to overcome this
problem a key aspect of the image correlation process is the interpolation of pixel
values in both the undeformed and deformed image. A wide variety of interpolation
schemes can be used, with the most common being a bi-cubic spline fitting
algorithm

30,31

and with the end result being a continuous variation in intensity

31

patterns .

Assuming the subset chosen is small enough so that the displacement gradients are
nearly constant, the undeformed intensity array can be related to the deformed intensity
array by uniform linear mapping. This uniform linear mapping is directly related to the
strain field that each individual subset undergoes. The correlation software iteratively
displaces each subset looking for a match between the reference and deformed image.
In addition, modern image correlation algorithms can also account for subset distortion
by applying a mathematical shape function to each subset before performing the
32

iterative search . A cross-correlation function is then used to characterize the quality
30

of the match between the reference and deformed images . Once this has been
completed over the entire area of interest, the displacement field obtained can be
30

differentiated to determine the full strain tensor .

30

2.5.2.2 Three-Dimensional Digital Image Correlation (DIC)
The photogrammetric component of three-dimensional image correlation is based on a
binocular vision model, similar to that used for human depth perception. By comparing
the location of corresponding subsets in images taken by both cameras, the surface
profile of a feature can be determined, in addition to calculating surface strains. One of
the fundamental differences between two and three-dimensional image correlation is
that, for the three-dimensional case, information about the orientation of the cameras is
required. To obtain this information a calibration process must be carried out for the
30

pair of cameras being used . The five parameters required for modelling the imaging
characteristics of the cameras, and their location relative to the sample plane, are
shown in Table 3. All these parameters describe the internal workings of the camera
30

and are camera specific values .

31

Table 3: Camera calibration parameters

Parameter

(1) Pinhole distance (phd)

Definition
distance from the imaging lens to the CCD
sensor array

(2) & (3) Co-ordinates of the

two dimensional location of the intersection

centre of the image (Cx,Cy)

between the optical axis and the sensor plane

(4) Lens distortion factor (K)

intrinsic camera parameter

(5) Aspect ratio

two dimensional location of the intersection
between the optical axis and the sensor plane

General error estimates are difficult to determine since there are many parameters that
can have a direct effect on accuracy. Basic error estimates have been derived, given
that the camera orientation remains within a prescribed boundary which includes:
(1) Pan angle between cameras: 30-60 degrees (2) Twist and tilt angles: -5 to 5
degrees (3) Object to camera distance (Z): 0.3 m to 3 m (4) Size of region of interest
(D): 10 mm to 500 mm and (5) Ratio of Z/D: Z/D > 5. When the camera orientation is
within the range of values given above, the typical uncertainty for in-plane displacement
is on the order of D/10 000, where D is the in-plane dimension of the object being
measured. Uncertainty in the out-of-plane displacement is on the order of Z/50 000
30

where Z is the distance from the object to the CCD .

32

3.0

LITERATURE REVIEW

This chapter reviews the available literature regarding hole cold expansion and riveting
in both aluminum and fiber metal laminate alloys. Special attention is paid to the areas
of residual stress measurement, and experimental strain measurements with the goal of
identifying the breadth and depth of engineering knowledge in these areas as well as
knowledge gaps where additional original research contributions are required.
3.1

Cold Expansion of Aluminum Alloys

A significant body of literature has been amassed over the years pertaining to hole cold
expansion and its effects on aluminum alloys. A broad overview of the different
33

methods that can be used for cold expansion is provided by Champoux . The most
common hole cold expansion methods mentioned by Champoux include solid
sleeve
48

20,34,35

36,37

, ballising

38

, split mandrel

as well as split sleeve cold expansion

39-

, which has been qualified for use in aerospace structures and has thus become the

focus of most current research articles. Research involving hole cold expansion can be
broadly categorized into three separate areas: fatigue performance after cold
expansion, experimental measurements of the cold expansion process, and computer
simulation of the cold expansion process; of which the first two will be of primary
interest.
3.1.1 Fatigue of Aluminum Alloys as a Result of Cold Expansion
From an aerospace perspective, determining the fatigue performance of any structural
modification is usually a key step in validating these modifications for use on flight
articles. Petrak and Stewart

49

laid the groundwork for fatigue studies with their

33

research looking at the effect of several types of cold expansion and interference fit
fastener systems. In their paper, several different interference fit fasters were tested,
along with a new type of rivet and most importantly two different cold expansion
systems: the split sleeve system developed by Boeing, as well as a solid sleeve system
developed by the J.O King Company. The results showed that both split sleeve and
solid sleeve cold expansion produced comparable fatigue results, which addressed the
concern regarding the creation of a longitudinal ridge or “pip” that occurs during split
sleeve cold expansion. In fact the results showed that compared to an open hole, any
system that produced some type of interference fit would provide an improvement in
fatigue life, with an apparent correlation between the degree of interference and the
amount of crack growth retardation. This broad conclusion drawn by Petrak and
Stewart

49

50

was supported by Wagner et al

in later studies, but did not answer some of

the more detailed questions about the split sleeve cold expansion process concerning
issues such as the effect of the split sleeve orientation, post cold expansion reaming,
and out of plane displacement resulting from the cold expansion process. These issues
51

were later investigated by Beaver et al

who looked at these three variables and their

role in determining the effectiveness of split sleeve cold expansion with respect to
fatigue life.

Statistical analysis of the fatigue data from a series of cold expanded

2214-aluminum alloy coupons showed that no statistically significant difference existed
between test groups on the basis of split sleeve orientation, post cold expansion
reaming or the removal of out of plane displacement. This proof of the robustness of
the split sleeve cold expansion process was likely one of the drivers for the widespread
51

adoption of this technique in aerospace manufacturing. Beaver et al

34

was also one of

the first to comment in the open literature on the fractographic differences between the
extent of cracking on the entry and exit faces of a test coupon, an observation that was
52

later confirmed quantitatively by Zhang and Wang

using replicas of the fracture

surfaces to determine crack growth curves for both the mandrel entry and exit faces.

On a parallel path, other researchers took a more quantitative view of the fatigue
performance of aluminum alloys after cold expansion and attempted to quantify the
effect of process variables, such as the degree of cold expansion on fatigue life. In the
late 1970’s Chandawanich and Sharpe

20

used solid sleeve cold expansion to perform a

detailed study on crack growth and the stress intensity factors on both the entry and exit
faces of a fatigue test coupon. The results showed that cold expansion appeared to
have little effect on “crack initiation” (defined as the number of cycles to a crack length
of 0.1 mm) but that crack growth rates as well as the stress intensity factor at the crack
tip were markedly reduced. A study by Chao and Xiulin

53

focused more thoroughly on

“fatigue crack initiation” (defined here as the number of cycles to a crack length of
20

0.25 mm), with the results corroborating the findings of Chandawanich and Sharpe
that cracks formed first on the entry face of the coupon. However, unlike
20

Chandawanich and Sharpe , Chao and Xiulin

53

found that cold expansion did play a

role in increasing the number of cycles required for “fatigue crack initiation”. A later
54

study by Lacarac et al , looking at the role of the applied stress and the stress ratio on
the effectiveness of cold expansion, found that cold expansion had only a small

35

influence on fatigue crack growth rates for cracks of less than 1 mm and had the largest
influence on cracks of between 1 - 2 mm. This finding was similar to that of Zhang and
52

Wang

who also showed that the benefits of cold expansion were due to the

decreased crack propagation rate of larger cracks on the order of 0.5 - 1.5 mm.
However, comparison of Lacarac et al’s
20

those of Chandawanich and Sharpe
54

Lacarac et al

54

results regarding cracks of similar length to

or Chao and Xiulin

53

is not possible since

used starter notches of 0.15 mm in their coupons. Overall there

appears to be a lack of consensus regarding the ability of cold expansion to extend life
in the early stage of the fatigue process. It is possible that in the short crack regime,
immediately after crack nucleation, process variables such as the degree of cold
expansion play a larger role. What does appear clear is that cold expansion is effective
for reducing fatigue crack growth rates in aluminum alloys and is most effective after
crack nucleation and crack growth past the short crack regime.
3.1.2 Strain measurements of the Cold Expansion Process
Although fatigue experiments are useful for quantifying the life extension that can be
achieved from cold expansion, a deeper understanding of the process requires
experimental measurements of the strain fields resulting from hole cold expansion.
Some of the earliest measurements of these strain fields were made using standard foil
gauges

34,44,55

. One of the difficulties with foil gauges is that they average the strain

over their entire gauge area, making them less suitable for measuring regions with large
strain gradients such as at the edge of a hole. Also, since each individual strain gauge
measures strain in only one direction, determining hoop and radial strains requires

36

strain gauge rosettes or even alternating strain gauge orientations as was done by
44

O’Brien . Another method used by several researchers for making full-field
42,43,56

measurements was the grid method

. In this method, photoresist techniques are

used to etch precisely spaced, high density grids around the area close to the hole.
Optical microscopy can then be used to determine displacements by measuring the grid
distance after cold expansion. These displacements can be differentiated with respect
to length to determine the strain fields. In some ways, grid methods can be seen as the
precursor to modern image correlation algorithms where a random dot pattern replaces
the pre-printed grid and correlation algorithms replace direct measurements of grid
spacing. Full-field strain measurements have also been successfully made by
researchers using moiré techniques

20,35,41

.

Using these techniques a significant body of information has been amassed regarding
the effect of cold expansion on aluminum alloys. One of the early areas of investigation
was in regards to the location of the elastic-plastic boundary after cold expansion.
34

Poolsuk and Sharpe

used both foil strain gauges and linear variable differential

transformed (LVDT) based surface profile measurements to determine the elasticplastic boundary around holes which had been cold expanded using the solid sleeve
cold expansion process. The technique used by Poolsuk and Sharpe

34

was fairly

simple in practice and relied on the assumption that for an isotropic material, in the
elastic region surrounding a cold expanded hole, the magnitude of the radial and
tangential stresses would be equal. Poolsuk and Sharpe

37

34

used strain gauges to

determine radial and tangential strain at discrete points, but the same technique could
be used with any full-field strain measurement system. Their determination of the
radius of plasticity using surface thickness relied on the fact that in the plastic region,
radial and tangential strains are no longer equal in magnitude and as a result of volume
constancy requirements, through thickness changes must be non-zero. The results of
this study showed that the radius of plasticity for solid sleeve cold expansion ranged
from 6.03 mm to 7.06 mm, varying slightly depending on the degree of interference. A
55

similar study performed by Arora et al

found similar results for holes expanded using

a split sleeve type process. Both experimental methods agreed with one another and
when compared to purely theoretical findings showed that Nadai’s
58

for plane stress situations while Rich and Impellizzeri

57

theory worked well

had the best theoretical results

for plane strain situations.

An overview of the full-field measurements using moiré
44,59

photoelasticity

and strain gauges

34,44,55

20,35,41

42,43,56

, grid methods

,

show very similar strain results

surrounding a cold expanded hole. As expected, radial strains are compressive and
tangential strains are tensile, with peak magnitudes related to the degree of cold
expansion. One of the interesting results noted by several researchers is that the
strains on the mandrel entry side of the coupon are consistently lower than results on
the mandrel exit side of the coupon

41,43,44,47,52,60-63

. Other researchers looking at

crack growth rates have confirmed that this strain differential results in faster crack

38

growth rates on the mandrel entry rather than on the mandrel exit faces of fatigue
coupons

51-53,64

. One possible explanation for this is presented by both Zhang and

52

65

Wang

and Forgues et al

is that the difference might be attributable to the level of

retained expansion and to the material volume carried by the mandrel movement, while
66

Babu et al

suggested that differences in the constraint conditions between the entry

and exit faces might be responsible for the formation of non-uniform through-thickness
residual stresses.

In conjunction with these “total” strain measurements, a significant amount of work has
been done looking at the (elastic) residual strain resulting from the cold expansion
process using either standard x-ray or neutron based diffraction
Sach’s type measurements

60-62,67,70

40,42,45,46,48,63,67-69

or

. X-ray diffraction measurements on aluminum

alloys are always challenging due to the large grain size and texture in the material that
typically results in high measurement inaccuracies, a fact documented by Ball and
42

who ended up using grid methods to back up their x-ray diffraction results.

Lowry

One of the more prolific users of x-ray diffraction technology was Stefanescu and his coworkers

45,46,48,63,69
47

radiation

who used a highly collimated x-ray beam as well as synchrotron

to investigate the residual strain field around cold expanded holes and

showed that the approximate difference between the entry and exit faces was on the
63

order of 60 MPa . With regards to the modified Sach’s method, Ozedmir and co-

39

60,62

workers used this method extensively to study surface

61,70

and through thickness

residual strains resulting from hole cold expansion. A comparison between Ozedmir
and Edwards

61

Sach method results and Stefanescu et al’s

46

x-ray diffraction results

showed very similar stress fields around a 4% cold expanded hole (Figure 9) and clearly
demonstrate the difference in stress fields between the mandrel entry (inlet) and
mandrel exit (outlet) faces.

200

0

0

-200

Hoop stress (MPa)

Hoop Stress (MPa)

200

Entry
Face
Exit
Face

-400

-200
Middle
-400

Exit Face
Entry Face

-600

-600
0

5

0

10

Distance from hole (mm)

2
4
6
Distance from hole (mm)
(b)

(a)

Figure 9: Residual stress measurements around a 4% cold expanded hole (a)
46
measured using x-ray diffraction from Stephanescu et al and (b) measured using a
modified Sach’s method from Odzemir and Edwards

40

61

3.2

Riveting of Aluminium Alloys

Although the use of riveting as a joining method is not new, many of the early papers
regarding riveting have dealt with the rivet material itself and/or the rivet material and
process issues. From a theoretical perspective, the riveting process shares some
fundamental similarities to cold expansion. In both cases, interference is created that
expands the initial diameter of the hole, this means that some of the early closed form
work looking at pressurization of holes could provide estimates of the residual strain
57,71,72

resulting from riveting

. One of the first papers to build on the similarity between

these two processes and to try and determine fatigue life differences was the work of
Petrak and Stewart

49

in 1974. They compared cold expanded and riveted coupons in

the zero load transfer configuration to prove their hypothesis that the degree of
expansion was the main driver in improving fatigue life. The results showed that in the
zero load transfer (ZLT) configuration, the rivets provided approximately the same
fatigue life benefit as hole cold expansion. This result agreed with their original test
hypothesis, since both treatments resulted in approximately the same degree of hole
expansion. Fox and Withers

73

also noticed the similarity between cold expansion and

riveting and showed, using synchrotron and neutron diffraction, that the residual
stresses resulting from cold expansion and riveting were similar in magnitude and
direction. In a follow up paper Fox and Withers

74

used riveted, zero load transfer

coupons to measure stress relaxation around the rivet after various numbers of fatigue
cycles. The results from x-ray diffraction showed that the residual stress profile around
the rivet was similar to that seen in cold expansion. Interestingly, although a relatively

41

high maximum applied stress (240 MPa) was used, crack nucleation was not biased
towards the rivet hole, but was varied in terms of location, an indication of the
effectiveness of the rivets compressive residual stress field to reinforcing the hole.

Given the difficulties making strain measurements in the region under the rivet head, the
few papers that do provide experimental measurements typically relied on either x-ray
73-76

diffraction

or strain gauges

23,77-79

to measure the strains resulting from the

riveting process. One interesting approach to obtain results closer to the rivet hole was
75

that of Fitzgerald and Cohen

who used x-ray diffraction to make residual stress

measurements of the rivet head itself. Although this did not address the issue of the
residual stresses beneath the manufactured head, it did provide experimental data as
close to the pilot hole as possible and showed that the compressive residual stress
close to the hole is a function of squeeze force. Fox and Withers

73

used the same

approach, except using both synchrotron x-ray and neutron diffraction, to make both inplane and through thickness residual strain measurements. A summary of the radial
and hoop strains surrounding the 7.9 mm diameter rivet used in Fox and Withers’

73

experiment is reproduced in Figure 10, and shows compressive strains in the immediate
vicinity of the rivet and tensile hoop strain as one moves away from the rivet center.

42

3000

Elastic Strain (x10e-6)

2000
1000
0
-1000
-2000
-3000

Radial Strain
Hoop Strain

-4000

Edge of Rivet

-5000
0

5

10

15

20

25

30

Distance from rivet Center [mm]
73

Figure 10: Radial and hoop strains due to the riveting process from Fox and Withers .
Vertical line denotes interface between rivet and coupon. Dashed lines are provided for
clarity only
The more common approach to estimating the strains resulting from riveting has been
to simulate the riveting process computationally using finite element software. Although
the focus of this research is experimental, a brief review of some of the analytical work
done on riveting can be helpful as it can provide some understanding of what is
happening under both the driven and manufactured head, as well as provide some
additional context for discussing the fatigue results that were obtained.
Attempts to better model the riveting process and take into account the through
thickness compression resulting from the formation of the driven head first entered the

43

open literature with Muller’s

23

work in 1995. This work in many ways appears to be

seminal publication on the effects of riveting, dealing with both experimental and
23

analytical aspects of riveting in aluminum and fiber metal laminate materials. Muller

used both closed form and finite element analysis to back up the results of his fatigue
tests on riveted lap joints, which demonstrated the importance of controlling riveting
squeeze force and showed that the fatigue life of a riveted joint could be correlated to
the squeeze force applied to the rivet.

Muller’s suggestion that the clamping force played an important role in fatigue life led
80

researchers such as Deng and Hutchinson

77

and Li and Shi

to work at developing
77

better finite element models to simulate the creation of this clamping force. Li and Shi
developed a 2D axisymmetric model that was validated using both strain gauges and
neutron diffraction and that could account for the compressive stress developed
between the driven and manufactured heads and the surface of the joint. The use of
strain gauges for validating various aspects of an FEA model is quite commonplace in
78

the literature with researchers such as Langrand et al

79

and Markiewicz et al

using

strain gauge instrumented coupons to validate the performance of their computer
models. Other validation approaches have included using the force-deflection history of
the rivet to validate the computer model; an approach that was used by Szolwinski and
81

82

Farris . Although more current papers by researchers such as Atre and Johnson
83

and Szymczyk et al

present 3D FEA models of the riveting process, there is little

44

experimental validation of the results and the results themselves are not quite
comprehensive enough to support the experimental work in this research. An older,
but more comprehensive research program on the residual strains induced during the
84

riveting process was presented by Rans and Straznicky
77

results of Li and Shi

who used the experimental

to validate their 3D FEA model. Of greatest interest from their

findings was the observation that the residual stresses beneath the rivet head were
primarily due to the rivet clamping force and not to the radial expansion of the rivet
shank.
3.3

Riveting of Fiber Metal Laminate Materials

A review of the open literature showed that only a small body of knowledge exists
focusing specifically on riveting and its effect on fiber metal laminate materials
23

The impetus for many of these investigations was sparked by Muller

23,85-88

who performed a

comprehensive series of tests as part of his doctoral dissertation looking at the fatigue
behaviour of riveted lap joints in both 2024-T3 aluminum and fiber metal laminate
materials. One of the key findings from his investigation was that rivet squeeze force
played a key role in controlling the fatigue life of riveted joints and that higher squeeze
forces could result in an order of magnitude increase in fatigue life. He also looked at
direct comparisons between 2024-T3 aluminum and FML 3 riveted joints and showed
that the qualitative response to riveting is similar in both materials, but that FML 3
riveted joints had a greater fatigue life with crack growth and residual strength
23

reductions occurring more slowly. Muller

also noted that the location of crack

nucleation tended to move away from the rivet center as the rivet squeeze force was

45

.

23

increased. Muller

inspected coupons after riveting and did not find any delamination

in FML due to the riveting process. The results of an experimental test program by
88

Lazzeri

on riveted FML and monolithic 2024-T3 coupons produced similar

conclusions. Ryan and Monaghan

85

built on this research with a finite element based

investigation looking at the potential failure modes in an unnamed grade of FML and
2024-T3 aluminum during the riveting process. They took a more basic approach to
modeling FML properties in that two FEA simulations were run, one with material
properties representative of the longitudinal direction and one representative of the
transverse direction in the material. Although Ryan and Monaghan

85

claim to have

derived material property information from actual tensile tests, the results do not
conform to those for any standard grade of FML

10

with a significant difference in elastic

modulus between the longitudinal direction (53.9 GPa) and the transverse directions
(9.4 GPa). This fact notwithstanding, Ryan and Monaghan’s

85

work suggests the

potential for internal delamination of the FML plies, a suggestion that was also
86

corroborated by Rans et al . Ryan and Monaghan’s

85

FEA models also showed a

non-homogenous expansion of the FML due to the radial expansion of the rivet, which
makes sense given the extremely orthotropic nature of the FML they used, but the
magnitude of which may vary when less orthotropic FML grades are used. The finite
86

element based study done by Rans et al

is the only published paper to date

examining and comparing the residual stresses due to riveting in both fiber metal
laminate and 2024-T3 aluminum materials. Although no direct experimental validation
46

was provided in this paper, the displacement of the rivet bucking bar was compared to
experimental data and showed very good agreement to the FEA results. Overall, the
finite element results showed that riveting in FML resulted in larger regions of plasticity
86

with smaller gradients of residual stress. Rans et al

attributed this behaviour to the

apparent strain hardening caused by the fiber layers. This was surmised to be because
of the redistribution of load to the fiber layers once the aluminum layers started yielding.
Experimental corroboration of this phenomenon will be difficult since the image
correlation results are limited to the region adjacent to the manufactured or formed head
of the rivet.
3.4

Cold Expansion of Fiber Metal Laminate Materials

A search of the literature regarding the effect of cold expansion on fiber metal laminates
revealed only two papers. The first was a Masters thesis by van der Kuip

89

that looked

at fatigue crack growth in FML 3-3/2, FML 3-5/4 and aluminum 2024-T3 coupons that
had been cold expanded. Overall, van der Kuip

89

noted that crack growth rates on the

entry and exit sides were noticeably different, with cold expansion extending the life in
the early stage of the fatigue process on the exit side of the coupon, but not as
significantly on the entry side. Mechanical removal of the individual aluminum layers
showed that a typical triangular delamination pattern existed with the base of the
triangle near the edge of the hole and the tip coincident with the crack tip.

90

The second paper was by Rans et al

who used computational methods to simulate
90

the cold expansion process in FML 3-2/1. Rans et al

47

noted that expansion of the

aluminum layers in the FML occurred as a result of two mechanisms: first was radial
pressure from the oversized mandrel and second was a shear-driven expansion from
the elastic expansion of the prepreg layer. Although delamination between the fiber and
90

aluminum layers was not modeled in this work, Rans et al

commented on the

likelihood that a small amount of delamination around the cold expanded hole could be
beneficial as this would extend the length over which the internal glass fibers could
stretch, thus serving to better retard any cracks that form. While delamination is
certainly helpful for reducing crack propagation, if delamination around the hole is
confirmed, this would suggest that cold expansion may not be able to extend life in the
early stage of the fatigue process. Overall Rans et al’s

90

study reinforced the suitability

of performing hole cold expansion process on FML.
3.5

Discussion: Identification of Knowledge Gaps

One of the main purposes for reviewing the literature regarding riveting and cold
expansion in both aluminum and fiber metal laminates was to identify gaps in the
current body of research that needed to be addressed. The concept behind cold
expansion is not new and a substantial body of knowledge has been built up looking at
both the fatigue performance as well as the strain fields generated by cold expansion.
The literature clearly shows that although cold expansion does provide an increase in
fatigue life, the most common method used for cold expansion, split sleeve cold
expansion, produces unequal residual compressive stresses on the entry and exit faces
of the coupon. The increased residual compressive stress on the exit face better serve
to retard crack formation, and, thus, crack nucleation and growth tend to occur first on
the entry face. This is one phenomenon that has not been deeply explored in fiber

48

metal laminate materials. A review of the literature shows that no full-field experimental
methods have been used to measure strains in fiber metal laminate materials and that
including this as part of the current research could help better understand the root
cause of this phenomena in both FML as well as in 2024-T3 aluminum. Another issue
that can be addressed by this research is whether cold expansion is more effective at
extending fatigue life during the early stage of the fatigue process or during the crack
propagation stage. This is an important question for FML materials because being able
to extend fatigue life during the early stage of the fatigue process would improve one
shortcoming with FML and increase the acceptance of this material in aerospace
structures. Although this issue has been addressed by researchers for aluminum, there
is some degree of contradiction in the conclusions. Two possible reasons for these
contradictions exist, the first is that the definition of short crack length is somewhat
arbitrary and is defined differently by researchers; the second is that not all researchers
have recognized the difference in residual stress between the entry and exit faces and
this difference can also play an important role in retarding short crack growth.

From a fatigue perspective, the riveting of aluminum and FML joints has been
addressed by many researchers. Experimentally the greater focus has been on the
fatigue life, while far fewer researchers have attempted to measure the strains during
the riveting process in aluminum. In FML, the experimental focus has been almost
entirely on the fatigue life of riveted FML coupons while only finite element models have
been used to estimate full-field strains during riveting. Experimentally measuring
riveting strains is difficult in general due to the fact that the rivet covers the region

49

closest to the hole, however the experimental methods used in this research should
provide some measure of the strain field surrounding the rivet, and, when combined
with analytical modeling, may provide some insight into what is occurring during the
riveting process. Although zero load transfer (ZLT) coupons are less popular since they
are representative of lower-load aircraft attachments, several researchers

49,91,92

have

used this geometry in 2024-T3 to study fatigue life during riveting. No researchers to
date have used this geometry in FML. Another area that has not been addressed is the
concept of optimizing FML for improved performance in cold expansion and riveting.
Ideally, the strain measurements taken both statically and during fatigue cycling will
provide suggestions for new FML layups that may improve both riveting and cold
expansion behaviour. Although the cold expansion and riveting of aluminum alloys are
topics of some familiarity to researchers, extending this research into the realm of fiber
metal laminates opens up a new avenue of original research.

50

4.0

RATIONAL DECISION MAKING PROCESS

For the static measurements of strain during the cold expansion and riveting process,
several possible experimental mechanics techniques were available for use. To better
evaluate each of these technologies in an objective manner, the rational decision
methodology put forward by Olden and Patterson

93

was used. This method involves

identifying essential (hard) and non-essential (soft) attributes for the technologies under
consideration. The hard attributes are used to narrow down the list of potential
technologies and then an expert panel is employed to rate the importance of each
non-essential (soft) attribute as well as to score each technology on a scale of 1-10 in
terms of its ability to fulfill each of the attributes.
4.1

Technology Selection for Measuring Strains During Cold Expansion

The essential attributes for measuring strains during cold expansion, included the ability
to measure strain quantitatively (Att 1) and the ability to measure strain both during and
after the cold working process (Att 2). The technique to be selected also had to be able
to deal with the geometric constraints imposed by the FTI cold expansion equipment
(Att 3) and had to be easily available (Att 4). Based on these criteria a wide range of
techniques were evaluated, with the results of the evaluation detailed in Table 4. A brief
summary of the reason for excluding some of the techniques is presented in Table 5.
The evaluation process resulted in the following techniques being chosen: digital image
correlation (DIC), in-plane moiré (MI), holographic interferometry (HI), reflection
photoelasticity (RP), electronic speckle pattern interferometry (ESPI) and strain gauges
(SG).

51

Table 4: Viability of various experimental mechanics techniques for measuring strains
during cold expansion
Technique

Att 1

Att 2

Att 3

Att 4

Viable

Brittle Lacqueur

N

N

N

N

N

Caustics

N

N

N

N

N

Electronic Speckle Interferometry

Y

Y

Y

Y

Y

Digital Image Correlation

Y

Y

Y

Y

Y

Moire - in plane

Y

Y

Y

Y

Y

Moire - shadow

N

N

Y

Y

N

Moire - projection

N

N

Y

Y

N

Holographic Interferometry

Y

Y

Y

Y

Y

Photoelasticity - transmission

Y

N

Y

Y

N

Strain gauges

Y

Y

Y

Y

Y

Thermoelasticity

Y

N

N

Y

N

Photoelasticity - reflection

Y

Y

Y

Y

Y

Table 5: Techniques excluded from decision making and reason for exclusion
Technique

Reason for Exclusion

Brittle Lacquer

Technique is qualitative only

Transmission Caustics

Requires a transparent specimen

Reflection Caustics

Optical access to singularity

Shadow Moiré

Measures surface deformation

Projection Moiré

Measures surface deformation

Transmission photoelasticity

Requires a transparent specimen

Thermoelasticity

Requires cyclic loading

For the techniques that were chosen, the following non-essential attributes were
selected for the next level of evaluation (Table 6):

52

Table 6: List of non-essential attributes for the techniques that met the essential
requirements
Non-essential (soft) attributes
Insensitive to test environment
High quality data
No limitation on loading type/amount
Ease of surface preparation
Low cost per test
Real time testing
Low capital cost
Ability to measure strains near hole edge
Compatible with FTI cold expansion tools

The list of non-essential attributes was provided to each member of the expert
committee and they were asked to rank the importance of each attribute on a scale of
1-5 (with 1 being the least important and 5 being the most) as well as to rank the
performance rating of each technique with respect to each attribute on a scale of 1-10
(with 1 being poor performance and 10 being excellent performance). For each
technique the average importance and the average performance were calculated and
plotted against one another as shown in Figure 11 to Figure 13. Ideally one would want
to see a technique have high performance for the most important attributes and thus a
cluster of dots in the upper right hand quadrant of the graphs.

53

5.0
Importance

Importance

5.0
2.5
Digital Image Correlation

0.0
0

5

2.5
Moire - In plane

0.0

10

0

Performance

5

10

Performance

Figure 11: Plot of importance versus performance for digital image correlation and inplane moiré

5.0
Importance

Importance

5.0

2.5
Holographic Interferometry

0.0
0

5

2.5
Reflection Photoelasticity

0.0

10

0

Performance

5

10

Performance

Figure 12: Plot of importance versus performance for holographic interferometry and
reflection photoelasticity
5.0
Importance

Importance

5.0

2.5
ESPI

0.0

2.5
Strain Gauges

0.0

0

5

10

Performance

0

5
Performance

Figure 13: Plot of importance versus performance for electronic speckle pattern
interferometry and strain gauges

54

10

In addition to examining the distribution of each attribute in terms of the importance and
the performance, it is also useful to use a metric that can quantitatively determine the
optimum technique for each situation. In this case a cumulative score for each
technique was determined by multiplying the average importance of each attribute by
the average score given by the expert panel and summing this up for each technique.
The final cumulative scores are given in Figure 14, and show that digital image
correlation is clearly the optimum technique. Holographic interferometry received the
lowest scores overall, while strain gauges were second best, with the remaining three
techniques all fairly close in score.

250

Score

200
150
100
50
0
DIC

HI

MI

RP

ESPI

SG

Technique
Figure 14: Cumulative scores for each technique evaluated using the rational decision
making process
4.2

Technology Selection for Measuring Strains During Riveting

A second case study was performed looking at the essential attributes for measuring
strains during the riveting process. These included the ability to measure strain
quantitatively (Att 1), the ability to measure strains both during and after the riveting

55

process (Att 2) as well as ease of availability (Att 3). Based on these criteria a wide
range of techniques were evaluated, with the results of the evaluation detailed in Table
7. The evaluation process resulted in the following techniques being chosen: digital
image correlation (DIC), reflection photoelasticity (RP), and strain gauges (SG). The
techniques that were excluded and the reason for their exclusion are provided in Table
8.

The distribution for each technique in terms of importance versus performance are
given in Figure 15 and Figure 16a. The final cumulative scores are given in Figure 16b,
and show that digital image correlation is clearly the optimum technique. Reflection
photoelasticity received the lowest scores overall, while strain gauges came in second
place. The overall results are supported in the literature which showed a number of
23,77-79

researchers who used strain gauges to corroborate their results
72

researcher who used photoelasticity .

56

and even one

Table 7: Viability of various experimental mechanics techniques for measuring strains
during riveting
Technique

Att 1

Att 2

Att 3

Att 4

Viable

Brittle Lacqueur

N

N

N

N

N

Caustics

N

N

N

N

N

Electronic Speckle Interferometry

Y

N

Y

Y

N

Digital Image Correlation

Y

N

Y

Y

N

Moire - in plane

Y

Y

Y

Y

Y

Moire - shadow

N

N

Y

Y

N

Moire - projection

N

N

Y

Y

N

Holographic Interferometry

Y

N

Y

Y

Y

Photoelasticity - transmission

Y

N

Y

Y

N

Strain gauges

Y

Y

Y

Y

Y

Thermoelasticity

Y

N

Y

Y

N

Photoelasticity - reflection

Y

Y

Y

Y

Y

Table 8: Techniques excluded from decision making and reason for exclusion
Technique

Reason for Exclusion

Brittle Lacquer

Technique is qualitative only

Transmission Caustics

Requires a transparent specimen

Reflection Caustics

Optical access to singularity

Shadow Moiré

Measures surface deformation

Moiré – in plane

Rivet makes grid installation difficult

Projection Moiré

Measures surface deformation

Transmission photoelasticity

Requires a transparent specimen

Thermoelasticity

Requires cyclic loading

57

5.0
Importance

Importance

5.0
2.5
Digital Image Correlation

5

Strain
Gauges

0.0

0.0
0

2.5

0

10

5

10

Performance

Performance

Figure 15: Plot of importance versus performance for digital image correlation and strain
gauges

200
Score

Importance

5.0
2.5
Reflection photoelasticity

5

100
50

0.0
0

150

0

10

DIC

Performance

RP
Technique

(a)

SG

(b)

Figure 16: a) Plot of importance versus performance for reflection photoelasticity b)
Cumulative scores for each technique evaluated using the rational decision making
process

4.3

Discussion

The outcome from the rational decision making process suggested that digital image
correlation should be explored for measuring strains during both the cold expansion and
riveting process. Both strain gauges and reflection photoelasticity scored highly during
both case studies, and the literature did highlight several researchers who used strain
gauges for making strain measurements after cold expansion

58

44,55,94

77-

and riveting

79,95

. Reflection photoelasticity was also used to better understand the strains after

cold expansion

44,96

. The outcome from the process is dependent on the parameters

provided as constraints, and different parameters may have resulted in the inclusion or
exclusion of one or more techniques. The results of this analysis are applicable to the
static testing of the cold expanded and riveted coupons and although these results have
some relevance to the fatigue testing portion of this research, thermoelastic stress
analysis was one technique that could only be used during the application of fatigue
loads. With only one image correlation system available, thermoelastic stress analysis
was used during the fatigue portion of the testing to measure strains on the opposite
face of the coupon. The selection of thermoelastic stress analysis was mainly due to
the availability of the equipment and its compatibility with fatigue loading.

59

5.0

EXPERIMENTAL METHODS

The experimental methods section details the procedures involved in both the static and
fatigue testing of the aluminum and fiber metal laminate coupons, including both the
cold expansion and riveting procedures as well information regarding both the digital
image correlation and thermoelastic stress analysis system. An overview of the
production methodology for the FML panels is also provided along with residual stress
measurements for each panel.

5.1

Static Test Setup

Identical test fixtures and digital image correlation (DIC) stereo camera setups were
used to measure surface strains during both the hole cold expansion and the riveting
process for both the aluminum and FML coupons (Figure 17). The DIC system was
comprised of two digital video cameras, mounted on tripods, (Retiga 1300, Qimaging
Inc, Burnaby BC) with resolutions of 1280 x 1024 pixels. For the field of view used in
the static test, the effective spatial resolution was 0.052 mm/pixel and the coupon
surface was illuminated using two high intensity LED light arrays (Siemens-Nerlite Inc,
Nashua NH). All coupons were positioned on a custom, three-pin support fixture, to
ensure consistent location of the specimens with respect to the cameras (Figure 17).
The sensitivity of a particular DIC setup is a function of the speckle distribution, the
image capture hardware and the correlation algorithm. The sensitivity of the DIC setup
used was determined empirically after system calibration by capturing multiple
reference images and processing them through the correlation algorithm. .The overall
strain sensitivity in all cases was better than ±50
(w) sensitivity was better than ±0.0015 mm .

60

and the out of plane displacement

Figure 17: Isometric diagram of coupon retention fixture

5.1.1 Hole Cold Expansion Procedure
The pilot hole for all coupons was drilled on a milling machine, using a carbide drill bit.
Drill speed was approximately 500-800 rpm, with a low feed force and no cutting fluid, to
97

avoid contaminating the fibre layers . Centre drilling was performed first, followed by a
starter drill and then a reamer to ensure consistent hole sizing.

Hole cold expansion was performed using a manual cold working tool (HP-10, FTI inc)
that was positioned behind the coupon and supported by a V block (Figure 18). This
43

manual cold expansion process has been used in previous research

and is fully

certified for aerospace use by the manufacture (Fatigue Technology Inc.). The split
sleeve was placed at the root of the mandrel and both were passed through the hole.
The mandrel was then pulled through the hole by turning the nut at the back of the
manual cold expansion tool. Images were captured at every 2 full turns until resistance
was felt as a result of the mandrel/split-sleeve contacting the hole. At that point, the

61

process continued with images taken every quarter turn (90º degree rotation) until the
mandrel passed completely through the hole. The split sleeve and mandrel were
removed from the coupon and a final image was taken.

Figure 18: Initial mandrel placement for hole cold expansion process

Mandrel displacement was calculated by measuring the axial displacement of the tool
caused by each rotation of the nut. Linear regression of the axial displacement versus
tool rotation data (Figure 19) showed that the mandrel displaced 1.25 mm/360º degree

Mandrel Disp. (mm)

of tool rotation and this value was used for subsequent cold expansion tests.

2.50
2.00
1.50
1.00

y = 3.452E-03x

0.50
0.00
0

90

180

270

360

450

540

Tool Rotation (degrees)
Figure 19: Mandrel displacement vs. tool rotation

62

630

720

Hole cold expansion was performed using a size 8-1-N split sleeve with a nominal
starting hole diameter of 6.40 mm and total interference of approximately 4.1%.
Incremental deformed images were taken from the mandrel entry side of the coupon as
the mandrel was displaced through the coupon thickness. The deformed images were
processed using Vic-3D software (Correlated Solutions Inc, Columbia SC) over an area
of interest spanning the entire height of the coupon. All images were processed with a
subset size of 17 pixels, a step size of 5 pixels and a strain window of 15 pixels.
5.1.2 Riveting procedure
The same test fixture and camera setup was used for the riveted coupons. Prior to
riveting, the coupons were painted white and speckled with black paint using a precision
spray gun. To ensure no paint adhered to the inner surface of the hole, a plug was
inserted into each hole during the painting process. A manual rivet tool was positioned
behind the coupon, supported by a V block (Figure 20). An initial image without the rivet
was used as the reference image when processing the data.

For the static testing, universal head rivets (MS20470AD-5) with a nominal diameter of
3.96 mm (0.156 inches) made from 2117 aluminum were used. These rivets were
positioned in pilot holes having a nominal diameter of 4.09 mm (0.161 inches) which left
approximately 0.12 mm of clearance around the rivet after installation. The decision to
focus on universal head rivets was made based on the difficulties other researchers had
using counter sunk rivets

86,87

. Although there is no doubt that for aerospace

applications countersunk rivets are important from an aerodynamic perspective,
producing the countersink can have negative implications if the countersink results in

63

the formation of a “knife-edge” at the metal/fiber laminate junction. Universal rivets
allow for a better comparison to the cold expansion results since the initial pilot hole
does not require any additional preparation and the confounding effect of the
countersink on the fatigue results is removed.

Figure 20: Manual riveting tool and coupon fixture
An initial measurement of the rivet protrusion was made before the riveting process
commenced. Riveting took place in two steps, with the first step being to use the
manual rivet press to set the rivet in the hole at which point an image was taken. Next,
the coupon was taken to a hydraulic rivet press were the final riveting was completed.
The coupon was brought back to the test frame where another image was taken and the
final rivet diameter and protrusion height were measured. If paint chips were visible,
compressed air was used to clean the coupon surface. Incremental deformed images
were taken from the driven side of the rivet as it was compressed to its final protrusion
height. The deformed images were processed using Vic-3D software (Correlated
Solutions Inc, Columbia SC) over an area of interest spanning the height of the coupon
with the rivet and rivet shadow removed, as shown in Figure 21. All rivet images were

64

processed with a subset size of 17 pixels, a step size of 9 pixels and a strain window of
15 pixels.

(a)

(b)

Note: For interpretation of the references to color in this and all other figures, the
reader is referred to the electronic version of this dissertation
Figure 21: Chosen area of interest for rivet processing. (a) area of interest showing
position of rivet and corresponding shadow and (b) actual reference image used.
5.2

Fatigue test setup

Fatigue experiments were conducted in an MTS servohydraulic frame equipped with a
90 kN load cell. Three load levels (8.3, 8.9 and 10 kN) were chosen with a load ratio of
R=0.1 and a loading frequency of 10 Hz. These corresponded to net section stresses of
168, 175 and 198 MPa respectively for the unexpanded coupon and approximately
0.8% higher net section stresses for the cold-expanded coupon. Net section stress was
defined as the applied load divided by the cross-sectional area (perpendicular to the
load) of the specimen at the position of the hole. On the mandrel entry face of the
aluminum coupons, optical images were captured using a single high resolution digital
video camera (Allied Vision Technologies, Newburyport, MA) with a 1000 x 1000 pixel
spatial resolution and a Canon FD zoom lens, coupled to a fiber optic based ring-light

65

(Olympus Highlight 3000, Center Valley, PA). The optical setup provided a resolution of
approximately 15.1 m/pixel; this combined with a light surface abrasion using 320 grit
sandpaper provided sufficient contrast to eliminate the need for any type of additional
speckle coating. Initial static images were captured at the maximum and minimum of
the prescribed loading cycle and then images were captured at maximum load in 600cycle increments for the unexpanded coupons and in 1200-cycle increments for the
cold-expanded coupons, using a synchronization module in the image capture software
(Correlated Solutions Inc, Columbia SC). Analysis of the images was performed using
Vic-2D image correlation software (Correlated Solutions Inc, Columbia SC). In addition,
the surface crack length was measured using Imagetool (University of Texas Health
Science Center, San Antonio, TX) image processing software. On the mandrel exit face
of the coupon, a thermoelastic stress analysis was used to measure strains. This
technology incorporated a Deltatherm 1410 infrared camera (Stressphotonics Ltd,
Madison WC) with a temperature resolution of 2 mK, an InSB detector with 256x256
pixel resolution and zoom lens providing a resolution of 74.8 m/pixel, was used to
perform thermoelastic stress analysis.

For the riveting portion of this test, individual coupons were riveted using an
instrumented arbor press (Figure 22a) with a squeeze force of approximately 13.3 kN.
Since the coupons were going to be used in fatigue, a special support fixture and
loading platen were integrated into the arbor press (Figure 22b) to help standardize the
riveting process and reduce any chance of bending the coupons. Standard 3.96 mm
diameter aircraft grade rivets (MS20470AD-5) requiring a clearance hole of 4.09 mm

66

diameter were used and all aluminum and standard FML 4 coupons were tested at a net
stress of 263 MPa. On the driven head side of the riveted coupon the same image
correlation system as above was employed to measure strain while on the
manufactured head side of the coupon the same thermoelastic stress analysis system
was used to provide a strain map proportional to the first strain invariant.

(a)

(b)

Figure 22: (a) Integral stop and support platen for the coupon during riveting with an (b)
instrumented arbor press with load cell
5.3

Production of FML and 2024-T3 Aluminum Coupons

Both the FML 3 and FML 4 grades, as well as the custom FML variants used in this test,
98

were produced at the National Research Council composite facility . All FML material
was manufactured using FM-94 film adhesive embedded with S2 glass fibers, along
with 0.3 mm thick 2024-T3 aluminum that had been phosphoric acid anodized (PAA)
and coated with BR127 primer to improve adhesion to the FM-94 film adhesive. Figure
23 shows the cure cycle used during the autoclave process for all FML sheets with a
maximum temperature of 121 ºC and a peak pressure of 517 KPa.

67

140

525

120

400

275

80
60

150

Pressure (KPa)

Temperature (C)

100

40
Temp (c)
20

25

Pressure (KPa)

0
0

50

100
Cure time (min)

150

-100
200

Figure 23: Standard cure cycle used for FML 3 and FML 4
5.4

Design of FML and 2024-T3 Aluminum Coupons

The design of both the static and fatigue test specimens was driven by the cost and size
constraints of the constituent materials used to produce the FML. The anodized
2024-T3 aluminum sheets used for FML production measured approximately 305 mm x
610 mm (12 inches x 24 inches) and were sheared in half to produce panels measuring
305 x 305 mm (12 inches x 12 inches) with the 0º degree orientation of the FML defined
by the rolling direction of the aluminum. Producing panels this size made the
constituent materials easier to handle while still maximizing the use of the FM-94
prepreg that measured 610 mm (24 inches) wide by approximately 200 m (656 feet).

In developing a design for the static coupons, the initial goal was to maximize the
number of coupons that could be produced from an individual panel. For the initial tests,

68

the coupon design was structured to provide six coupons in a given direction, with two
additional coupons in an orthogonal direction (Figure 24). Additional cut plans were
used to produce coupons oriented at 45° degrees to the rolling direction of the
aluminum, however, this design greatly reduced the number of available coupons
(Figure 25). Both the FML and aluminum coupons were cut using a waterjet cutting
system, which left a relatively rough finish that required milling 3.175 mm of material on
either edge of the coupons. This required that the coupons be made slightly oversized
(44.45 mm) so that they could be machined down to their final width of 38.10 mm
(1.50 inch). The final static coupon dimensions are shown in Figure 26.

The coupons used for fatigue testing had similar orientations and shape but were cut to
203 mm (8.0 inch) in length to allow them to be gripped in the servohydraulic load
frame. To compensate for the extra length of the fatigue coupons, only one transverse
coupon per sheet could be produced (Figure 27). The dimensions of the post water jet,
machined coupons are provided in Figure 28. For the final phase of fatigue testing
coupons were cut in the 0º, 45º and 90º degree orientation and a separate cut plan was
used that allowed for only two coupons in each material orientation (Figure 29).

69

Figure 24: Layout for standard static test coupons (dimensions in inches)

70

Figure 25: Layout for 45º static coupons (dimensions in inches)

Figure 26: Dimensions of static test coupon after machining (dimensions in inches)

71

Figure 27: Layout for standard fatigue test coupons (dimensions in inches)

Figure 28: Dimensions of fatigue test coupon after machining (dimensions in inches)

72

Figure 29: Layout for multi directional fatigue coupons (dimensions in inches)
5.5

Residual Stress Measurement of FML Panels

The literature on FML clearly acknowledges the effect that tensile residual stress in the
aluminum layers, caused by the manufacturing process, plays on fatigue life

1-3,99

.

Measuring the residual stress experimentally is a difficult procedure that is often done
using strain gauges. For the purpose of this research program, strain gauges were not
ideal since they would have had to be mechanically removed before water jet cutting,
possibly damaging the thin aluminum layer. The non-contact nature of the DIC
technique seemed to suggest that it would be an appropriate technology for measuring
residual strains on the FML panels, however a fair number of challenges still existed. In
order to ensure the integrity of the panels, the edge of each panel was masked off after
assembly and just before autoclaving. At this point the panels were speckled. Early

73

testing with standard spray paints (Krylon Flat Industrial Acrylic Lacquer Spray Paint,
Krylon Inc) showed that the heat from the autoclave caused the pattern to distort, but
this was solved by moving to high temperature paints (Tremclad High Heat Enamel Flat
Black, Tremclad Inc). Although the high temperature paints did not distort after
autoclaving, the breather cloth placed over the panels caused the background finish to
fade slightly and affected the overall contrast pre- and post-test. The eventual solution
was to speckle only the panels with black paint, which provided enough contrast for the
correlation algorithm to process the images. A rigid mounting frame was built to
precisely locate each panel both pre- and post-autoclaving (Figure 30)

Figure 30: Experimental setup for FML panel residual strain measurement
Although the overall results were adequate, the small changes in the paint colour due to
the high temperature, as well as the relatively low strain values in the FML panels
resulted in more background noise, increasing the strain sensitivity to ±150

. As a

result, strain values over the entire area of each panel were extracted and averaged
out. Since the average residual strain values extracted from each panel were in the

74

elastic range, Hooke’s law for orthotropic materials was used to perform strain to stress
conversion using the material properties from Table 1 and the following equations:

σ1 =

E1
ν E
⋅ ε1 + 12 2 ⋅ ε 2
1 − ν12ν 21
1 − ν12ν 21

5.5.1

σ2 =

ν12E2
E1
⋅ ε1 +
⋅ε
1 − ν12ν 21
1 − ν12ν 21 2

5.5.2

where 1 and 2 are the principal directions,

is the principal stress, E is the elastic

modulus and v is Poisson’s ratio.

Sample maximum and minimum principal strain images are shown in Figure 31 and
overall results for each panel are given in Table 9.

(a)

(b)

Figure 31: Sample strain results from DIC for (panel 35) FML 4 [-60/0/+60] (a) maximum
principal strain and (b) minimum principal strain

75

Table 9: Summary residual stress results for various types of FML panels
Residual
FML type
FML 3
FML 4
FML 4 EXP

1

2

Avg (MPa)

22.5

8.9

Std Dev

3.8

5.4

Avg (MPa)

19.6

1.4

Std Dev

9.8

6.8

Avg (MPa)

22.3

13.5

Std Dev

2.5

4.1

A review of the literature on this subject shows several approaches to measuring
residual stresses, including x-ray diffraction
102

methods

100

101

, neutron diffraction

103

and by measuring coupon deflection after processing

, analytical

. Comparing these

values for FML 4 to those in the literature shows a reasonable correspondence with the
analytical method

102

, which calculated an estimated residual stress of 20.26 MPa, and

the deflection measurement, which determined an estimated residual stress of 15.1
MPa.

76

6.0

STATIC TEST RESULTS

All static cold expansion and riveting results were post-processed in two ways. First,
qualitative information regarding the maximum and minimum principal strains was
provided using color images of the strain fields. Secondly, quantitative information was
provided using data extracted from an annulus, centered on each cold expanded and
riveted hole, with a circle radius of 125 pixels or 6.0 mm. The decision to use an
annulus instead of a line profile was due to the asymmetry of the strain field resulting
from cold expansion. The radial co-ordinate system used to extract data from around
the cold expanded and riveted holes is shown in Figure 32.

The extracted data from each of the coupons were grouped so that specific engineering
questions could be answered with the results. For the cold expansion results, one initial
concern was determining the degree of variability inherent in the cold expansion
process. Next, differences in the strain field between the two principal material
orientations were examined, along with a comparison of the resulting strain fields in
FML and aluminum after cold expansion. Additional information was obtained by
examining the differences between FML 3 and FML 4, looking at the effect of cold
expanding coupons in the 45º degree orientation, and examining the strain differences
between the entry and exit face after cold expansion.

77

Figure 32: Radial co-ordinate system of the annular data extraction
6.1

Process Variability

The issue of process variability is important for drawing valid conclusions from the
experimental data presented. The main source of variability in this stage of the
experiment was assumed to be due to the cold expansion process itself. Differences in
initial hole diameter, variations in mandrel size, rotation of the split sleeve and other
sources of human error were among the likely contributors to any variability in the data.
In order to determine the amount of variability in the data that was collected, two
separate FML 3 coupons (specimen GAL1 and specimen GAL3) were selected and
their strain fields compared. Looking at the plot of maximum principal strain (Figure 33)
one notices that the overall pattern of the residual strains are quite similar. Both
coupons exhibit the same “butterfly” pattern with the strain field from specimen GAL1
showing a slightly more prominent dip at zero degrees. The two plots of minimum
principal strain (Figure 34) also look almost identical, with the compressive strains
forming a slight cross shape around the cold expanded hole. Radial line profiles
extracted from both sets of data highlight some of the subtle differences between the
residual strain fields. The plot of maximum principal strains (Figure 35) shows how

78

similar the two strain fields are, with the data points overlapping except at 135° degrees
where a drop of approximately 300

is noted. The plot of minimum principal strains

(Figure 35) shows greater variability, with a larger strain difference occurring at
approximately 320° degrees. Close examination of Figure 34 corroborates this, as in
this area the region of compressive residual strain is slightly expanded compared to
specimen GAL3. Even though this difference is approximately 2500 microstrain, the
relative error in this small region is only about 12% compared with the peak
compressive strains seen after cold expansion. Greater variability is to be expected in
this region as it is very close to the split sleeve, and the strain data could be influenced
by slight variations in sleeve orientation.

(a)

(b)

Figure 33: Plot of maximum principal strains on the entry face for two FML 3 coupons
(a) specimen GAL1 and (b) specimen GAL3

79

(a)

(b)

Figure 34: Plot of minimum principal strains on the entry face for two FML 3 coupons (a)
specimen GAL1 and (b) specimen GAL3

-4000
1 [ strain]

0

6000
1 [ strain]

8000

4000

-8000

2000

-12000

0

-16000
0

90

180 270
Degrees

FML 3 (GAL1)

0

360

90

180

270

360

Degrees
FML 3 (GAL1)

FML 3 (GAL3)

FML 3 (GAL3)

(b)

(a)

Figure 35: Plot of principal strains for two FML 3 coupons, specimen GAL1 and
specimen GAL3) (a) maximum principal strain and (b) minimum principal strain

80

The same type of comparison was made with the 2024-T3 aluminum coupons in order
to verify that the variability was material independent. Figure 36 and Figure 37 show
the maximum and minimum principal strains for two aluminum coupons. The overall
shape of the strain fields appears to be very comparable, with only small variations
evident. The circular line extraction from the data (Figure 38) shows little difference
between the strain results, with the greatest difference occurring in the plot of minimum
principal strain between 225º and 315º degrees. This corresponds to the location of the
split sleeve and reinforces the hypothesis that variability in this area is due to split
sleeve orientation or due to the interaction between the edges of the split sleeve and the
open hole.

(a)

(b)

Figure 36: Plot of maximum principal strains on the entry face for two 2024-T3
aluminum coupons (a) specimen AL1 and (b) specimen BL1

81

(a)

(b)

Figure 37: Plot of minimum principal strains on the entry face for 2024-T3 aluminum
coupon (a) specimen AL1 and (b) specimen BL1

-4000
2 [ strain]

0

6000
1 [ strain]

8000

4000

-8000

2000

-12000

0

-16000

0

90

180 270
Degrees

2024-T3 (AL1)

0

360

90

180

270

360

Degrees

2024-T3 (BL1)

2024-T3 (AL1)

(a)

2024-T3 (BL1)

(b)

Figure 38: Plot of principal strains for two 2024-T3 aluminum coupons, specimen AL1
and specimen BL1 (a) maximum principal strain and (b) minimum principal strain

82

6.2

Material Orientation

To study the effect of changing material orientation with respect to the split sleeve
direction, a number of FML and 2024-T3 aluminum coupons were produced with the
transverse grain direction parallel to the long axis of the coupon. In these cases, the
split sleeve direction remained unchanged (to the right in all images) and Figure 39 and
Figure 40 show a comparison between the maximum and minimum principal strain
results for these longitudinal and transversely oriented coupons.

L

T

T

L

(a)

(b)

Figure 39: Maximum principal strain on the entry face for two FML 4 coupons (a)
specimen GBL1 (longitudinal orientation) and (b) specimen GBT1 (transverse
orientation)

83

L
T
T
L

(a)

(b)

Figure 40: Minimum principal strain on the entry face for two FML 4 coupons (a)
specimen GBL1 (longitudinal orientation) and (b) specimen GBT1 (transverse
orientation)
Relatively little difference can be seen between the maximum and minimum principal
strain patterns of both longitudinal and transverse coupons. This is likely due to the
small difference (approximately 11%) in elastic modulus between the longitudinal and
transverse material directions. At most this difference would result in a change of
approximately 1100

, which is less than the difference of one color bar in the above

figures, making it difficult to detect qualitatively. Figure 41 shows the results of a
circular line extraction from both the longitudinal and transversely oriented coupons.
The maximum principal strains are tensile and very little difference is seen between the
longitudinal and transverse coupons. The strain profile is very similar to other FML
specimens with a trough in the strain field located at 270° degrees. This trough
corresponds to the location of the split in the split sleeve and is surrounded by two

84

peaks; likely from the thin, sharp edges of the split sleeve causing a strain concentration
in this localized region of a magnitude just over 8000

.

8,000

-2,000
2 [ strain]

0

1 [ strain]

10,000

6,000
4,000

-4,000
-6,000

2,000

-8,000

0

-10,000
0

90

180

270

0

360

90

270

360

Degrees

Degrees
FML 4 (Long)

180

FML 4 (Trans)

FML 4 (Long)

(a)

FML 4 (Trans)

(b)

Figure 41: Plot of principal strains for two FML 4 coupons, specimen GBL1 and
specimen GBT1 (a) maximum principal strain and (b) minimum principal strain
The same experiment was repeated using aluminum coupons, with the strain results
shown in Figure 42 and Figure 43. Comparing the two results, one sees very little
evidence of a change in the strain field as a result of varying the material orientation.
An examination of the circular line extraction in Figure 44 shows even less variability
between the two orientations than with the FML 4 results. The basic shape of the graph
is quite representative of a cold expanded aluminum coupon, with a trough in the strain
field where the split is located, surrounded by regions of higher strain on either side.
The results are not unexpected when one considers that although rolled aluminum has
slightly orthotropic properties, the difference in elastic modulus between the longitudinal
and transverse directions is negligible compared to FML 4.

85

T

L
T

L

(a)

(b)

Figure 42: Maximum principal strain on the entry face for 2024-T3 aluminum coupons
(a) specimen AL3 (longitudinal orientation) and (b) specimen AT3 (transverse
orientation)

T

L
T

L

(a)

(b)

Figure 43: Minimum principal strain on the entry face for 2024-T3 aluminum coupons (a)
specimen AL3 (longitudinal orientation) and (b) specimen AT3 (transverse orientation)
86

12,000

0
-4,000

8,000

e2 [ strain]

e1 [ strain]

10,000

6,000
4,000

-8,000

-12,000

2,000

-16,000

0
0

90

180

270

0

360

90

270

360

Degrees

Degrees
2024-T3 (Long)

180

2024-T3 (Long)

2024-T3 (Trans)

2024-T3 (Trans)

(b)

(a)

Figure 44: Plot of principal strains for 2024-T3 coupons, specimen AL6 (Longitudinal)
and Specimen AT6 (Transverse) for (a) maximum principal strain and (b) minimum
principal strain
6.3

Comparison Between FML 3 and FML 4

Two grades of FML, FML 3 and FML 4, were tested to determine the differences in
residual strain after cold expansion. Table 1 provides the basic laminate layup of these
two variants while Table 2 details their mechanical properties. From these tables it is
clear that FML 4 has a higher elastic modulus and yield strength in the longitudinal (L)
direction and a lower elastic modulus and yield strength in the longitudinal transverse
(LT) direction. As a result of being laminate materials, both of these FML variants
exhibit orthotropic behaviour, with the lowest yield strength occurring at 45° degrees to
the longitudinal direction. Since FML 4 has a greater difference in elastic modulus
between the L and LT direction, it would not be surprising to see a slight difference in
the residual strain fields between these two FML grades. Indeed, a close examination

87

of Figure 45 shows that the maximum principal strain field for FML 4 is slightly
elongated in the transverse direction compared to FML 3. The same effect is evident
when examining Figure 46, which shows the minimum principal strain for both materials.

T

T

L

L

(a)

(b)

Figure 45: Maximum principal strains on the entry face for (a) FML 3 (specimen GAL2)
and (b) FML 4 (specimen GBL1)

T

T

L

L

(a)

(b)

Figure 46: Minimum principal strains on the entry face for (a) FML 3 (specimen GAL2)
and (b) FML 4 (specimen GBL1)
88

From the plot of the residual strain data extracted from around the cold expanded hole
(Figure 47) it is very difficult to directly note the effect of this elongation. The effect of
this elongation in the transverse direction should be most noticeable in either the 0º
degree or 180º degree directions and although a very slight difference may exist, there
is still enough variability in the cold expansion process to make this determination
inconclusive.

8,000

0
-2,000

1 [ strain]

2 [ strain]

6,000
4,000

2,000

-4,000
-6,000
-8,000

-10,000

0
0

90
180 270
Degrees
FML 3

0

360

90

180

270

360

Degrees
FML 4

FML 4

FML 3

(b)

(a)

Figure 47: Plot of principal strains for FML 3 (specimen GAL2) and FML 4 (specimen
GBL1) for (a) maximum principal strain and (b) minimum principal strain
6.4

FML 45º Orientation

In order to further investigate the orthotropic nature of FML and the residual strains after
cold expansion, additional coupons were machined with the longitudinal direction
oriented at 45° degrees to the long axis of the coupon. The split sleeve direction
remained the same (to the right in the image), and Figure 48 shows the dramatic
change this causes in the maximum principal strain field. From a structural point of
89

view, rotating the coupons’ axes effectively orients the split in the split sleeve in the
direction of minimum elastic modulus and minimum yield strength. The effect of this
can be seen clearly in Figure 49, where the typical butterfly shape that results from the
split sleeve is replaced with a more concentric annulus of compressive residual strain.

T

T

L

L

(a)

(b)

Figure 48: Maximum principal strains on entry face for FML 3 (a) specimen GAL2
(standard orientation) and (b) specimen GCF2 (45° orientation). Note: Dotted line
shows orientation of split sleeve

90

T

T

L

L

(a)

(b)

Figure 49: Minimum principal strains on entry face for FML 3 (a) specimen GAL2
(standard orientation) and (b) specimen GCF2 (45° orientation). Note: Dotted line
shows orientation of split sleeve
In the plot of maximum principal strain (Figure 50a), the typical strain concentration
seen between 225º - 315º degrees has almost completely disappeared. In the plot of
minimum principal strain (Figure 50b), a smaller strain concentration exists in that
region, but overall, the strains appear to be much more uniform than with the
longitudinally or transversely oriented FML coupons.

91

0

8,000

-2,000
2 [ strain]

1 [ strain]

6,000
4,000

-4,000
-6,000

2,000

-8,000

0

-10,000
0

90 180 270
Degrees
STD

0

360

90

180

270

360

Degrees

45 Deg

STD

(a)

45 Deg

(b)

Figure 50: Plot of principal strains for FML 3 specimens GAL2 (longitudinal) and GCF2
(transverse) with (a) maximum principal strains and (b) minimum principal strains
These results reinforced the idea that the orthotropic nature of FML makes it a difficult
material to cold expand predictably, at least without some forethought concerning the
grade of FML and its material properties. It was this result that led to the idea of
changing the material properties of FML to be more isotropic in the plane of the
laminate, and to reduce the need to clearly define material direction before cold
expansion.
6.5

Mandrel Entry and Exit Face Results (2024-T3 and FML)

Although a plane stress assumption would appear to be appropriate for the 1.59 mm
thick material being used in this research, the open literature cites many
researchers

41,43,44,47,61-63

who have demonstrated that the compressive residual

strains after cold expansion are higher on the exit face than on the entry face. The
implication for this, in fatigue, is that crack growth rates on the exit and entry face may
92

differ, a fact that has also been observed by several researchers

51-53,64

. To verify

whether this phenomenon was present for our thin (1.59 mm) FML 3 and 2024-T3
aluminum coupons, entry and exit face strains were measured and compared for both
materials. Figure 51 and Figure 52 show the maximum principal and minimum principal
strains on the entry and exit faces of an FML 3 coupon. Visual comparison of the two
faces shows very similar strain patterns, making it difficult to detect whether strains on
the exit face are indeed higher.

(b)

(a)

Figure 51: Maximum principal strains for (specimen 15-A-7) FML 3 coupon (a) mandrel
entry face and (b) mandrel exit face

93

(a)

(b)

Figure 52: Minimum principal strains for (specimen 15-A-7) FML 3 coupon (a) mandrel
entry face and (b) mandrel exit face
Examination of the radial extractions for FML 3 (Figure 53), shows that overall the
maximum principal strains are slightly higher on the exit face, whereas for the minimum
principal strains, the differences on the exit face are greatest between 0º-180º degrees.
A further clarification is achieved by extracting data from a vertical line starting at 180º
(in the circular co-ordinate frame) and extending to the edge of the hole. This line
profile (Figure 54) shows that, immediately adjacent to the edge of the hole, both the
minimum and maximum principal strains on the exit face of the coupon are of greater
magnitude than those on the entry face.

94

-2000

10,000

-4000
2 [ strain]

1 [ strain]

8,000
6,000
4,000

-6000
-8000
-10000

2,000

-12000
-14000

0
0

90

180
270
Degrees
Entry

0

360

90

180
270
Degrees
Entry

Exit

360

Exit

(b)

(a)

Figure 53: Plot of entry and exit face principal strains for (specimen 15-A-7) FML 3 (a)
maximum principal strains and (b) minimum principal strains
0.01

Strain [mm/mm]

0.005
0
-0.005
e1 [entry]

-0.01

e2 [entry]
e1 [exit]

-0.015

e2 [exit]

-0.02
0

2

4
6
8
Distance from hole edge [mm]

10

Figure 54: Vertical line profile (180º) of entry and exit principal strains for FML 3 coupon
(specimen 15-A-7)

95

Examining the strain fields from the 2024-T3 aluminum coupons, it is apparent that the
overall extent of both the maximum principal strains (Figure 55) and the minimum
principal strains (Figure 56) are greatest on the exit face.

(b)

(a)

Figure 55: Maximum principal strains for (specimen AL-T-7) 2024-T3 aluminum (a)
mandrel entry face and (b) mandrel exit face

96

(b)

(a)

Figure 56: Minimum principal strains for (specimen AL-T-7) 2024-T3 aluminum (a)
mandrel entry face and (b) mandrel exit face

From the radial strain extraction of the 2024-T3 aluminum (Figure 57), it is apparent
that, overall, both the maximum and minimum principal strains are higher on the exit
face. The line profile taken from the edge of the hole (Figure 58) shows that at the
point immediately adjacent to the edge, the maximum and minimum principal strains on
the exit face are slightly higher than those on the entry face, in a manner similar to FML.

97

5000

0
e1 [entry]
e1 [exit]

4000

-2,000

3000

2 [ strain]

1 [ strain]

e2 [entry]
e2 [exit]

-1,000

2000

-3,000
-4,000
-5,000
-6,000

1000

-7,000
0
0

90

180 270
Degrees

-8,000

360

0

90

(a)

180 270
Degrees

360

(b)

Figure 57: Plot of entry and exit face principal strains for (specimen AL-T-5) 2024-T3
aluminum (a) maximum principal strains and (b) minimum principal strains

Principal Strain
[mm/mm]

0.025
0.015
0.005
-0.005
-0.015
-0.025
0

2

4

6

8

10

Distance from hole edge [mm]
e1 [entry]

e2 [entry]

e1 [exit]

e2 [exit]

Figure 58: Plot of entry and exit principal strains for 2024-T3 aluminum coupon
(specimen AL-T-5)

98

One ramification of this result that was not completely appreciated until during the
fatigue testing was that the higher overall residual strains on the exit face was more
effective at extending the life in the early stage of the fatigue process compared to the
entry face.
6.5.1 Effect of Increased Edge Distance
The initial design of experiments dictated that all static and fatigue coupons should have
similar widths to make comparing results more meaningful. Given a nominal cold
expanded hole diameter of 6.64 mm (0.2616 inches) and a coupon width of 38.1 mm
(1.50 inches) all coupons had a nominal edge ratio (defined as the ratio of edge
distance to hole radius) of approximately 5.73. To determine the effect of increasing the
edge distance, additional 2024-T3 aluminum and FML 3 coupons were machined with a
width of 63.5 mm (2.50 inches) providing an edge ratio of 9.55.

Full-field images of the maximum principal strain surrounding the low and high edge
ratio coupons are shown in Figure 59. It is clear that the change in boundary constraint
provided by the difference in edge ratios has an impact on the tensile strain at the edge
of the coupon. The change in edge ratio also likely has an impact on the tensile strains
close to the edge of the cold expanded hole, but the full extent of this is more difficult to
determine due to the different magnifications used for each coupon. This change in
magnification (CL3: 0.08 mm/pixel and AL3: 0.05 mm/pixel) has an impact on strain
resolution, especially in high strain gradient areas such as at the hole edge.

99

(a)

(b)

Figure 59: Plot of maximum principal strain on entry face for a) high edge ratio coupon
(specimen CL3) and b) low edge ratio coupon (specimen AL1)
Vertical line profiles through the central notch of the aluminum coupons (Figure 60)
show that the low edge ratio coupons have maximum principal strains approximately
500

greater at the coupon edge than those of the high edge ratio coupons.

100

Principal Strain (microstrain)

5,000
e1 (high edge)
e1 (low edge)

4,000
3,000
2,000
1,000
0
0

10
20
30
40
50
60
Distance from coupon edge (mm)

70

Figure 60: Vertical line profile showing variation in maximum principal strain through
coupon center for both high edge ratio (specimen CL3) and low edge ratio (specimen
AL1) 2024-T3 aluminum coupons
By contrast, the same line profile plotting the minimum principal strains (Figure 61)
shows that at the edge of the coupon, the minimum principal strains are more similar,
with a difference of less than approximately 300

101

.

Principal Strain (microstrain)

0
-2,000
-4,000
-6,000
-8,000

e2 (high edge)
e2 (low edge)

-10,000
0

10
20
30
40
50
60
Distance from coupon edge (mm)

70

Figure 61: Vertical line profile showing variation in minimum principal strain through
coupon center for both high edge ratio (specimen CL3) and low edge ratio (specimen
AL1) 2024-T3 aluminum coupons
Figure 62 shows a full-field plot of the maximum principal strains in both FML 3
coupons, clearly highlighting the difference in tensile strain caused by the difference in
boundary constraint. Line extractions taken from the high and low edge ratio FML 3
coupons show much the same behaviour as in the aluminum coupons. A comparison of
the vertical line profile taken from both of these coupons (Figure 63) shows maximum
principal strains approximately 700

greater at the edge of the low edge ratio coupon

than at the edge of the high edge ratio coupon. The same line profile extraction for the
minimum principal strains (Figure 64) shows a smaller difference, on the order of 200
at the coupon edge.

102

(a)

(b)

Figure 62: Plot of maximum principal strain on the entry face for FML 3 a) high edge
ratio coupon (specimen GCL2) and b) low edge ratio coupon (specimen GAL1)

Principal Strain (microstrain)

5,000

e1 (high edge)
e1 (low edge)

4,000
3,000
2,000
1,000
0
0

10
20
30
40
50
60
Distance from coupon edge (mm)

70

Figure 63: Vertical line profile showing variation in maximum principal strain through
coupon center for both high edge ratio (specimen GAL1) and low edge ratio (specimen
GCL2) FML 3 aluminum coupons
103

Principal Strain (microstrain)

0
-2,000
-4,000
-6,000
-8,000

e2 (high edge)
e2 (low edge)

-10,000
0

10

20

30

40

50

60

70

Distance from coupon edge (mm)
Figure 64: Vertical line profile showing variation in minimum principal strain through
coupon center for both high edge ratio (specimen GAL1) and low edge ratio (specimen
GCL2) FML 3 aluminum coupons
The results with FML are similar to those with 2024-T3 aluminum, in that both seem to
show an increase in maximum principal strain at the coupon edge, as well as at the
edge of the cold expanded hole. Although the different magnifications used for both
images changed the strain resolution and makes quantification of the effect difficult at
104

the edge of the hole, a computer simulation of this situation by Ayatollahi and Arian

appears to confirm both the increase in tensile strain at the edge of the coupon as well
as the increase in strain at the edge of the hole and suggests that edge ratio needs to
be taken into consideration during the cold expansion process as to small an edge ratio
may reduced the effectiveness of the cold expansion process.

104

6.6

Static Riveting Results

For the static riveting results, fewer comparisons were made than for cold expansion.
With the theoretically uniform nature of the riveting process, the main focus for the static
riveting tests was to determine how much variability could be expected as well as to
determine the resultant strain field for the different materials.
Unlike with cold expansion, the final diameter of the manufactured and driven head
covered the region closest to the pilot hole and made it impossible to measure the
strains in this region. It should be noted that, for clarity, some of the full-field strain
results have been overlaid over the original pilot hole to provide a better sense of the
relationship between the pilot hole and the measured strain field.
6.6.1 Process Variability Rivet Results
As with the cold expanded coupons, process variability was quantified by comparing
two different coupons. In the rivet process, the amount of compression generated from
a rivet of a specific size is related to both the height of the protruding head as well as
the diameter of the protrusion created during the compression process. Although every
attempt was made to use the same amount of displacement, the riveting process is very
sensitive to even small changes in insertion angle which can then influence both the
final rivet protrusion as well as the uniformity of the strain field.

In the case of the aluminum coupons, the overall shape of the strain field is quite
similar, with the maximum principal strain field (Figure 65) appearing to be slightly larger
in diameter than the minimum principal strain field (Figure 66). In both cases the strain
field appears to be uniform and circular without the typical cardioid shape seen after

105

split sleeve cold expansion. The radial line extraction of the strain data (Figure 67)
supports this conclusion, showing only small undulations in the strain fields with
relatively consistent strains between the two aluminum coupons.

(b)

(a)

Figure 65: Maximum principal strains for 2024-T3 aluminum riveted coupons on driven
head side for (a) specimen BL17 and (b) specimen BL19

106

(a)

(b)

Figure 66: Minimum principal strains for 2024-T3 aluminum riveted coupon on driven
head side for (a) specimen BL17 and (b) specimen BL19
-600

1200

-900

2 [ strain]

1 [ strain]

1500

900

-1200
BL19

BL19
BL17

600
0

90
180 270
Degrees

BL17
-1500

360

0

(a)

90
180 270
Degrees

360

(b)

Figure 67: Plot of principal strains for riveted 2024-T3 coupon BL17 and BL19 (a)
maximum principal strain and (b) minimum principal strain

107

6.6.2 Comparison Between FML 3 and FML 4 Rivet Results
Qualitative examination of the maximum principal strain (Figure 68) field shows that the
strains surrounding the rivet in the aluminum are radially quite symmetric while those
surrounding the rivet in FML show evidence of increased strain at 45° degree
increments around the circumference of the rivet. The minimum principal strains
surrounding the rivet in the FML coupon show slightly more bias, forming what could be
described as a cross pattern around the rivet (Figure 69). Quantitative examination of
the data from the radially extracted strains (Figure 70), shows an undulating strain field
with reductions in minimum principal strain at 45° degree increments, corresponding
with the direction of minimum modulus and minimum yield strength.

(b)

(a)

Figure 68: Maximum principal strains on the driven head side for (a) FML 3 (specimen
GAL4) and (b) FML 4 (specimen GBL5)

108

(a)

(b)

Figure 69: Minimum principal strains on the driven head side for (a) FML 3 (specimen
GAL4) and (b) FML 4 (specimen GBL5)

2,500

0
FML 3
FML 4

-500
e2 [ strain]

e1 [ strain]

2,000
1,500
1,000

-1000
-1500
-2000

500
FML 3
FML 4

0
0

90

180
270
Degrees

-2500

360

(a)

0

90

180
270
Degrees
(b)

Figure 70: Plot of principal strains for riveted FML 3 (specimen GAL4) and FML 4
(specimen GBL5) for (a) maximum principal strain and (b) minimum principal strain

109

360

7.0

THEORETICAL ANALYSIS AND COMPARISON TO STATIC RESULTS

Any discussion regarding the theoretical basis behind hole cold expansion and riveting
is best served by a brief foray into elasticity and plasticity theory as well as an
examination of the yield criteria concept. A review of closed form solutions for the cold
expansion process is provided, as well as a detailed overview of the approach used to
model cold expansion and riveting in aluminum and FML materials as well as a
comparison to the experimental results. The final section in the chapter provides an
overview of classical laminate theory as it applies to FML and its application to the
design and characterization of new FML 4 variants.
7.1

Discussion of Yield Criterion

One of the foundations behind elastic-plastic material models is the concept of a yield
criterion that defines the combination of stresses that will cause a material to deform
105

plastically. Mendelson

discusses some of the history behind the development of

modern day yield criteria, which go back as far as Coulomb in 1773. The problem with
many of these early yield criteria is that they were developed for brittle materials and
then applied directly to ductile ones resulting in large errors between the theories and
the experimental results. Coulomb’s theory predicted failure of a specimen when the
maximum shear stress reached the value of the maximum shear stress under uniaxial
tensile loading. Although the maximum shear (Tresca) criterion has shown fair
agreement with experimental results, its applicability is limited to ductile materials
whose yield stress in tension and compression are equal (Figure 71). Another early
yield criterion was the maximum strain energy theory which predicted failure when the
strain energy per unit volume equalled the strain energy per unit volume as determined

110

by an axial tensile or compressive test of the same material. Since the maximum strain
energy theory has not been verified by experiment, it has been largely supplanted by
106

the maximum distortion energy theory

.

7.1.1 Distortion Energy Yield Criteria
The majority of current elastic-plastic material models use a yield criterion generically
called the maximum distortion energy theory. This theory is also referred to as the
Huber-Hencky-Von Mises theory since it was first proposed by Huber in 1904 and also
independently by Von Mises of Germany in 1913

106

. The theory was further developed

by both Von Mises and Hencky in later years and is most commonly called the Von
Mises failure criteria in recognition of his contribution to the development of this theory.

What differentiates the maximum distortion energy theory from other failure theories is
the recognition that the portion of strain energy producing volume change does not
produce failure by yielding in isotropic materials. This has been proven experimentally
in experiments by Bridgman

107,108

who showed that isotropic, homogenous materials

can withstand high hydrostatic pressures without yielding. This finding reinforced the
concept that yielding in a material results from the deviatoric portion of the total strain
energy applied to a material.

The maximum distortion energy theory can be derived by using strain energy concepts,
which provides background for a brief discussion of stress invariants and their
relationship to plasticity theory.

111

Using superposition, the standard stress tensor consisting of the three principal stresses
1,

2,

3 can be imagined to consist of two additive component tensors, one

hydrostatic and one dilatational. The elements of the hydrostatic tensor are defined as
the mean “hydrostatic” stress:

σ +σ +σ
σ= 1 2 3

7.1.1

3

The elements of the deviatoric or dilatational tensor are ( 1- σ ), ( 2- σ ) and ( 3- σ )
which are shown in matrix representation in Equation 7.1.2:

σ1
0
0

0

σ2
0

σ

0

0

0

= 0 σ 0 +
σ3
0 0 σ
0

σ1 − σ
0
0

0

0

σ2 −σ

0
σ3 − σ

0

7.1.2

With the principal stress state resolved into two components, it is now possible to
calculate the strain energy due to the dilatational component of the stress tensor. First,
the total strain energy must be derived, by integrating the area under the elastic portion
of the stress-strain curve to get:
1
1
1
U total = σ1ε1 + σ 2ε 2 + σ 3ε 3
2
2
2

7.1.3

Using the generalized Hooke’s law for isotropic, linearly elastic materials, Equation 7.1.3
can be rewritten completely in terms of stress:
U total =

(

)

1
2
2
2 ν
σ1 + σ 2 + σ 3 − (σ1σ 2 + σ 2σ 3 + σ 3σ1 )
2E
E

112

7.1.4

Determining the strain energy of the dilatational component of the stress tensor can be
approached by re-arranging the equation for the total internal energy to produce:

U distortional = Utotal − U hydrostatic

7.1.5

A state of stress will result in distortion only (no volume change) if the sum of the three
normal stresses is zero. The total change in volume associated with these normal
stresses is referred to as the volumetric strain ( v), and is simply the sum of the normal
strains:

εv =

dV
= εx +ε y +εz
V

7.1.7

For an isotropic material the volumetric strain can be expressed in terms of stresses by
using the generalized Hooke’s law

εx =

(

1
σ x −ν σ y + σ z
E

)

7.1.8a

εy =

1
σ y − ν (σ x + σ z )
E

7.1.8b

εz =

1
σ z −ν σ x + σ y
E

(

7.1.8c

)

and substituting Equation 7.1.7 into Equation 7.1.8 and collecting like terms to obtain
Equation 7.1.9, which expresses the volumetric strain in terms of the hydrostatic
stresses

106,109

.

εv =

1
(1 − 2ν ) p
E

7.1.9

113

The internal energy resulting from the hydrostatic stress (volume change) can be
calculated from the expression for the total energy (Equation 7.1.4) by setting principal
stresses 1= 2= 3=p, and then replacing p by Equation 7.1.1, which gives the
following expression for the internal energy due to hydrostatic stress

U hydrostatic =

3 (1 − 2ν ) 2 (1 − 2ν )
p =
(σ1 + σ 2 + σ 3 )2
2E
6E

110

:
7.1.10

By subtracting Equation 7.1.10 from Equation 7.1.4 and simplifying, an expression for
the distortion energy can be obtained:

U distortional =

1 +ν
6E

(

σ1 − σ 2

) (
2

+ σ 2 − σ3

) (
2

+ σ 3 − σ1

)

2

7.1.11

The maximum distortion energy theory of failure states that plasticity will occur when the
internal energy given by Equation 7.1.11 exceeds the limiting value from a uniaxial
tensile test. In uniaxial tension, all but one of the principal stresses are zero. If we call
this stress the yield stress ( yp) and set the other principal stresses to zero the internal
energy of distortion is equal to:

U distortional =

1 +ν 2
σ yp
3E

7.1.12

Substituting this value in Equation 7.1.11 and re-arranging, one obtains the more
recognizable form of the maximum distortion energy yield criteria (7.1.13)

σ yp =

1
2

(

σ1 − σ 2

) (
2

+ σ 2 − σ3

) (
2

+ σ 3 − σ1

)

2

7.1.13

For plane stress, 3=0, and Equation 7.1.13 in dimensionless form becomes:

114

σ1
σ yp

2

σ1 σ 2
σ2
−
⋅
+
σ yp σ yp
σ yp

2
=1

7.1.14

Equation 7.1.14 is an equation of an ellipse as shown in Figure 71. Any stress falling
within the ellipse indicates that the material behaves elastically and points on the ellipse
boundary indicate that the material is yielding. As a result, the maximum distortion
energy theory does not predict changes in material response when hydrostatic tensile or
compressive stresses are added, since Equation 7.1.13 is based only on the differences
in the stress state.

Figure 71: Comparison of Maximum Shear and Maximum Distortion Energy yield criteria
7.2

Failure Criteria for Fiber Metal Laminates

The Maximum Distortion Energy yield criterion has proven to be an effective tool in
predicting failure for isotropic materials, as long as the yield stress is known and the
given state of stress can be transformed into its principal directions. In the case of FML

115

or other composite materials the assumption of isotropy does not hold and a more
generalized failure criterion is required.

111

As Tsai and Wu

pointed out, failure criteria in general do not address the

microscopic failure modes of a material, they just provide a method for estimating load
carrying capacity. The majority of reference handbooks on material strength agree with
one another in terms of uniaxial and shear properties measured along a materials’ axis
of symmetry, however, these strength values are of little use when trying to determine
failure for the combined stress state of a composite material.

112

Cortes and Cantwell

used three different yield criteria in an effort to predict failure in
113

titanium based fiber metal laminate composites and showed that both the Tsai-Wu
111

and the Tsai-Hill

failure criteria offered improvements over the maximum stress

failure model for these types of materials. Since these two failure criteria have shown
good applicability for use with fiber metal laminate materials in these and other
studies

112,114,115

, the following sections provide some background information on their

use.
7.2.1 Tsai-Hill Failure Criteria
113

Azzi and Tsai

put forward a generalized theory of anisotropic strength that used

material properties derived from uniaxial tests to evaluate the strength of a composite

116

116

material. Building on the work of Hill

, who postulated that the yield condition for

anisotropic materials could be assumed to be a quadratic in the form of:

(

)

2
2
2
2
2
2
F (σ 2 − σ 3 ) + G (σ 3 − σ1 ) + H (σ1 − σ 2 ) + 2 L ⋅τ 23 + M ⋅τ13 + N ⋅τ12 = 1

7.2.7

where F,G,H,L,M,N are material strength parameters, and 1,2,3 are the principal axes
117

of symmetry

. Expanding and collecting like terms from Equation 7.2.7 results in:

2
2
2
(G + H )σ1 + ( F + H )σ 2 + ( F + G )σ 3 − 2 [ H σ1σ 2 + Fσ 2σ 3 + Gσ1σ 3 ]
2
2
2
+2 Lτ 23 + M τ13 + Nτ12 = 1

7.2.8

If the failure strengths in the material axes are denoted by X,Y,Z, with shear failure
denoted by S then Equation 7.2.8 can be solved experimentally by applying a uniaxial
tensile stress in each of the three principal directions while keeping all other stresses
zero. These conditions applied to Equation 7.2.8 yield the following three equations:
G+H =

H + F=
F +G =

1
X2

1
Y2

1
Z2

7.2.9a
7.2.9b
7.2.9c

Solving for the unknowns G,H and F yields the following three equations:
G=

1 1
1
1
⋅
+
−
2 Z2 X 2 Y2

H=

1
1
1
1
⋅
+
−
2 X 2 Y2 Z2

F=

1 1
1
1
⋅
+
−
2 Y2 Z2 X 2

117

7.2.10

Assuming a state of plane stress in the laminate ( 3= 13= 23=0), then the plane stress
version of the failure criteria (Equation 7.2.8) can be written as:
2
2
2
G ⋅ σ1 + Fσ 2 + H (σ1 − σ 2 )2 + 2 Nτ12 =1

7.2.11

Application of a pure shear stress τ12 , with 1= 2=0 results in an expression for the
remaining parameter, N:
2N =

1
S2

7.2.12

Substituting the failure parameters from Equation 7.2.10 and Equation 7.2.12 into the
plane stress failure criteria (Equation 7.2.11), results in a generalized form of the TsaiHill failure criteria

117

σ1 2
X

:

−

σ
1
1
1
+
−
σσ + 2
2 Y2 Z2 1 2
Y
X

2

+

τ12 2
S

=1

7.2.13

For the case of an isotropic material, Equation 7.2.13 reduces to the standard Von
Mises yield equation

113

. If the assumption can be made that the material properties in

the through thickness (z direction) transverse to the fiber direction are equal, then the
material can be considered to be transversely isotropic. As a consequence the normal
strengths in the Y and Z direction would be considered equal, reducing Equation 7.2.13
to the more common form of the Tsai-Hill criteria for fiber metal laminate materials:
2
σx

X2

−

σ xσ y
X2

+

2
σ 2 τ xy
y
Y2

+

S2

=1

7.2.14

This Tsai-Hill failure criteria (Equation 7.2.14) was used successfully by Cortes and
112

Cantwell

in estimating the failure stress of titanium based fiber metal laminates.

118

112

Cortes and Cantwell

also showed that the Tsai-Wu failure criteria correlated well with

experimental results.
7.2.2 Tsai-Wu Failure Criteria
The Tsai-Wu theory is based on a postulated failure envelope of the form:

Fiσ i + Fijσ iσ j =1

7.2.15

where Fi and Fij are strength tensors that are related to the material strengths in the
principal lamina directions and must be determined experimentally. For an orthotropic
lamina subjected to plane stress ( 3= 13= 23=0) Equation 7.2.15 reduces to:
2
2
2
F11σ1 + 2 F12σ1σ 2 +F22σ 2 +F66τ12 +F1σ1 +F2σ 2 =1
111

Tsai and Wu

7.2.16

postulated that simple uniaxial strength experiments could be

performed to determine the majority of the stress components. By measuring tensile
failure in the principal material direction (X) and assuming all other stress components
to be zero the failure criteria (Equation 7.2.16) reduces to :

F11 X 2 + F X = 1
1
F11 X '2 − F X ' = 1
1

(for tension)

7.2.17a

(for compression)

7.2.17b

These two equations can be solved simultaneously to give the following values for F1
and F11 in terms of the ultimate strength in the X direction:

F11 =

1
XX '

and

F1 =

1
1
−
X X'

119

7.2.18

A similar procedure can be performed to determine ultimate tensile strength in the
orthogonal material principal direction (Y). Again assuming that all other stress
components are zero, Equation 7.2.16 now becomes:

F22Y 2 + F2Y = 1
F22Y '2 − F2Y ' = 1

(for tension)

7.2.19a

(for compression)

7.2.19b

These two equations can again be solved to give the following values for F2 and F22 in
terms of the ultimate strength in the Y direction:

F2 =

1 1
1
−
and F22 =
Y Y'
YY '

7.2.20

A similar procedure can be performed for an application of a pure shear stress (S),
again assuming that all other stress components are zero, reducing Equation 7.2.16 to:

F66 S 2 + F6 S = 1
F66 S '2 − F6 S ' = 1

(for +τ )

7.2.21a

(for − τ )

7.2.22b

Solving Equations 7.2.21a and 7.2.21b simultaneously produces the following values for
F6 and F66:
F66 =

1
S2

and F6 = 0

7.2.22

The only remaining term is F12, and in theory this could be determined by applying a
biaxial stress state so that 1= 2=0, however this poses practical difficulties and various
values (Equations 7.2.23a-c) have been proposed for this term.

120

F12 = −
F12 = −
1
F12 = − ⋅
2

(

1
2X 2
1

2X ⋅ X '
1
X ⋅ X ' Y ⋅Y '

)( )

7.2.23a
7.2.23b
7.2.23c

The correct value is material dependent and requires experimental validation, with
112

Cortes and Cantwell

applying the formulation in Equation 7.2.23c for use with

titanium based fiber metal laminates.
7.3

Elastic-Plastic Material Models

The next step in building a closed form solution for the stresses and strains during cold
expansion is to be able to mathematically describe material behaviour beyond the linear
region. In 1943, Ramberg and Osgood

118

published a report detailing some simple

formulas for describing the stress-strain ( - ) curve of a material in terms of Young’s
modulus (E) and two parameters (n and K – strain hardening coefficients) relating to the
behaviour of the material during plastic deformation. The classic Ramberg-Osgood
expression is shown in Equation 7.3.1

ε=

σ
E

+K

σ n

7.3.1

E

and has since been modified to take into account the yield stress ( y) of the material in
question. This modified Ramberg-Osgood parameter was first proposed by
119

Budiansky

in 1971 and it separates the material behaviour into linear and non-linear

components:

121

ε=
σ

σ
E

σ
ε=
E σy

for σ ≤ σ y

7.3.2

n −1

7.3.3

for σ > σ y

Analytical models trying to represent material behaviour after a reversal in the stress
field or during cyclical plasticity need some way to account for the potential changes in
material properties. If one performs a uniaxial tension or compression test and plots
true stress versus true strain, it would be noted that for most materials the yield point in
tension and compression are very similar. However, if one first deforms a material in
uniform tension, unloads it and then deforms it in compression, the yield point in
compression is typically reduced. This is referred to as the Bauschinger effect, and is
120

most clearly illustrated in the case of a tensile specimen. Hill

suggested that this

effect may be due to the distortion of the crystallographic planes into a preferred
orientation, resulting in the material becoming increasingly anisotropic. Hill also
hypothesized that this crystallographic distortion caused microscopic residual stresses
to remain in the material, and, if the material was then loaded differently, for example in
compression as opposed to tension, these residual stresses would significantly
influence plastic yielding. There are two main models used to describe the
Bauschinger effect; isotropic and kinematic hardening (Figure 72). In kinematic
hardening it is assumed that the elastic unloading range will be double the initial yield
stress. If the initial yield stress is 0, and the yield point during a subsequent loading
cycles is 1 then the specimen will yield in compression according to the path ABCDE
(Figure 72) after being stressed in tension. At the other end of the spectrum is the

122

theory of isotropic hardening that assumes that the mechanism that produces hardening
acts equally in tension and compression. As a result, if the tensile yield stress during a
load cycle is 1 then compressive yielding would occur at a stress of - 1 as shown by
the path ABCFG (Figure 72). Although this is the simplest theory to use and apply to
closed form solutions, test results show that the compressive yield stress lies between
105

points H and D in Figure 72

105

Figure 72: Effect of isotropic versus kinematic hardening on the yielding of a material
7.4

Review of Closed Form Solution for Cold Expansion
57

The basis for the current closed form solutions for cold expansion rests with Nadai

in

1943; whose interest in characterizing the joining of boiler tubes using radial expansion
led him to first explore much of the theoretical groundwork that is used today. Hsu and

123

71

Forman

improved upon Nadai’s

57

work by using a modified Ramberg-Osgood

material model to better enable them to characterize material behaviour beyond yield.
Although the work by Hsu and Forman

71

modeled the unloading step, they assumed

that it was elastic and thus did not address reverse yielding or the development of a
121

reverse yield zone next to the hole. Budiansky

122

and Ball

put forward a closed

form solution that took into account elastic-plastic unloading and thus the creation of a
reverse yield zone, caused by the removal of the oversized mandrel from the expanded
hole. Ball’s

122

derivation started by dividing up the cold expansion process into elastic
123

and plastic regions, with separate equations for each region. Guo

developed a very

complete solution that took into account finite boundary conditions, but did not
completely deal with mandrel unloading. Zhang et al’s
framework and attempted to complete Guo’s

123

124

paper explicitly built upon this

work by taking into account both the

insertion of the mandrel and the reverse unloading that takes place when the mandrel is
removed, as well as further subdividing the region around the hole into plastic, elasticplastic and elastic regions, thus providing a slightly more rigorous result than that
122

achieved by Ball

or Guo

123

.

The basic assumptions remain the same as those initially presented by Hsu and
71

Forman , namely that the cold expansion process begins with a hole in a finite circular
plate with radius r, inner radius a, subjected to an internal pressure p that represents the
122

action of the oversized mandrel. Both Ball

124

and Hsu and Forman

71

represented the

124

plate as being infinite in radius while Zhang et al

explicitly defined an outer radius of

the plate (b).

An overview of the closed form solution begins with the definition of a polar co-ordinate
system as shown in Figure 73, with the initial boundary conditions as follow:
r= 0 at r = b

7.4.1

r = -p at r = 0

7.4.2

Figure 73: Free body diagram of a finite plate with circular hole

125

124

In all cases, the material properties are modeled using the modified Ramberg-Osgood
relationship:

ε=

σ
E

σ

σ
ε= ⋅
E σy

where

is the true strain,

for σ ≤ σ y

7.4.3

n −1

for σ ≥ σ y

7.4.4

is the true stress, E is the elastic modulus, y is the initial
122

yield stress and n is the strain hardening exponent. Both Ball

124

and Zhang et al

started the derivation of their respective closed form solutions by providing the
fundamental relationships between strain and displacement in polar coordinates:
du
dr
u
εθ =
r

εr =

7.4.5a
7.4.5b

where u is the displacement in the radial direction and r is the distance from the center
of the hole. The total strains are then defined as the sum of both the elastic and plastic
strains in both the radial and tangential directions:

ε r = ε r el + ε r pl

7.4.6a

εθ = εθ el + εθ pl

7.4.6b

In the elastic region, the relationship between stresses and strains can be defined using
the generalized Hooke’s law model:

126

(
(

1
⋅ σ r −ν ⋅ σ θ
E
1
εθ el = ⋅ σθ −ν ⋅ σ r
E

ε r el =

)
)

7.4.7a
7.4.7b

where E is the Young’s modulus of the material and

is the Poisson’s ratio. The

relationship between stresses and strains in the plastic zone is more complex, for which
122

both Ball

124

and Zhang et al

71

rely on a model first put forward by Hsu :

ε r pl =

1 1
−
Es E

⋅ σr −

R
⋅ σθ
1+ R

7.4.8a

εθ pl =

1 1
−
Es E

⋅ σθ −

R
⋅σ r
1+ R

7.4.8b

In Equations 7.4.8a and 7.4.8b, R is defined as the ratio of in-plane transverse plastic
strain to through thickness plastic strain in much the same way that the Poisson’s ratio
defines the ratio of lateral to transverse elastic strains. A value of R=1 would represent
a purely isotropic material and an R=0 would represent anisotropic plastic behaviour.
Testing a range of R values showed that R=0.5 provided the optimal match to the
experimental strain values for FML while R=1 was optimal for 2024-T3 aluminum. Es is
the secant modulus at a point ( , ) on the stress strain curve and can also be obtained
from the modified Ramberg-Osgood model as:

1
ε 1 σ
= =
⋅
Es σ E σ y

127

n-1

7.4.9

Since

has no effect on the stress solution =R/(1+R) can be used in conjunction with

Equation 7.4.6, Equation 7.4.7 and Equation 7.4.8 to produce a relationship between
the total strains and stresses

123

as shown:

εr =

122

7.4.10a

εθ =
Both Ball

1
R
⋅ σr −
⋅ σθ
Es
1+ R
1
R
⋅ σθ −
⋅σ r
Es
1+ R

7.4.10b

124

and Zhang et al

divided the derivation of the residual stress field into

two distinct parts – the first representing the insertion of the oversized mandrel and the
second representing the reverse unloading in the material that occurs when the
oversized mandrel is removed and the material exhibits some elastic spring back.
7.4.1 Stresses Due to Loading of Plate by Mandrel
The closed form solution for the stresses resulting from the oversized mandrel may also
be suitable for describing the stresses induced through the riveting process or any other
process where an oversized mandrel or fastener is inserted into a hole.

122

Although Ball

123

, Guo

124

derivation, Zhang et al

124

and Zhang et al

all started off with essentially the same

expanded the analysis to include plates of finite size b,

instead of merely assuming an infinite plate. If a uniform pressure p applied at the hole
boundary results in elastic deformation then the elastic solution for the radial and
tangential stresses is

124,125

:

128

( b2 r 2 ) − 1 ⋅ p
σr = −
( b2 a 2 ) − 1
( b2 r 2 ) + 1 ⋅ p
σθ = −
(b2 a2 ) − 1

7.4.11a

7.4.11b

In the case where the plate undergoes elastic-plastic deformations, the stress solutions
in the elastic domain (rp r

b), with variables depicted graphically in Figure 74, are:

(b2 r 2 ) − 1 ⋅ p p
σr = −
( b2 a 2 ) − 1
( b2 r 2 ) + 1 ⋅ p p
σθ = −
( b2 a 2 ) − 1

7.4.12a

7.4.12b

where pp represents the pressure at the boundary between the elastic and plastic
domain at r=rp. To determine pp, the first step is to calculate the effective stress, which
in the plastic domain (a

r

rp), is defined as:
2R

2
2
σ = σ r + σθ −
⋅ σ r ⋅ σθ
1+ R

0.5

7.4.13

The yield criterion for the effective stress is:

σ = σy

7.4.14

Since FML is a hybrid of aluminum and glass fibers and has a distinct yield point, this
formulation should be applicable for both aluminum and FML.

129

Figure 74: Diagram of the variables associated with elastic-plastic deformation

124

The elastic solution for Equation 7.4.12 at r=rp should also satisfy Equation 7.4.13 and
Equation 7.4.14 because of the continuity of the stress field at the elastic-plastic
124

boundary

. By combining Equation 7.4.12, Equation 7.4.13 and Equation 7.4.14, it is

possible to obtain the pressure at the elastic-plastic boundary (pp) in terms of the yield
stress:

pp = σ y

b2
a2

−1 ⋅ 2 ⋅

b4
4
rp

+2+

b4

2R
⋅
−1
1 + R r4
p

130

−0.5

7.4.15

By substituting Equation 7.4.15 into Equation 7.4.12a and Equation 7.4.12b it is
possible to obtain an expression for the radial and tangential stresses in the elastic
zone:

σ r = −σ y ⋅

σθ = σ y ⋅

b2
r2
b2
r2

−1 ⋅ 2 ⋅

+1 ⋅ 2 ⋅

b4
4
rp
b4
4
rp

+2+

+2+

-0.5

b4

2R
⋅
−1
1+ R r4
p

7.4.16a
-0.5

b4

2R
⋅
−1
1+ R r4
p

7.4.16b

122

In order to generate a solution for the stresses in the plastic zone, both Ball
124

and Zhang et al

, Guo

123

used Budiansky’s technique of writing the effective stress in terms of

a parameter , which varies monotonically from a at the edge of the hole to p at the
edge of the plastic zone, to give the following two equations:

σr = σ ⋅

1+ R
1
⋅ cos(α ) −
⋅ sin(α )
2
1+ 2⋅ R

7.4.17a

σθ = σ ⋅

1+ R
1
⋅ cos(α ) +
⋅ sin(α )
2
1+ 2 ⋅ R

7.4.17b

124

Zhang et al

combined Equation 7.4.16 and Equation 7.4.17 with

= p and r = rp to

produce two intermediate equations relating p and rp:

sin(α p ) = 1 + 2 ⋅ R ⋅

b
rp

2

⋅ (1 + 2 ⋅ R ) ⋅

131

b
rp

-0.5

4
+1

7.4.18a

cos(α p ) = (1 + 2 ⋅ R ) ⋅

122

Both Ball

b
rp

-0.5

4
+1

7.4.18b

where, 0 < α p ≤ π
2
124

and Zhang et al

used Equation 7.4.9, Equation 7.4.10 and Equation

7.4.17 along with the stress equilibrium equation:
dσ σ r − σ θ
+
=0
dr
r

7.4.18c

and the compatibility equation:
dεθ εθ − ε r
+
=0
dr
r

7.4.19

To produce an expression that could be differentiated in terms of the effective stress ( )
and the parameter

1

σ

⋅ dσ =

to give:

2 ⋅ (1 + R ) ⋅ sin(α )

( n + 1 + 2 ⋅ R ) ⋅ cos(α ) + ( n − 1) ⋅

1 + 2 ⋅ R ⋅ sin(a )

⋅ dσ

7.4.20

This can then be integrated to produce an expression relating the effective stress to the
yield stress:

(

µ
2a1 ⋅ (1 + R ) ⋅ α a − α p
a1 ⋅ sin(α p ) + a2 ⋅ cos(α p )
σ
=
exp
σy
a1 ⋅ sin(α a ) + a2 ⋅ cos(α a )
a2 + a2
1

where
a1 = ( n − 1) 1 + 2 R
a2 = n + 1 + 2 R

µ=

2a2 (1 + R )
2 2
a1 + a 2

132

2

)

7.4.21

The relationship between the pressure p, and the parameter a and p can be derived
using Equation 7.4.17a and Equation 7.4.21 along with the initial conditions provided by
Equation 7.4.2 to give:

a1 ⋅ sin(α p ) + a2 ⋅ cos(α p )
a1 ⋅ sin(α a ) + a2 ⋅ cos(α a )

1 + R sin(α a )
⋅
− cos(α a )
p =σy
2
1 + 2R

(

2a1 ⋅ (1 + R ) ⋅ α a − α p
× exp
2
a1 + a 2
2

µ
7.4.22

)

The next step in the derivation is to produce an expression relating the edge ratio r/a to
the parameter . Combining Equation 7.4.18c and Equation 7.4.17 and integrating the
resultant from

= a at r=a gives the following generalized equation:

sin(α a )
a1 ⋅ sin(α ) + a2 ⋅ cos(α )
r
=
⋅
a
sin(α )
a1 ⋅ sin(α a ) + a2 ⋅ cos(α a )

γ

( n2 −1) ⋅
exp

(

1 + 2 R ⋅ (α a − α

2 ⋅ n 2 + 1 + 2R

)

)
7.4.23

where

γ=

n ⋅ (1 + R )
n2 + 1 + 2R

If r is set equal to rp and

is set equal to a, then the relationship between rp, a, and

p can be defined as:
sin(α a ) a1 ⋅ sin(α p ) + a2 ⋅ cos(α p )
=
⋅
a
sin(α p ) a1 ⋅ sin(α a ) + a2 ⋅ cos(α a )

rp

γ

( n2 −1) ⋅
exp

(

(

1 + 2R ⋅ α a − α p

2 ⋅ n2 + 1 + 2R

)

)
7.4.24

The maximum value of , max, can be determined from Equation 7.4.24 by calculating
the limit as b

,p

, and rp

resulting in the following equation:

133

α max = tan −1
124

Zhang et al

n + 1 + 2R
(1 − n ) 1 + 2 R

7.4.25
122

proposed a slightly different solution than Ball

who solved for rp, a,

and p by using Equation 7.4.24, Equation 7.4.22 and Equation 7.4.18. In Zhang et
al’s

22

solution, the trigonometric functions for p in Equation 7.4.18a and Equation

7.4.18b are substituted into Equation 7.4.21 and Equation 7.4.23 and then solved using
an iterative solver routine with p < a < max. Since Ball’s analysis

122

assumed b

,

an iterative solution was possible by simply using Equation 7.4.22. With rp, a, and p
determined, the radial and tangential stresses in the plastic zone can be calculated
using Equation 7.4.23, Equation 7.4.21 and Equation 7.4.17 with the elastic stresses
calculated using Equation 7.4.16.

124

The approach used by both Zhang et al

122

and Ball

up to this point, simulated the

stress resulting from the insertion of an oversized fastener or rivet into a hole. This
portion of the closed form solution may prove to be very useful in modeling the strain
response in FML since stress-strain solutions can be calculated in each of the principal
material directions by simply modifying the Ramberg-Osgood material model.
7.4.1.1 Calculation of the Interference Ratio
The next step in generating a closed form solution is to determine the interference ratio
122

resulting from the insertion of the oversized mandrel. Although both Ball
124

et al

solve the problem similarly, Zhang’s work provides the more explicit

134

and Zhang

explanation. In both cases the main goal is to determine a relationship between the
interference generated by the mandrel and the subsequent pressure applied at the edge
of the hole.

The interference (Ia) should be equivalent to the difference between the radial
displacement of the plate, up(a), and the radial contraction of the mandrel, um(a), at the
edge of the hole (r=a). This relationship can be represented mathematically as:
I a = am − a = u p ( a ) − um ( a )

7.4.26

where am is the radius of the mandrel and a is the radius of the hole. Both Zhang et
124

al

122

and Ball

made the assumption that the displacement of the mandrel was

elastic and so um could be calculated using:
a ⋅p
um ( a ) = − m ⋅ (1-ν m )
Em

7.4.27

where Em and m are the elastic modulus and Poisson’s ratio of the mandrel
respectively. The radial displacement of the plate can be calculated by rearranging and
using Equation 7.4.5b at r=a:
u p ( a ) = a ⋅ εθ ( a )

7.4.28

Zhang provides two analytical expressions for up, one assuming that the plate
undergoes only an elastic deformation, and the other assuming that the plate undergoes
a plastic deformation. The equation for up assuming plastic deformation takes into
account the contribution due to both the elastic and plastic strains and is derived by

135

combining Equation 7.4.6b, Equation 7.4.7b and Equation 7.4.8b with Equation 7.4.17
and Equation 7.4.21 to give the following expression at
u p (a) =

a ⋅σ y
E

⋅

= a and r=a:

1+ R
1+ λ
⋅ (1 − λ ) ⋅ cos(α a ) +
⋅ sin(α a )
2
1 + 2R

a1 ⋅ sin(α p ) + a2 ⋅ cos(α p )
a1 ⋅ sin(α a ) + a2 ⋅ cos(α a )

µ

(

2 ⋅ a1 (1 + R ) ⋅ 1 + 2 R ⋅ α a − α p
exp
2
2
a1 + a2

)

n

7.4.28a

where

λ=

R
R
−
−ν
1+ R 1+ R

a1 ⋅ sin(α p ) + a2 ⋅ cos(α p )
a1 ⋅ sin(α a ) + a2 ⋅ cos(α a )

µ
⋅ exp

(

2 ⋅ a1 ⋅ (1 + R ) ⋅ α a − α p
2
2
a1 + a2

)

1− n

Assuming only elastic deformation in the plate, it is possible to derive an equation for
the radial displacement of the plate at r=a from Equation 7.4.7b and Equation 7.4.16:
u p (a) =

a ⋅σ y
E

b2
b2
b4
2 R b4
⋅
+ 1 +ν ⋅
−1 ⋅ 2 ⋅
+2+
⋅
−1
4
1+ R r4
a2
a2
rp
p

−0.5

7.4.28b

The undeformed mandrel size, am can now be calculated using Equation 7.4.24 and
Equation 7.4.27 substituted into Equation 7.4.26 to produce the following expression
am =

up ( a ) + a
1−

p
⋅ (1 −ν m )
Em

7.4.29a

The interference ratio, I0, can now be easily calculated from:
I
a −a
I0 = a = m
a
a

136

7.4.29b

122

:

In practice, the above equations are solved by deciding on a desired interference level
(I0) and iteratively varying the pressure (p) until the desired interference ratio is
obtained.
7.4.2 Closed Form Solution for Elastic-Plastic Unloading
124

Both Zhang et al

122

and Ball

71

built upon the solution presented by Hsu and Forman

by explicitly dividing the cold expansion process into a loading regime (insertion of the
122

mandrel) and an unloading regime (removal of the mandrel). Ball

divided his closed

124

form solution into both a plastic and elastic regime while Zhang et al

went one step

further and provided a closed form solution for an elastic-plastic transition regime. Due
to the reverse yielding resulting from the withdrawal of the mandrel, the equation for the
*
reverse yield stress ( σ y ) depends on whether a point is in the elastic or plastic region.

For points that were elastic during the loading process (i.e. insertion of the oversized
mandrel) the equation for the reverse yield stress is:
σ* = σ +σ y
y

where

7.4.30

is the effective stress as calculated from Equation 7.4.13. For points that

underwent plastic deformation during the loading process, the equation for the reverse
yield stress is:
σ * = (1 + β ) ⋅ σ y + (1 − β ) ⋅ σ
y

Equation 7.4.31 includes a

7.4.31

term that represents the Baushinger parameter. This

parameter takes into account the strain hardening of the material due to plasticity. A

137

Baushinger parameter of =0 implies isotropic hardening while a =1 represents
kinematic hardening.

The closed form solution for the unloading process is very similar to that followed for the
loading process. All equations and variables used specifically for the unloading process
are denoted with an “*”. The relationship between the applied pressure, p, the
*

*

parameter a at the hole edge (r=a), and the parameter p at the edge of the plastic
*

zone (r=rp ) during the unloading process is defined as:
*
1 + R sin(α a )
*
p = σ*
⋅
− cos(α a )
y
2
1 + 2R

× exp

(

*
2a1 ⋅ (1 + R ) ⋅ α a − α *
p
2
a1 + a 2
2

)

a1 ⋅ sin(α * ) + a2 ⋅ cos(α * )
p
p
*
*
a1 ⋅ sin(α a ) + a2 ⋅ cos(α a )

µ

7.4.32

*

The boundary of the reverse yield plastic zone, rp , can be found using Equation 7.4.33
which is the same equation as Equation 7.4.24 except that all variables have a “*”
denoting the unloading process:
r*
p

*
*
*
sin(α a ) a1 ⋅ sin(α p ) + a2 ⋅ cos(α p )
=
⋅
a
sin(α p ) a ⋅ sin(α * ) + a ⋅ cos(α * )
1
a
2
a

γ

( n2 −1) ⋅
exp

(

(

*
1 + 2R ⋅ α a − α *
p

2 ⋅ n2 + 1 + 2R

*

)

*

)

7.4.33
*

An iterative solver can now be used to solve for both rp and a . The value of p can
then be calculated using either Equation 7.4.18a or Equation 7.4.18b. For points at
a

r

*

rp , the unloading is plastic and the resulting radial and tangential stresses are

given by:

138

*
σ r = −σ * ⋅

1+ R
1
⋅ cos(α * ) −
⋅ sin(α * )
2
1+ 2 ⋅ R

7.4.34a

*
σθ = −σ * ⋅

1+ R
1
⋅ cos(α * ) +
⋅ sin(α * )
2
1+ 2 ⋅ R

7.4.34b

Where the effective stress for the unloading step ( σ * ) can be calculated using:

a1 ⋅ sin(α * ) + a2 ⋅ cos(α * )
p
p
=
*
*
σ*
a1 ⋅ sin(α a ) + a2 ⋅ cos(α a )
y

σ*

(

µ

*
2a1 ⋅ (1 + R ) ⋅ α a − α *
p

exp

2
a1 + a 2
2

)

7.4.35

*
where the reverse yield stress ( σ y ) is calculated using Equation 7.4.31. The
relationship between the radius r and the unloading Budiansky parameter

*

is defined

in a similar manner to Equation 7.4.33:
*
sin(α a ) a1 ⋅ sin(α * ) + a2 ⋅ cos(α * )
r
=
⋅
*
*
a
sin(α * ) a1 ⋅ sin(α a ) + a2 ⋅ cos(α a )

122

Ball
(rp

*

r

γ

( n2 −1) ⋅
exp

(

(

*
1 + 2R ⋅ αa − α *

2 ⋅ n 2 + 1 + 2R

)

)

7.4.36

treated points between the reverse yielded zone and the plastic zone
124

rp) as completely elastic whereas Zhang et al

treated this region as elastic

with a yield point based on the reverse yield criterion. The equations for the radial and
tangential stresses in the elastic-plastic region include the yield criterion from Equation
7.4.31 and are given by:

*
σ r = (1 + β ) ⋅ σ y + (1 − β ) ⋅ σ ⋅

× 2⋅

b4
r*
p

4
+2+

b2
−1
2
r

2R
⋅
1+ R

b4
r*
p

139

-0.5

4
−1

7.4.37a

*
σθ = - (1 + β ) ⋅ σ y + (1 − β ) ⋅ σ ⋅

× 2⋅

b4

4

r*
p

+2+

b2
+1
r2

2R
⋅
1+ R

b4
r*
p

For all points located outside the plastic zone (r

-0.5

4

7.4.37b

−1

rp), the unloading is purely elastic and

the equations for the radial and tangential stresses include the reverse yield criterion
from Equation 7.4.30 and are given by:

(

)

*
σr = σ +σ y ⋅

(

)

*
σθ = - σ + σ y ⋅

b2
r2

−1 ⋅ 2 ⋅

b4
r*
p

b2
b4
+1 ⋅ 2 ⋅
r2
r*
p

4
+2+

2R
⋅
1+ R

4
+2+

2R
⋅
1+ R

b4
*
rp
b4
r*
p

-0.5

4

7.4.38a

−1
-0.5

4
−1

7.4.38b

The final radial and tangential residual stresses can now be calculated by simply
summing up the stresses during both the loading and unloading portion of the cold
expansion process:
res
*
σ r = σ r +σ r

7.4.39a

res
*
σθ = σθ +σθ

7.4.39b

7.4.3 Calculation of Radial and Tangential Strains
For the purposes of making a comparison between experimental and theoretical results,
it was critical to have an explicit formulation for the strain values in both the elastic and
plastic regimes. During the loading phase, the plastic strains can be calculated by using
Equation 7.4.10 with the Ramberg-Osgood relationship for the secant modulus

140

(Equation 7.4.9), which results in the following explicit expression for the radial and
tangential strains:
1 σ
εr = ⋅
E σy
1 σ
εθ = ⋅
E σy

n-1
⋅ σr −

R
⋅ σθ
1+ R

7.4.40a

R
⋅σ r
1+ R

7.4.40b

n-1
⋅ σθ −

The elastic strains can then be calculated from the generalized Hooke’s Law
relationship given in Equation 7.4.7, except that the Poisson’s ratio, , is replaced
71,123

by

:
ν=

R
1+ R

7.4.41

The calculation of the elastic and plastic strains for the unloaded case proceeds in a
similar manner, with the inclusion of the corresponding stresses from unloading used in
Equation 7.4.40 and Equation 7.4.42. The final residual strains are then simply the
summation of the residual strains during loading and unloading, in a manner analogous
to Equation 7.4.39.
1
R
⋅ σr −
⋅ σθ
E
1+ R
1
R
εθ = ⋅ σθ −
⋅σ r
E
1+ R

εr =

7.5

7.4.42a
7.4.42b

Development of Closed Form Model for Riveting

Modifying the closed form solution used for the cold expansion process provided one
possible method for developing an analytical solution for calculating the stresses and
strains during the riveting process.

141

In the first stage of the closed form solution for cold expansion, an analytical solution
was developed for calculating the stresses and strains during the insertion of an
oversized mandrel into the fastener hole. In many ways this describes the riveting
process, where an undersized rivet is placed into a hole, and compressed so that the
rivet shank expands circumferentially. The key piece of information required is the final,
expanded diameter of the rivet. This was measured by carefully polishing down the
protruded head of the rivet until it was flush with the coupon. The coupon was then
photographed using a stereomicroscope (Figure 75) with the lighting adjusted so that
the expanded shank of the rivet was visible. A scale left in the field of view allowed for
easy calibration between pixels and inches, and a macro written for ImageTool allowed
the diameter to be calculated by selecting three opposing points on the circumference.

Figure 75: Polished surface used for rivet measurement with rivet diameter highlighted
in red
Using the value of the expanded diameter of the rivet shank, the percent interference
was calculated for the rivet in both the aluminum and the FML coupons. The average
rivet diameter measured using this method was 4.191 mm in aluminum and 4.27 mm in
FML 3, giving an average expansion of 3.0% and 4.5% respectively. The same closed

142

form solution used to calculate the strains during cold expansion was then used with
only minor changes. In the case of riveting, there is no elastic-plastic spring back since
the rivet remains in the coupon, so this portion of the closed form solution was removed.
The material properties for the rivet were input in place of the mandrel properties and
the starting diameter was set to be equivalent to the initial (oversized) hole size for the
of rivet. The applied pressure was then varied iteratively until the calculated rivet radius
(post expansion) matched the measured radius.

7.6

Closed Form Modelling of FML Properties

The properties of any fiber metal laminate material can be analytically predicted using
an approach that combines micromechanic strength of materials methods along with
classical laminated plate theory. The strength of materials approach is used to model
the properties of the prepreg material (resin + glass fiber) while classical laminated plate
(CLP) theory is used to determine the properties of the entire fiber metal laminate based
on the number of plies and their orientation. As with any closed form approach, certain
limitations exist: (1) the predicted FML properties are reliant on the accuracy of the fiber
and matrix properties used (2) an assumption is made that the glass fibers behave
isotropically and (3) the predicted properties and predicted strengths are upper bounds.

7.6.1 Micromechanics Approach to Modeling Prepreg Properties
Assuming that the elastic modulus of the glass fibers (Ef), the elastic modulus of the
resin matrix (Em), the volume fraction of glass fiber (Vf), the volume fraction of the resin
matrix (Vm), the shear modulus of the glass fiber (Gf) and the shear modulus of the
resin matrix (Gm) are known, then many of the prepreg properties, starting with the

143

modulus of the prepreg (E1) in a direction parallel to the fibers can be calculated using a
rule of mixtures approach. The derivation for the material properties of the prepreg is
based on the representative volume element (RVE) approach that assumes the fibre,
matrix and prepreg to be of the same height, but of different thicknesses (tf, tm and tp)
as shown in Figure 76.

Figure 76: Representative volume element (RVE) showing applied stress in the
direction of the fiber
If a unidirectional stress ( p) is applied to the RVE in the direction of the fiber, then it
can be assumed that the corresponding force applied to the prepreg is equal to the sum
of the force applied to the fiber and the force applied to the matrix. With the assumption
of linear-elastic isotropic constituents, the force relationship can be re-written as:
E1ε p Ac = E f ε f A f + Emε m Am

where

7.6.1

is the applied strain and A is the area of each component in the RVE. With the

assumption that the displacements and thus the strains in each component of the RVE

144

are equal one can re-write Equation 7.6.1 in terms of the volume fraction (V) to produce
an expression for the elastic modulus in the fiber direction:
E1 = V f ⋅ E f + Em ⋅ (1 − V f )

7.6.2

For the elastic modulus transverse to the fiber direction, a force applied in this direction
will be distributed equally among all the components of the RVE (Figure 77) such that
the force in the prepreg equals the force in the matrix which equals the force in the
fibers.

Figure 77: Representative volume element (RVE) showing applied stress transverse to
the direction of the fiber

As a result the displacement of the prepreg in this direction is equal to the sum of the
displacements of the fiber and the matrix components. The individual components of
the displacement can be related to the strain in each component using:

δ p = t p ⋅ε p

δ f = t f ⋅ε f

δ m = tm ⋅ ε m

The strains can also be expressed using Hooke’s law as:

145

7.6.3

σ
ε p= c

εf =

E2

σf
Ef

σ
εm = m

Em

7.6.4

The equation for the displacement of the RVE under a transverse load can then be rewritten in terms of the stresses as follows:

δ p = δ f + δm
σf
σc
tp

E2

=tf

σ
+ tm m
Ef
Em

7.6.5

Since the stresses are equivalent, they cancel out of Equation 7.6.5 and the ratio of the
thicknesses can be equated to the volume fraction of the constituents, which after some
rearranging, gives the modulus of the prepreg orthogonal (E2) to the fiber:
E2 =

Em ⋅ E f
V f ⋅ Em + (1 − V f ) ⋅ E f

7.6.6

An analogous derivation can be used to determine the shear modulus of the prepreg
(Gp):
Gp =

Gm ⋅ G f
V f ⋅ Gm + (1 − V f ) ⋅ G f

7.6.7

A similar type of derivation can also be used to determine the Poisson’s ratio for the
prepreg ( p) which is given by:

ν p = V f ⋅ν f + (1 − V f ) ⋅ν m

7.6.8

If additional information is known regarding the coefficient of thermal expansion of both
glass fiber ( f) and the matrix ( m) then the coefficient of thermal expansion of the

146

prepreg in the direction parallel to ( 1) and perpendicular to the orientation of the glass
fibers ( 2) can be determined using:
α1 =

α f ⋅ E f ⋅V f + α m ⋅ Em ⋅ (1 − V f )

E1
α 2 = (1 + ν f ) ⋅ α f ⋅V f + (1 + ν m ) ⋅ α m ⋅ (1 − V f ) − α1 ⋅ν p

7.6.9
7.6.10

With the four independent material constants (E1, E2, vp and Gp) of the prepreg
(unidirectional glass + resin matrix) determined, Hooke’s law for orthotropic materials
can be used to determine both the compliance matrix [S] and the stiffness matrix [Q] of
the prepreg:
1
E1

−ν p

E1
0

[S ] =

E1
1
E2
0

−ν p

0
0

7.6.11

1
Gp

E1
1 −ν 2
p

[Q ] =

ν p E2

ν p E2

E2
1 −ν 2
p

0

0

Gp

1 −ν 2
p
0

1 −ν 2
p

0

7.6.12

In order to more generally relate [S] and [Q] to any orientation a transform matrix [T] is
required, where

is the angle between the x-axis to the principal fiber axis. In general

for laminated plate analysis, the directions 1,2,3 refer to the principal fiber direction, the

147

in-plane perpendicular direction and the out-of-plane perpendicular direction
respectively. The loading direction for the entire laminate is designated using x,y,z.
cos 2 (θ )
[T ] =

sin 2 (θ )

2 ⋅ cos(θ ) ⋅ sin(θ )

sin 2 (θ )

cos 2 (θ )

−2 ⋅ cos(θ ) ⋅ sin(θ )

7.6.13

− cos(θ ) ⋅ sin(θ ) cos(θ ) ⋅ sin(θ ) cos 2 (θ ) − sin 2 (θ )

The transform matrix [T] can be used to convert stress in the principal direction to that at
an arbitrary angle

as shown:

σ1
σx
σ 2 = [T ] ⋅ σ y
τ12
τ xy

7.6.14

The same transformation can also be used to convert strains in the principal direction to
strains at an arbitrary angle

in a similar manner. The only change is the addition of

the Reuter’s matrix [R] which allows one to transform the tensorial shear strain tensor
instead of the engineering shear strain tensor.

[ R] =

1 0 0
0 1 0

7.6.15

0 0 2

With the addition of the Reuters matrix one can convert strain in the principal direction
to that in an arbitrary direction, in a manner similar to that done with the principal stress:

ε1
εx
−1
ε 2 = [ R ] ⋅ [T ] ⋅ [ R ]
εy
γ12
γ xy

7.6.16

Based on Hooke’s law for angled lamina, one can relate the principal strains to the
principal stresses using the compliance matrix [S]:

148

ε1
ε2 = [S ]⋅
γ12

σ1
σ2
τ12

7.6.17

Ideally one would like to determine the compliance matrix in the x-y-z system such that:

εx
εy

σx
_
= S ⋅ σy

γ xy

τ xy

7.6.18

_

The value for [ S ] can be determined by replacing the stress and strain terms in
Equation 7.6.17 using Equation 7.6.14 and Equation 7.6.16 respectively and rearranging the equation to solve for strains in the x-y-z system as shown:

εx
εy

−1

= [ R ] ⋅ [T ]

−1

⋅ [ R]

⋅ [ S ] ⋅ [T ]

γ xy

σx
σy
τ xy

so,

7.6.19

_
−1
−1
S = [ R ] ⋅ [T ] ⋅ [ R ] ⋅ [ S ] ⋅ [T ]

The same basic derivation can be performed for the stiffness matrix [Q], so that we can
determine the stiffness matrix in the x-y-z co-ordinate system.

σ1
σ 2 = [Q ]
τ12

ε1
ε2
γ12

so,

σx
εx
−1 ⋅ Q ⋅ R ⋅ T ⋅ R −1 ε
σ y = [T ] [ ] [ ] [ ] [ ]
y
τ xy
γ xy
so,
_
_ −1
−1
−1
Q = [T ] ⋅ [Q ] ⋅ [ R ] ⋅ [T ] ⋅ [ R ] = S

149

7.6.20

7.6.2 Classical Laminated Plate Approach to Laminate Properties
The approach so far has yielded the local and global stiffness [Q] and compliance [S]
matrices, allowing for a complete theoretical characterization of the stresses and strains
in an entire laminate or an individual ply. Next, a standard classical laminated plate
(CLP) approach will be used to determine the engineering constants of the lamina (Ex,
126-128

Ey, Gxy, xy)

. The approach to determining the engineering constants of a

laminated composite material (like FML), can be best understood by examining the
stress – strain relations for an individual ply as shown:

1
Ex

εx
εy
ϒ xy

−

ν xy
Ex
1
Ey

=
Sym

0
0
1
Gxy

σx
⋅ σy

7.6.21

τ xy

To apply Equation 7.6.21 to a complete laminated composite material, one needs to
take into account that the stresses vary through the thickness, so one needs to define
the average stresses and relate them to strains. The average stresses ( σ ) can be
approximated by integrating the stresses in the x,y,z direction over the thickness (t) of
the laminate, which by definition are related to N, the average force/unit width acting on
a specific face of the laminate:

150

_ 1 t /2
N
σx ≡ ⋅
σ x ⋅ dz = x
t
t
−t /2
_ 1 t /2
Ny
σy ≡ ⋅
σ x ⋅ dz =
t
t
−t /2
_ 1 t /2
N xy
τ xy ≡ ⋅
σ x ⋅ dz =
t
t
−t /2

7.6.22

If we assume that the laminate is orthotropic and that the laminate layup is symmetric, it
is possible to express the relationship between the laminate strains and the average
stresses in a similar manner to that for an individual ply:

εx
εy

1
Ex
1
= ⋅
t

ϒ xy

−

ν xy
Ex
1
Ey

Sym

0
Nx

0
1
Gxy

⋅ Ny
N xy

7.6.23

The next step is to express Equation 7.6.23 in terms that can be solved explicitly,
allowing one to determine the engineering constants by inspection. To do this it is
instructive to examine the derivation used to determine stresses and strains in a
laminated composite beam.

Classical beam theory is built on several fundamental assumptions including:
1. plane sections remain planar after deformation
2. plate thickness (t) remains constant
3. plate deformations are small enough that small angle assumptions are valid

151

In this case, for a uniform plate under a bending deformation, the strain at any point in
the thickness (z) can be related to the mid-plane strains ( º) and the curvature ( ) as
shown:

0
εx

εx

κx
0 +z κ
εy = εy
y
κ xy
ϒ xy
ϒ0
xy

7.6.24

If one is dealing with a laminated plate, an assumption that there is perfect bonding
between each of the laminate layers must be made. Stresses applied to a section of
the beam will lead to an equivalent axial force (N) and a bending moment (M)
t /2

N=

M=

−t /2
t /2

σ x ⋅ dz = axial load / unit width

−t /2

7.6.25

σ x ⋅ z ⋅ dz = moment / unit width

One can use a Hookean definition for stress to substitute for x in the equations for N
and M and obtain the following relationships:
N=

t /2
−t /2

σ x dz =

t /2
−t /2

Eε x dz =

t /2
−t /2

(

)

E ε x − zκ x dz

7.6.26

which can then be re-arranged as:
N=

t /2
−t /2

E ⋅ dz ⋅ ε x +

t /2
−t /2

E ⋅ z ⋅ dz ⋅ κ x

N = A ⋅ε x + B ⋅κ x

the same can be done for M, which gives:

152

7.6.27

M=

M=

t /2

(

)

E ε x + z ⋅ κ x ⋅ z ⋅ dz

−t /2
t /2

−t /2

t /2

E ⋅ z ⋅ dz ⋅ ε x +

−t /2

7.6.28

E ⋅ z 2 ⋅ dz ⋅ κ x

M = B ⋅ε x + D ⋅κ x

In matrix form the above equations can be written as:
N
M

A

=

B

B D

⋅

εx

7.6.29

κx

Where [A] is termed the extensional stiffness of the laminated plate, [B] is the coupling
stiffness of the laminated plate and [D] is the bending stiffness of the laminated plate.
Overall the stiffness expressions for [A], [B] and [D] can be generalized by replacing the
constant of integration as follows:
t /2

A=

E ⋅ dz =

−t /2

B=

t /2

E ⋅ z ⋅ dz =

−t /2

D=

t /2
−t /2

E ⋅ z 2 ⋅ dz =

N
k =1

N
k =1

Ek ⋅

Ek ⋅

N
k =1

Zk

Z k −1

Ek ⋅

dz =

Z k −1
Zk

Zk
Z k −1

N
k =1

z ⋅ dz =

(

Ek ⋅ zk − zk −1

)

1 N
2 2
Ek ⋅ zk − zk −1
2
k =1

(

z 2 ⋅ dz =

7.6.30

)

1 N
3 3
Ek ⋅ zk − zk −1
3
k =1

(

7.6.31

)

7.6.32

Where the thickness of the kth layer is defined as tk=zk-zk-1. Through the use of the [A],
[B], and [D] matrices we now have a way to use the engineering constants of the
individual plies to determine the overall engineering constants of the laminate. The

153

overall stiffness matrix of the laminated plate is given by Equation 7.6.29 and the
individual stiffness components can be written as:

[ A] =

N
k =1

_
Q ⋅ ( zk +1 − zk )

7.6.33

[ B] =

1 N _
2
2
Q ⋅ zk +1 − zk
2
k =1

(

)

7.6.34

[ D] =

1 N _
3
3
Q ⋅ zk +1 − zk
3
k =1

)

7.6.35

(

where [Q ] is given in Equation 7.6.20. If one inverts the stiffness formulation of the
laminate stress-strain relationship, one obtains the compliance formulation as shown:

{ }
ε0

{k }

=

[ A]3x3 [ B ]3x3
[ B ]3x3 [ D ]3 x3

−1
⋅

{N}
{M }

A'
=

B'

3 x3
3 x3

B'
D'

3 x3

⋅

{N }
{M }

7.6.36

3 x3

Some additional matrix algebra is required to calculate the inverse of the [A], [B], and
[D] matrices and a summary of these operations is provided below:
A*
B*
C*
D*

= [ A]−1
3 x3
3 x3
3 x3
3 x3

= − A*
= − B*

3 x3

⋅[ B]
3 x3

7.6.37a

3 x3

= [ D]
− B
⋅ A*
⋅ [ B]
3 x3 [ ]3 x3
3 x3
3 x3
3 x3

154

D'
B'
C'
A'

−1
= D*
3 x3
3 x3
*
= B
⋅ D'
3 x3
3 x3
3 x3
T
= B'
3 x3
3 x3
3 x3

= A*

3 x3

+ B'

7.6.37b

T
⋅ B*
3 x3
3 x3

For symmetric laminates the coupling matrix [B]=0 and the compliance formulation of
the stress strain relationship can be expressed as:
'
A11

εx
εy
γ xy

=
Sym

'
A12
'
A22

'
A16
Nx
Nx
'
A26 ⋅ N y = A1 ⋅ N y
'
A66
N xy
N xy

7.6.38

Equation 7.6.38 can now be written in a similar form to Equation 7.6.23 and by
inspection, one can determine the following values for the in-plane engineering
constants of the laminate:

Ex =

1

7.6.39a

'
t ⋅ A11
1
Ey =
'
t ⋅ A22
− A'
ν xy = 12
'
A11
1
Gxy =
'
t ⋅ A66

7.6.39b
7.6.39c
7.6.39d

The above equations and approach was used to estimate the material properties of
FML with various layups, which will be further discussed in Chapter 9.0.

155

7.7

Comparison of Closed Form Results to Experimental Measurements

Based on the development of a closed form solution for cold expansion and riveting
(Chapter 7.4), sample experimental strain data obtained from DIC measurements on the
entry face (Chapter 6.0) of 2024-T3 aluminum and FML 3 coupons were compared to
the closed form results. In addition to strain data, each comparison graph shows the
location of the elastic-plastic boundary (rp/a) as well as the reverse yielding elastic*

plastic boundary (r p/a) determined from the closed form solution (where r is the
distance from the center of the open hole and a is the radius of the open hole).

In order to gain better fidelity in the comparison between the closed form solution and
the experimental results, material property data for both the 2024-T3 aluminum

129

and

FML coupons were taken in both the longitudinal and transverse direction.
Modifications were then made to account for material property changes and edge
distance changes in each direction.

7.7.1 Comparison to Cold Expansion Strains: 2024-T3 Coupons
The results for the 2024-T3 aluminum coupon (Figure 78 and Figure 79) shows the best
corroboration in the elastic region, with some hint of divergence as the data gets closer
to the plastic zone. The overall correlation between the two results is better for the
maximum principal strains since the overall strain magnitude is lower. Greater
divergence from the measured data is seen in the plot of minimum principal strain
possibly due to the extremely high strain gradient near the edge of the hole and the
limited strain resolution that was available at the magnification that was used. The
average magnification was approximately 0.05 mm/pixel and the subset size measured

156

2

17 pixels x 17 pixels, meaning that each subset covered approximately 0.78 mm . The
closed form solution shows a predicted exponential increase in strain as one
approaches the edge of the hole (r/a=1). In the region of plastic strain between
approximately r/a=1 and r/a = 2.2 (linear distance of approximately 3.8 mm) only slightly
more than four full subsets cover this region. The magnification used for testing is
always a compromise between having a field of view large enough to view the full extent
of the cold expansion residual strains and having enough strain resolution to capture
some detail regarding what is happening at the edge of the cold expanded hole.
0.04
Strain (mm/mm)

0.02
0
radial (closed form)
hoop (closed form)
hoop (experimental)
radial (experimental)
rp/a
rp*/a

-0.02
-0.04
-0.06
-0.08
-0.1
1

1.5

2

2.5
Distance (r/a)

3

3.5

4

Figure 78: Comparison between closed form and experimental measurements for
aluminum coupon in transverse direction (specimen AL1)
The same effect is seen in the plot of the longitudinal strains (Figure 79) which shows
very similar results in both magnitude and form to those from the transverse direction.
This is to be expected since aluminum has similar properties between the longitudinal
and transverse directions.

157

0.04
Strain (mm/mm)

0.02
0
radial (closed form)
hoop (closed form)
hoop (experimental)
radial (experimental)
rp/a
rp*/a

-0.02
-0.04
-0.06
-0.08
-0.1
1

1.5

2

2.5
Distance (r/a)

3

3.5

4

Figure 79: Comparison between closed form and experimental measurements for
aluminum coupon in longitudinal direction (specimen AL1)

7.7.2 Comparison to Cold Expansion Strains: FML 3 Coupons
The same comparisons were made with an FML 3 coupon, and overall results showed
much better corroboration than with the 2024-T3 aluminum coupons. As with the
aluminum coupons, the experimental results for FML 3 (Figure 80 to Figure 82) show
some divergence, especially as one approaches the plastic region. To make the
comparisons more accurate, the experimental strain results were extracted in the
longitudinal and transverse direction, as well as in the 45º degrees direction. This
allowed for more accurate material properties to be used in the closed form solution.
The results for the transverse direction (Figure 80) showed similar values to the closed
form solution until near the reverse yield elastic-plastic boundary (rp_/a). At that point
the experimental strain results started to diverge, with the maximum principal strains
being overestimated by the closed form solution and the minimum principal strains
being underestimated.

158

0.02
Strain (mm/mm)

0.01
0
radial (closed form)
hoop (closed form)
hoop (exp)
radial (exp)
rp/a
rp*/a

-0.01
-0.02
-0.03
-0.04
-0.05
1

1.5

2

2.5
Distance (r/a)

3

3.5

4

Figure 80: Comparison between closed form and experimental measurements for FML
3 coupon in transverse direction (specimen GAL1)
The results from the longitudinal direction (Figure 81) showed excellent corroboration
with the closed form predictions, with only a slight deviation in the maximum principal
strains just past the reverse yield elastic-plastic boundary.

0.02
Strain (mm/mm)

0.01
0
radial (closed form)
hoop (closed form)
hoop (experimental)
radial (experimental)
rp/a
rp*/a

-0.01
-0.02
-0.03
-0.04
-0.05
1

1.5

2

2.5
Distance (r/a)

3

3.5

4

Figure 81: Comparison between closed form and experimental measurements for FML
3 coupon in longitudinal direction (specimen GAL1)

159

The results in the 45º degree direction (Figure 82) corroborated well with the closed
form solution up to the elastic-plastic (rp/a) boundary, at which point the closed form
results appeared to underestimate both the maximum and minimum principal strains.
Extracting data at exactly 45º degrees is difficult and certainly one likely source of error
is the actual angle at which the data was extracted.

This approach to modeling the effect of cold expansion in FML appears reasonable and
provided good corroboration of the experimental data. It should also be noted that the
strains at 45º degrees were significantly higher than in either the longitudinal or
transverse direction, meaning that this model was capturing the inherent orthotropy of
the material to some extent.

Overall, the experimentally measured cold expansion strains in FML were lower than in
the aluminum coupons. Since both the FML and the aluminum coupons were
measured with the same experimental setup and had the same strain resolution, the
lower strain gradient in FML may account for why better corroboration was seen with
this material.

160

0.04

Strain (mm/mm)

0.02
0
radial (closed form)

-0.02

hoop (closed form)

-0.04

hoop (experimental)

-0.06

radial (experimental)
rp/a

-0.08

rp_/a

-0.1
1

1.5

2

2.5
Distance (r/a)

3

3.5

4

Figure 82: Comparison between closed form and experimental measurements for FML
3 coupon in 45 degree direction (specimen GAL1)

7.7.3 Comparison to Riveting Strains: 2024-T3 Coupons
One difficulty in validating a closed form model for riveting stemmed from the inability to
measure strains under the driven or manufactured head. Compared to the cold
expansion results, the experimental measurements for the riveted coupons tended to
begin much farther away from the edge of the pilot hole, in the range of
1.75 < r/a < 2.75, which is well within the elastic range for both aluminum and FML.
The same approach was followed for the comparison to the riveting strains, where both
longitudinal and transverse strain data were extracted so that the closed form model
could be run with the appropriate material models. In the transverse direction (Figure
83) the experimental strain results appear to corroborate very well up to the elasticplastic boundary (r/a=1.89).

161

0.04
Strain (in/in)

0.02
0
hoop (closed form)
radial (closed form)
hoop (experimental)
radial (experimental)
r/a

-0.02
-0.04
-0.06
-0.08
1

1.5

2

2.5
3
Distance (r/a)

3.5

4

Figure 83: Comparison between closed form and experimental measurements for
riveted aluminum 2024-T3 coupon in transverse direction (specimen AT8)
In the longitudinal direction (Figure 84) the experimental strain results also appear to
corroborate very well up to the elastic-plastic boundary (r/a=1.97). The strain results
from both directions appear to be quite similar overall, with only a small change in the
location of the elastic-plastic boundary to suggest that different material properties were
used for each direction.

162

0.04

Strain (mm/mm)

0.02
0
hoop (closed form)

-0.02

radial (closed form)

-0.04

hoop (experimental)
radial (experimental)

-0.06

r/a

-0.08
1

1.5

2

2.5
3
Distance (r/a)

3.5

4

Figure 84: Comparison between closed form and experimental measurements for
riveted aluminum 2024-T3 coupon in longitudinal direction (specimen AT8)
7.7.4 Comparison to Riveting Strains: FML 3 Coupon

The same procedure was used with the riveted FML coupons as with the cold expanded
coupons, where material models in the transverse (Figure 85), longitudinal (Figure 86)
and in the 45º degree direction (Figure 87) were input into the closed form solution. In
the elastic range, the closed form solution seems to corroborate very well to the
experimentally measured strains. The larger minimum principal strains predicted in the
45º direction are indicative that the approach used with the closed form model allows for
better predictions with orthotropic materials such as FML.

163

0.06
Strain (mm/mm)

0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
1

1.5

2

2.5

3

3.5

4

Distance (r/a)
hoop (closed form)
radial (experimental)

radial (closed form)
r/a

hoop (experimental)

Figure 85: Comparison between closed form and experimental measurements for FML
coupon in transverse direction (specimen GAL4)

Strain (mm/mm)

0.06
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
1

1.5

2

2.5

3

3.5

4

Distance (r/a)
hoop (closed form)
hoop (experimental)
r/a

radial (closed form)
radial (experimental)

Figure 86: Comparison between closed form and experimental measurements for FML
coupon in longitudinal direction (specimen GAL4)

164

Strain (mm/mm)

0.06
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
-0.1
1

1.5

2

2.5
Distance (r/a)

hoop (closed form)
hoop (experimental)
r/a

3

3.5

4

radial (closed form)
radial (experimental)

Figure 87: Comparison between closed form and experimental measurements for FML
coupon in 45º degree direction (specimen GAL4)

165

8.0

BASELINE FATIGUE BEHAVIOUR

The baseline fatigue phase of this research program involved the fatigue testing of both
aluminum and fiber metal laminate coupons at a net section stress ranging from 168198 MPa, a loading frequency of 10 Hz and a load ratio of R=0.1 (see chapter 5.2 for
additional details). The results from the aluminum coupons provided a baseline for
comparing the fatigue life, the crack growth and the crack nucleation mechanisms of the
FML coupons. The baseline fatigue testing involved screening 2024-T3 aluminum and
FML coupons to determine their fatigue life after cold expansion and riveting. In
addition, strain measurements made on either face of the coupons provided important
information that was used to better understand the mechanism behind the fatigue life
improvement seen from cold expansion and riveting
8.1

Fatigue Behaviour After Cold Expansion

Fatigue results are provided for both aluminum and FML, with detailed strain information
provided for select coupons for the purpose of more in-depth discussion. As a concise
way of presenting the large number of data sets, sample results from both the DIC and
TSA systems are presented for both FML 3 and FML 4 at one stress level (198 MPa)
and for one sample specimen.
For each specimen, results are presented pre-crack and at crack lengths of
approximately 1, 2, and 3.7 mm. The final crack length of 3.7 mm was chosen as it
represented the longest crack length that could be discerned in all coupons, given the
field of view of the camera. In all cases, the data collected simultaneously from the TSA
system was reflected about the loading (vertical) axis for ease of comparison to data
from the DIC system on the opposite face. From an analysis perspective, the main
166

focus was on the maximum principal strains, since these are largely responsible for
crack growth and provide the most information about what is occurring in the region
close to the crack tip.
8.1.1 Aluminum: Cold Expansion Strain and Fatigue Results
8.1.1.1 Aluminum: Overall Fatigue Results

Overall fatigue results showing the number of cycles to failure against the net section
stress are shown in Figure 88. Although the number of coupons tested at each stress
level is relatively small (n=3 for the cold expanded coupons and n=2 for unexpanded
coupons), the improvement in fatigue life as a result of cold-expansion, especially at
lower stress levels, is still evident. These findings are supported by a number of
researchers who have used residual stress measurements, using either the Sachs
62,130

method

46,68,122

or x-ray diffraction

, to show that the effectiveness of the cold

expansion process is as a result of the compressive residual stresses created around
the hole.

167

Net Section Stress (MPa)

220
Cold Expanded

210

Unexpanded
200
190
180
170
160
0

250,000

500,000

750,000

1,000,000

1,250,000

Cycles to Failure

Figure 88: Mean fatigue results for aluminum coupons both with and without coldexpansion of the hole
8.1.1.2 Aluminum: Crack Growth Curves

Sample crack growth curves comparing the rate of crack growth for open hole and cold
expanded coupons at each of the three net stress levels are given in Figure 89a,b and
Figure 89c. The results support the overall fatigue results showing retardation in crack
growth as a result of cold expansion. What is less clear is whether the cold expansion
process is effective in extending life during the early stage of the fatigue process. The
literature on this subject is also ambiguous, with researchers such as Chandawanich
and Sharpe

20

showing that cold expansion has no effect on what they termed “fatigue
131

crack initiation”, while others such as Amrouche et al

suggesting that cold expansion

does have an effect on “crack initiation”. The optical measurements used for the current
test program provided accurate results for cracks of 0.4 mm in length or greater, but

168

detecting the formation of cracks below that threshold was less consistent. The other
important point is that all optical crack growth measurements were made on the entry
face, and given that the exit face had higher residual strains, it seems likely that cold
expansion would extend the early stage of the fatigue process on the exit face. Trying
to verify this by simply examining the crack growth curves of Figure 89 can be
misleading due to the difficulties in measuring very small initial crack sizes. However, if
one arbitrarily uses 1 mm as the definition of a short crack, then it is possible to
determine the number of cycles required to grow a crack of this size both before and
after cold expansion. Figure 90 clearly shows that cold expansion increases the
number of cycles required to grow a 1 mm crack, and that this increase appears to be
related to the net section stress. Calculating the crack growth per number of cycles
(da/dN) for all coupons also shows how cold expansion significantly reduces the overall
rate of crack propagation in the aluminum coupons (Figure 90).

169

Crack Length
(mm)

5.0

Net Stress = 165 MPa

4.0

2024-T3 (Open Hole)
2024-T3 (Cold Expanded)

3.0
2.0
1.0
0.0
0

100,000

200,000

300,000

400,000

500,000

600,000

Cycles
(a)

Crack Length
(mm)

5.0

2024-T3
(Open Hole)

4.0
3.0

2024-T3
(Cold
Expanded)

2.0
1.0

Net Stress = 176 MPa

0.0
0

50,000

100,000
Cycles

150,000

200,000

Crack Length (mm)

(b)

5.0

Net Stress = 198 MPa

4.0

2024-T3 (Open
Hole)

3.0
2.0

2024-T3 (Cold
Expanded)

1.0
0.0
0

20,000

40,000

60,000

80,000

100,000

120,000

Cycles
(c)
Figure 89: Crack growth curves for 2024-T3 aluminum coupons (a) Net Stress 165
MPa: Open Hole (specimen Al-L-20) and cold expanded (specimen Al-L-28) coupons
(b) Net Stress 176 MPa: Open Hole (specimen AL-L-26) and cold expanded (specimen
AL-L-29) coupons and (c) Net Stress 198 MPa: Open Hole (specimen AL-L-36) and
cold expanded (specimen AL-L-35) coupons

170

6.0

375,000

5.0

300,000

4.0

225,000

3.0

150,000

2.0

75,000

1.0

0

0.0
198 (MPa)

176 (MPa)
Stress Level

Al 2023 OH
Al 2023 OH

da/dN (mm/10,000 cycle)

7.0

450,000
Cycle Count

525,000

165 (MPa)
Al 2023 CX
Al 2023 CX

Figure 90: Variation in number of cycles to 1 mm crack length (columns) versus da/dN
(symbols) for 2024-T3 aluminum at various stress levels
8.1.1.3 Aluminum: DIC and TSA Measurements During Fatigue Loading
Although, it is possible to quantify the corresponding total residual strains using image
correlation by selecting a reference state prior to cold expansion and collecting and
processing multiple images during the cold expansion process

132

, in this study, the

reference state was chosen to be post cold expansion, so that data from image
correlation would be analogous to that from thermoelastic stress analysis; i.e. the
reference image was collected at the minimum (889 N), and the deformed image at the
maximum (8896 N) load in the fatigue cycle. Thus the data from both digital image
correlation and thermoelastic stress analysis represent the strain difference or the
amplitude of strain during the cycle.

171

The maximum principal strains measured with DIC on the entry face of an aluminum
coupon are shown in Figure 91 for unexpanded (UH) (left column) and cold-expanded
(CX) (right column) holes precrack and for crack lengths of 1 mm, 2 mm and 3.7 mm.
The crack lengths were obtained from the image of the coupon captured at maximum
load and subsequently used for digital image correlation. As expected, based on the
data shown in Figure 90, the number of cycles required to grow the fatigue crack with a
cold-expanded hole is substantially greater than for an unexpanded hole; by a factor of
two for a crack length of 1 mm rising to a factor of three for a crack length of 3.7 mm.
Full-field maps of the thermoelastic stress analysis signal (in camera A/D units)
captured during the same cycles are shown in Figure 92. These data maps are directly
proportional to the amplitude of the temperature, T, during the loading cycle, which in
turn is proportional to the amplitude of the first stress invariant, ∆ (σ11 + σ 22 ) .

172

Unexpanded Hole

Cold-expanded

Microstrain
Uncracked

(a) 0 cycles

(b) 0 cycles

(c) 63,101 cycles

(d) 103,301 cycles

(e) 64,901 cycles

(f) 191,501 cycles

(g) 67,901 cycles

(h) 212,501 cycles

1.0 mm
crack

2.0 mm
crack

3.7mm
crack

Figure 91: Maximum principal strains obtained from digital image correlation from
aluminium coupons with both an unexpanded (left, specimen AL-L-25 ) and cold–
expanded (right, specimen AL-L-27 ) hole pre-crack and with crack lengths of 1, 2 and
3.7 mm

173

Uncracked

Unexpanded Hole

Cold-expanded

2.0 mm
crack

3.7 mm
crack

(a) 0 cycles

(b) 0 cycles

(c) 63,101 cycles

(d) 103,301 cycles

(e) 64, 901 cycles

(f) 191,501 cycles

(g) 67,901 cycles

1.0 mm
crack

TSA

(h) 212,501 cycles

Figure 92: Full-field maps of the thermoelastic signal (A/D units) from the exit face for
unexpanded (left) and cold-expanded (right) holes. Date reflected about the loading
axis for ease of comparison vertical) axis for ease of comparison

174

8.1.1.4 Discussion
There is little difference between the precrack coupons with the unexpanded (UH) and
cold expanded (CX) holes (Figure 91), and the difference that does exist is likely due to
the approximately 0.8% higher net section stress for the cold-expanded coupon. When
the crack extends to 1 mm, a clear difference exists between the results for the UH
(Figure 91c) and CX (Figure 91d) coupons. In the UH coupon a crack is clearly visible,
with a circular contour of both maximum principal strain (Figure 91c) and TSA signal or
first stress invariant (Figure 92c) at its tip. It is interesting to note that the strain
amplitude deduced from TSA associated with the crack tip is lower than at the
uncracked side of the hole. This effect is likely due to crack tip plasticity, which creates
a small residual stress field ahead of the crack tip, so that when it is unloaded the
plastic zone is compressed circumferentially and the surrounding elastic material
experiences tension. The tension raises the minimum stress experienced during the
cycle and thus lowers the stress amplitude. This behaviour has been observed
133

previously

in TSA data in the vicinity of propagating cracks, however, the resolution

of these images is too low for the plastic region to be visible. The data in Figure 92b
and Figure 92d from the exit face of the cold-expanded hole exhibit no apparent
difference between the uncracked case and when a 1 mm long crack was observed on
the entry face. This implies that the crack did not extend to the exit face, and evidence
for this is provided by the fracture surface for the coupon shown in Figure 93. The
fracture surface was obtained after final failure of the coupon at which point the crack
was considerably longer on the entry face than on the exit face with a maximum length
in the mid-section. The crack front barely reached the exit face prior to final failure,

175

probably as a consequence of the substantially higher compressive residual stresses on
the exit face. Thermoelastic stress analysis is not based on a purely surface
phenomena but is sensitive to strain concentrations through the thickness, though this is
dependent on loading frequency, as heat transfer needs to occur towards the surface in
order for the through-thickness variation of strain and hence temperature to register.
However, at the frequency employed in these tests (10Hz) it is inevitable that there
would be a substantial three-dimensional non-adiabatic zone associated with the crack
133

tip plasticity

.

Additional fractographic analysis of an unexpanded coupon (Figure 94) shows a straight
crack front perpendicular to the faces of the specimen; a fact supported by both the DIC
and TSA results, which show approximately equal lengths of crack on each face at each
increment of fatigue life shown in Figure 91 and Figure 92.

The extent of the plastic zone created during the cold expansion process was calculated
from digital image correlation measurements made during the expansion process44.
The strain tensors evaluated from the DIC data were converted to stress using the
material properties of the 2024-T3 aluminum and then the von Mises yield criteria was
used to determine where the onset of plasticity would occur. The plastic zone was
found to extend about 2.5 mm from the hole edge so that for crack lengths of about
2 mm and less probably there is no distinct crack tip plastic zone and hence the
classical crack tip stress/strain pattern is not seen until the crack grows out of this
region. This is supported by the DIC data for the expanded hole in Figure 91 (right

176

column) which does not exhibit a crack tip strain distribution comparable to the
unexpanded hole as in Figure 91 (left column) until the crack is of length 3.7 mm. There
is some evidence in the TSA data (Figure 92h) that the crack tip plastic zone is
beginning to emerge from this region at a crack length of 3.7 mm on the entry face.

When the crack extends in both the UH and CX coupons the load distribution
becomes asymmetric as the cracked (left) ligament reduces in stiffness and more load
is borne by the uncracked (right) ligament. This effect is magnified for the CX coupon
because the extent of the uncracked and elastic ligament is also reduced by the plastic
zone around the hole arising from the cold expansion. By the time the crack extends to
3.7 mm (Figure 91h), the stress in the previously uncracked ligament of the CX coupon
has become so great that a small crack appears. This is not visible in the TSA data
(Figure 92h) because the crack front is curved such that the crack has not reached the
exit face as shown in Figure 93.

In the UH coupons, there is an increase in crack tip strain with increasing crack length
as would be expected since the stress intensity factor is a function of crack length.

177

1.0 mm

Figure 93: Fracture surface of the coupon with cold-expanded hole orientated as in
Figure 92 with the exit face on the lower side and with increasing levels of magnification
from top to bottom

178

Figure 94: Optical (top) and SEM (bottom) images of the fracture surfaces for the
coupon with the unexpanded hole at increasing levels of magnification from top to
bottom and orientated with the exit face on the lower side
8.1.2 FML: Cold Expansion Strain and Fatigue Results
8.1.2.1 FML: Overall Fatigue Results
Overall fatigue results showing the number of cycles to failure against the net section
stress are plotted for both FML 3 (Figure 95a) and FML 4 (Figure 95b). Although the
number of coupons tested at each stress level is small, the improvement in fatigue life
as a result of cold-expansion, especially at lower stress levels, is still evident. The
overall results suggest that the cold expansion process is effective at increasing fatigue
life for both grades of FML.

179

Net Stress (MPa)

200
FML 3 (Open Hole)

190

FML 3 (Cold Expanded)

180
170
160
0

100,000

200,000
300,000
Cycles to Failure

400,000

500,000

(a)
Net Stress (MPa)

200
FML 4 (Open Hole)

190

FML 4 (Cold Expanded)

180
170
160
0

200,000

400,000

600,000
800,000
Cycles to Failure

1,000,000

1,200,000

(b)
Figure 95: Mean fatigue results. (a) FML 3 [90/0] longitudinal coupons both with and
without cold-expansion of the hole and (b) FML 4 [0/90/0] longitudinal coupons both with
and without cold-expansion of the hole
8.1.2.2 FML: Crack Growth Curves
A closer examination of some typical crack growth curves, from open hole and cold
expanded coupons for both FML grades (Figure 96 and Figure 97) at the three net
stress levels, shows how difficult it can be to definitely comment on the effectiveness of
cold expansion at extending life on the entry face, in the early stage of the fatigue
process. However, in almost every case, short crack growth (defined as crack growth to
1 mm) appears to occur at the same cycle count in both the unexpanded and cold
180

expanded coupons. A better overview of the data is provided for FML 3 in Figure 98,
which shows the overall number of cycles (taken from all FML 3 crack growth curves)
required to grow a 1 mm crack as well as the crack growth rates, both before and after
cold-expansion. From Figure 98 it appears that although cold expansion does have an
effect at reducing short crack growth (on the entry face), for net stress levels less than
176 MPa, it is much less pronounced than in aluminum (Figure 90), where the reduction
in short crack growth rates ranged from 50,000 to over 200,000 cycles, depending on
the net stress level. However, from the crack growth curves in Figure 98, it appears that
cold expansion is effective at reducing crack propagation rates for all net stress levels,
with a slight increase in effectiveness at the highest net stress level (198 MPa). The
same analysis performed for all the FML 4 crack growth curves (Figure 99) shows that
cold-expansion has a relatively minimal effect on reducing short crack growth, with only
small reductions of less than 10,000 cycles at all load levels. However, as with FML 3,
cold-expansion is more effective at reducing crack propagation rates at all net stress
levels, with a slight increase in effectiveness at the highest net stress (198 MPa). This
suggests that the compressive residual stresses induced by cold expansion on the entry
face are most effective when the crack has grown past 1 mm and crack bridging can
become fully effective.

181

Crack Length
(mm)

5.0
Net Stress = 165 MPa

4.0
3.0
2.0

FML 3 Open Hole

1.0

FML 3 CX

0.0
0

50,000

100,000
150,000
Cycles to Failure

200,000

250,000

(a)

Crack Length
(mm)

5.0
Net Stress = 176 MPa

4.0
3.0
2.0

FML 3 Open Hole
FML 3 CX

1.0
0.0
0

50,000

100,000

150,000

200,000

250,000

Cycles to failure
(b)

Crack Length
(mm)

5.0
Net Stress = 198 MPa

4.0
3.0
2.0

FML 3 - Open Hole

1.0

FML 3 - CX

0.0
0

20,000

40,000

60,000

80,000

100,000

Cycles to Failure
(c)
Figure 96: Crack growth curves for FML 3 coupons (a) Net Stress 165 MPa: Open Hole
(specimen 15-A-3) and cold-expanded (specimen 15-A-6) coupons (b) Net Stress 176
MPa: Open Hole (specimen 15-A-2) and cold-expanded (specimen 15-A-5) coupons
and (c) Net Stress 198 MPa: Open Hole (specimen 15-A-1) and cold-expanded
(specimen 15-A-4) coupons

182

Crack Length (mm)

5.0

FML 4 Open Hole

4.0

FML 4 CX

3.0
2.0
1.0

Net Stress = 165 MPa

0.0
0

50,000

100,000

150,000

200,000

Cycles to Failure
(a)

Crack Length
(mm)

5.0

Net Stress = 176 MPa

4.0
3.0
2.0

FML 4 Open Hole

1.0

FML 4 CX

0.0
0

20,000

40,000
60,000
Cycles to Failure

80,000

100,000

(b)

Crack Length
(mm)

5.0
Net Stress = 198 MPa

4.0
3.0
2.0

FML 4 - Open Hole

1.0

FML 4 - CX

0.0
0

20,000

40,000
Cycles to Failure

60,000

80,000

(c)
Figure 97: Crack growth curves for FML 4 [0/90/0] longitudinal coupons (a) Net Stress
165 MPa: Open Hole (specimen 16-B-4) and cold expanded (specimen 13-B-3)
coupons (b) Net Stress 176 MPa: Open Hole (specimen 16-B-6) and cold expanded
(specimen 13-B-2) coupons and (c) Net Stress 198 MPa: Open Hole (specimen 16-B5) and cold expanded (specimen 13-B-1) coupons

183

3.5

60,000

3.0

50,000

2.5

40,000

2.0

30,000

1.5

20,000

1.0

10,000

0.5

0

0.0
198 (MPa)

FML 3 OH

176 (MPa)
Stress Level
FML 3 CX

da/dN (mm/10,000 cycle)

4.0

70,000
Cycle Count

80,000

165 (MPa)

FML 3 OH

FML 3 CX

Figure 98: Variation in number of cycles to 1 mm crack length (columns) versus da/dN
(symbols) for FML 3 at various stress levels

1.5

40,000

1.2

30,000

0.9

20,000

0.6

10,000

0.3

0

0.0
198 (MPa)

176 (MPa)
Stress Level

FML 4 OH
FML 4 OH

da/dN (mm/10,000 cycle)

1.8

50,000
Cycle Count

60,000

165 (MPa)
FML 4 CX
FML 4 CX

Figure 99: Variation in number of cycles to 1 mm crack length (columns) versus da/dN
(symbols) for FML 4 [0/90/0], cut in the longitudinal direction, at various stress levels

184

8.1.2.3 FML: DIC and TSA Measurements During Fatigue Loading
As with the aluminum coupons, digital image correlation was used to capture strains on
the entry face of the FML coupons and thermoelastic stress analysis (TSA) was used to
capture strain information on the exit face during fatigue loading. One sample coupon
for each material was selected at the 198 MPa net stress level. On the entry face of the
sample FML coupon, the maximum principal strain measured using DIC is presented
pre-crack, and at 1 mm, 2 mm and 3.7 mm crack growth intervals. Information from the
TSA system is presented for the exit face at the same intervals. In all cases the
unexpanded coupon is shown in the left-column and the cold-expanded coupon is
shown in the right column. The crack lengths were obtained from images of the coupon
captured at maximum load and subsequently processed using digital image correlation.
8.1.2.3.1 FML 3 Results
In the pre-crack condition, a slightly larger difference in the strain field exists between
the unexpanded coupon (Figure 100a), and the cold expanded coupon (Figure 100b).
Part of this difference can be attributed to the slightly higher net stress in the cold
expanded coupon (~0.8 %) as a result of the slightly enlarged hole. Overall, the strains
at the crack tip on the entry face of the cold expanded coupon (Figure 100d,f,h) are
slightly lower than those of the unexpanded coupon (Figure 100c,e,g) likely as a result
of the compressive residual strains imparted during cold expansion. In addition, a
region of lower maximum principal strain on the unexpanded hole coupons, at the 0º
and 180º degree positions seems to grow in area along with the crack (Figure 100c,e,g).
This area of lower maximum principal strain may be indicative of through-crack growth,
which is an observation supported by the TSA data on the exit face (Figure 101c,e,g) as
185

the TSA signal shows a reduction in magnitude and movement of the peak TSA signal
away from the hole in the 90º and 270º degree direction, which is indicative of crack
growth.

186

Unexpanded Hole

Cold-expanded

Microstrain
Uncracked

(a) 0 cycles

(b) 0 cycles

(c) 22,301 cycles

(d) 22,301 cycles

(e) 25,301 cycles

(f) 39,101 cycles

(g) 31,301 cycles

(h) 64,301 cycles

1.0 mm
crack

2.0 mm
crack

3.7mm
crack

Figure 100: Maximum principal strains obtained from digital image correlation
measurements on the entry face of FML 3 coupons with both an unexpanded (left,
specimen 12-A-1) and cold–expanded (right, specimen 12-A-4) hole with crack lengths
of 0, 1, 2 and 3.7mm

187

Unexpanded Hole

Cold-expanded

(a) 0 cycles

(b) 0 cycles

(c) 22,301 cycles

(d) 22,301 cycles

(e) 25,301 cycles

(f) 39,101 cycles

(g) 31,301 cycles

(h) 64,301 cycles

Uncracked

1.0 mm
crack

2.0 mm
crack

3.7mm
crack

Figure 101: Full-field maps of the thermoelastic signal (A/D) units from the exit face for
both unexpanded (left, specimen 12-A-1) and cold-expanded (right, specimen 12-A-4)
FML 3 holes

188

8.1.2.3.2 FML 4 Results
In the pre-crack condition, only a very slight difference in the strain field exists between
the unexpanded coupon (Figure 102a) and the cold expanded coupon (Figure 102b),
which can be attributed to the slightly higher net stress in the cold expanded coupon
(~0.8 %) as a result of the enlarged hole. As with the FML 3 coupons, overall, the
strains at the crack tip on the entry face of the cold expanded coupon (Figure 102d,f,h)
are overall slightly lower than those of the unexpanded coupon (Figure 102c,e,g), likely
as a result of the compressive residual strains imparted during cold expansion. In the
FML 4 unexpanded coupon (Figure 102c), a secondary crack appears to form beneath
the main crack, but the propagation appears to arrest as soon as the crack length
approaches 1 mm, likely as a result of crack bridging (Figure 102e and Figure 102f).
The corresponding cold-expanded FML 4 coupon (Figure 102d and Figure 102f) only
shows evidence of a primary crack forming and although there is a stress intensity at
the crack tip in all cases, the stress intensity factor is lower than that of the unexpanded
coupons. In addition, as with FML 3, a region of lower maximum principal strain on the
unexpanded hole at the 0º and 180º positions seems to grow in area along with the
crack (Figure 102c,e,g). This area of lower maximum principal strain may be indicative
of through crack growth, an observation supported by the TSA data on the exit face
(Figure 103c,e,g) that shows a reduction in magnitude of the TSA signal and movement
of the peak TSA signal away from the hole.

189

Unexpanded Hole

Cold-expanded

Microstrain
Uncracked

(a) 0 cycles

(b) 0 cycles

(c) 21,101 cycles

(d) 27,101 cycles

(e) 27,101 cycles

(f) 45,101 cycles

(g) 39,101 cycles

(h) 73,901 cycles

1.0 mm
crack

2.0 mm
crack

3.7mm
crack

Figure 102: Maximum principal strains obtained from digital image correlation
measurements on the entry face of FML 4 coupons with both an unexpanded (left, 16B-5) and cold–expanded (right, specimen 13-B-1) hole with crack lengths of 0, 1, 2 and
3.7 mm

190

Unexpanded Hole

Cold-expanded

(a) 0 cycles

(b) 0 cycles

(c) 21,101 cycles

(d) 27,101 cycles

(e) 27,101 cycles

(f) 45,101 cycles

(g) 39,101 cycles

TSA

(h) 73,901 cycles

Uncracked

1.0 mm
crack

2.0 mm
crack

3.7 mm
crack

Figure 103: Full-field maps of the thermoelastic signal (A/D) units from the exit face for
both unexpanded (left, 16-B-5) and cold-expanded (right, specimen 13-B-1) FML 4
holes

191

8.1.2.3.3 Ultrasonic Inspection of FML Coupons
Non-destructive evaluation performed post test, using pulse echo ultrasound (PE-UT),
clearly highlighted the resulting area of delamination. Sample ultrasonic images for
both unexpanded and cold expanded FML 3 (Figure 104) and FML 4 (Figure 105)
specimens on both the entry and exit faces are provided. The color scale used for the
pulse echo ultrasound (PE-UT) is qualitative, and visually denotes the differences in
signal amplitude of the ultrasound wave. Although the disbond area appears greater
89

than that measured by van der Kuip , this difference is likely due to the different failure
criteria used for the coupon. Van der Kuip

89

used an automatic crack measurement

system and was able to stop the fatigue cycles as soon as the crack reached the
coupon edge, while for this test, a displacement limit of 0.89 mm (0.035 inches) was
used to determine when fatigue cycling would stop. The extra fatigue cycles applied to
these coupons likely allowed the disbond area to grow beyond that measured by van
89

der Kuip . Measurements of the disbond area were made by scaling the ultrasound
images appropriately and using ImageTool (Department of Dental Diagnostic Science at
The University of Texas Health Science Center, San Antonio, Texas) image analysis
software to measure the area. The results are displayed in Table 10, and show no
statistical difference in disbond area between the cold expanded and unexpanded
coupons or between the entry and exit faces, although the disbond area and shape did
differ between the two grades of FML.

192

Unexpanded Hole

Cold-expanded

(a)

(b)

(c)

(d)

Pulse Echo
Entry Face
Pulse Echo
Exit Face

Figure 104: Pulse echo ultrasonic scans of FML 3 specimen 12-A-1 (open hole) and
specimen 12-A-4 (cold expanded). Image (a) unexpanded entry face (b) cold expanded
entry face (c) unexpanded exit face and (d) cold expanded exit face
Unexpanded Hole

Cold-expanded

(a)

(b)

(c)

(d)

Pulse Echo
Entry Face
Pulse Echo
Exit Face

Figure 105: Pulse echo ultrasonic scans of FML 4 specimen 16-B-5 (open hole) and
specimen 13-B-1 (cold expanded). Image (a) unexpanded entry face (b) cold expanded
entry face (c) unexpanded exit face and (d) cold expanded exit face
Table 10: Disbond area for cold expanded and unexpanded coupon
2

Average
Std. Dev.

Unexpanded Coupon: Disbond Area (cm )
Entry Face
Exit Face
19.10
18.76
2.90
3.65

Average
Std. Dev.

Cold-Expanded Coupon: Disbond Area (cm )
Entry Face
Exit Face
18.00
15.98
2.46
1.50

2

8.1.2.4 Discussion
For fiber metal laminates, the crack opening that occurs during the crack propagation
phase is due to shear deformation and delamination growth between the laminate

193

layers. Load transfer between the aluminum and the fiber prepreg induces cyclic shear
9

stresses in the adhesive layer of the prepreg and results in a shear deformation . This
shear deformation serves to constrain the crack tip opening, but it is non-zero and thus
there is a stress intensity at the crack tip in the aluminum layer that one can measure
using image correlation.

The typical assumption for FML materials is that fatigue cracks propagate concurrently
9,134

in the metal layers only, while the fiber layers remain intact to bridge the crack

.

This assumption is supported by the results from the unexpanded FML coupons. Using
the TSA images from the unexpanded FML 4 coupon as an example, at 1 mm of crack
growth (Figure 103c) there is a small decrease in magnitude and a change in shape of
the stress concentration on the left hand side of the hole. At 2 mm of crack growth
(Figure 103e) there is an even greater decrease in magnitude and a slight elongation of
the stress concentration, clearly suggesting the presence of a crack, perhaps with fiber
bridging causing the elongation. At 3.7 mm of crack growth (Figure 103g) the crack has
propagated far enough that the crack tip stress distribution is no longer adjacent to the
central hole and a clear unloaded zone between the crack tip and the edge of the hole
suggests that fiber bridging has become less effective as a result of a possible
through-crack in the aluminum layers. Similar evidence is apparent in the maps of
maximum principal strain obtained from DIC. By contrast, for the cold expanded
coupon, at 1 mm of crack growth the TSA results (Figure 103d) are essentially identical
to the precracked image (Figure 103b). At 2 mm (Figure 103f) and at 3.7 mm of crack

194

growth (Figure 103h), the magnitude of the stress concentration on either side of the
cold expanded hole has decreased in magnitude slightly. This change is indicative of
the existence of a small crack, probably with fiber bridging, but is definitely a smaller
effect than seen on the entry side of the coupon. These observations are repeated with
both grades of FML and suggest that cold expansion effectively changes the fatigue
crack mechanism in FML from one where all the metal layers show similar fatigue crack
growth

1,3,9

, to one where only one surface, in this case the entry face, shows significant

crack growth.

The work by van der Kuip

89

also showed that in the early stages of the fatigue process,

a difference existed in the fatigue life between the exit and entry face of the cold
expanded coupons. This phenomena has been well-documented in monolithic
materials in terms of both the residual strain
fields

46,62,68,122,130

41,42,44

and have shown that the cold expansion process leads to a triaxial

stress/strain state even for relatively thin coupons
Kuip

89

and residual stress

135

. The testing done by van der

showed that in most cases the area of delamination on the exit face of the cold

expanded coupons was much less than on the entry face; however, what van der Kuip
did not address was whether or not this difference was attributable to differences in the
residual strain imparted by the cold expansion process.

195

Overall, the cold expansion of FML shares many similarities with cold expansion in
monolithic aluminum materials. As with 2024-T3 aluminum, residual strains on the entry
face are lower than those on the exit face and, as a result, crack propagation on the exit
face is delayed with respect to the entry face. This is less of an issue with monolithic
aluminum since the bulk of its fatigue life is in the crack nucleation phase, as opposed
to the crack propagation phase, and the fact that the compressive residual stresses
from cold expansion are able to retard crack propagation, makes it a desirable process
from a manufacturing standpoint. The situation is reversed in FML where the bulk of its
fatigue life is spent in the crack propagation phase; and, although cold expansion has a
clear, beneficial effect on the overall fatigue life of FML, its effect on short crack growth
on the entry face is not as straightforward. For FML 3 at stress levels of less than 176
MPa, cold expansion appears to delay the formation of short cracks (defined as cracks
of 1 mm), while for FML 4, the effect of cold expansion on short crack growth is less
pronounced, with a retardation in short crack growth of less than 10,000 cycles in all
cases.
8.2

Fatigue Results After Riveting

Due to material supply constraints, the decision was made to test only a reduced set of
coupons for the baseline riveting fatigue tests, so only 2024-T3 aluminum and FML 4
were tested for benchmark and comparison purposes.

The riveting and cold expansion processes share several similarities in terms of their
effect on the underlying material. In both cases, the hole is expanded, but in the case of
riveting, there is no re-collapse of the material surrounding the hole as the rivet shank
remains in place, unlike with cold expansion. Another difference is the clamping force
196

generated around the hole as a result of the formation of the rivet driven head. In the
136

case of a riveted joint, de Rijck et al

23

and Muller

have clearly outlined the positive

role played by the rivet clamping force in reducing fretting fatigue. For the case of zero
load transfer (ZLT) coupons with a rivet, the study by Petrak and Stewart

49

compared

the fatigue life of ZLT coupons with Stress Wave rivets to those with cold expanded
holes and showed that although the Stress Wave rivet improved fatigue life, it did not do
so by as much as hole cold expansion. Little information was given regarding the
Stress Wave rivet so it is difficult to determine how applicable these results would be to
the current investigation.

Surprisingly, the initial fatigue testing of the riveted coupons at the same net stress
levels used for the cold expanded coupons consistently resulted in run-out (defined as
any coupon surviving 1,000,000 fatigue cycles with no failure). As part of this initial pilot
study, additional fatigue testing at various stress levels was performed and the results
showed (Figure 106) that to achieve fatigue life similar to that of cold expanded
coupons, the net stress would need to be increased to approximately 263 MPa, almost
69 MPa higher than with the open hole coupons. Even at these higher stress levels,
crack nucleation tended to occur away from the open hole, sometimes even starting at
the edges of the coupon and gradually moving inward. Due to this variability in the
crack nucleation location and due to the formation of multiple cracks, it was not possible
to make crack growth measurements in a manner similar to the open hole coupons
(where all cracks nucleated from the open hole). As a result, the riveted coupons were
compared on the basis of percentage of life remaining. For the current results, 75% of
197

total life was used as the basis for comparing the aluminum and the FML coupons. This
means that full-field strain images of the coupons were extracted and compared at a
number of cycles equivalent to 75% of their total life as opposed to at set crack lengths.

Net Section Stress (Mpa)

500

400

300

200
y = -25.649Ln(x) + 562.65
100
1

10

100

1,000

10,000

100,000

1,000,000 10,000,000

Cycles

Figure 106: S-N curve for riveted aluminum 2024-T3 coupons at various stress levels
8.2.1 Aluminum: Rivet Fatigue Results
The average fatigue life of the (n=8) riveted 2024-T3 aluminum coupons tested at a net
stress of 263 MPa was 199,763 ± 56,631 cycles. This value is overlaid on an S-N curve
of the aluminum cold expansion fatigue results (Figure 107). This comparison between
the riveted and cold expanded coupons serves to highlight the improvement in fatigue
life achieved with riveting as opposed to cold expansion. As mentioned previously,
another key difference between the riveted and cold expanded coupon was the location
of the crack nucleation sites. With the cold expanded coupon, every coupon failed as a
result of a crack nucleating from close to the diameter of the hole, and propagating in a
direction perpendicular to the load application, until it reached the edge of the coupon.
The aluminum coupons suffered from multi-site damage with some cracks initially

198

nucleating from the region of the rivet hole and others nucleating at random locations
throughout the coupon and eventually linking up to cause coupon failure. The strain
measurements from the driven and manufactured head face of the coupons (Figure
108) show how much more uniform the surface strains are, with a much more

Net Section Stress (MPa)

concentric strain concentration immediately around the hole.

280
Open Hole
240

Cold Expanded
Rivet

200

160
10,000

100,000

1,000,000

10,000,000

Cycles to Failure
Figure 107: S-N curve for open hole, cold expanded and riveted 2024-T3 aluminum
coupons

199

Precracked Condition

75 % of cycles to failure

(a)

(b)

(c)

(d)

Driven
Head
(DIC data)

Manufactured
Head
(TSA Data)

Figure 108: a-b) Maximum principal strain from rivet driven face and c-d) TSA strain
information from rivet manufactured head face for the aluminum 2024-T3 coupon, at
pre-crack formation and at 75% of the number of cycles to failure (specimen Al-L-15).
Note: Net stress of 263 MPa
Several of the failed coupons were examined with both an optical and scanning electron
microscope (SEM) to better determine the origin of the crack. A sample image of one
specimen is shown in Figure 109.

200

(a)

(b)

(c)

Figure 109: (a) Optical micrograph of failure surface of AL-L-14 (b) Scanning electron
micrographs of left hand specimen surface below manufactured head. (c) Right hand
side of specimen. Note: Crack nucleation origin highlighted in red
Four coupons underwent fractographic analysis and the results of these tests are
summarized in Table 11. Overall, the initial cracks nucleated from somewhere in the
vicinity of the rivet hole, with no one location being dominant. The multi-site nature of
the failure made it impossible to measure crack growth, since often a secondary crack
growing from the edge or middle of the coupon would propagate inwards towards the

201

rivet, linking up with cracks growing from the rivet hole and causing coupon failure. One
important point to note is the effectiveness of the rivet at protecting the hole from fatigue
damage as highlighted by the variability in the crack nucleation locations.
Table 11: Summary failure locations from fractography of aluminum coupons
Specimen Identifier

Failure location(s)

AL-L-14

Below manufactured head

AL-L-15

Below manufactured head and internal

Al-L-16
AL-L-17

Multi site: Below driven and manufactured
head and internal
Below manufactured head and internal

8.2.2 FML: Rivet Fatigue Results
The average fatigue life of the (n=5) riveted longitudinal FML 4 [0/90/0] coupons was
161,325 ± 21,080 cycles and this datum was overlaid on an S-N curve for the cold
expanded FML coupons (Figure 110) to demonstrate how effective the riveting process
was for this material. The crack nucleation location was just as varied as with the
aluminum coupons, so comparisons were performed in the same way, taking data from
images corresponding to 75% of the cycles to failure. Figure 111 shows the maximum
principal strain field pre-crack growth (Figure 111a) and at 75% cycles to failure (Figure
111b). Even with the apparent strain concentration centered on the rivet, no clear
fatigue cracks have formed in this area. The TSA images obtained from the
manufactured head face show even less change between the pre-crack condition
(Figure 111c) and the coupon at 75% of its cycles to failure (Figure 111d). One
possible hypothesis is that the compression afforded by the rivet head could be the
main driver in changing the nucleation region from under the rivet head to the edge of

202

the coupon. This effect is interesting in light of the consistent failure mode for the cold
expanded coupons, where crack nucleation consistently occurred at the outer diameter
of the cold expanded hole and may suggest a mechanism for future improvements in

Net Section Stress (M Pa)

fastener technology.
280
FML 4 (CX)

260

FML 4 (Rivet)

240
220
200
180
160
10,000

100,000
1,000,000
Cycles to Failure

10,000,000

Figure 110: Fatigue results for FML 4 [0/90/0] riveted coupon, overlaid on S-N curve
data for FML 4 cold expanded coupon fatigue data

203

Precracked Condition

75 % of cycles to failure

(a)

(b)

(c)

(d)

Driven
Head
(DIC data)

Manufactured
Head
(TSA Data)

Figure 111: a-b) Maximum principal strain information from rivet driven face and c-d)
TSA strain information from rivet manufactured head face for the FML 4 [0/90/0]
coupon, at pre-crack formation and at 75% of the number of cycles to failure (specimen
13-B-5). Note: Net stress of 263 MPa
Table 12 summarizes the crack nucleation location in both the aluminum and FML
coupons and shows that the rivet is effective at retarding crack formation, shifting the
crack nucleation location away from central rivet hole in many instances. Post-test
ultrasonic inspection was used to further support this observation by determining the

204

areas of disbond in the coupon on both the driven and manufactured faces, which are
associated with crack formation. A sample image was provided for an FML 4 coupon in
Figure 112. For the ultrasonic results, sharp colour changes delineate the area of
disbond and by this measure show the dispersed nature of the disbond around the rivet.
Examining the ultrasound images in general, it is evident that the disbonded regions are
spread out more randomly in the central section of the coupon which is in contrast to the
constrained disbond pattern seen with the cold expanded coupons (Figure 104 and
Figure 105).
Table 12: Summary of crack nucleation locations for aluminum and FML riveted
coupons
FML 4
2024-T3 AL

Rivet
3
8

Edge
2
1

Multi Site
1

Driven
Face
(a)

Manufactured
Face
(b)
Figure 112: Pulse-echo ultrasonic images post test for: (a) FML 4 coupon (Specimen
13-B-5 driven face and (b) FML 4 manufactured face

205

9.0

DESIGN AND TESTING OF A NEW FML VARIANT

The observation that drove the design of a new FML variant was the effect that cold
expansion had on the FML coupons in the 45º degree orientation (Figure 48 and Figure
49). In this orientation the split sleeve was aligned with the direction of lowest elastic
modulus and lowest yield strength and the characteristic butterfly shape of the strain
field was replaced with a lower and more uniform maximum and minimum principal
strain field. These observations reinforced the idea that the orthotropic nature of FML
made it difficult to predict the results of cold expansion without having full knowledge of
the orientation and properties of the FML grade being used. These observations also
presented an opportunity for mitigating the situation, if it was possible to reduce the
orthotropy of the material and design a more isotropic layup.
9.1

Theoretical Design of New FML 4 Variants

One of the first steps in the design process for a new FML variant was to determine a
114

method of estimating FML material properties analytically. Kawai et al

had success

using a classical laminated plate approach to model FML properties, and this approach
was adopted in this work to estimate the elastic modulus, shear modulus and Poisson’s
ratio of any new FML material (Chapter 7.6.2). As part of the brainstorming process,
the first FML variant was designed to reinforce the ±45º degree direction with a
proposed layup sequence of [+45/90/-45]. The second variant was an accidental
discovery and was produced as a result of the inadvertent misorientation of two of the
prepreg layers in an early attempt at producing a quasi-isotropic material.
Measurements of the ply angles after ultrasonic inspection showed that a layup
sequence of [+30/0/-30] had been made instead of the desired prepreg layup. Since

206

two panels had been produced, the decision was made to include this material as part
of the investigation.

The final proposed FML variant stemmed from a review of classical laminated plate
theory, specifically the concept of a quasi-isotropic composite

126-128

. It has been

shown in classical laminated plate theory that if three or more identical plies are stacked
at equal angles (i.e the angle separating each of the n plies is /n radians) then the inplane properties of the laminate are isotropic. For an FML 4 variant with n=3 plies, this
would mean an angle of 60º between plies. From a theoretical perspective, a
[+60/0/-60] layup would ensure that the in-plane stiffness coefficients were constant
(i.e [Aij]=constant), however, this new material would only be considered to be quasiisotropic since the bending stiffness coefficients [Dij] would not be constant.

Looking at tables of standard FML layup orientations it was evident that no FML variants
used non-orthogonal plies except for FML 6 which uses a [-45/45] ply orientation and
that the idea of a quasi-isotropic FML did not appear in the open literature. Classical
laminate plate (CLP) theory was then used to generate a theoretical modulus
distribution for the three new FML variants for comparison to standard FML 4 (Figure
113).

From a theoretical perspective the initial concept of adding more glass fibers along the
±45º degree direction did appear to reduce the degree of orthotropy, between the

207

material orientations of highest and lowest modulus. Compared to FML 4 which has a
difference of approximately 13 GPa between orthogonal material directions,
FML 4 [-45/90/+45] only had a difference of approximately 7 GPA. Unfortunately, this
new FML 4 is strongest along the 60º degree direction, which makes it difficult to use in
a practical setting. The FML 4 [+30/0/-30] that was produced accidentally, showed a
fairly monotonic decrease in elastic modulus with a difference of approximately 14 GPa
between the 0º degree (most stiff) and 90º degree (least stiff) directions. The results
from the CLP analysis of the quasi-isotropic FML 4 [+60/0/-60] showed a constant
elastic modulus of approximately 50 GPa, slightly lower than that of FML 4 [0/90/0] in
the 0º degree orientation (58 GPa) but with the advantage of having a uniform elastic
modulus regardless of material orientation. Classical laminate plate theory also
predicted that this material would have a shear modulus of 19 GPa and a Poisson’s
ratio of 0.33, both values theoretically constant regardless of material direction.

208

Elastic Modulus (GPa)

60.00

FML 4 [0/60/-60]s
FML 4 [0/90/0]
FML 4 [-45/90/45]
FML 4 [30/0/-30]

55.00

50.00

45.00

40.00
0

15

30
45
60
Angle (degrees)

75

90

Figure 113: Theoretical modulus as a function of orientation for FML 4 [0/60/-60],
FML 4 [-45/90/45], FML 4 [30/0/-30], and standard FML 4-3/2 [0/90/0]
9.1.1 Baseline Mechanical Testing of New FML 4 Variants
From the analytical work done on all three FML 4 layups, it was clear that the quasiisotropic FML 4 had material properties that would likely best address our needs with
regards to cold expansion and riveting. However, as part of this investigation, two
panels of FML 4 [45/90/-45] and FML 4 [-30/0/+30] were produced in addition to the
quasi-isotropic FML 4 [-60/0+60] . Fatigue coupons in the 0º degree orientation
(longitudinal direction) were cut from each panel so that a basic S-N curve comparing
unexpanded and cold expanded fatigue life could be determined. The strains after hole
cold expansion were also measured using digital image correlation.

209

9.1.1.1 Static and Fatigue Behaviour of FML 4 [-45/90/+45]
Figure 114 shows the maximum principal strains on the entry and exit face of the
FML 4 [-45/90/+45] after cold expansion. Although the strain field no longer displays the
classic butterfly shape evident with FML 4 [0/90/0], a small degree of asymmetry is
evident in the strain field at 135º from the split sleeve (white arrow in Figure 114). The
minimum principal strains (Figure 115) appear much more radially symmetric and
except for the relatively poor fatigue performance (Figure 116) and the difficulty caused
by the orientation of the peak modulus at 60º degrees, this FML 4 layup would appear
promising.

(b)

(a)

Figure 114: Maximum principal strains for cold expanded FML 4 [-45/90/+45] (specimen
17-C-7) on the (a) entry face and (b) exit face

210

(b)

(a)

Figure 115: Minimum principal strains for cold expanded FML 4 [-45/90/+45] (specimen
17-C-7) on the (a) entry face and (b) exit face

Net Section Stress (MPa)

210
FML 4 [-45/90/45] CX

200

FML 4 [-45/90/45] OH

190
180
170
160
150
0

20,000

40,000

60,000

80,000

Cycles to Failure
Figure 116: Mean fatigue results for FML 4 [-45/90/45] coupons both with and without
cold-expansion of the hole

211

9.1.1.2 Static and Fatigue Behaviour of FML 4 [-30/0/+30]
The maximum principal strain results for FML 4 [-30/0/+30] after cold expansion are
shown in Figure 117 and also show a more concentric strain field than FML 4 [0/90/0],
with only a small amount of asymmetry. The minimum principal strain results (Figure
118) are even more concentric and even the fatigue results in Figure 119 show
reasonable fatigue performance for coupons cut in the longitudinal (0º degree) material
orientation. However, the closed form solution shows that the elastic modulus drops
monotonically between the 0º degree and 90º degree direction and in the 90º degree
direction is even lower than in FML 4 [-45/90/45], suggesting that the corresponding
fatigue life would be lower as well.

(b)

(a)

Figure 117: Maximum principal strains for cold expanded FML 4 [-30/0/+30] (specimen
18-D-7) on the (a) entry face and (b) exit face

212

(a)

(b)

Figure 118: Minimum principal strains for cold expanded FML 4 [-30/0/+30] (specimen
18-D-7) on the (a) entry face and (b) exit face

Net Stress (MPa)

200
FML 4 [-30/0/+30] OH

190

FML 4 [-30/0/+30] CX

180
170
160
0

250,000

500,000
Cycles to Failure

750,000

1,000,000

Figure 119: Mean fatigue results for FML 4 [-30/0/+30] coupons both with and without
cold-expansion of the hole
9.1.1.3 Static and Fatigue Behaviour of FML 4 [-60/0/+60]
The maximum principal strain results after hole cold expansion for the quasi-isotropic
FML 4 [-60/0/+60] are given in Figure 120 and show a much more uniformly concentric

213

strain field than FML 4 [0/90/0] . The same is true for the plot of full-field minimum
principal strains (Figure 121), where only a small strain concentration is seen to the right
of both images near the location of the split in the split sleeve. An examination of the
radial strain extraction (Figure 122) shows the typical drop in strain at 270º degrees,
coincident with the location of the split in the split sleeve. Otherwise, there is little
indication of the repeating strain concentrations at 45º degree increments as was seen
with FML 4 [0/90/0] (Figure 47).

(b)

(a)

Figure 120: Maximum principal strains for cold expanded FML 4 [-60/0/+60] (specimen
26-D-1-T) on the (a) entry face and (b) exit face

214

(b)

(a)

Figure 121: Minimum principal strains for cold expanded FML 4 [-60/0/+60] (specimen
26-D-1-T) on the (a) entry face and (b) exit face
One panel of FML 4 [-60/0/+60] was used to determine the baseline fatigue
performance of unexpanded and cold expanded coupons at three net stress levels
ranging from 165 MPa to 198 MPa (Figure 123). Overall, fatigue life in the longitudinal
direction, for this material was better than for FML 4 [-45/90/45] but not as good as for
either FML 4 [0/90/0] or FML 4 [-30/0/+30]. To more fully evaluate the fatigue life of this
quasi-isotropic FML 4 [-60/0/+60], it needs to be compared to a baseline grade of FML,
such as FML 4 [0/90/0], in all three primary material orientations (longitudinal,
45º degree and transverse). This is because, given the static properties of FML 4
[-60/0/+60], it is expected that the fatigue life should be fairly constant, irrespective of
material orientation.

215

0

10000

e2 [entry]

9000

e2 [exit]
-5000

8000

6000

e2 [ strain]

e1 [ strain]

7000

5000
4000

-10000

-15000

3000
-20000

2000
e1 [entry]

1000

e1 [exit]

-25000

0
0

45 90 135 180 225 270 315 360
Degrees

0

45 90 135 180 225 270 315 360
Degrees

(a)

(b)

Figure 122: Plot of entry and exit face principal strains for (specimen 26-D-1-T)
FML 4 [-60/0/+60] (a) maximum principal strains and (b) minimum principal strains

216

210
Net Stress (M Pa)

200

FML 4 [-60/0/+60] CX

190

FML 4 [-60/0/+60] OH

180
170
160
150
140
0

50,000

100,000

150,000

200,000

Cycle Count
Figure 123: Baseline fatigue data for FML 4 [-60/0/+60]. Comparison between
unexpanded and cold expanded coupons
The encouraging initial results with FML 4 [-60/0/+60] led to an additional test to
determine the strain field after riveting. The maximum principal strain result from the
riveted FML 4 [-60/0/+60] is shown in Figure 124 and qualitatively, appear more
uniformly concentric than the strain results from standard grade FML 4 (Figure 69)
without the slight undulations in strain at every 45º degree increment as seen with
FML 3 and FML 4.

217

(b)

(a)

Figure 124: Maximum principal strains due to riveting for FML 4 [-60/0/+60] (specimen
26-D-7-L) coupons (a) driven and (b) manufactured head face
A summary of the fatigue data from all the various FML variants (including FML 4 and
FML 3) is provided in Figure 125. This data provides insight into the fatigue
performance of the FML coupons in only one orientation, and it is important to consider
that fatigue performance in other orientations could be adversely affected by a drop in
the elastic modulus. Considering the analytical and experimental results for
FML 4 [-45/90/45] and FML 4 [-30/0/30], it was clear that neither of these FML 4 variants
completely met our design intent and that the quasi-isotropic FML 4 [-60/0/60] was the
best option for additional testing and analysis. Note: from this point on the term FML 4
variant will be used to refer to an FML 4 with a [-60/0/+60] layup unless otherwise
specified.

218

200

FML 4 [-30/0/+30] OH
FML 4 [-30/0/+30] CX
FML 4 [-60/0/+60] OH
FML 4 [-60/0/+60] CX

Net Stress (M Pa)

190

FML 4 [-45/90/+45] OH
FML 4 [-45/90/+45] CX
FML 4 [0/90/0] OH
FML 4 [0/90/0] CX

180

FML 3 OH
FML 3 CX

170

160
0

250,000

500,000

750,000

1,000,000

1,250,000

Cycles

Figure 125: Summary fatigue graph highlighting fatigue performance of all grades of
FML tested, both in the open hole and cold expanded configuration. Note: Dotted lines
are for visualization purposes only and FML 4 [-60/0/60] is highlighted with blue symbols
9.2

Validation of New Prepreg Batch

For the fatigue testing of the new FML 4 variant, additional FML panels were required
and thus additional FM-94 prepreg had to be procured from the manufacturer. A
rigorous validation procedure was used to ensure that the new prepreg material would
allow for the production of FML panels with similar static and fatigue properties to those
produced previously.

219

For this portion of the research program several additional FML 4 [90/0/90] panels were
produced. Soon after it was discovered that a manufacturing error had occurred early
on and that the original FML 4 panels were produced with a [0/90/0] orientation instead
of a [90/0/90]. The material properties of these two grades of FML 4 are identical but
oriented at 90º degrees to one another. As a result, in addition to verifying the
performance of the prepreg, these results also serve to confirm that FML 4 [0/90/0] in
the 0º degree orientation (longitudinal) is identical to FML 4 [90/0/90] in the 90º degree
(transverse).

A review of the manufacturer’s quality certificate from both batches of prepreg showed
similar constituent proportions of both matrix and fiber as detailed in Table 13.
Table 13: Summary material information regarding Cytec FM-94
FM-94 (Old)
2

Matrix Wt (avg)

255.7 g/m

Fiber Wt (avg)

186.2 g/m

2

FM-94 (new)
2

258.9 g/m

2

188.9 g/m

% Diff.
1.2%
1.4%

Although no static strength data existed for the initial FML 4 [0/90/0] panels, test data
from a previous experimental program

11

was obtained which provided comprehensive

elastic modulus and yield strength data for FML 4 in orientations ranging from 0º
degrees to 90º in 15º increments. Separate plots were prepared for the elastic modulus
measurements (Figure 126), combining data from the previous FML 4 coupons (old
prepreg) with data from the new FML 4 (new prepreg) and in the case of the elastic

220

modulus, overlaid with predictions from classical laminated plate theory. Comparison
between FML 4 [90/0/90] made with the new batch of FM-94 prepreg and the previous
batch of FM-94 showed little difference in the elastic modulus results, with a maximum
difference of less than 5% for FML 4 in the 90º orientation.

Elastic Modulus (GPa)

60.00
55.00
50.00
45.00
40.00
35.00
30.00
0 deg

15 deg

30 deg

45 deg

60 deg

75 deg

90 deg

Material Orientation
FML 4

FML 4 (NRC OLD)

FML 4 (CALC)

Figure 126: Experimentally determined elastic modulus for current FML 4 [90/0/90] with
11
new prepreg and FML 4 [90/0/90] made from old prepreg with analytical results.
Note: Dotted line for visualization purposes only
Several baseline fatigue tests were carried out at a net section stress of 198 MPa on
FML 4 [90/0/90] coupons made with the new prepreg material. A small sample size
(n=2) of coupons were tested with both unexpanded and cold expanded holes and the
information from the test was compared to the FML 4 (old prepreg) results from
Chapter 8.0. Ultrasonic inspection of both sets of coupons allowed the total disbond

221

area to be measured (Figure 127) and showed no significant difference between FML 4
(new prepreg) and FML 4 (old prepreg) coupons on the basis of the disbond
measurements.

Disbond Area (mm^2)

2500
2000
1500
1000
500
0
FML 4 (OH)

FML 4 (CX)

FML 4 [90/0/90], Transverse, New Prepreg
FML 4 [0/90/0], Longitudinal, Old Prepreg
Figure 127: Disbond measurements for FML 4 made with old and new prepreg
Crack growth rates were also compared between the coupons made with the two
batches of prepreg, and crack growth curves for the unexpanded (Figure 128a) and cold
expanded (Figure 128b) coupons showed very similar trends.

222

4
Crack Length (mm)

5

4
Crack Length (mm)

5

3
2
[0/90/0] Long (Old
Prepreg)
[90/0/90] Trans
(New Prepreg)

1
0
0

20,000

40,000

[0/90/0] Long (Old
Prepreg)
[90/0/90] Trans (New
Prepreg)

3
2
1

60,000

0
0

20,000

40,000

60,000

Cycles to Failure

Cycles to Failure

(a)

(b)

Figure 128: Comparison between old and new batches of prepreg (a) in FML 4
unexpanded coupons and (b) in FML 4 cold expanded coupons
The elastic modulus estimated from classical laminated plate theory also appeared to
be a reasonable match for the experimental data thus suggesting that variables such as
volume fraction of glass fiber and glass fiber mechanical properties have remained
constant between prepreg batches. With the fatigue results showing that both prepreg
batches produced FML coupons with similar fatigue lives, two overall conclusions were
reached: first, the two batches of prepreg were identical and produced FML 4 with
similar properties and second, FML 4 [0/90/0] and FML 4 [90/0/90] have identical
mechanical properties at 90º degrees to one another.

9.2.1 Manufacture of a New FML 4 Variant
Building the new quasi-isotropic FML 4 [-60/0/+60] variant encompassed the same
basic steps as building standard FML 3 and FML 4. The phosphoric anodized
aluminum sheets were sheared to 305 mm x 305 mm (12 inches x 12 inches) and set
aside. A special template was designed and built to allow for easy and accurate cutting

223

of the 60º degree prepreg plies (Figure 129). The combined [-60/0/+60] plies were
debulked separately and then layered between the aluminum sheets before being
debulked again. The final FML panels were then vacuum bagged and readied for the
autoclave. After this, all panels were inspected ultrasonically before being sent for
waterjet cutting and then finally milled to their final size.

Figure 129: Template tool for cutting precise 60º plies

9.3

Static Strength of FML 4 Variant

Static strength tests were performed on n=2 FML 4 [90/0/90] and n=2 FML 4 variant
[-60/0/60] coupons in the longitudinal, transverse and 45º direction to determine the
actual variation in elastic modulus with coupon orientation. The analytical results
corroborated well with the experimental findings (Figure 130), with less than 1.5% error
for the FML 4 variant results and less than 3% error for the FML 4 results.

224

Elastic Modulus (GPa)

60.00
55.00
50.00
45.00
40.00
35.00
30.00
0 deg

15 deg 30 deg 45 deg 60 deg 75 deg 90 deg
Material Orientation

FML 4
FML 4 Variant (CALC)

FML 4 Variant
FML 4 (CALC)

Figure 130: Elastic modulus for FML 4 [90/0/90] and FML 4 [-60/0/60] measured from
static failure tests (columns) combined with results from elastic modulus calculated
using classical laminated plate theory (symbols). Note: Dotted line for visualization
purposes only
Yield stress for the material was calculated from the stress-strain curves using the 0.2%
offset methodology and the results for FML 4 [90/0/90] and the new FML 4 variant are
shown in Figure 131.

225

Yield Strength (MPa)

300
260
220
180
140
100
0 deg

15 deg 30 deg 45 deg 60 deg 75 deg 90 deg
Material Direction (Deg)
FML 4

FML 4 Variant

Figure 131: Yield strength plotted against laminate direction for FML 4 [90/0/90] and
FML 4 variant [-60/0/60]

226

10.0

FATIGUE TESTING AND RESIDUAL STRENGTH OF FML 4 [-60/0/60]

The static strength tests (Figure 130) showed that the in-plane elastic modulus of the
new FML 4 variant was independent of material orientation. The resultant strain field
after cold expansion and riveting was more uniform than with other grades of FML, and
appeared to more closely resemble that of monolithic aluminum. Based on these
results it was expected that the new FML 4 variant would have a fairly constant fatigue
life irrespective of material orientation, both in the unexpanded and cold expanded
configuration.

For this phase of fatigue testing, additional panels of FML 4 [90/0/90] and FML 4 variant
[-60/0/60] were produced. The cut plan for the coupons was modified (Figure 29) to
allow n=2 coupons to be produced in the longitudinal, transverse and 45º degree
directions respectively. With the reduced number of coupons per panel, fatigue testing
of the new FML 4 variant was focused on only one stress level (198 MPa) and two
conditions: unexpanded and cold-expanded open hole. The hole diameter after cold
expansion and reaming was measured using a ball gauge and the applied load was
reduced in order to ensure that both the unexpanded and cold expanded coupons had a
net stress of 198 MPa.

Although all the FML coupons in this phase of testing were fatigued until a displacement
limit of 0.89 mm, fatigue life comparisons for the unexpanded and cold-expanded
FML 4 [90/0/90] and the FML 4 variant, were based on the number of cycles to a crack
size of 3.7mm as this provided a basis of comparison that was less affected by changes

227

in modulus. The riveted coupons, due to their distributed crack growth, used a
displacement limit of 0.89 mm as the basis for determining their fatigue life. Residual
strength testing was then performed on several coupons after the completion of the
fatigue testing.
10.1 FML 4 and FML 4 Variant Overall Fatigue Results
The fatigue testing was designed to determine the off-axis fatigue performance of both
FML 4 [90/0/90] and the new FML 4 variant. Although transversely oriented
FML 4 [90/0/90] coupons had over twice the life of transversely oriented FML 4 variant
coupons (Figure 132), the FML 4 variant coupons tested in the longitudinal and 45°
degree orientation showed an improvement in fatigue life over FML 4 [90/0/90] and both
grades of FML 4 showed an improvement in fatigue life as a result of cold expansion.
80,000

Cycles to Crack length = 3.7 mm

70,000

FML 4 (Unexpanded)
FML 4 Variant (Unexpanded)

60,000

FML 4 (Cold Expanded)

50,000

FML 4 Variant (Cold Expanded)

40,000
30,000
20,000
10,000
0
Long

45 Deg

Transverse

Coupon Orientation

Figure 132: Fatigue results for unexpanded and cold expanded FML 4 and FML 4
variant tested at a net stress of 198 MPa

228

For the riveted FML 4 variant coupons, a significant increase in fatigue life was seen
when compared to that of an unexpanded or cold expanded coupon (Figure 133).

250,000

Cycles to Failure

200,000
150,000

Open Hole
Cold Expanded
Rivet
Net Stress = 198 MPa

100,000
50,000
0
FML 4 Variant

Figure 133: Comparison of fatigue results for FML 4 variant (longitudinal) showing
cycles to failure of open hole, cold expanded and riveted coupons tested at a net stress
of 198 MPa
Individual crack growth curves from both grades of FML were analyzed with and without
cold expansion to determine the number of cycles required to grow a 1 mm crack, as
well as the crack propagation rate (da/dN). The results for standard FML 4 [90/0/90] are
provided in Figure 134 and the results for the new FML 4 variant are provided in Figure
135. The results for FML 4 [90/0/90] in the transverse orientation are, as expected,
similar to those of FML 4 [0/90/0] in the longitudinal direction, as seen in the first round
of fatigue testing (Figure 99). Since FML 4 [90/0/90] has a lower modulus in the
longitudinal and 45º degree orientations, crack growth rates are significantly higher
when compared to found in the transverse direction; however, cold expansion is still
effective at reducing crack growth rates. Cold expansion appears minimally effective at

229

retarding short crack growth (crack growth to 1 mm), with retardation of no greater than
5,000 cycles on average. The same analysis performed for all the FML 4 variant
coupons showed more constant crack propagation rates (da/dN) in all material
orientations, and a fairly uniform decrease in crack propagation rates (da/dN) after cold
expansion. As with the FML 4 [90/0/90] coupons, the effect of cold expansion on short
crack growth was fairly minimal with crack growth being retarded by no more than 6,500
cycles on average.
The overall conclusions from this more comprehensive data set are similar to what was
concluded earlier; cold expansion is effective at reducing crack propagation rates in
FML, in all material orientations, but is only minimally effective at retarding short crack
growth on the entry face.

30,000

25.0
20.0

20,000

15.0

15,000
10.0

10,000

5.0

5,000
0

da/dN (mm/10,000 cycle)

Cycle Count

25,000

0.0
Long

Trans
Coupon Orientation

45 Degree

FML 4 OH

FML 4 CX

FML 4 OH

FML 4 CX

Figure 134: Variation in number of cycles to 1 mm crack length (columns) versus da/dN
(symbols) for FML 4 in various material orientations

230

18,000

7.0

16,000

Cycle Count

5.0

12,000
10,000

4.0

8,000

3.0

6,000

2.0

4,000

1.0

2,000
0

da/dN (mm/10,000 cycle)

6.0

14,000

0.0
Long

Trans
Coupon Orientation

45 Degree

FML 4 Variant OH

FML 4 Variant CX

FML 4 Variant OH

FML 4 Variant CX

Figure 135: Variation in number of cycles to 1 mm crack length (columns) versus da/dN
(symbols) for the FML 4 variant in various material orientations
10.2 Residual Strength Results
Since the end of fatigue cycling for all FML coupons was defined on a compliance basis,
meaning that fatigue cycling was stopped when coupon displacement reached 0.89 mm
(0.035 in), all FML coupons were left with a certain degree of residual strength. In order
to quantify the degree of residual strength each “failed” FML coupon was submitted to a
uniaxial tensile test to failure, at a pseudo-static loading rate of 0.025 mm/sec
(0.001 in/sec). The data for FML 3 only includes data in the longitudinal direction, while
the data for FML 4 [90/0/90] and the new FML 4 variant includes data for all three
material orientations. An initial review of the results, segregated according to net stress
as well as condition (i.e unexpanded or cold-expanded), did not show a noticeable
effect from either factor, but the sample size was too small to draw a definitive
conclusion. Since elastic modulus was a function of material orientation, the decision

231

was made to separate the coupons on the basis of material orientation but aggregate
them across net stress and condition thus allowing for a minimum of n=5 specimens in
each group. By measuring the initial gauge length of the coupon and calculating the
cross-sectional area through the central hole, the force and displacement data from the
servohydraulic testing machine could be converted into stress and strain. This
conversion allowed for the residual elastic modulus (Figure 136) as well as the peak
load at failure (Figure 137) to be estimated.

The classical laminated plate (CLP) solution for the elastic modulus was modified in an
attempt to predict the residual elastic modulus of the fatigued coupons. By reducing the
modulus of the aluminum sheets, it was possible to determine the effective modulus
with varying contributions from the aluminum layer. Two scenarios were attempted, in
the first, all aluminum layers had their elastic modulus reduced to near zero. In the
second, only the outermost aluminum layers had their elastic modulus reduced. This
second scenario provided results that best fit the experimental findings and suggested
that in the majority of cases, the edge to edge cracking seen on the entry and exit face
was not present on the inner aluminum layer. Since the closed form solution does not
take into account fiber damage or breakage, it was assumed that the modulus derived
from the CLP solution would form an upper bound on the experimental values. It was
interesting to note that for this was essentially true for coupons in the longitudinal and
transverse direction, but not for coupons in the 45º degree direction. One possible
explanation is that although a complete surface crack was evident in the 45º degree
coupons, nearest to the hole, the outermost aluminum layers nearest to the outer edges

232

may not have cracked completely through and may have actually retained some
residual strength. The closed form model showed that if the entry/exit aluminum layers
retained even 40% of their elastic modulus it would explain these results for the 45º
degree coupons. This phenomenon may have been biased to the 45º degree coupons
since FML 4 has the lowest modulus in this orientation and would be more likely to
displace enough to meet the 0.89 mm displacement limit as the surface cracks in the
outermost aluminum layers propagated towards the edge of the coupon.

Residual Elastic Modulus (GPa)

40
35
30
25
20
15
10
Longitudinal

Transverse

45 Degree

Direction
FML 3
FML 4 Variant
FML 4 Theoretical

FML 4
FML 3 Theoretical
FML 4 Variant Theoretical

Figure 136: Residual elastic modulus for FML 3, FML 4 [90/0/90] and FML 4 variant
coupons after fatigue failure. Note: Analytical results overlaid with dotted lines for
visualization purposes only

233

Residual Peak Load (N)

20000
16000
12000
8000
4000
0
Longitudinal

Transverse

45 Degree

Direction

FML 3

FML 4

FML 4 Variant

Figure 137: Residual peak load for FML 3, FML 4 [90/0/90] and FML 4 variant coupons
after fatigue failure
10.3 FML 4: DIC and TSA Measurements
10.3.1 FML 4: Unexpanded Coupons

Maximum principal strain measurements from DIC are provided for the entry face of the
FML 4 unexpanded coupons in Figure 138. Strain measurements are provided for
coupons in all three material orientations (longitudinal, transverse and 45º degree) in
both pre-crack and cracked conditions. A small variation is seen among the precracked FML 4 coupons (Figure 138a,e,i), but this is to be expected given the difference
in elastic modulus between the three material directions. This difference becomes more
noticeable as the crack length increases, with the difference being the most striking for
a crack length of 3.7 mm (Figure 138d,h,l). At this crack length the coupon in the
transverse direction (which has the highest modulus) shows the lowest crack tip strains,
while the longitudinal coupon has slightly higher crack tip strains, and the 45º degree
coupon has the highest crack tip strains, with the strain field extending out at angles of

234

45º degrees from the horizontal crack tip, in line with the longitudinal and transverse
orientations of the material.

The TSA images provide a corresponding view of the strain field on the exit surface of
the coupon. Comparing the precrack images from coupons in all three material
orientations (Figure 139a,e,i) to those at 1 mm of crack growth on the entry face (Figure
139b,f,j), little evidence of crack growth is seen. At 2 mm of crack growth on the entry
face, both the longitudinal and the 45º degree coupon show movement of the TSA
signal at the crack tip, away from the left side of the hole, clearly indicative of crack
growth (Figure 139c,k). The transverse coupon shows a change in magnitude and
shape of the TSA signal, which is indicative of a smaller crack forming in the same
location. At 3.7 mm of crack growth on the entry surface, TSA images from the
longitudinal and 45º degree coupon both show signs of bilateral crack growth (Figure
139d,l). The transversely oriented coupon shows clear signs of crack growth on the left
hand side of the hole, and a change in magnitude and shape of the TSA signal on the
right hand side, indicative of the formation of a smaller crack in this area (Figure 139h).

Overall the results for the unexpanded hole show that crack growth on the exit face lags
only slightly behind that seen on the entry face of the coupon, behaviour that
corresponds to that seen with the previous batch of fatigue coupons.

235

Longitudinal

Transverse

45º Degree

(a) 0 cycles

(e) 0 cycles

(i) 0 cycles

(b) 10,300 cycles

(f) 16,900 cycle

(j) 4,300 cycles

(c) 12,100 cycles

(g) 21,100 cycles

(k) 4,900 cycles

(d) 14,500 cycles

(h) 30,700 cycles

(l) 5,500 cycles

PreCrack

1.0 mm
crack

2.0 mm
crack

3.7 mm
crack

Figure 138: FML 4 [90/0/90] maximum principal strains from the entry face (a-d)
unexpanded longitudinal coupon (Specimen 30-B-3-L), (e-h) unexpanded transverse
coupon (Specimen 30-B-1-T) and (i-l) unexpanded 45º degree coupon (Specimen 27B-4-F)

236

Longitudinal

Transverse

45º Degree

(a) 0 cycles

(e) 0 cycles

(i) 0 cycles

(b) 10,300 cycles

(f) 16,900 cycle

(j) 4,300 cycles

(c) 12,100 cycles

(g) 21,100 cycles

(k) 4,900 cycles

(d) 14,500 cycles

(h) 30,700 cycles

(l) 5,500 cycles

PreCrack

1.0 mm
crack

2.0 mm
crack

3.7 mm
crack

Figure 139: FML 4 [90/0/90] TSA images from the exit face (a-d) unexpanded
Longitudinal coupon (Specimen 30-B-3-L), (e-h) unexpanded transverse coupon
(Specimen 30-B-1-T) and (i-l) unexpanded 45º degree coupon (Specimen 27-B-4-F)

237

10.3.2 FML 4: Cold Expanded Coupons

Examining a similar series of images after cold expansion, one can clearly see the
effect that the cold expansion process has on the crack tip strains. Compared to the
results of Figure 138, the strain field at the crack tip after cold expansion shows a
significant reduction in size and magnitude in all cases. Even for the cracks at 3.7 mm
(Figure 140d,h,l), the crack tip strains show a slight reduction in magnitude in all
material orientations compared to the unexpanded coupons (Figure 138d,h,l). As with
the unexpanded coupons, the differences in strain at the crack tip appear to follow the
same trend as the elastic modulus, with the transverse direction (highest modulus)
showing the lowest crack tip strain, and the coupons cut in the 45º degree orientation
showing the highest crack tip strain.

The TSA images taken on the exit side of the cold expanded hole, show a slight delay in
crack formation on this face. As with the unexpanded hole, no clear indication of crack
formation exists when a 1 mm crack is present on the entry face, except on the
longitudinal coupon (Figure 141b) where a reduction of the strain field on the left hand
side may indicate the presence of a small crack. At 2 mm of crack growth, the
longitudinal and transverse coupons show additional signs of crack growth (Figure
141c,g). At 3.7 mm of crack growth, bilateral cracks are visible with the longitudinal and
45º degree coupons (Figure 141d,l), however, the transverse coupon (Figure 141h) only
shows clear signs of crack growth on the left hand side of the hole. Overall, the results
after cold expansion show a retardation in crack propagation as well a slight extension
of the fatigue life in the early stage of the fatigue process.

238

Longitudinal

Transverse

45º Degree

(a) 0 cycles

(e) 0 cycles

(i) 0 cycles

(b) 13,900 cycles

24,700cycle

(c) 18,700 cycles

(g) 36,700 cycles

(k) 7,900 cycles

(d) 27,700 cycles

(h) 69,741 cycles

(l) 9,400 cycles

No
crack

1.0 mm
crack
(f)

(j) 6,400 cycles

2.0 mm
crack

3.7 mm
crack

Figure 140: FML 4 [90/0/90] maximum principal strains from the entry face (a-d) cold
expanded longitudinal coupon (Specimen 33-B-3-L), (e-h) cold expanded transverse
coupon (Specimen 30-B-2-T) and (i-l) cold expanded 45º degree coupon (Specimen 33B-6-F)

239

Longitudinal

Transverse

45º Degree

(a) 0 cycles

(e) 0 cycles

(i) 0 cycles

(b) 13,900 cycles

(f) 24,700cycle

(j) 6,400 cycles

(c) 18,700 cycles

(g) 36,700 cycles

(k) 7,900 cycles

(d) 27,700 cycles

(h) 69,741 cycles

(l) 9,400 cycles

No
crack

1.0 mm
crack

2.0 mm
crack

3.7 mm
crack

Figure 141: FML 4 [90/0/90] TSA images from the exit face (a-d) cold expanded
longitudinal coupon (Specimen 33-B-3-L), (e-h) cold expanded transverse coupon
(Specimen 30-B-2-T) and (i-l) cold expanded 45º degree coupon (Specimen 33-B-6-F)

240

10.4 FML 4 Variant: DIC and TSA Measurements
10.4.1 FML 4 Variant: Unexpanded Coupons

Maximum principal strain measurements from DIC are provided for the entry face of the
FML 4 variant unexpanded coupons in Figure 142. Strain measurements are provided
for coupons in all three material orientations (longitudinal, transverse and 45º degree) in
both pre-crack and cracked conditions. A small variation in strain is also seen among
the pre-cracked FML 4 variant coupons (Figure 142a,e,i), which is somewhat surprising,
given that static testing showed the difference in elastic modulus between the various
directions to be within 1 GPa. However, the differences may be reflective of this small
difference since the longitudinal direction had the (nominally) highest modulus, followed
by the transverse coupon, and the 45º degree coupon, which had the lowest modulus
(and the correspondingly highest strains).

The region of relatively low maximum principal strain at 0º and 180º degrees tends to
grow with increasing crack growth. This is often indicative of through crack growth in
the coupon, as the applied load is now being more fully transferred to the crack tip and
away from the top (0º degree) and bottom (180º degree) of the hole. The TSA images
(Figure 143) that provide a corresponding view of the exit surface seem to support this
hypothesis.

Equipment failure from the TSA camera meant that no information is available for the
45º degree precrack condition (Figure 143i). However, comparing the precrack images
from coupons in the other two material orientations (Figure 143a,e) to those at 1 mm of
crack growth on the entry face (Figure 143b,f,j) show little evidence of crack growth on
241

the exit face. At 2 mm of crack growth on the entry face, both the longitudinal and the
45º degree coupon (Figure 143c,k) show movement of the TSA signal at the crack tip,
away from the left side of the hole, clearly indicative of crack growth. The transverse
coupon (Figure 143g), shows a change in magnitude and shape of the TSA signal,
indicative of a small crack forming in that location. At 3.7 mm of crack growth on the
entry surface, TSA images from the longitudinal and 45º degree coupon (Figure 143d,l)
both show signs of bilateral crack growth. The transverse coupon (Figure 143h) shows
clear signs of crack growth on the left hand side of the hole, and a change in magnitude
and shape of the TSA signal on the right hand side of the hole are indicative of the
formation of a small crack in this region.

Overall the results for the unexpanded hole show that crack growth on the exit face lags
slightly behind that seen on the entry face of the coupon, behaviour that corresponds to
that seen with the previous batch of fatigue coupons.

242

Longitudinal

Transverse

45º Degree

(a) 0 cycles

(e) 0 cycles

(i) 0 cycles

(b) 10,000 cycles

(f) 8,500 cycle

(j) 8,500 cycles

(c) 12,400 cycles

(g) 10,300 cycles

(k) 10,000 cycles

(d) 17,200 cycles

(h) 15,100 cycles

(l) 13,000 cycles

No
crack

1.0 mm
crack

2.0 mm
crack

3.7 mm
crack

Figure 142: FML 4 variant maximum principal strains on entry face for (a-d) unexpanded
longitudinal coupon (Specimen 32-D-2-L), (e-h) unexpanded transverse coupon
(Specimen 32-D-4-T) and (i-l) unexpanded 45º degree coupon (Specimen 32-D-6-F)

243

Longitudinal

Transverse

No
crack

45º Degree

Image Not Available

(a) 0 cycles

(e) 0 cycles

(i) 0 cycles

(b) 10,000 cycles

(f) 8,500 cycle

(j) 8,500 cycles

(c) 12,400 cycles

(g) 10,300 cycles

(k) 10,000 cycles

(d) 17,200 cycles

(h) 15,100 cycles

1.0 mm
crack

2.0 mm
crack

3.7 mm
crack

(l) 13,000 cycles

Figure 143: FML 4 variant TSA images on exit face for unexpanded (a-d) longitudinal
coupon (Specimen 32-D-2-L), (e-h) transverse coupon (Specimen 32-D-4-T) and (i-l)
45º degree coupon (Specimen 32-D-6-F)

244

10.4.2 FML 4 Variant: Cold Expanded Coupons

After cold expansion, the maximum principal strains for the pre-crack FML 4 variant
coupons (Figure 144a,e,i) appeared fairly similar among all three material orientations,
with only the transverse orientation showing slightly lower strains. Overall, cold
expansion appears to have significantly reduced crack tip strains up to 3.7 mm, at which
point crack tip strains started to increase, possibly as a result of the crack growing past
the elastic-plastic boundary (approximately 3.3 mm from hole edge) created by the cold
expansion process. Examination of the TSA images (Figure 145) for supporting
evidence of this found that after 2 mm of crack growth on the entry face (Figure 145g),
coupons from all three material orientations start to show subtle indications of crack
growth, consisting of a reduction in magnitude and a slight change in shape of the TSA
signal on the exit surface. When the crack had grown to 3.7 mm on the entry face, the
transverse coupon (Figure 145h) showed the clearest indication of crack growth, with a
bilateral separation of the TSA signal away from the edge of the hole. The longitudinal
and 45º degree coupon (Figure 145d,l), showed a change in shape as well as a
reduction in the magnitude of the TSA signal, clearly indicative of early crack formation
on this face

245

Longitudinal

Transverse

45º Degree

(a) 0 cycles

(e) 0 cycles

(i) 0 cycles

(b) 13,900 cycles

(f) 13,600 cycle

(j) 16,300 cycles

(c) 21,400 cycles

(g) 19,900 cycles

(k) 21,700 cycles

(d) 33,400 cycles

(h) 30,400 cycles

(l) 30,700 cycles

No
crack

1.0 mm
crack

2.0 mm
crack

3.7 mm
crack

Figure 144: FML 4 variant maximum principal strains for (a-d) cold expanded
longitudinal coupon (Specimen 29-D-2-L), (e-h) cold expanded transverse coupon
(Specimen 29-D-3-T) and (i-l) cold expanded 45º degree coupon (Specimen 35-D-3-F)

246

Longitudinal

Transverse

45º Degree

(a) 0 cycles

(e) 0 cycles

(i) 0 cycles

(b) 13,900 cycles

(f) 13,600 cycle

(j) 16,300 cycles

(c) 21,400 cycles

(g) 19,900 cycles

(k) 21,700 cycles

(d) 33,400 cycles

(h) 30,400 cycles

(l) 30,700 cycles

No
crack

1.0 mm
crack

2.0 mm
crack

3.7 mm
crack

Figure 145: FML 4 variant TSA images for (a-d) cold expanded longitudinal coupon
(Specimen 29-D-2-L), (e-h) cold expanded transverse coupon (Specimen 29-D-3-T) and
(i-l) cold expanded 45º degree coupon (Specimen 35-D-3-F)

247

10.4.3 FML 4 Variant: Riveted Coupons

A sample size of n=3 FML 4 variant coupons were riveted and then fatigue tested at a
net stress of 198 MPa and of the three coupons tested, two failed in the grip region.
Figure 146 shows the strain results from DIC and TSA on both the manufactured and
driven face of the coupon that failed in the gauge area. At 75% cycles to failure, crack
nucleation has occurred near the outer edge of the coupon and the crack has begun
propagating towards the rivet hole, demonstrating how effective the rivet is in increasing
fatigue life.
Microstrain

Uncracked Condition

75 % of cycles to failure

(a)

(b)

(c)

TSA

(d)

Driven
Head
(DIC)

Manuf.
Head
(TSA)

Figure 146: a-b) Maximum principal strain information from rivet driven face and c-d)
TSA strain information from rivet manufactured head face for the FML 4 variant coupon,
at pre-crack formation and at 75% of the number of cycles to failure (specimen 35-D-2L). Note: Net stress of 198 MPa

248

An earlier comparison between the fatigue lives of FML 4 variant coupons in the
unexpanded, cold-expanded, and riveted configuration (Figure 133) clearly showed
almost a 350% increase in fatigue life for the riveted coupons versus unexpanded
coupons. These results demonstrate that the mechanism behind the fatigue life
increase in cold expansion and riveting is also effective with the new FML 4 variant
coupons.
10.5 Ultrasonic Inspection of FML 4 and FML 4 Variant Coupons

Non-destructive evaluation was again performed post test, using pulse echo ultrasound
to highlight the area of delamination. Sample ultrasonic images are provided for the
entry and exit faces of unexpanded FML 4 (Figure 147) and cold expanded FML 4
(Figure 148) as well as unexpanded FML 4 variant (Figure 149) and cold expanded
FML 4 variant (Figure 150) coupons in all three material orientations. The color scale
used for the pulse echo ultrasonic is qualitative only and visually denotes differences in
signal amplitude of the ultrasound wave.

From a qualitative perspective, little difference appears to exist between the shape and
area of disbond for the open hole or cold expanded FML 4 coupons. As well, the
ultrasound signal appears to be slightly less pronounced on the exit side of the coupon
compared to the entry side. The transverse coupon shows the largest area of disbond
in both the unexpanded (Figure 147c,d) and cold expanded coupons (Figure 148c,d).
The longitudinal coupon shows the second largest area of disbond in both unexpanded
(Figure 147a,b) and cold expanded (Figure 148a,b) coupon while the 45º degree
coupons shows the smallest area of disbond in both unexpanded (Figure 147e,f) and
cold expanded (Figure 148e,f) coupons.
249

Pulse Echo UT Entry Face

Pulse Echo UT Exit Face

(a) Nf=23,770

(b)

(c) Nf=194,448

(d)

(e) Nf=7,891

(f)

Long.

Trans
.

45º

Figure 147: FML 4 open hole tested at a net stress of 198 MPa with cycles to failure (Nf)
provided. Longitudinal (specimen 30-B-3-L), transverse (specimen 30-B-1-T) and 45º
degree (specimen 27-B-4-F)

Pulse Echo UT Entry Face

Pulse Echo UT Exit Face

Long.

(b)

(a) Nf=43,187
Trans
.
(c) Nf=613,298

(d)

(e) Nf=12,611

(f)

45º

Figure 148: FML 4 cold expanded hole tested at a net stress of 198 MPa with cycles to
failure (Nf) provided. Longitudinal (specimen 33-B-3-L), transverse (specimen 30-B-2-T)
and 45º degree coupon (specimen 33-B-6-F)

250

From a qualitative perspective, the area of disbond around the unexpanded open hole
in the FML 4 variant are more similar in size and shape to that of the FML 4 coupons
oriented at 45º degrees. As with the FML 4 coupons, the ultrasound signal on the exit
face appears to be slightly less pronounced than on the entry face. The FML 4 variant
cold expanded coupons all have self-similar disbond areas and shapes, but these
appear to be slightly larger than those from the FML 4 variant unexpanded coupons.

The ultrasound results for the riveted FML 4 variant coupons are shown in Figure 151
for all three coupons. Of these three coupons, two failed in the grip region (Figure
151a,b and Figure 151e,f) with the red disbond region clearly visible in these images. A
closer visual examination of the failure region showed what appeared to be fretting byproducts in the grip area, suggesting that perhaps micro-slip in this region may have
precipitated failure. Even the one coupon that appeared to fail in the gauge area
(Figure 151c,d) showed some signs of disbonding in the grip region, along with an
indication of disbonding (due to crack growth) at the edge of the coupon. If grip failures
could be eliminated from future tests, there is a possibility that the actual fatigue life
might even be higher than what was reported here.

251

Pulse Echo UT Entry Face

Pulse Echo UT Exit Face

(a) Nf=36,432

(b)

(c) Nf=27,582

(d)

(e) Nf=24,724

(f)

Long.

Trans
.

45º

Figure 149: FML 4 variant open hole tested at a net stress of 198 MPa with cycles to
failure (Nf) provided. Longitudinal (specimen 32-D-2-L), transverse (specimen 32-D-4-T)
and 45º degree coupon (specimen (32-D-6-F)
Pulse Echo UT Entry Face

Pulse Echo UT Exit Face

Long.
(b)

(a) Nf=60,367
Trans
.
(d)

(c) Nf=56,802
45º

(f)

(e) Nf=60,716

Figure 150: FML 4 variant cold expanded hole tested at a net stress of 198 MPa with
cycles to failure (Nf) provided. Longitudinal (specimen 29-D-1-L), transverse (specimen
35-D-1-T) and 45º degree coupon (35-D-4-F)

252

Spc #

Pulse Echo UT Manuf. Head Face

Pulse Echo UT Driven Head Face

(a) Nf=196,189

(b)

(c) Nf=236,750

(d)

(e) Nf=217,704

(f)

26-D7-L.

35-D2-L.

35-D5-L
Figure 151: Ultrasonic inspection of FML 4 Variant coupons post riveting tested at a net
stress of 198 MPa with cycles to failure (Nf) provided. Note: Only coupon 35-D-2-L
failed in grip
10.6 Discussion

One interesting aspect, revealed by the multiple phases of fatigue testing, is the
occasional difference in strain between the unexpanded and cold expanded coupons
under the initial static load. In theory, there should be no detectable difference under
static loading after cold expansion, since the compressive residual strains do not
change the material properties in a way that would be measurable under a simple static
load. A review of the initial aluminum and FML coupons showed that the small
difference detected was likely due to the increase in hole size due to cold expansion,
which resulted in a 0.8% increase in the net section stress and a corresponding
increase in strain. For this most recent phase of the fatigue testing the loads were
adjusted to compensate for the slightly larger hole in the cold expanded coupons and
the net section stresses were equivalent between the open hole and cold expanded
coupon. While many FML coupons now showed essentially equivalent strains between
253

the unexpanded and cold expanded coupons during static loading, in some cases there
still appeared to be some small differences in strain during static loading, with the cold
expanded coupons typically showing slightly higher strains. One hypothesis that seems
plausible is that cold expansion increases the amount of disbonding that occurs around
the hole and effectively “enlarges” the hole by reducing the structural integrity around its
circumference, thereby reducing the net section area through the hole, raising the net
section stress and consequently the net section strain. The research by van der Kuip

89

used chemical etching and mechanical milling to remove the aluminum layers and
visualize the disbonding around the hole. Van der Kuip

89

observed that even drilling

the initial open hole caused an annular region of disbonding around the hole (no
measurement provided), with cold expansion increasing the disbond to 0.3 mm from the
hole edge.

The first approach to verifying this aspect of the drilling/cold expansion process involved
cross-sectioning several FML coupons, and performing a microscopic examination of
the area around the hole at various magnifications. Figure 152 shows an unexpanded
FML 3 coupon at x10 and x20 magnification. The two plies in this FML 3 coupon are
easily differentiated as in one ply the fibers are oriented normal to the plane of the
cross-section, and appear as small pin heads, and in the other ply the fibers run in the
plane of the cross-section, and appear as long strands. A small area of disbond is
assumed to exist in the top ply, as a result of the disruption in the orientation of the
fibers adjacent to the hole (see highlighted region in Figure 152b). Measurement of the

254

disbond length was done using ImageTool image analysis software and that the
disbond measured approximately 0.06 mm in length.

(a)

(b)

Figure 152: Cross-section of an unexpanded hole in FML 3 (a) x10 magnification and
(b) x20 magnification with area of possible disbond highlighted in red

Next, an FML 3 coupon that had been cold expanded but not reamed was crosssectioned and viewed microscopically at the same magnifications (Figure 153). In this
case, the fiber plies now appeared to extend out from the edge of the hole on the exit
side. Given the mismatch in elastic modulus between the 2024-T3 aluminum (72 GPa)
and the FM-94

90

prepreg (51 GPa), it would appear that the compressive residual

strains induced by the oversized mandrel had elastically compressed the prepreg layer,
while at the same time plastically deforming the aluminum layer. With the removal of
the oversized mandrel, the prepreg attempted to spring back, with the spring back force
exceeding the shear strength of the aluminum-prepreg interface (approximately
45 MPa), resulting in a small amount of prepreg extending past the aluminum at the
outer edge of the hole. Analysis of the image showed that the length of fiber extending

255

into the hole measured approximately 0.06 mm, which suggests that this is the same
region of fiber that disbonded during the initial open hole drilling process.

(a)

(b)

Figure 153: Cross-section of FML 3 coupon (exit side) after cold expansion but before
reaming at (a) x10 magnification and (b) x20 magnification with area of disbond
highlighted with arrows
Finally, two additional FML 3 coupons were cold expanded, reamed and
cross-sectioned for microscopic examination (Figure 154). It is apparent that the
reaming process removed any fibers in the hole, along with remnants of the “pip”
created by the split in the split sleeve. The area of disbond appears to be less
consistent, with approximately 0.09 mm of fibers disrupted in Figure 154a, and a smaller
length (approximately 0.05 mm) of disrupted fiber in Figure 154b. What is difficult to
ascertain is whether the fibers to the left of the disbond region are actually bonded to
the aluminum or whether the adhesive bond has been disrupted resulting in a situation
often referred to as a “kissing bond”.

256

(a)

(b)

Figure 154: Cross-section of two FML 3 coupons (exit face) at x20 magnification (a)
specimen with 0.09 mm disbond length and (b) specimen with 0.05 mm disbond length

Another approach to quantify this disbond area and to verify van der Kuip’s

89

results

was attempted using two non destructive inspection (NDI) methods. Both high
resolution ultrasonics and pulsed thermography methods were used, but neither could
conclusively detect the area of disbond. The difficulty detecting the area of disbond
likely stems from the small size of the disbond, an assumption based on both the
current microscopic examination (0.06 mm) as well as from van der Kuip’s

89

results

(0.30 mm). Although there is a large difference between the current disbond estimate
89

and that of van der Kuip’s , his etching/milling method is better suited to reveal “kissing
bonds” and it is not inconceivable that cold expansion results in an 0.30 mm radius of
89

disbond surrounding a cold expanded hole. What van der Kuip

did not address was

the variability in this measurement, and the current results seem to suggest that there
may be a degree of variability associated with the area of disbond.

257

Reviewing the cases where the static strains appeared to be different before and after
cold expansion, one interesting observation was made. It was noted that as part of the
experimental procedure, immediately after cold expansion, static loads identical to those
placed during the fatigue cycle were applied. The strain field at this point, often
appeared to be more similar to the unexpanded strains. Also, the pre-crack images
were taken after at least 100 fatigue cycles had been applied to help seat the coupon in
the hydraulic grips, and it is possible that in some cases these fatigue cycles caused the
disbond to grow slightly and lowered the observed strains. Although this phenomena is
of interest, it did not adversely affect the fatigue life of the cold expanded specimens, as
in all cases the specimens with cold expanded holes outlasted those with unexpanded
holes.

A final approach used to investigate the potential disbond around the hole after cold
expansion involved subjecting both open hole and cold expanded coupons to static
loads until failure, and measuring the resultant elastic modulus. For this experiment two
groups of three (n=3) longitudinal FML 4 [90/0/90] coupons were produced. The
unexpanded coupons were reamed such that their central hole was of the same
diameter (6.63 mm) as the hole produced after cold expansion. The engineering stressstrain curve that would be used to determine the elastic modulus was based on the net
section stress through the central hole in the coupons, and the strain was based on the
global elongation of the coupons measured by crosshead displacement. It was
recognized early on that to successfully prove the hypothesis that the disbond resulting

258

from cold expansion could affect the mechanical properties of a notched coupon, the
modulus results would have to have little scatter and the difference between
unexpanded and cold expanded coupons would have to be quite large. The results
showed very similar material properties between the two coupons, with the unexpanded
coupons having an average elastic modulus of 50.04 ±0.46 GPa and an average max
load of 31.27 ± 0.41 kN, while the cold expanded coupons had an average elastic
modulus of 50.43 ± 1.5 GPa and an average max load of 31.27 ± 0.24 kN. Although the
results of this experiment did not conclusively prove or disprove the existence of a
disbond around cold expanded holes in FML, at a minimum, it showed that the static
strength of FML is not significantly affected by the cold expansion process.

The pulse echo ultrasonic inspection used to inspect all coupons after fatigue failure
was very useful at highlighting the differences in the disbond area for coupons with
different material orientations and different FML grades. What is known about fatigue
failure in FML is that the cyclic shear stresses in the adhesive layer are related to the
fiber bridging stresses. It is these cyclic shear stresses that are responsible for the
growing delamination between the aluminum and fiber layers. As this delamination area
grows, the length over which the fibers are elongated increases, lowering the fiber
strains. In essence, there is a balance between delamination growth in the prepreg and
9

the bridging strains . For the FML 4 [90/0/90] in the transverse direction, the area of
delamination is greatest (Figure 147d,c) and correspondingly so is the fatigue life. As
the transverse coupon is being fatigued, two of the three fiber plies are aligned parallel
to the loading direction and the prepreg has the highest elastic modulus. When loaded

259

in tension, tensile stress in the aluminum layer is transferred to the fiber prepreg layer
through shear, causing elongation of the fibers. In the transverse direction, the fibers
are aligned to best resist the load and to most effectively bridge any cracks that form in
the aluminum. Conversely, in the 45º degree direction (Figure 147e,f), the same
mechanisms are in place to transfer load, except in this orientation the fiber prepreg has
a lower elastic modulus and does not transfer the load as effectively. The effectiveness
of the fiber bridging in the aluminum layer is thus reduced, and crack propagation
occurs more quickly. This reduction in fiber bridging effectiveness also means that the
delamination area is reduced, since, except for the local region near the propagating
crack, the fiber prepreg layer is more elastic and less likely to cause adhesive shear
failure.

For the FML 4 variant coupons, all fiber orientations (Figure 148) have essentially the
same elastic modulus and thus provide an equivalent degree of fiber bridging in all
material orientations. Consequently the delamination area is also fairly consistent as all
material orientations result in approximately the same degree of shear strain at the
aluminum/prepreg interface. The slight difference that appears between the
unexpanded and cold expanded coupons is likely a result of the longer fatigue life in the
cold-expanded coupons. An increased number of fatigue cycles results in more cyclic
adhesive stresses, and thus an increased disbond area. Measurement of the disbond
area for both the FML 4 [90/0/90] (Figure 155) and the FML 4 variant (Figure 156)
coupons confirms that overall, cold expanded coupons do show a slight increase in
disbond area over that of the unexpanded coupons.

260

One possible approach to increasing the fatigue life would be to use a higher stiffness
reinforcement material in the prepreg. This would both increase the modulus of the
prepreg and improve fiber bridging and effectively lower the stress in the aluminum
layer under the applied load. While this approach may have theoretical merit, the
greatest drawback is that both steps would require changing the constituent
components of FML. Over the long term this approach may result in a fundamental
improvement to the FML being used today, it would also require recertification of this
new material, where perhaps a more pragmatic approach would be to examine and
modify the current process parameters to improve overall material performance.

Overall, a comparison between the unexpanded and cold expanded coupons from each
FML grade showed qualitatively similar disbond patterns with only small increases in
disbond area after cold-expansion. This supports the idea that the effectiveness of
cold- expansion in FML is related to its effect on the monolithic aluminum layers and
does not affect crack bridging or overall disbond of the fiber layers.

261

Disbond area (mm^2)

2500
OH
CX

2000
1500
1000
500
0
Longitudinal

Transverse

45 degree

FML 4

Disbond area (mm^2)

Figure 155: Measured area of disbond from pulse echo ultrasound for FML 4 [90/0/90]
in both unexpanded and cold expanded conditions [combined entry and exit face
average of n=2 coupons]
2500

OH
CX

2000
1500
1000
500
0
Longitudinal

Transverse

45 degree

FML 4 variant

Figure 156: Measured area of disbond from pulse echo ultrasound for FML 4 variant in
both open hole and cold expanded conditions [combined entry and exit face average of
n=2 coupons]

262

11.0

DISCUSSION

The motivation for this research was the increasing use of fiber metal laminates in
aircraft structures, with the corresponding suggestion that fiber metal laminate materials
could be used as direct replacements for aluminum; suitable for riveting or cold
expansion as the need arose. A review of the literature surrounding riveting and cold
expansion showed that although these processes were well understood for monolithic
materials, little research had been performed to ascertain the effect of riveting on fiber
metal laminates and even less research had been performed to determine the effect of
cold expansion.

These gaps in the current body of knowledge led to this research program, which was
aimed at understanding the effects of cold expansion and riveting on FML, using both
experimental and analytical methods, to see if the information gained could be used to
design an FML variant optimized for use with cold expansion and riveting.

The results obtained met all the objectives of this research program and extended the
body of scientific knowledge in this area. Although the research was constrained to the
stated objectives and did not directly set out to examine the underlying mechanism
behind cold expansion in FML, several observations made during the course of this
investigation addressed this issue and are discussed further. An overall discussion of
the results is provided which centers on the primary research objectives and discusses
what has been achieved in each area as well as how this information was related to the
ultimate goal of producing an optimized FML variant.

263

11.1 Cold Expansion of FML
The results from the static tests provided a unique opportunity to measure full-field
strains in real time during the cold expansion process. Although measuring full-field
strains in aluminum coupons during cold expansion and riveting was not new, using the
image correlation technique to gather this information provided a unique insight into
both processes. For the FML coupons, only two researchers had explored the cold
expansion process in FML

89,90

and neither had made experimental measurements of

the strains resulting from this process. Although manual cold expansion equipment had
43

previously been used by Beaver et al , it had never been used in the current manner,
where individual strain measurements were taken at specific increments of mandrel
displacement through the coupon. This allowed the low speed (5 frames per second)
video cameras, used for image correlation, to effectively “slow down” the cold expansion
process and provide a more complete visualization of the change in residual strains
during this process.

The pseudo-static measurement of the surface strains during cold expansion showed
several similarities between the aluminum and FML coupons. In the case of the
aluminum coupon, insertion of the mandrel (Figure 157a) resulted in an expansion of
the elastic-plastic boundary as predicted by the analytical solution. Withdrawal of the
mandrel (Figure 157b) resulted in recollapse of the material surrounding the hole, and
reverse yielding, with a new elastic-plastic boundary being created close to the hole.

264

(a)

(b)

Figure 157: Maximum principal strains in aluminum coupon (specimen AL1): (a)
mandrel fully inserted and (b) mandrel removed
Interestingly, the same mechanism appears to be at work in the FML coupon. Complete
mandrel insertion (Figure 158a) results in a larger elastic-plastic boundary, and
withdrawal of the mandrel (Figure 158b) results in recollapse of the material surrounding
the hole, causing reverse yielding in the aluminum layer and formation of a new elasticplastic boundary closer to the hole. Although the processes have similarities, the
change in strain field symmetry is a clear indication that the material properties of this
FML 3 coupon are much more orthotropic than aluminum. Another difference between
FML and aluminum after cold-expansion, is the delamination that occurs at the
aluminum/prepreg interface due to the cold-expansion process (Chapter 10.6).

265

(a)

(b)

Figure 158: Maximum principal strains in FML 3 coupon (specimen GAL1): (a) mandrel
fully inserted and (b) mandrel removed
The observations and measurements made seem to support the hypothesis that the
improvement in fatigue life for FML is because of the compressive residual stresses
imparted by the oversized mandrel into the aluminum layer. Cold-expansion appears to
play a fairly minimal role in extending life in the early stage of fatigue process on the
entry face, possibly as a result of the delamination at the aluminum/prepreg interface
adjacent to the hole. The reason this does not have a detrimental affect on fatigue life
is that crack bridging in FML is not fully effective until a crack has reached a radial
length of approximately 1.0 mm, which is significantly longer than the radial length of the
disbond area. The TSA results from the exit face of the coupon suggest that cold
expansion may better extend life in the early stage of the fatigue process, an
observation that has been confirmed by van der Kuip

89

during his fatigue testing of

cold-expanded FML. This difference may be due to the higher residual strains on the
41,43,44,47,52,60-63

exit face, a phenomena well documented in aluminum coupons

266

.

Although it has been shown in this research that cold expansion does result in higher
residual strains on the exit face, it seems likely that the higher residual strains would
need to act in tandem with a reduction in the level of disbond on this face. Conclusively
proving this would likely need to be done using chemical etching to remove the
aluminum layers after cold-expansion to determine the exact area of disbond on both
faces.

The static testing provided a means of measuring the surface residual strains resulting
from cold-expansion and allowed for a comparison to be made between the aluminum
and FML. These results graphically demonstrated the effect of material orthotropy on
the residual strains. Material data sheets about the standard FML grades often provide
only material properties in the two principal directions, and the cold expansion results
were a graphic reminder that, as a laminated composite, the in-plane material response
can be anisotropic with both elastic modulus and yield strength being a function of the
material orientation.

Static testing clarified that although FML 3 and FML 4 are often referred to as
quasi-isotropic

137,138

, due to their similar material properties in the longitudinal and

transverse direction, they are not quasi-isotropic in the classical laminate sense. By
definition, a quasi-isotropic laminate is one with three or more identical plies at equal
angles (i.e the angle separating each of the n plies is /n) with the resulting in-plane
properties being isotropic. Changing material orientations made it clear that the high
strains at the split in the split sleeve were reduced if it was aligned with the 45º direction,

267

coincident with the material orientation with the lowest elastic modulus. This key
observation, that the residual strain field due to cold expansion was much more uniform
with coupons cut in the 45º degree material orientation, eventually led to the design of a
true, quasi-isotropic FML 4 [-60/0/60] variant.
11.1.1 Influence of Mandrel Geometry
The use of a manual cold expansion tool, combined with strain measurements
performed at regular increments of mandrel insertion, made it possible to observe a
relationship between the size and shape of the strain field and the position of the
mandrel. By attempting to understand the effect mandrel geometry may play in the cold
expansion process one gains a more complete understanding of this dynamic process,
including a possible explanation for the difference in strain field between the entry and
exit face. Relatively little attention has been paid to mandrel geometry in the open
literature, although O’Brien

44

published the basic dimensions of the mandrel he used for

cold-expanding thick section aluminum coupons (Figure 159a). Manufacturer data
regarding the actual dimensions of each mandrel are not given, likely due to the
proprietary nature of the information. For this research program, a laser measuring
system (LT-9030M, Keyence Inc, Osaka Japan) was used to determine the profile of the
mandrel (Figure 159b and Figure 159c) to see if the dimensions of the mandrel could
help explain some features of the cold expansion process. The design of this mandrel,
designated as type 8-1-N (FTI Inc, Seattle WA) is similar in function to the one used by
44

O’Brien , but with very different overall dimensions. The same gradually increasing
taper region exists (designated as region A and B in Figure 159c) but the flat region,
which produces the maximum interference (Region C in Figure 159c) is significantly

268

44

longer than on the mandrel used by O’Brien . In this case, the flat region is long
enough (4.8 mm) to ensure that the full thickness of the coupon (t=1.64 mm) is
expanded at the same time. Another interesting difference is at the tail end of the
mandrel (region D in Figure 159c), which is much shorter and more blunt than the
mandrel used by O’Brien

44

(Figure 159a), which had a much more gradual taper.

During the cold expansion process, the gradual slope of the mandrel (region A in Figure
159c) ensures that both the entry and exit faces are gradually expanded up to the
maximum expansion. As soon as the mandrel is displaced past the flat landing
(region C Figure 159c) the blunt nose of the mandrel, results in the rapid recollapse of
the material. By the time the mandrel is poised to leave the exit face of the coupon, the
majority of the material radially constraining the hole has been expanded and plastically
deformed by the mandrel and has subsequently recollapsed as a result of its removal.
44

In contrast, the mandrel used in O’Brien’s study

had a gradual taper on either side of

the flat landing, that allowed the material to gradually recollapse during mandrel removal
process. Further investigation may be warranted to determine if the addition of a
gradual taper to the cold expansion mandrel has an effect on delamination in fiber metal
laminate materials.

The manner in which the geometry of the mandrel interacts with the material
surrounding the open hole may influence the resultant residual strains and explain why
there is a difference between the entry and exit face. An examination of the situation
immediately before the mandrel leaves the entry face (Figure 160a) shows how the rigid

269

steel mandrel in conjunction with the tool housing provides constraint in the axial
direction (through shear) during the reverse yielding of the material at the entry surface.
This more uniform three-dimensional constraint may lead to a greater hydrostatic
component of strain, and hence less yielding, resulting in lower and less extensive
residual stresses at the entry surface. The situation is reversed at the exit surface
(Figure 160b) where reverse yielding of the exit face material occurs at the instant that
the mandrel leaves the coupon. With the rigid steel mandrel no longer providing
constraint in the axial direction, increased shear deformation and thus increased
yielding can occur, resulting in higher and more extensive residual strains on the exit
face.

270

(a)

(b)

(c)

Figure 159: Mandrel profile used for cold expansion process with schematic of the full
mandrel overlaid

271

(a)
(b)
Figure 160: Geometric constraint conditions for a nominal material element (a) at the
entrance face and (b) at the exit face
11.2 Fatigue Testing of Cold Expanded Coupons
The fatigue test was the final phase in the research program and was broken down into
two stages. The first stage was the baseline fatigue stage, designed to generate
baseline fatigue information for unidirectional coupons of 2024-T3 aluminum, FML 3 and
FML 4 in the open hole configuration (unexpanded and cold expanded) and determine
baseline fatigue life for three different net stresses (S-N curves). Fatigue information
was also gathered for riveted coupons made from the same materials, but tested at only
one net stress level (263 MPa) due to the significantly improved fatigue life after
riveting. One constraint on the design of these experiments was the limited amount of
raw materials for making FML as well as limited fatigue test frame availability.

To make efficient use of the available load frame access, FML coupons were fatigued
until a crack had extended across the full width of the specimen. During initial pilot

272

testing, a peak displacement of 0.89 mm (0.035 inches) was associated with bilateral
crack propagation to the outer edge of the coupon for all specimens and thus this
displacement was used as the failure criteria. In effect, failure for FML coupons, was
defined as a change in coupon compliance, while for the aluminum coupons, failure was
defined as crack propagation across the full width and complete physical separation of
the specimen. Thus the number of cycles to failure for aluminum and FML are not
directly comparable, with the FML coupons still retaining substantial residual strength
after “fatigue failure”, with residual failure loads ranging from 11.6 kN for FML 3, to
9.6 kN (minimum) for FML 4 [90/0/90] to 11.4 kN (minimum) for the FML 4 variant. The
residual elastic moduli ranged from 22.2 GPa for FML 3, to 21.4 GPa (minimum) for
FML 4 [90/0/90] and 24.12 GPa (minimum) for the FML 4 variant (Chapter 10.2).
11.3 Fatigue Testing of Riveted Coupons
The initial static measurements of the strains during riveting highlighted that riveting is a
manufacturing operation that is very sensitive to the initial placement of the rivet and to
the riveting force. The static riveting results showed more concentric strains around the
rivet hole and stood in contrast to the strain distribution from cold expansion, which
showed a large strain gradient at the location of the split in the sleeve. Unfortunately,
the true magnitude of the strains adjacent to the rivet hole are difficult to measure since
this region is obscured by the driven head on one face and the manufactured head on
the other.

The inclusion of riveting in this research program was deemed important as it is still one
of the dominant fastening methods in the aerospace industry, and one of the benefits of
FML is that it can be riveted in much the same way as monolithic aluminum. From an

273

experimental mechanics perspective, riveting combines aspects of hole cold expansion
from the expanded rivet shank with through-thickness compression from the driven and
manufactured heads. The study of riveted joints is a well-established field and although
few researchers have published work looking at the effect of riveting with FML,
139

researchers such as Lanciotti and Lazzeri

88

and Lazzeri

have clearly shown that this

is a viable process and provides a life improvement compared to riveted 2024-T3
aluminum joints.
Although the literature on riveting and the effects of fatigue on riveted joints is relatively
extensive for aluminum alloys, often this work has focused on the performance of the
23

joint itself as opposed to the riveting process. However, researchers such as Muller

have focused on the applied compression as a variable in the fatigue life of a riveted
joint. For a joint, rivet compression can influence the degree of fretting that occurs as
well as the degree of expansion of the rivet shank. Schijve

16

in his book on the fatigue

of structures discusses how the location of initial crack nucleation can be influenced by
rivet compression, with higher degrees of compression moving the crack nucleation
location away from the rivet hole. In the idealized case of a zero load transfer joint,
compression is still an important variable in fatigue life. Consistent rivet compression
ensures that the expansion and degree of interference of the rivet shank is consistent,
ensuring proper hole filling. For a zero load transfer rivet, the compression of the rivet
and formation of a driven head likely serves to generate a triaxial strain field around the
initial pilot hole. The expansion of the rivet shank provides in-plane compression
around the pilot hole and the compression provided by the driven head adds a through

274

thickness strain component. Given the hydrostatic nature of these triaxial strains, it
seems likely that less yielding would occur in the material surrounding the rivet hole
compared to the cold expansion process.

Proving or disproving the above hypothesis is difficult since in the region of highest
strain, near the rivet hole, the area is obscured on one face by the driven head and on
the other face by the manufacture head. In an attempt to verify this hypothesis
regarding the nature of the strain field close to the hole, an innovative approach using a
2024-T3 aluminum coupon was attempted to measure strains in this region. Using the
same static test fixture described in Chapter 5.2.1, a higher resolution camera (PCI
Imaging, Sensicam QE, 1280x1024 resolution) along with high magnification optics
were used to take a reference image of an aluminum coupon at a magnification of
0.0094 mm/pixel. After the reference image was taken the coupon was coated with
high strength tape to protect the surface and then riveted. After riveting the coupon was
placed on a mill and both the rivet driven and manufactured heads were carefully milled
away, leaving just a small section of the rivet shank in the hole. The coupon was then
mounted back in the static test fixture and a “deformed” image was taken and
processed using the Vic-2D correlation software (Correlated Solutions Inc). At this
magnification, surface disparities on the coupon itself were adequate to perform image
correlation and the resultant maximum and minimum strain fields are shown in Figure
161. The images were scaled similarly to the cold expanded coupon results to highlight
how much lower the strain values were close to the hole. Of course, these strain values

275

cannot take into account the compression provided by the rivet head and so a separate
approach was used to measure its contribution.

Given the uniformly high rivet squeeze force of approximately 13.3 kN it is reasonable to
assume that the manufactured head of the rivet, which is in direct contact with the
coupon body, not only compresses the material under the manufactured head but also
provides resistance to the extensional load being applied to the coupon during fatigue.
To get an approximate sense of the magnitude of this load, pressure sensitive film was
placed on both sides of the aluminum coupon to measure the resultant normal pressure
after riveting.

276

e1 (um/m)

Driven Face

Manufactured Face

(a) Max Principal Strain

(b) Max Principal Strain

(c) Min Principal Strain

e2 (um/m)

(c) Min. Principal Strain

Figure 161: Minimum principal strains for an aluminum coupon (specimen AL-L-64) on
both the driven and manufactured faces with shank
Pressure sensitive film comes in various grades, rated according to the pressure it is
sensitive to. When a normal force is applied to the film, ink capsules within the film
rupture and cause the film to turn a reddish-pink color. The intensity of the film stain can
be measured using a scanner, which can digitize the film, allowing the stain to be
converted to pressure using a previously determined calibration curve. As part of a
previous research program

140

a calibration equation (Equation 11.3.1) and

277

corresponding coefficients (Table 14) were determined for use in calibrating low,
medium and high pressure film.

P = a + b ⋅ y + cy 2 + d ⋅ y3 + ex + fxy + gxy 2 + hxy3

11.3.1

where P is the pressure in MPa, x is the humidity at the time the stain was taken, y is
the grayscale pixel intensity value from the pressure film stain and a,b,c,d,e,f,g,h are the
coefficients from Table 14.

Table 14: Coefficients for determining pressure from pixel intensity values
Coefficient
a
b
c
d
e
f
g
h

Low
1.189E+02
-1.555E+00
7.538E-03
-1.263E-05
-1.082E+00
1.469E-02
-7.255E-05
1.225E-07

Medium
1.379E+02
-1.384E+00
6.862E-03
-1.325E-05
2.074E-01
-5.519E-03
3.126E-05
-5.442E-08

High
-3.357E+02
7.378E+00
-3.595E-02
5.033E-05
2.310E+01
-3.260E-01
1.524E-03
-2.350E-06

Figure 162 shows a greyscale representation of the various grades of pressure film
placed under the manufactured head, while Figure 163 shows the corresponding
pressure distribution from these images. Pressure film was also placed under the
driven head of the rivet, but the pressure distribution was so localized around the rivet
hole that a discernable pressure stain could not be measured.

278

(a)

(b)

(c)

Figure 162: Pressure film stains from (a) low (b) medium and (c) high grade films taken
from the manufactured head of a rivet

Pressure [MPa]

200
160
120
80
40
0
0.00

0.50

1.00

1.50

2.00

2.50

Dist from Rivet Edge [mm]
Figure 163: Pressure distribution for consolidated pressure film stains on manufactured
head of a riveted coupon. Regression line for visualization purposes only

At this point, two separate measurements are now available. The first is the in-plane
residual strain field surrounding the rivet (after the manufactured and driven heads have
been removed) and the second is the normal pressure distribution measured under the
manufactured head of the rivet.

279

For the case of the rivet, a linear-elastic superposition approach was used to estimate
the total strain field under the rivet head. The total strain field was assumed to be
comprised of radial ( r), hoop ( h) and through thickness strains ( z). For the in-plane
measurements, the radial and hoop strains were measured using image correlation.
Assuming from the magnitude of these strains that some plastic deformation was
occurring close to the hole, the triaxial strains ( z) in the through-thickness direction
34,109

were estimated by assuming volume constancy
0 = ε z + εr + εh

:
11.3.2

It is interesting to note that this approach suggests that the through-thickness strains
closest to the hole are actually tensile in nature due to the large radial and hoop strains
34

being applied. This finding seems to support the work done by Poolsuk and Sharpe

who used a linear variable displacement transducer (LVDT) to measure the change in
thickness near cold expanded holes.

The compression applied by the manufactured head of the rivet was assumed to result
in radial and hoop strains as well as strains in the through thickness direction. Since the
normal stresses measured with pressure film were well in the elastic range for
aluminum, a very simple linear elastic approach was used to calculate the applied
strains using the equations below:

280

σ
εz = N

11.3.3a

σ
ε r = −ν N

11.3.3b

σ
ε h = −ν N

11.3.3c

E

E

E

where N is the normal stress measured using pressure sensitive film, v is the
Poisson’s ratio of the aluminum and E is the elastic modulus.

The linear superposition of the strains due to the compression of the rivet and the
strains due to the expansion of the rivet shank provided an estimate of the total strain
field underneath the rivet head. Radial and hoop strains from a cold expanded coupon
with a similar interference ratio (rivet – 3.0%, cold expansion – 4.0%) were measured
previously using image correlation techniques. The same approach was used to
estimate the through thickness strains and a comparison of rivet and cold expansion
strains is shown in Figure 164. An analysis of the Von Mises stresses shows that the
elastic-plastic boundary is located at approximately 0.4 mm from the hole edge for the
riveted coupons, but that for cold expansion, the strains in the entire region shown in
Figure 164 are beyond yield.

281

0.02
Principal strain [mm/mm]

0.015
0.01
0.005
0
-0.005
-0.01
-0.015
-0.02
-0.025
-0.03
0.00
e1 [rivet]

0.50

1.00

1.50

2.00

Distance from hole edge [mm]
e2 [rivet] e3 [rivet] e1 [CX] e2 [CX]

2.50
e3 [CX]

Figure 164: Hoop (e1), radial (e2) and through thickness strains (e3) for both a riveted
and cold expanded (cx) coupon. Note: dotted line denotes the elastic-plastic boundary
for the riveted coupon only

From a fatigue perspective, the cold expansion process appears to be more successful
in plastically deforming the material around the hole and creating a large region of
compressive residual stress. However, under fatigue loading, the strain field around the
rivet also shows some significant differences from that after cold expansion. After cold
expansion, and before the formation of a crack, the strain field due to the applied load
(excluding residual stresses) is essentially identical to that of an open hole, which is not
the case after riveting as shown in Figure 165. Research by Lanciotti and Polese

91

91

provides an interesting perspective on these results, as Lanciotti and Polese

performed a series of tests using interference fit steel pins to provide varying degrees of

282

interference ranging from 0.5-2.5%, in zero load transfer aluminum coupons. Their
research showed that hole cold expansion (performed with a similar level of
91

interference) was more effective in increasing fatigue life , but since the results from
this research program show the opposite effect, it seems likely that it is not just the
radial expansion of the shank, but also the compression afforded by the rivet head that
92

plays a role in improving fatigue life. A recent paper by Keshavanarayna et al , looking
at fatigue-based severity factors for different types of joints, also noted the effectiveness
92

of riveted zero load transfer coupons. Keshavanarayna et al

explained the improved

fatigue performance on the reduction in the stress amplitude and the increase in mean
stress level that occurs locally due to hole filling by the expanded rivet shank.
Aluminum Cold Expanded

Aluminum Rivet

(Net Section Stress = 198 MPa)

(Net Section Stress = 263 MPa)

(a)

(b)

Figure 165: Comparison of maximum principal strains between (a) cold expanded
aluminum (specimen AL-L-27) and riveted aluminum (AL-L-9)

283

To verify Keshavanrayna et al’s

92

hypothesis, horizontal strain profiles along lines

perpendicular to the load were obtained from the image correlation measurements
during fatigue loading for both a riveted and a cold expanded coupon. The strain
information was extracted at both the minimum and maximum of the load cycles and the
strain measurements were converted to hoop stress ( 1) using Hookes law and
assuming linear-elastic isotropic behaviour:

σ1 =

E
⋅ (1 −ν ) ε1 + νε 2
(1 +ν )(1 − 2ν )

11.3.4a

Clearly, a linear elastic stress-strain conversion is not completely valid for the cold
expansion results due to plasticity close to the hole, so the Von Mises failure criteria
(Equation 7.1.13) was used to determine the elastic-plastic boundary. The hoop stress
results for both cold expansion and riveting are shown in Figure 166 with the dotted line
representing the elastic-plastic boundary. At the elastic-plastic boundary both the mean
stress (Equation 11.3.5) and the stress amplitude (Equation 11.3.6) were determined for
the cold expanded and riveted coupon and the results presented in Table 15.

284

500

Stress (MPa)

400

300

200

100

0
0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

Distance from Hole Edge (Driven Side) [mm]
CX - Low Load

CX - High Load

Rivet - Low Load

Rivet - High Load

Figure 166: Cold expansion (specimen AL-L-27) and rivet strains (specimen AL-L-41) at
high load (10 kN) and at low load (1 kN). Note: Dotted line denotes elastic-plastic
boundary for cold expansion only

σ
− σ min
σ mean = max

11.3.5

σ amplitude = σ max − σ min

11.3.6

2

Table 15: Comparison between cold expansion and riveting stress values during fatigue
loading
Cold Expansion

Riveting

Mean Stress ( mean)

150 MPa

100 MPa

Stress Amplitude ( amp)

299 MPa

199 MPa

Stress Ratio (Reff)

0.14

0.15

285

These results clearly confirm Keshavanarayna et al’s

92

hypothesis, showing that both

the mean stress, and more importantly the stress amplitude, are significantly reduced in
the riveting case. Interestingly, the effective stress ratio (Reff= max/ min) is very
similar in both cases, but according to Schijve

16

it is the reduction in stress amplitude

that plays the largest role in determining fatigue life.

It appears clear that two possible factors play a role in the enhanced fatigue
performance seen with the riveted coupons. The first is the interference from the rivet
shank and the second is due to the compression created by the formation of the driven
head. Our previous measurements and analysis have shown that the residual strains
due to the riveting process are lower than those from cold expansion so a closer
investigation of the role of the rivet head is in order.

Given the uniformly high rivet squeeze force of approximately 13.3 kN it is reasonable to
assume that the manufactured head of the rivet, which is in direct contact with the
coupon body, not only compresses the material under the manufactured head but also
provides resistance to the extensional load being applied to the coupon during fatigue
and as a result reduces any potential crack opening displacements.
One means of quantifying this is to estimate the change in the net section stress due to
hole filling and due to friction between the rivet manufactured head and the coupon.
From the pressure distribution shown in Figure 163, the average normal stress ( n)
under the rivet head was estimated to be approximately 87 MPa.

286

Figure 167: (a) Front view of riveted coupon highlighting pressure affected zone and (b)
side view of rivet showing line of action of frictional force
The average area (Aavg) over which the normal stress from the rivet head acts, is
shown graphically in Figure 167, with the actual average area measured directly from
the pressure film stain and determined to be approximately 3.22 x 10

-5

2

m . The

average normal force (FN) could then be estimated from FN= n Aavg which gave an
average force of 2801 N. The coefficient of kinetic friction ( k) between the aluminum
head and the rivet, assuming no lubrication between the surfaces, is k=1.4 and thus
the frictional force (Ff) can be determined from Ff = kFN which gives a frictional force
acting opposite the applied load of approximately 3.9 kN. Given that the applied load to
the coupons is 14.2 kN, simple superposition of the forces shows that in the local area
under the rivet the net applied load would be reduced to 10.3 kN. If one uses the

287

original net section area of the riveted coupon (taken through the center of the rivet
hole) equal to 5.4 x 10

-5

2

m then the local net section stress has been reduced to

( net=Fnet/A=10.3kN/5.4x10

-5

2

m ) to 191 MPa (27% reduction) and if one assumes

perfect hole filling from the rivet, the net section area increases to 5.79 x 10

-5

2

m , which

reduces the local net section stress to 178 MPa (32% reduction), further supporting the
hypothesis that the clamping force of the rivet and the frictional force it generates, is the
root mechanism behind the increased fatigue life of the riveted coupons.
11.4 Effectiveness of New FML 4 [-60/0/60] variant
It is interesting that so few papers in the open literature deal with property optimization
141

of fiber metal laminates. Van Rooijen et al

approached the topic of property

optimization in FML by focusing mainly on improvements in the constituent components;
determining the effects that changes to the aluminum or glass fibers would have on
material properties, without addressing the conventionally accepted layup sequence of
142

the various FML grades. More recent work Nam et al

looked at optimizing the

stacking sequence in FML 3 by combining a classical laminated plate approach for
determining material properties with a finite element method, using a Tsai-Hill failure
criterion to determine material failure, and a genetic algorithm to predict the optimum ply
142

sequence. As an outcome Nam et al

presented several possible stacking

sequences, each optimized for a specific type of loading, emphasizing the importance of
having several grades of FML to choose from depending on the application.

288

One possible reason that more isotropic FML laminates have not been pursued is the
reluctance of composite engineers to produce quasi-isotropic materials. The
quasi-isotropic approach for standard carbon fiber reinforced polymers (CFRP) is a
design philosophy that is typically used as a last resort when there is a lack of
information regarding a component’s loading history. More modern design practice with
composite materials relies on having some information regarding the applied loads and
the design stresses so that the stacking sequence of the CFRP can be designed
accordingly. A typical example would be a monocoque composite bike frame where
each joint will typically have a specific layup based on typical rider loads and the design
intent of the frame (i.e. optimized for weight or stiffness). Although fiber metal laminates
are a class of composite, they are often referred to as hybrid materials, since they are
hybrids of monolithic metal and glass fibers. As a hybrid material, FML do not have the
same degree of customization as typical CFRP’s, and the results of this study would
certainly support the adoption of a new grade of quasi-isotropic FML 4 based on the
[-60/0/60] stacking sequence.

Comparisons between the FML 4 variant and FML 4 [90/0/90] are complicated by the
orthotropic nature of FML 4 [90/0/90]. Although the elastic modulus of the FML 4
variant is approximately 13% lower than FML 4 [90/0/90] in the transverse direction, a
comparison of the off-axis properties of both materials shows a significantly better
performance for the quasi-isotropic FML 4 variant, both of in terms of modulus and yield
strength in the longitudinal and 45º degree orientation. From a fatigue perspective, the
quasi-isotropic FML 4 variant also has superior fatigue life in the longitudinal and

289

45º degree orientations, but has a lower fatigue life in the transverse direction. Although
the difference in fatigue life may preclude immediate use in aerospace, the isotropy of
this new layup would certainly be suitable for static applications or applications involving
low cycle fatigue.
11.5 Error Analysis
The potential errors in various aspects of this research are assessed and discussed in
this section.
11.5.1 Static Testing and Measurements
Static strain measurements were made using digital image correlation and any error
analysis needs to focus on the potential errors associated with this measurement
technique. For the 3D image correlation measurement, the system sensitivity was
determined by taking multiple reference images and processing these images to
determine the level of strain below which measurements were difficult to discern from
noise in the system (CCD, variations in lighting, vibration etc). As mentioned previously
in all cases, the strain sensitivity for the 3D DIC setup was better than ±50

and the

out of plane displacement (w) sensitivity was better than ±0.0015 mm. Given that our
camera setup met the parameters stated in Chapter 2.5.2.2, the typical uncertainty for
in-plane displacement was estimated from the ratio D/10,000, where D is the in-plane
dimension of the object being measured. Uncertainty in the out-of-plane displacement
was estimated from the ratio Z/50 000 where Z is the distance from the object to the
30

CCD . For the current, setup D was approximately 66 mm and Z was approximately
112 mm, giving an out of plane uncertainty on the order of 0.6% and an in-plane
displacement error on the order of 0.2%

290

For 2D image correlation, one of the largest sources of error is out-of-plane
displacement. Since 2D DIC was used only for the fatigue testing, a digital dial gauge
(Mitutyo Inc) was used to determine the average out-of-plane displacement during a
fatigue cycle, which measured approximately 0.02 mm. The ratio ( z/z) where z is the
out of plane displacement and z is the distance from the CCD to the coupon face can be
used to provide an estimate for the uncertainty in the measured strain results. With a
CCD to coupon distance of 250 mm the effect of out of plane displacement is
-5

approximately 8.0 x 10

mm/mm which is more than two orders of magnitude smaller

than the peak strains measured on these coupons.
11.5.2 Closed Form Solution
Although the chosen approach for modeling the rivet strains was similar to that used by
23

Muller , in that he also only considered expansion of the shank and did not take into
account compressive stresses from the rivet head, results from the fatigue test suggest
that for zero load transfer rivets, the compression from the driven head is an important
variable and this was discussed in detail in Chapter 11.3. Although the analytical model
used did not take this variable into account,the calculated strains still corroborated well
with the measured strains. This was not surprising since the strains that were measured
were in the region outside of the driven and manufactured head, and it is likely that the
strains in this region were predominately due to the interference from the rivet shank
and not due compression from the rivet head. The strain due to compression from the
rivet head appeared to be lower and more localized than that due to expansion of the
rivet shank, and it is likely that that a more sophisticated model may be required to
attain a more accurate strain solution close to the rivet hole.

291

In addition, the fidelity of the closed form model was limited by the available material
property data. For this work, a materials handbook

129

was consulted for aluminum

material properties in both the longitudinal and transverse orientation. These material
values are average values from many material batches and may not provide an exact
match to the material that was used here. For modeling FML, material properties were
obtained from an earlier test performed at NRC on various FML grades which provided
elastic modulus and yield strength information at 15º degree increments. The same
prepreg batch was used in our initial test coupons, ensuring fairly good accuracy for the
material information.
11.5.3 Fatigue Testing
The largest source of uncertainty in the fatigue testing was the relatively small sample
size available, which precluded determining the statistical significance of the differences
seen among the test groups. To compensate to some degree for the small number of
specimens, additional effort was made to reduce experimental variability.
Cold-expansion of the coupons was done in-situ in the load frame, using a precision
alignment jig to ensure that the mandrel was orthogonal to the coupon. For riveting, a
precision support fixture was designed to support the coupon, and rivets were milled to
size for each coupon, so that the amount of shank protruding was identical. The
instrumented arbor press also helped assure that consistent compressive loads were
applied to the rivet. The test plan required static loads identical to the fatigue loads be
applied to all coupons before the start of fatigue testing and this generated a benchmark
strain field that could be used to independently verify that the fatigue test machine was

292

applying the correct loads during the fatigue cycle and that the image capture system
was capturing images at maximum load during the fatigue cycle.

The displacement limit of 0.89 mm, that was used to define fatigue failure, is adequate
for coupons of the same material, cut in the same orientation. However, when
comparing coupons of different orientations or different grades of FML some uncertainty
will be introduced since displacement for a given load is a function of the material
modulus. For the final phase of testing, the fatigue life comparison between the FML 4
[90/0/90] and the FML 4 variant was redefined on the basis of crack growth to remove
this small bias.
11.6 Innovation and Contribution to Scientific Knowledge
Several innovations were developed as part of this research program. The largest
innovation was the development and testing of a new quasi-isotropic FML 4 variant.
Another innovation was the use of digital image correlation to measure cure induced
residual stress in FML panels. Measuring surface strain during the cold expansion
process had never been attempted using DIC, and both the static and fatigue strain
measurements revealed information to better help understand this process in FML.
11.6.1 Scientific publications and conference proceedings
As part of this research program, several scientific publications and conference
proceedings have been prepared and presented. The following is a list of the published
and submitted scientific publications:

293

Journal Articles Accepted
1. Backman D, Liao M, Crichlow L, and Patterson EA The use of digital image

correlation in a parametric study on the effect of edge distance and thickness on
residual strains after hole cold expansion. Journal of Strain Analysis for Engineering
Design, vol 43, number 8, 2008.

2. Backman D, Cowal C, and Patterson EA. Analysis of the effects of cold expansion of

holes using thermoelasticity and image correlation. Fatigue and Fracture of
Engineering Materials and Structures,In-press.

Conference Proceedings Accepted
1. Backman D and Patterson EA. Measuring residual strains in aluminum and fiber

metal laminate materials during cold expansion and riveting, 2008 Society of
Experimental Mechanics Annual Conference, Orlando, Florida.

2. Backman D and Patterson EA. Fatigue life enhancement of fiber metal laminate

materials as a result of hole cold expansion, 2009 Society of Experimental Mechanics
Annual Conference, Albequrque, New Mexico.

3. Backman D and Patterson EA. Fatigue cracks in fibre metal laminates in the

presences of rivets and cold expanded holes, 2010 Society of Experimental Mechanics
Annual Conference, Indianapolis, Indiana.

294

4. Backman D, Sears T, and Patterson EA. Development of a new fiber metal laminate

variant optimized for cold expansion and riveting, 2011 International Conference on
Aeronautical Fatigue, Montreal, Quebec.

295

12.0

RECOMMENDATIONS AND FUTURE WORK

The results from these tests suggest several avenues of investigation for future work in
this area. These areas can be broadly categorized as cold expansion process changes,
FML material changes, and new avenues of investigation.
12.1 Cold Expansion Process Changes
The results of both the static and fatigue portion of this research show that aluminum
and FML could benefit from an improved cold expansion process. Although there is no
doubt that the current split sleeve cold expansion process is effective in extending
fatigue life of both 2024-T3 and FML materials, the TSA data from the exit face shows
that the current cold expansion process is more effective at extending life in the early
stage of the fatigue process on the exit face. Crack growth information from the entry
face shows that, for cracks of less than approximately 1 mm, the number of cycles
required is only minimally decreased. Differences in the strain field between the two
faces, also show up on the static coupons and the current hypothesis for this
phenomenon is that a difference in geometric constraint exists between the material on
the entry and on the exit face.

As mentioned in the literature survey, the idea that the cold expansion process results in
an asymmetrical three dimensional strain field through the thickness of a specimen has
been noticed by other researchers. Although no research has looked at whether
specimen thickness plays a role in this phenomenon, there is no doubt that there is a
difference in residual strain between the entry and exit faces of the coupon, even for the
thin 1.42-1.70 mm coupons used and that this difference plays a role in limiting the

296

fatigue life of a cold expanded coupon. One interesting approach to this problem has
been “double cold expansion” which involves performing cold expansion twice, but
changing the direction of the mandrel so that each face of the coupon has been both an
exit and an entry face. This type of procedure was modeled analytically by Jang and
Kim

143

144

and used experimentally by both Bernard et al

and Stefanescu

45

to extend

the fatigue life of open hole coupons. This “double cold expansion” is not that practical
in a production environment and cannot be used where only one face of a structure is
accessible. The fact that it does improve fatigue life supports the need to develop a
viable modification to the cold expansion process that could achieve this in a more
efficient manner.

One possible avenue of research would be to examine if the split sleeve cold expansion
mandrel could be modified to reduce the additional geometric constraint on the entry
face and thereby provide a more three dimensionally uniform cold expansion process.
96

This approach was examined briefly by O’Brien , who investigated reducing the
degree of taper at the mandrel head from 30º to 15º (Figure 159) as way of reducing the
strain rate during the cold expansion process. Although he did not directly compare the
effect that this modification had on the exit strains from a standard mandrel, a review of
his data indicated that this modification reduced the exit strains and may have a positive
96

145

effect on fatigue life . Chakherlou and Vogwell

tried a similar approach, modifying

the mandrel more significantly and reducing the taper to just over 1º. Although no
145

corroborating strain measurements were presented, Chakherlou and Vogwell

297

presented FEA and fatigue results that demonstrated a more even strain field around
the entry and exit faces, as well as fatigue crack nucleation occurring away from the
central hole.

Another possible approach would be to look at cold expansion methods that eliminate
the split sleeve. The strain measurements clearly showed that the split sleeve and the
material deformation resulting from it (Figure 168) have an effect on the residual strain
field. Although modifying the cold expansion process to remove the split has been the
146

subject of research by Karabin et al

, who showed some potential improvements with

a modified “split sleeve-less” method, in the current research, the strain concentration at
the location of the split did not appear to influence crack nucleation during fatigue
loading.

(b)

(a)

Figure 168: (a) Overview of open hole at the end of the cold expansion process.
Location of the split sleeve highlighted in white box. (b) Close up view of split sleeve
region with arrows highlighting deformation caused by the sleeve

298

The static setup used in this research program to make strain measurements during
cold expansion would be ideally suited to determining the effectiveness of new mandrel
designs. Using the same laser profilometer, the shape of the new mandrel could be
measured and through the use of that information, the resulting strain on the entry face
could be recorded and correlated to the effective interference of the mandrel as it
displaces through the coupon. Using a mirror setup, it might also be possible to make
concurrent measurements of the strain on the exit face as well. Investigation of a
chemical etching capability would also be complementary to many of the investigations
above, as this method could quantitatively address the issue of how much disbond
occurs on the entry and exit face after cold expansion.
12.2 FML Process Changes
During the manufacturing process, fiber metal laminate materials are particularly
susceptible to residual stress effects due to the mismatch in the coefficients of thermal
expansion between the 2024-T3 aluminum and the S2 glass prepregs. The proof of
concept work that was performed to measure these residual stresses using image
correlation showed that the new FML 4 variant has tensile residual stresses
approximately equal to those of FML 3 or FML 4. Lowering the tensile residual stresses
in the aluminum layer of the new FML 4 variant would be a simple way of improving its
fatigue performance compared to standard grade FML 3 or FML 4. A new lower
temperature cure process has been developed at NRC, specifically for FML and other
hybrid-like materials, and the residual stress measurement method mentioned above
would be ideal to quantify the change in residual stress resulting from this or other cure
cycles.

299

A more advanced possibility would be to look at new prepreg systems that could be
bonded to the aluminum without the need for a high temperature cure cycle. Combining
this with new more fatigue resistant grades of aluminum might allow for a more fatigue
resistant quasi-isotropic FML 4 variant, one that could perhaps be used in fatigue rated
applications.
12.3 Future work
One possible area for future investigation would be to examine non-destructive
evaluation technologies that would allow for real-time determination of the delamination
state in the outer and inner aluminum plies during fatigue cycling. Of special interest
would be an inspection process that could reveal the condition of the inner aluminum ply
in FML 4. Currently no non-destructive technology exists to do this, and researchers
who have examined the middle plies have had to rely on chemical etching of the
147

aluminum and mechanical abrasion of the prepreg

. One possible candidate

technology for looking at delamination in the outer aluminum plies would be lock-in
thermography or a variant thereof which might be capable of real time disbond
measurement.

Another area of investigation was inspired by an observation from the fatigue testing of
FML 4 [90/0/90] in various material orientations and the difference in fatigue life
between coupons from each of the orientations. This observation regarding the off-axis
fatigue life of FML was supported by the results of the ultrasonic inspection which
showed a significantly different area of disbond between coupons from the different
material orientations. However, relatively little regarding this phenomenon has been

300

discussed in the literature with the most comprehensive work to date done by
148,149

Kawai et al

who focused solely on FML 2 in addition to a paper by

147

Chang et al
147

et al

, who focused on notched FML 4 and FML 4 with starter cracks. Chang

made the observation that for off-axis laminates, the applied stress level in the

aluminum is increased leading to earlier “crack initiation”. From an engineering design
perspective, determining the stress in the aluminum layer of an FML is relatively
straightforward, using the analytical solution presented in Chapter 7.6. If a relationship
could be determined between the effective stress in the aluminum layers and the
corresponding fatigue life, then it might be possible to use this as a generic method to
predict the fatigue life of other FML 4 variants

301

13.0

CONCLUSIONS

The aim of this thesis was to produce a new FML variant optimized for both cold
expansion and riveting. To achieve this aim, three research objectives were proposed:

1. Experimentally measuring the strains in fiber metal laminates due to both the cold
expansion and riveting process and establishing the effect of these processes on
structural performance.
2. Developing a theoretical model that could be used to analytically predict the strains
resulting from the hole cold expansion and riveting process.
3. Develop and test new variants of FML, optimized with regards to standard
manufacturing processes such as cold expansion and riveting.
The broader conclusions from this research program have been grouped according to
each of the objectives and detailed below:
13.1 Experimental Measurements
The full-field strains resulting from cold-expansion and from riveting on various grades
of FML were measured using the digital image correlation technique. The
cold-expansion results showed how the residual strain field was dependent on the split
sleeve direction relative to the material orientation. These static strain measurements
showed that changing the direction of the split sleeve could significantly reduce the
magnitude of the residual strains, especially if the split was oriented at 45º degrees to
the longitudinal axis, which in FML 3 and FML 4, corresponded to the orientation with
lowest elastic modulus and lowest yield strength. It was this observation that

302

suggested that designing a more isotropic fiber metal laminate material would improve
performance after cold expansion and riveting.

An explanation for the mechanism behind the cold expansion process in FML was
provided by observing cross-sectioned micrographs of the interior plies in FML after
cold expansion. Indications of disbond close to the edge of the cold expanded hole
suggested that it was the introduction of compressive residual stresses into the
aluminum layers by the oversized mandrel that played the dominant role in extending
fatigue life, as it appeared that the glass fibers in the immediate vicinity of the cold
expanded hole disbonded due to the cold-expansion process.
13.2 Development of a Theoretical Model
An effective closed form solution for modeling stresses and strains in both aluminum
and FML 3 was presented. Reasonable corroboration was shown between the
analytical and experimental results for aluminum, while the best was corroboration was
achieved for FML 3.

Classical laminated plate theory was used to analytically predict the elastic modulus of
various grades of FML 4, each with a different prepreg layup. A comparison between
the results calculated using CLP and the experimental measurements showed that the
CLP derivation provided excellent estimates of the elastic modulus in all material
orientations. CLP theory was also used to estimate the residual strength of the panels
post-test and comparing the analytical results to those determined experimentally
provided valuable evidence to suggest that the inner aluminum was largely intact after
“fatigue failure”.

303

13.3 Development and Testing of New FML Variants
13.3.1 Fatigue Testing
The fatigue test results conclusively showed that the cold expansion process is effective
for all grades of FML tested, including the new FML 4 variant. Detailed correlation of
TSA and DIC data to fractography was used to elucidate crack development after both
cold expansion and riveting and proved that cold expansion extended life in the early
stage of the fatigue process more effectively on the exit face than on the entry face,
especially in aluminum.

For riveting, the combination of in-plane strains from the expansion of the rivet shank
and the compression from the rivet head was shown to be very effective at delaying
crack nucleation and shifting the nucleation location away from the central rivet hole.

Static tensile testing, post “fatigue failure”, showed that the compliance basis for
determining failure left all coupons with a significant amount of residual strength, with all
coupons showing a residual elastic modulus of at least 35% of their original value.

Analysis of the crack growth curves showed that, while cold expansion was effective at
reducing crack propagation rates, it was only minimally effective extending life in the
early stage of fatigue crack growth (defined as a crack growth to 1 mm). One possible
explanation for this was that the cold expansion process may result in delamination of
the aluminum in the annular region next to the cold expanded hole. As a result, while
the compressive residual stresses induced by cold expansion are quite effective at

304

reducing crack propagation for longer cracks, crack nucleation is only minimally
affected.
13.3.2 Effectiveness of Quasi-Isotropic FML 4 [60/0/-60]
Static tensile testing showed that the FML 4 variant with a quasi-isotropic layup had an
elastic modulus similar to that predicted by the closed form solution. Strain
measurements after cold expansion and riveting showed that this FML 4 variant had a
much more uniform residual strain field after cold expansion than either standard FML 3
or FML 4. Fatigue testing results showed that the fatigue life of the FML 4 variant was
relatively constant, independent of material orientation, and that it held significant
residual strength and stiffness after complete fatigue crack growth on both coupon
faces. Although a quasi-isotropic FML may not be ideal in high-cycle fatigue
applications, such as in an airplane fuselage, for static design applications or
applications with multiaxial loading and or unknown loading, this FML 4 [-60/0/60] may
prove to be extremely useful.
13.4 Summary
The aim of this research program, laid out in the introduction was met. Based on
experimental measurements of the strain field during cold expansion and riveting,
several new candidate FML variants were analyzed, manufactured, and tested. Of
these, a quasi-isotropic FML 4 variant [-60/0/60] showed promising results and was
subjected to additional testing. Comprehensive static and fatigue testing of this
FML 4 [-60/0/60] variant demonstrated that it did indeed show quasi-isotropic behaviour.
Although the modulus and fatigue life were lower than FML 4 [90/0/90] in the transverse
orientation, the static and fatigue properties were similar or better in all other
orientations. Overall, the FML 4 [-60/0/60] variant developed proved to be better suited

305

for cold expansion and riveting and would be an excellent addition to the standard
grades of FML that exist currently.

306

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