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This is to certify that the

dissertation entitled

THE INFLUENCE OF PROCESSING, CHEMISTRY,
AND INTERPHASE MICROSTRUCTURE ON THE
ADHESION OF CARBON FIBERS TO THERMOSET
AND THERMOPLASTIC MATRICES

presented by

MARK CORNELL WATERBURY

has been accepted towards fulfillment
of the requirements for

 

PH.D mgmem MATERIALS SCIENCE

W7. 9%

Major professor U

 

Date AIIGHSI 2. 1991

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emails-9.1

 

THE INFLUENCE OF PROCESSING, CHEMISTRY, AND INTERPHASE
MICROSTRUCTURE ON THE ADHESION OF CARBON FIBERS
TO THERMOSET AND THERMOPLASTIC MATRICES

By

Mark Cornell Waterbury

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Metallurgy, Mechanics, and Materials Science

1991

ABSTRACT
THE INFLUENCE OF PROCESSING, CHEMISTRY, AND INTERPHASE
MICROSTRUCTURE ON THE ADHESION OF CARBON FIBERS TO
THERMOSET AND THERMOPLASTIC MATRICES
By

Mark Cornell Waterbury

The adhesion of surface treated PAN-based carbon fibers to DGEBA epoxy,
a thermoset polymer, BPA-polycarbonate, an amorphous thermoplastic, and Nylon
6,6, a semicrystalline thermoplastic was investigated with an integrated set of surface
analysis and mechanical tests. Intermediate modulus Hercules 1M6 carbon fibers with
different amounts of electrochemical oxidative surface treatment were subjected to
XPS surface composition analysis and micro-Wilhelmy surface energy measurements,
and, along with treated and sized fibers, single fiber fragmentation tests, interlaminar
shear, transverse flexural, and mode II fracture toughness tests.

Increasing surface treatment increased surface oxygen, polar surface free
energy, and interfacial shear strength. Mode II fracture toughness increased with
increasing treatment, and with sizing. Interlaminar shear and transverse flexural
strengths increased with initial surface treatment, but leveled off as treatment
proceeded.

Carbon fiber adhesion to thermoplastic matrices was investigated with the
single fiber fragmentation test, and by observation of the failure modes by polarized
light microscope for amorphous polycarbonate, and by Confocal Scanning Optical
Microscopy (CSOM) for semicrystalline Nylon 6,6. Polycarbonate specimens were
fabricated by solvent deposition and by hot pressing, Nylon 6,6 Specimens by hot
pressing.

Carbon fiber adhesion to Lexan was found to reach a limiting value, regardless

of processing. Solvent deposition specimens showed very poor adhesion. Pure

Mark Cornell Waterbury
polycarbonate specimens showed adhesion increasing with consolidation time and
temperature.

Carbon fiber adhesion to Nylon 6,6 increased with development of a
transcrystalline sheath and with fiber surface treatment. CSOM observations of
fragmentation specimens revealed radial matrix cracks that interacted with the
interphase and spherulitic microstructure.

An experimental method was developed to measure fiber volume fractions in
unidirectional composites by an image analysis technique, Optical Numeric Volume
Fraction Analysis (ONVfA). An In Situ Fiber Strength test (ISFS) was developed to
accurately measure the strengths of fibers at short gage lengths, in situ.

An analysis of the single fiber fragmentation process was performed, failure
modes were discussed, and reproducible parameters associated with interfacial

properties were identified.

DEDICATION

To all who came before, for all who will follow.

iv

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LIST OF TABLES
LIST OF FIGURES

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TABLE OF CONTENTS

THE INFLUENCE OF THE FIBER-MATRIX INTERFACE ON

THE PROPERTIES OF FIBER REINFORCED COMPOSITE ......

SYNQPSIS ......................................
m IfRQDLlCTIQN .................................
CQMPQSITE PERFQRMANCE AND INTERFACE PRQPERIIES . .

CHEMISTRY CF THE FIBER/MATRIX INTERFACE ..........
MATERIALS IENCE OF THE FIBER/MATRIX INTERFA E . . .

SCALE EFFECTS ON INTERPHASE PROPERTIES ...........
CONSTRAINT EFFECTS ON INTERPHASE PROPERTIES ......
MICROSTRUCTURAL EFFECTS ON INTERPHASE PROPERTIES .
EXPERIMENTAL PRQGRAM OVERVIEW .................
ANALYSIS OF THE FRAGMENTATION TEST ..............
IN SITU FIBER STRENGTH TESTING ...................
OPTICAL NUMERIC VOLUME FRACTION ANALYSIS ........
FIBER SURFACE TREATMENT EFFECTS ON IM6/EPOXY .....
AMORPHOUS THERMOPLASTIC, BPA-POLYCARBONATE .....
SEMICRYSTALLINE THERMOPLASTIC, NYLON 6,6 .........

ON THE ACQUISITION AND INTERPRETATION OF
INFORMATION FROM THE SINGLE FIBER FRAGMENTATION

INTERFACIAL SHEAR STRENGTH TEST .................

ERACMENTATION TEST SYNOPSIS ....................
ERACMENTATION TEST INTRODUCTIQN ................

QVERVIEW QF THE SINCLE FIBER FRACMENTATIQN TESI

F_RA§MENTATION "PET FAILQRE MQDES . . . . . . . . . . . . . .' .'
INTERFACIAL FAILURE ............................

RADIAL MATRIX CRACKING ........................
INT ERPHASE YIELDING ............................

EIBER STRENGTH DISTRIBU I ICN EFFECTS ..............
EAILLJ RE MQDE INTERACTIQNS ......................

SFF SPECIMEN FABRICATION EFFECTS .................
FIBER SURFACE CONTAMINATION ....................

FIBER DAMAGE
STRESSES INDUCED BY MATRIX COOLING AND CURING

MEASURABLE FRAGMENTATION TEST PARAMETERS ......

STRESS BIREFRINGEN CE PATTERN

QBSERVAIIQN AND RECQRDINC .....................

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[EST DATA ACQUISITIQN .......................... 42
RELATIONSHIP TQ QTHER INTERFACIAL ADHESIQN TESTS . . 43
RA MENTATI N TE T N L I NS ................. 55
ON THE DETERMINATION OF FIBER STRENGTHS
BY IN-SITU FIBER STRENGTH TESTING ................. 56
N- I FIBER TRENG H TE T YN P I ............... 56
F INTR DU TI N ............................. 56
ISFS EXPERIMENTAL PRSEEDURE .................... 58
SINGLE FIBER FRAGMENTATION TEST ................. 58
IN-SIT U FIBER STRENGTH TEST ...................... 59
ISFS SPECIMEN FABRICATION ....................... 61
ISFS DATA ACQUISITION ........................... 62
ISFS CALCULATIONS .............................. 64
COMPUTER TENSION TEST SIMULATION ............... 65
ACOUSTIC EMISSION DETECTION ..................... 66
I FS RESULTS AND DIS U SI N ...................... 68
CQMPARISON OF ISFS AND CQNVENTIQNAL TENSICN TESTS . 74
I F N L I NS ............................... 75

DETERMINATION OF FIBER VOLUME FRACTIONS BY
OPTICAL NUMERIC VOLUME FRACTION ANALYSIS (ONVfA) . 76

QNVfA SYNOPSIS ................................. 76
QNVfA INTRODUCTIQN ............................ 76
QNVfA EXPERIMENTAL ............................ 83
NVfA E IPMENT ............................... 84
QNVfA SAMPLE CALCULATIONS ..................... 85
NVfA RES LT AND DI S l N .................... 86
ECTURE QNVFA WQRK ............................ 91
F N I N ............................. 92

EFFECTS OF OXIDATIVE SURFACE TREATMENTS ON FIBER
SURFACE CHEMISTRY, FIBER-MATRIX ADHESION AND
COMPOSITE MECHANICAL PROPERTIES OF INTERMEDIATE

MODULUS 1M6 CARBON FIBERS IN DGEBA/MPDA EPOXY . . . . 93
M6 YN P IS ................................... 93
1M6 INTRQDUCTIQN .............................. 94
1M6 EXPERIMENTAL PRQCRAM ........... , ........... 97
1M6 EXPERIMENTAL MATERIALS ..................... 97
CHARACTERIZATION OF FIBER SURFACE PROPERTIES ..... 100
XPS Surface Composition Analysis ....................... 100
Chemical Composition ............................... 101
Chemical Group Deconvolution ......................... 101
Micro-Wilhelmy Surface Energy Measurements ............... 101
Micro-Wilhelmy Balance System ......................... 105
Micro-Wilhelmy Experimental Program .................... 108
Fiber Surface and Cross Section Examination ................. 108
1M6 MECHANICAL TESTING ......................... 109
Fiber Tensile Strength Tests ........................... 109
Interfacial Shear Strength Tests .......................... 110
Fragmentation Specimen Fabrication ...................... 111

vi

5.3.3
5.3.3
5.3.3
5.3.3
5.3.3
5.3.3
5.3.3
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5.4.1
5.4.2
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Fabrication of Composite Specimens ...................... 113
Volume Fraction Analysis by ONVfA ..................... 116
Mode 11 Fracture Toughness Tests ........................ 116
Transverse Bending Tests ............................. 116
Short Beam Shear Tests .............................. 116
SEM Fractography of Mode II and Trasverse Flexure Surfaces ...... 117
Birefringence Evolution Sequence Acquisition ................ 117
IMQ RESULTS AND INTERPRETATIQN ................. 120
FIBER SURFACE ANALYSIS RESULTS .................. 120
Surface Chemical Composition Results ..................... 120
Chemical Group Deconvolution Results .................... 124
Micro-Wilhelmy Surface Energy Results .................... 126
Fiber Surface and Cross Section Examination Results ............ 130
MECHANICAL TEST RESULTS ........................ 133
Fiber Tensile Strength Results .......................... 133
Fiber Volume Fractions and Distributions ................... 135
Interfacial Shear Strength Results ........................ 139
Birefringence Evolution Sequence Interpretations ............... 144
Mode 11 Fracture Toughness Results ...................... 153
Transverse Flexural Results ............................ 155
Interlaminar Shear Strength Results ....................... 158
SEM Fractographic Analysis ........................... 160
W ............................... 171

THE INFLUENCE OF PROCESSING TIME, TEMPERATURE,
AND MATRIX COMPOSITION ON THE ADHESION OF

 

CARBON FIBERS TO BlSPHENOL-A POLYCARBONATE ...... I76
POLYCARBONATE SYNOPSIS ........................ 176

LY ARB NATE INTROD CTI N .................... 176
BQLYCARBONATE EXPERIMENTAL MATERIALS .......... 178
EQLYCARBQNATE EXPERIMENTAL PROCEDURE .......... 179
HOT PRESSED SPECIMEN FABRICATION ................ 179
SOLVENT DEPOSITED SPECIMEN FABRICATION .......... 182
DATA ACQUISITION AND ANALYSIS ................... 182
BIREFRINGENT IMAGE ACQUISITION .................. 183

LY ARBONATE RE LT AND Dl I N ........... 183
SOLVENT PROCESSED SPECIMENS .................... 183
SOLVENT-FREE SPECIMENS ......................... 186
INTERPRETATION OF BIREFRINGENCE PATTERNS ......... 189
EQLYCARBQNATE CONCLUSIQNS ..................... 195

THE INFLUENCE OF FIBER NUCLEATED CRYSTALLIZATION
ON INTERFACIAL SHEAR STRENGTHS AND FAILURE MODES

OF CARBON FIBERS IN NYLON 6,6 .................... 196
NYLON YN PSIS .............................. 196

YL N INTR D TI N ......................... 196

YL N EXPERIMENTA PR ED RE ............... 199
NYLONN 6,6 EXPERIMENTAL MATERIALS ............... 199
FABRICATION OF NYLON 6,6 188 SPECIMENS ............ 200
NYLON 6,6 FRAGMENTATION TESTING ................. 201
NYLON 6,6 RESULTS AND DISCUSSION ................. 202
NYLON 6,6 188 RESULTS ........................... 202

vii

RI. "I. Nil. . . . . .

7.4.2 MICROSTRUCTURE AND FAILURE MODE OBSERVATIONS . . . 205
7.4.3 HEATED STAGE MICROSCOPE OBSERVATIONS ........... 221
7.5 N N I .......................... 221
8.0 CONCLUSIONS .................................. 222
8.1 ERACMENTATIQN TEST CONCLUSIUNS ................. 222
8.2 ISFS CQNCLUSIQNS ............................... 223
8.3 QNVFA CONCLUSIONS ............................. 223
8.4 1M6 CONCLUSIONS ............................... 223
8.5 P LY ARB NATE ON L 1 NS ..................... 224
8.6 NYLON 6,6 CONCLUSIQNS .......................... 225
8.7 M THERM PL TI MA X N L I N . 225
APPENDICES

APPENDIX A. SOURCE CODE FOR FIBERTRACK, SINGLE FIBER
FRAGMENTATION TEST DATA ACQUISITION AND ANALYSIS SYSTEM . 228

APPENDIX B. SOURCE CODE FOR FIBERLINK, IN SITU FIBER
STRENGTH FRAGMENTATION TEST DATA ANALYSIS SYSTEM ....... 245

APPENDIX C. SOURCE CODE FOR OPTICAL NUMERIC
VOLUME FRACTION ANALYSIS SYSTEM ....................... 263

APPENDIX D. SOURCE CODE FOR WILHELMY WETTING
BALANCE DATA ACQUISITION AND ANALYSIS SYSTEMS ........... 294

REFERENCES .......................................... 3 12

viii

Table 1.
Table 2.
Table 3.
Table 4.
Table 5.
Table 6.
Table 7.
Table 8.
Table 9

Table 10.
Table 11.
Table 12.
Table 13.
Table 14.
Table 15.
Table 16.

LIST OF TABLES

Flaws per 25 mm @ strain increment for A84 fibers. ........... 68
In situ and ex situ A84 fiber strengths. .................... 72
Volume fractions by ONVfA and acid digestion. .............. 87
Void volume fractions by areal analysis and acid digestion. ....... 90
Properties of 1M6 carbon fibers summarized from Hercules data sheet. 98
Surface oxygen, nitrogen, and functional groups on 1M6 fibers. . . . . 121
Polar, dispersive, and total surface free energy on 1M6 fibers. ..... 127
Critical lengths, Lch’s, tensile strengths, and 188 for 1M6 fibers. . . . 135
Fiber and void volume fractions by ONVfA. ................ 136
Mode 11 fracture toughness for IM6/epoxy composites. .......... 154
Transverse fiexural strengths and moduli for IM6/epoxy composites. . 157
Interlaminar shear strengths for IM6/epoxy composites. ......... 159
Properties of Lexan 141 polycarbonate resin. ................ 179
Matrix type, processing, L,/D’s, and 188 for A84 in Lexan 141. . . . . 184
Matrix type, processing, LJD’S, and 188 for A84 in PC. ........ 187

Processing, LJD, and 188 for Nylon 6,6 matrices. ............ 204

ix

Figure 1.
Figure 2.
Figure 3.
Figure 4.
Figure 5.
Figure 6.
Figure 7.
Figure 8.
Figure 9.

Figure 10.
Figure 11.
Figure 12.
Figure 13.
Figure 14.
Figure 15.
Figure 16.
Figure 17.
Figure 18.
Figure 19.
Figure 20.
Figure 21.
Figure 22.
Figure 23.
Figure 24.
Figure 25.
Figure 26.
Figure 27.
Figure 28.
Figure 29.
Figure 30.
Figure 31.
Figure 32.
Figure 33.
Figure 34.
Figure 35.
Figure 36.
Figure 37.
Figure 38.
Figure 39.
Figure 40.
Figure 41.
Figure 42.

LIST OF FIGURES

Cross sectional diagram of fiber, interphase, and matrix. ......... 13
Diagram of single fiber fragmentation specimen. .............. 16
Approximate tensile stress distribution in fragmentation test.
Slightly more realistic tensile stress distribution in fragmentation test. . 18

Interfacial failure by stick-slip Mode 11 cracking. ............. 22
Fiber failure strain energy effects on interfacial failure ........... 28
Fiber strain energy effects at higher coupon strain. ............ 28
Diagram of fiber strain energy effects on shear stress transfer. ..... 29
Diagram of fiber failure strain effects on interphase yielding. ...... 30

Birefringence patterns for 8 breaks in A84 fiber, 1.3% coupon strain. 36
Birefringence patterns for 8 breaks in A84 fiber, 1.5% coupon strain. 36
Birefringence patterns for 8 breaks in A84 fiber, 1.8% coupon strain. 37
Birefringence patterns for 8 breaks in A84 fiber, 2.0% coupon strain. 37
Birefringence patterns for 8 breaks in A84 fiber, 2.3% coupon strain. 38
Birefringence patterns for 8 breaks in A84 fiber, 2.5% coupon Strain. 38
Birefringence patterns for 8 breaks in A84 fiber, 2.7% coupon strain. 39
Birefringence patterns for 8 breaks in A84 fiber, 3.0% coupon strain. 39

Rasterized integration of birefringence patterns to detect yielding. . . . 41
Symmetric mode 11 crack in homogeneous material. ............ 45
Asymmetry of mode 11 crack between dissimilar materials. ....... 45
Crack growth habits for 4 crack initiation and loading conditions. . . . 47
Symmetry of interfacial cracking for fragmentation test. ......... 49
Symmetry of interfacial cracking for pullout test. ............. 51
Symmetry of interfacial cracking for droplet pullout test .......... 52
Symmetry of interfacial cracking for short fiber. .............. 53
Symmetry of interfacial cracking for indentation test. ........... 54
Fragmention stresses and polling lengths. .................. 59
Straining stage for single fiber fragmentation test. ............. 60
Block functional diagram of FiberTrack/FiberLink. ............ 63
Fiber break positions recorded by F iberTrack. ............... 64
AE trace from carbon fiber failure. ...................... 67
Flaws vs strain increment by specimen in PC. ............... 69
Flaws vs strain for A84 fibers in PC and epoxy. .............. 70
Flaws vs strain and exponential curves. ................... 71
In-situ and ex-situ fiber strengths. ....................... 72
Digitized image of graphite/epoxy composite ................. 79
Same image with fibers counted and tagged. ................ 79
Boxes shaded to indicate number of fibers. ................. 80
Fiber map, one white pixel per fiber. ..................... 81
Block areal density map, (fibers/box). .................... 82
Fiber areal density distribution function. ................... 82
Fiber maps and distributions for HP], 2, and 3. .............. 88

Figure 43.
Figure 44.
Figure 45.
Figure 46.
Figure 47.
Figure 48.
Figure 49.
Figure 50.
Figure 51.
Figure 52.
Figure 53.
Figure 54.
Figure 55.
Figure 56.
Figure 57.
Figure 58.
Figure 59.
Figure 60.
Figure 61.
Figure 62.
Figure 63.
Figure 64.
Figure 65.
Figure 66.
Figure 67.
Figure 68.
Figure 69.
Figure 70.
Figure 71.
Figure 72.
Figure 73.
Figure 74.
Figure 75.
Figure 76.
Figure 77.
Figure 78.
Figure 79.
Figure 80.
Figure 81.
Figure 82.
Figure 83.
Figure 84.
Figure 85.
Figure 86.
Figure 87.
Figure 88.
Figure 89.
Figure 90.
Figure 91.
Figure 92.
Figure 93.
Figure 94.

Fiber maps and distributions for AC1, 2, and 3. ............. 89
Fiber fractions by ONVfA and Acid Digestion ................ 91

Chemical structures of epoxy precursors. .................. 99

Surface tension influence on contact angles. ................. 102
Fiber wetting force and contact angle measurement. ............ 104
Block diagram of micro-Wilhelmy wetting balance. ............ 106
Single fiber fragmentation test specimen .................... 111
Mechanical test specimen diagrams. ...................... 115
Surface oxygen percentage by XPS. ...................... 122
Surface nitrogen percentage by XPS. ..................... 123
Surface functional groups versus surface treatment. ............ 125
Fiber surface free energy versus surface treatment. ............ 127
Polar free energy versus surface oxygen percentage. ........... 129
SEM of fiber surface morphology #1. .................... 131
SEM of fiber surface morphology #2. .................... 131
SEM of fiber cross-section, #1. ........................ 132
SEM of fiber cross-section, #2. ........................ 132
Extrapolation of fiber tensile Strengths to critical lengths. ........ 134
Fiber volume fractions and distributions for 24 ply laminates. ...... 137
Fiber volume fractions and distributions for 12 ply laminates. ...... 138
Interfacial shear strengths for 1M6 fibers. .................. 140
Interfacial shear Strengths for 1M6 and A4. ................. 141
I88 versus surface oxygen and polar surface free energy. ........ 142
188 and functional groups versus surface treatment. ............ 143

Birefringence sequence for Untreated 1M6 fiber. .............. 147
Birefringence sequence for 20%ST 1M6 fiber. 148

Birefringence sequence for 100%8T 1M6 fiber. .............. 149
Birefringence sequence for 200%8T 1M6 fiber. .............. 150
Birefringence sequence for 600%8T 1M6 fiber. .............. 151
Birefringence sequence for lOOGST 1M6 fiber. ............... 152
Mode 11 fracture toughness for 1M6 composites. .............. 154
Transverse flexural strengths for 1M6 composites. ............. 157
Interlaminar shear strengths for 1M6 composites ............... 159
SEM @ 200x, untreated mode 11 fracture. ................. 161
SEM @ 200x, 20% treated mode 11 fracture. ............... 161
SEM @ 200x, 100% treated mode 11 fracture. ............... 162
SEM @ 200x, 200% treated mode II fracture. ............... 162
SEM @ 200x, 600% treated mode 11 fracture. ............... 163
SEM @ 200x, 100% GST sized mode 11 fracture .............. 163
SEM @ 1000X, untreated mode 11 fracture. ................. 164
SEM @ 1000X, 20% treated mode 11 fracture. ............... 164
SEM @ 1000X, 100% treated mode 11 fracture. .............. 165
SEM @ 1000X, 200% treated mode 11 fracture. .............. 165
SEM @ 1000X, 600% treated mode 11 fracture. .............. 166
SEM @ 1000X, 100% GST sized mode 11 fracture. ............ 166
SEM @ 500x, Untreated transverse flexural fracture. .......... 168
SEM @ 500x, 20%ST transverse flexural fracture. ............ 168
SEM @ 500x, 100%ST transverse flexural fracture. ........... 169
SEM @ 500X, 200%ST transverse flexural fracture. ........... 169
SEM @ 500x, 600%ST transverse flexural fracture. ........... 170
SEM @ 500x, lOOGST transverse flexural fracture. ........... 170
Mode 11 fracture toughness versus 188. .................... 172

xi

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Figure 95.
Figure 96.
Figure 97.
Figure 98.
Figure 99.

Figure 100.
Figure 101.
Figure 102.
Figure 103.
Figure 104.
Figure 105.
Figure 106.
Figure 107.
Figure 108.
Figure 109.
Figure 110.
Figure 111.
Figure 112.
Figure 113.
Figure 114.
Figure 115.
Figure 116.
Figure 117.
Figure 118.
Figure 119.
Figure 120.
Figure 121.
Figure 122.
Figure 123.
Figure 124.
Figure 125.
Figure 126.
Figure 127.
Figure 128.
Figure 129.

Interlaminar shear strength versus 188. .................... 174
Summary of mechanical test results versus surface treatment. ...... 175
Chemical structure of BPA polycarbonate. .................. 179
Fixture for hot pressing single fiber specimens. .............. 181
Spin coating fixture for solvent deposition specimen fabrication. . . . . 182
Interfacial shear strengths for A84 in Lexan 141. ............. 185
Interfacial shear strengths for A84 in pure polycarbonate. ........ 186

Solvent deposited Lexan matrix birefringence pattern ............ 191

Fast cooled Lexan matrix birefringence pattern. .............. 191
Slow cooled Lexan matrix birefringence pattern. .............. 191
Pure polycarbonate matrix birefringence pattern. .............. 191
Surface of annealed polycarbonate. ...................... 192
Possible polycarbonate crystalline sheath around A84 fiber. ....... 193
Crazed polycarbonate fragmentation specimen. ............... 194
Chemical structure of Nylon 6,6 - poly(hexamethyl adipamide). . . . . 200
Interfacial shear strengths of carbon fibers in Nylon 6,6. ......... 204
Four CSOM micrographs of transcrystallinity in Nylon 6,6. ....... 206
TOM of AU4 breaks in Nylon 6,6. ...................... 208
TOM of A84 break in rapidly cooled Nylon 6,6 ............... 209
TOM of A84 break in Nylon 6,6 slowly cooled from 275 °C. ..... 210
TOM of A84 in Nylon 6,6 cons. @ 275 °C, iso-xtal @ 225 °C. . . . . 211
TOM of A84 in Nylon 6,6 cons. @ 300 °C, iso-xtal @ 225 °C. . . . . 212
Interfacial shear strength versus radial crack diameter. .......... 214
CSOM of A84 break initiated interspherulitic crack #1. ......... 215
CSOM of A84 break initiated interspherulitic crack #2. ......... 215
CSOM of A84 break initiated intraspherulitic cracks #1. ......... 216
CSOM of A84 break initiated intraspherulitic cracks #2 ......... 216
CSOM of A84 break initiated transcrystalline crack #1. ......... 217
CSOM optical section of A84 break in Nylon 6,6, Z: 2.35. ...... 218
CSOM optical section of A84 break in Nylon 6,6, Z= 3.6. ....... 218
CSOM optical section of A84 break in Nylon 6,6, Z= 4.8. ....... 219
CSOM optical section of A84 break in Nylon 6,6, Z= 6.0. ....... 219
CSOM optical section of A84 break in Nylon 6,6, Z= 7.2. ....... 220
CSOM optical section of A84 break in Nylon 6,6, Z= 8.45 ....... 220
188 of AU4 and A84 fibers in thermoset and thermoplastic matrices. . 226

xii

CHAPTER 1

THE INFLUENCE OF THE FIBER-MATRIX INTERFACE ON THE
PROPERTIES OF FIBER REINFORCED COMPOSITES

1.1 SYNOPSIS

An outline of the research program, and its motivation is given in this section.

The background of the research effort in this area is briefly described.

1.2 INIRODUCTIQN

The fiber/ matrix interface may be thought of as the center of a composite
material. Since a composite is, by definition, a material with at least two distinct
phases, separated by an interface, all composites rely upon some degree of interfacial
adhesion. Depending on the desired properties, the optimal value of this adhesion for
a given composite application may be as high as possible, or it may be much lower
to deliberately facilitate debonding. An intermediate level of interfacial adhesion that
provides good strength values while preventing brittle failure modes is commonly the
most desirable compromise.

The complexity of failures in composites, even under the idealized conditions
of carefully controlled laboratory tests, makes the understanding of composite failure
in terms of basic mechanisms extremely difficult. Since the interface lies at the core
of the most complex interactions within the composite, interfacial effects are even
more difficult to adequately model than those involving failure initiated within the
fibers or matrix.

While the motivation for this research is driven partly by the necessity to
improve the understanding of the linkage between interface and composite properties

to insure adequate and predictable composite performance, there are also opportunities

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to achieve significant property improvements which are not yet fully exploited.

1.3 CQMPQSIIIE PERFQRMANCE AND INTERFACE PRQPERIIES
The relationship between the performance of composite materials and

interfacial properties is under intensive investigation. Composite behavior models
have often met with little quantitative success, however, due to the inherent
complexity of the mechanics and failure of multiphase materials. Attempts have been
made to develop performance models based on integrated micromechanical and
macromechanical criteria, developed along the lines of Griffith’s criterion for failure
[Mahishi, 1986], and using finite element method models [1(olle, 1990]

A more common, and less abitious approach is based on the investigation of
changes in composite failure mode with differences in interfacial adhesion. For
instance, Shih [1986] found that a change from compressive to flexural failure
occurred in unidirectional composites subjected to four point bending when interfacial
strengths were reduced. A failure mode transition diagram was constructed to
represent this process.

Another approach to understanding composite performance has been to perform
integrated sets of mechanical tests on a range of composites [Curtis, 1987]. By noting
relationships between the fiber, matrix and interface characteristics of a variety of
systems and the resultant composite performance, conclusions about the influence of
each were drawn.

Numerous researchers have used the single fiber fragmentation test to evaluate
failure mode transitions along with interfacial shear strengths, including [Dibenedetto,
1985, 1986], [Drzal, 1980 (B), 1982], [Wimolkiatisak, 1989] and many others. While
fragmentation test failure modes may, or may not, directly correspond to changes in

behavior of the macroscale composite, due to the differences in loading conditions,

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this technique allows composite failures to be studied in microcosm.

1.4 EMI TRY F FIBER/MATRIX INTERFACE

The chemistry of the fiber/ matrix interface region has been the object of
extensive investigation and is the basis for many of the models of fiber/matrix
adhesion. Chemically based fiber/matrix bonding may involve primary chemical
bonds, hydrogen bonding, or the various forms of dispersion bonding (dipole-dipole,
dipole-induced dipole, etc.). There have been numerous attempts reported in the
literature to resolve adhesion into these components.

The reinforcing fibers used in modern composites include the PAN-based
carbon fibers investigated in this study, glass fibers, liquid crystal polymer fibers
(Kevlar), other polymer fibers (U HMW polyethylene), and inorganic, crystalline
materials, (Silicon carbide, alumina, etc.). Each class of fiber presents its own set of
adhesion challenges. In some cases these challenges have largely been met, i.e., the
success of silane coupling agents with glass fibers. In others interfacial adhesion is
generally sufficient, as with metal matrix composites, but other problems such as fiber
degradation by diffusion of the matrix continue to present problems. For carbon
fibers the adhesion issue presents a ”moving target” as a result of changing processing
methods for the fibers continue to increase the axial properties, strength and modulus,
while tending to degrade the transverse properties, such as interlaminar shear strength
and toughness.

A general model of adhesion of polymers to inorganic surfaces has been
proposed by Plueddemann, based on the behavior of silane coupling agents and glass
reinforcements [Plueddemann, 1970]. This model proposes that a dynamic
equilibrium exists at the interface and that resistance to an aqueous environment, for
instance, results from the equilibrium favoring coupling of polar groups within the

polymer to the surface.

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The nature of bonding to fibers is the object of extensive investigation and
debate. Fibers treated with bromine, have been shown to have improved adhesion
and to change in electrical conductivity. These changes have been attributed both to
the formation of an intercalant with bromine situated between graphite planes,
[Jaworske, 1986] and to primary chemical bond formation, [Jaworske, 1987]. The
structure of carbon fibers involves some degree of microporosity, [Denison, 1988],
[I-lughes, 1990], as indicated by a somewhat lower density than that for solid graphite.
Denison, et al have suggested that these micropores may absorb polymer chains and
promote bonding. With polymer chains sufficiently deeply absorbed, interfacial shear
strengths may approach those expected for primary chemical bonds even when only
dispersion type forces are active.

The chemical properties of graphite edge planes have been investigated by
Raman spectroscopy, [Katagiri, 1988]. They have found that Raman spectra from the
edges of graphite planes differ from those of the cleaved basal planes in displaying
bands at 1355 cm" and 1620 cm". They attribute this difference to the discontinuity
in the structure, and suggest that Raman spectra may serve as an indication of the
degree of graphitization.

The acid-base properties of surface treated carbon fibers have been investigated
by [Wesson, Allred, 1990], (Watts, 1991] and many others. Adhesion may also be
attributed to London dispersion forces, especially with thermoset matrices where small

monomer units can interact with a high proportion of surface sites.

1.5 MATERIALS SCIENCE CF THE FIBERZMATRIX INTERFACE
The understanding of the properties of the fiber/ matrix interface region, or

”interphase” or ”mesophase" as it is now called, is largely dependent upon
extrapolation of material properties measured in macro-scale specimens. This

extrapolation is complicated by differences in chemical composition, size, constraint

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conditions, and microstructure that are often unknown and immeasurable. As
discussed in the previous section, differences in chemical composition can arise from
segregation to or away from the interface, or physisorption or chemisorption of matrix
constituents by the fiber surface. These differences can lead to an interphase with
significantly changed basic material properties from the bulk material.

Even in the absence of compositional differences, however, the properties of
the matrix in the vicinity of a surface may be substantially different. Some sources
of these differences include scale effects, constraint effects, and microstructural

effects. These influences are discussed in the following sections.

1.5.1 SCALE EFFECTS ON INTERPHASE PROPERTIES

The limiting properties of composite interphases have often been compared
with the strength and other failure characteristics of the bulk matrix. This
interpretation neglects the changes in material behavior that occur in identical systems
at different size scales, because smaller specimens tend to have smaller flaws. Glass
in macroscopic form, for example, is extremely brittle and low in strength, 7 to 140
MPa for "off the shelf" glass rods. Surface defect free silica, in contrast, Shows
strengths in the 3-5 GPa range [Kelley, 1986]. While this strength increase does not
result from smaller specimens [Kelley, 1986] but from the greater stress concentration
at the tip of larger defects [Griffith, 1921, 1924], similar effects appear to influence
the strength and extent of plastic deformation of adhesives [Stringer, 1985] and
matrices [Bascom, 1985].

1.5.2 CONSTRAINT EFFECTS ON INTERPHASE PROPERTIES
The constraint imposed on the low modulus polymeric matrix by the much
higher modulus fiber causes a change in material properties within the "interphase” ,

the matrix material in close proximity to the fiber. The thickness of this interphase

'Il‘an

6

depends to some degree upon how it is defined, that is, on how much different its
properties must be from the bulk matrix material. A theoretical approach to
determining the interphase thickness has been proposed, however, and may be used
to analytically evaluate this thickness and compare it with experimental properties
[Theocaris, 1985, 1986]. This model is based on measurements of the moduli of the
fiber, matrix, and composite along with basic assumptions about the continuity of
properties between the interphase, the fiber, and the bulk matrix. The interphase-
thickness has also been evaluated by a thermal analysis technique, [Sideridis, 1988]
which is based upon measurements of discontinuities in the heat capacity at the glass
transition temperature that result from the decreased mobility of the polymer chains
in the vicinity of the fiber.

1.5.3 MICROSTRUCTURAL EFFECTS ON INT ERPHASE PROPERTIES
Although the surfaces of carbon fibers generally appear to be smooth, except
for axial striations, at all size scales visible by either optical or scanning electron
microscopy, at smaller scales considerable topographic roughness is evident.
Scanning tunneling microscope (STM) of carbon fibers are beginning to appear in the
literature and should help to clarify the role of mechanical interlocking in fiber/ matrix
adhesion. Hoffman, Elings, and Gurley [Hoffman, 1988] have published STM images
of pitch—based Amoco P-55 carbon fibers at size scales ranging from the tens of
nanometers to atomic scales. The apparent roughness was found to vary considerably
depending on size, being very rough at the nanometer scale, and much smoother as
the image came to include only the surface of a single graphite crystallite. Although
these images were very difficult to produce, the increased availability of STMS should
make their application to comparative studies of carbon fibers commonplace.
Semicrystalline therrnoplastics generally develop what has been termed a

"transcrystalline" interphase resulting from nucleation of polymer crystals by the

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surface of the fiber or by Shear strains along the fiber surface. This interphase has
a strongly oriented structure with anisotr0pic moduli and strengths. These values may
not be determined by measurement of bulk material properties due to the
fundamentally diffement microstructures.

Microstructural changes also occur as a result of segregation of low molecular
weight components of the matrix toward the interface. The decrease in chain mobility
of these components in the fiber vicinity is less than that of the higher Mw
constituents, resulting in a free energy driving force. This segregation may occur for
thermosets during the curing process, and for amorphous or semicrystalline

thermoplastics during consolidation.

1.6 E ALP RAM VE VEW

This section provides an overview of the experimental and theoretical program
undertaken for this work and attempts to show how the several parts of the program
are directed toward an improved understanding of the influence of fiber/ matrix
interface characteristics on composite performance. The program consists of three
sections that are intended to enhance the experimental tools available for composite
interface research, and three sections that are applications of these tools to different
classes of matrices. The experimental tools investigated are the fragmentation test
described in Chapter 2 which is used as a probe of the fiber/ matrix interphase
properties and failure modes, the in situ fiber strength test in Chapter 3 which can be
used to obtain information on the short gage length fiber strengths that are required
by models of composite properties, and the optical numeric volume fraction analysis
method in Chapter 4 that can be used to investigate the influence of fiber fraction and
distribution on composite properties. The applications consist of investigations of
fiber/ matrix adhesion for carbon fibers to thermoset epoxy (Chapter 5), to
polycarbonate, an amorphous thermoplastic (Chapter 6), and to Nylon 6,6, a

 

53

8
semicrystalline thermoplastic (Chapter 7). These systems were chosen to represent
the three most common classes of polymer matrices in an effort to develop an
understanding of the similarities and differences in fiber/ matrix adhesion for these
cases.
The motivation and background for these investigations are outlined in the

following sections.

1.6.1 ANALYSIS OF THE FRAGMENTATION TEST

The single fiber fragmentation interfacial Shear strength test has formed the
basis of many fiber/ matrix interface studies in recent years, and is exploited in the
current work as well. Although its principal advantage is the relative Simplicity of a
system comprised of only a single fiber compared with vastly more complex
composite systems, there is still enough complexity to generate a wide range of
interpretations among researchers.

In the course of these investigations the author has developed his own
interpretations and insights into the mechanisms involved in the fragmentation test and
into the kinds of information that may be available from it. This analysis of the
fragmentation test is intended to convey these insights in the hopes that they will
benefit future work. The analysis is not intended to be a complete review of the

method, which is beyond the scope of this work.

1.6.2 IN SITU FIBER STRENGTH TESTING

Perhaps the most fundamental of the properties of the constituents of composite
materials is the strength of the reinforcing fibers. The remarkably high strengths of
modern, low defect fibers is the foundation on which the entire composites industry
is built. The development of models of the strength of composites usually depends

upon information about fiber strengths at the Shortest gage lengths that can be fully

9
loaded through the interface. The Weibull analysis of fragmentation tests also
requires information about short gage length fiber strengths.

In addition to theoretical interest, direct measurements of fiber strengths in situ
may prove to be a powerful tool for process optimization. Although the fibers in
polymer matrix composites are generally only damaged to a minimal degree by
handling during the fabrication process, in metal matrix composites fiber surfaces are
subjected to diffusion and attack by the melt as an integral part of the consolidation
process. Indeed, the development of good interfacial strength is dependent upon the
same diffusional penetration of the fiber by the matrix that eventually leads to the
degradation of fiber strength. The in situ strengths of fibers in such systems will, in
general, be significantly different from their ex situ, virgin values. A great deal of
work has been done to develop coatings to protect metal matrix reinforcement fibers
from diffusional damage. The assesment of the performance of these coatings
requires that the fiber strengths be measured in situ, following the complete
consolidation process.

Numerous researchers, including the author, have recently independently
suggested that fiber strength information is available from the fragmentation test
[Waterbury, 1990], [Wagner, 1989], [Henstenburg, 1989], [Figueroa, 1990]. A
theoretical development of a simple, robust experimental technique for single fiber
fragmentation in situ fiber strength testing and an experimental verification of this

approach appears in Chapter 3.

1.6.3 OPTICAL NUMERIC VOLUME FRACTION ANALYSIS

The distribution of fibers within the matrix material must be sufficiently
uniform for the translation of the high performance properties of the fibers to the
composite material to be efficient. High performance aerospace-grade composites

require a high volume fraction of well distributOd fibers with low void content and

10
minimal direct fiber-fiber contact.

Fiber volume fractions have largely been measured by digestion of the matrix
material by an acid or other solvent, providing only averaged values with no
information on the distribution of fibers and voids. Optical numeric volume fraction
analysis (ONVfA) measures volume fractions by counting the numbers of fibers in
optical microscope images of composite cross sections. These measurements are
accurate and reproducible, and provide information on the volume fraction distribution
at the finest possible scale, that of the fibers. By comparisons with the distribution
of voids measured by areal image analysis, it is possible to develop a complete
mapping of the fibers, voids, and matrix components in a composite. These data may
be used in the interpretation of mechanical test results to gain an improved
understanding of the influence of matrix rich areas, voids, and other distribution

effects on composite performance.

1.6.4 FIBER SURFACE TREATMENT EFFECTS ON IM6/EPOXY

The carbon fiber/epoxy resin interface has been one of the most extensively
studied composite interfaces. This activity has been motivated by the difficulty of
achieving adequate bonding to a fiber surface that is mostly comprised of extremely
unreactive graphitic carbon, and by the wide usage of these materials as high
performance composites. Although the problem is far from intractable, many
effective surface treatments having been developed, no completely successful
approach, such as the use of silane coupling agents with glass fibers, has been
developed. Moreover, changes in carbon fiber production methods have tended
toward higher moduli, higher strength fibers with more highly oriented graphitic
carbon surfaces that are more difficult to adhere to.

The core of this research effort consists of an integrated set of

micromechanical and macromechanical tests on intermediate modulus, Hercules

1 1
Magnamite" 1M6 fibers with different surface treatments, coupled with measurements
of the fiber surface atomic and molecular compositions and free energies. The
surface treatments investigated include a series of electrochemical oxidative treatments
that are proprietary to Hercules0 and so cannot be fully reported, but which represent

different extents of the standard commercial preparation for these fibers.

_ 1.6.5 AMORPHOUS THERMOPLASTIC, BPA POLYCARBONATE

Although most current composite matrices are thermoset polymers, there are
numerous advantages to thermoplastic materials for this application. Chief among
these is a substantial reduction in fabrication time, an essential development for the
use of composites in high volume, low cost applications. An additional advantage
involves the greater toughness of thermoplastics compared with thermosets. The
exploitation of this advantage requires that improvements are made in fiber/ matrix
adhesion for thermoplastic matrix systems.

Adhesion in thermoset matrix composites may involve the formation of primary
chemical bonds between the fiber surface, or chemisorbed surface species, and the
highly reactive matrix precursors. Thermoplastics, in contrast, have already
undergone polymerization and are much less reactive. Primary chemical bond
formation is therefore extremely unlikely. Adhesion is probably dependent entirely
upon physisorption driven by dispersion forces and upon mechanical interlocking.
Mechanical interlocking may be significantly augmented by the possibility of partial
intercalation of the polymer chains into the graphitic "mosaic" structure, however.
Levels of adhesion in thermoplastics that approach those of thermoset matrices have

been reported.

1.6

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12
1.6.6 SEMICRYSTALLINE THERMOPLASTIC, NYLON 6,6

Fiber/ matrix adhesion in semicrystalline thermoplastic matrices is complicated
by the intricate morphology of the spherulitic microstructures of the bulk matrix and
by the influence of fiber-nucleated crystallization of the matrix. Failure modes within
both macro and micro composites must interact in some way with this anisotr0pic and
inhomogeneous interphase. Even in the absence of failure, changes may still be
expected in the transfer of shear stresses between the fiber and matrix because of the
anisotropy in the moduli of the oriented transcrystalline structure.

A schematic ”cartoon" of some of the factors involved in fiber/ matrix adhesion
appears in Figure 1. Adhesion may be effected by primary chemical bonds,
secondary, London dispersion forces or acid-base interactions, mechanical
interlocking, the stiffness of the interphase region, or any combination of these

factors. An attempt to elucidate the roles of these factors comprises this dissertation.

l3

  
 
 
 
 
 
     
    
 
 

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Axial Striations

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Graphitic mosaic surface structure.
atomically smooth within crystallites
but rough on larger scales.

"Onion" skin-core
morphology

Figure 1. Cross sectional diagram of fiber, interphase, and matrix.

CHAPTER 2

ON THE ACQUISITION AND INTERPRETATION OF INFORMATION
FROM THE SINGLE FIBER FRAGMENTATION
INTERFACIAL SHEAR STRENGTH TEST

2.1 FRAGMENTATIQN TEST SYNOPSIS

An analysis of the single fiber fragmentation interfacial shear strength test is
performed. Competing and cooperating failure modes are identified. Potential
approaches to improving data acquisition and analysis are described. Several
reproducible parameters associated with interfacial properties which may be recorded

during properly controlled fragmentation experiments are defined.

2.2 FR MENTATION T T INTROD ION

The single fiber fragmentation interfacial shear strength test, (SFF-ISS) has
been used by an increasing number of laboratories for the characterization of fiber—
matrix interface properties. In recent years the qualities of this test have been the
object of intensive investigation, and even more intensive debate.

Each of the current interfacial shear strength testing techniques, including
pullout testing, droplet pullout, indentation testing, and fragmentation testing, suffers
from its own set of experimental limitations. Many of these result from the small size
and brittleness of modern reinforcing fibers, factors which are increasing with the
trend toward higher moduli and smaller diameters.

Numerous experimental factors complicate the performance of fragmentation
tests and the interpretation of results. While some of these complications are widely
appreciated, if not fully understood, others have received little or no attention in the

literature. Failure to adequately control all relevant experimental variables can lead

14

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15
to generation of misleading and confusing data.

The final average fragment length and the fragment length distribution are
frequently subjeeted to sophisticated statistical analyses based upon idealized models.
The validity of these analyses is compromised by the differences in the failure modes
exhibited by real microcomposites with varying surface treatments, matrices, and
processing conditions.

The SFF-ISS test proceeds as a complex admixture of Simultaneous failures
which compete in some cases, cooperate in others, and which sometimes involve the
interface, and sometimes do not. All failures that occur during the test contribute to
the final microcomposite defect structure. These defects tend to accommodate the
coupon tensile strain, influencing the fiber fragment lengths. The final critical length
is a function of the material properties of the fiber, matrix, interphase, and interface,
and of the failure modes operative in them.

A more complete understanding of the failure processes in single fiber
composites can improve the application of this tool for the study of methods to
enhance composite performance. This paper is a review of some of the possible
single fiber fragmentation test failure modes and an assessment of their influence on
the final test results. An attempt will also be made to identify viable approaches to

refining SFF-ISS information acquisition and analysis.

2.3 OVERVIEW OF THE SINGLE FIBER FRAGMENTATION TEST
As described in numerous other publications [Fraser, 1983], [DiBenedetto,
1986], [Drzal, 1980] the Single fiber fragmentation test proceeds as follows.
Separated single fibers are embedded in a small tensile coupon of epoxy or
other, usually transparent matrix, parallel to the gage section (Figure 2). As the
coupon is raised to a strain level greater than the failure strain of the fiber, the fiber

repeatedly fails. This fragmentation process stops when the lengths of the remaining

l6

Tensile coupon made One or more isolated fibers

from matrix material

 

 

 

 

 

 

 

Fiber repeatedly fragments
within gage length of specimen

 

Figure 2. Diagram of single fiber fragmentation specimen.

fragments approach an average limiting value, often called the critical length, L,.
This length, along with the strengths of the fiber fragments, forms the basis of the
single fiber fragmentation interfacial shear strength test.

A diagram of the approximate normal stresses in fiber fragments appears in
Figure 3. This simple diagram is based on a constant shear stress transfer along the
entire length of the fragments. The constant stress distribution is derived from the
assumption of a perfectly bonded interface to a perfectly plastic matrix. The matrix
is assumed to yield at all highly stressed regions until shear tractions equalling the
shear strength of the matrix are uniformly attained. A shear lag model in which the
tensile strength of the final fragments multiplied by the fiber cross sectional area is
taken to be equal to the interfacial shear strength multiplied by the surface area of
each half of the fragment is then used to calculate the 188. Since a fragment can fail
at any point greater than L,/2 from the end, the final range of fragment lengths ranges
from L,/2 to L,. A constant term of 3/4 is therefore sometimes introduced to

compensate for this.

I7

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I- AA/—\A/""\
EAA/\AA/\/\

Figure 3. Approximate tensile stress distribution in fragmentation test.

A constant shear traction never occurs in actual fragmentation tests that always
involve some combination of elastic and plastic behavior and often include some
degree of interfacial debonding. The constant traction assumption has, nevertheless,
played an integral role in most of the data reduction methods in use. A slightly more
realistic distribution of tensile stresses is shown in Figure 4. Allowance is made for
some indeterminate amount of interfacial failure at the fragment ends and for the lack
of shear stress at the fragment midpoints.

In one improvement on the shear lag analysis, a Poisson-Weibull treatment,
developed for use with optical fibers [Medrano, 1987], has been applied to allow for
the distribution of fiber strength [Drzal, 1980]. This treatment corrects for the fact

that fiber fracture occurs over a range of stress levels, rather than at a unique

18

 

_L. [\/"—\/ _______ \
I Ass/\A/"K

L AAA AAAA

 

 

 

Figure 4. Slightly more realistic tensile stress distribution in fragmentation test.

strength. Although the Poisson-Weibull analysis has the considerable advantage of
being applicable to all SFF-ISS specimens, regardless of failure mode, there are a
number of approximations made in this treatment. Some of the more important of

these are the following:

1) The assumption that tractions equal to the interfacial shear strength are uniformly
attained along the fragment length. Interfacial debonding near the fiber ends reduces
the maximum possible tractions within these regions to those transferred by friction
alone. The low moduli of matrices compared with fibers also limit their stress
transfer abilities even without debonding. Transverse matrix cracks can further reduce

stress transfer near fiber ends. Near the fragment midpoints, shear stresses approach

19

zero because of symmetry.

2) The assumption that the entire fiber fragment is subject to failure when, near the
completion of the test, only a narrow region at the midpoint is highly stressed. Fiber
strengths as a function of length are based on the largest flaw present within the entire
gage length. The fully stressed regions in SFF fragments are vanishingly small, and

yet the strength at critical length is the value used in the equation.

3) The use of the strength of a randomly selected fiber with a gage length equal to
the critical length in the analysis. In fact the fragments remaining at the end of the
SFF test are non-random segments without any large flaws, which would have failed
in the course of the test. This proof testing of fibers has described in detail [Fraser,
1980]. A computer program which corrects this difference to perform in-situ fiber
strength measurements has also been developed (see Chapter 3) [Waterbury, 1991].

Determinations of more accurate shear traction distributions have been
attempted by a number of researchers. A detailed analysis of stress transfer in single
fiber composites by a finite difference approach was performed by Termonia [1987].
This analysis found that stress transfer is a function of the ratio of Young’s moduli
for the case of perfect interfacial bonding. For the case of interfacial failure, a non-
linear relationship between interfacial adhesion and critical length was predicted. A
very large increase in critical length was predicted for interfacial bonding less than
30% of the matrix strength.

Shear tractions have been determined experimentally by the use of the Raman
optical strain gage [Galiotis, 1989]. This technique measures shifts in Raman spectra
of carbon or Kevlar fibers to produce plots of the tensile stresses along the lengths of
fragments during the course of the test. These stresses can be differentiated as a

function of length to determine the actual shear traction. This extremely promising

20
experimental technique can be used to directly verify the predictions of finite element
and other theoretical mechanics predictions. The maximum Shear tractions measured
by this method can be interpreted as the Shear strength of the interface with much less

ambiguity.

2.4 FBACMENTATIQN TQT FAILURE MCDE

Several different failure modes occur within fragmentation specimens,
depending upon the interface and other properties, sometimes within the same
specimen. A list of the basic modes and some comments about them comprises this

section.

2.4.1 INTERFACIAL FAILURE

The most common mode of failure in fragmentation tests is interfacial failure
by the propagation of mode 11 cracks starting at the ends of fragments and advancing
some distance along the fiber. When a fiber breaks the freed ends snap back and
subject the fiber-matrix interface to both a sudden shock wave of shear stresses and
to continued stress after the passage of the shock. Interfacial cracking may be
initiated either by this shock wave or, statically, by the increasing interfacial stresses
as coupon strain is raised throughout the test.

Interfacial failure may occur either extremely close to the actual, atomically-
thin interface or at some small distance within the interphase. Distinguishing between
these nearly identical failure modes is the object of some interest. Crasto, et a1,
detected and correlated emissions of photons and even electrons with acoustic events
accompanying fiber failures in model composites with 1 to 300 fibers [Crasto, 1987].
The photon emissions were taken to be indications of adhesive failures, since the light
was probably emitted when dissimilar materials with different electron affinities were

separated.

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21

The locus of interfacial failure may also be distinguished by microtomy of
fragmentation test specimens and subsequent TEM observations [Drzal, 1983]. In the
case of failure within the fiber surface, fiber surface fragments may be seen to be
adhering to the matrix material, while interfacial failure within the interphase or
matrix leaves some matrix material adhered to the fiber and a gap between this and
the bulk matrix.

Following the initial failure of the fiber/ matrix interface adjacent to fiber
breaks, shear tractions continue to be transmitted to the fiber across the failed
interface by friction. These tractions have a maximum value limited by the interfacial
static coefficient of friction. The actual traction is effected by the displacement of the
fiber during interfacial failure. For a small amount of failure and a low sliding
coefficient of friction, the fiber end may be almost completely moved to a relaxed
state, resulting in negligible tractions until coupon strain is significantly increased.

Mechanical interlocking after interfacial failure may occur as a result of the
generation of irregular fracture surfaces, or from relief structures etched into fibers
by surface treatments. Ismael and Vangsness [Ismael, 1987] for instance, have found
the presence of elliptical pits aligned with the fiber axis after high temperature
oxidative surface treatment. The smoother surface of Hercules A84 fibers in
comparison with A81 fibers has been found to lead to a reduction in interfacial shear
strength, as measured by the fragmentation test of approximately 10% [Drzal, 1983].

Piggot [1986] has claimed that interfacial failure accompanies virtually all
single fiber failures, and that the test only provides an indication of frictional shear
strengths as a result.

For many fiber/ matrix combinations, interfacial failure proceeds by what has
been called "stick-slip" behavior. Stick-slip debonding is usually associated with un-
sized fibers, and with higher modulus fibers with poor interfacial shear strengths. A
birefringence sequence of a typical stick-slip debonding crack appears in Figure 5.

E. 3 Int I... u .___L — - I - ..

22

 

Figure 5. Interfacial failure by stick-slip mode 11 cracking.

23

This failure mode is related to stick-slip crack advance in isotropic materials,
and is a consequence of the difference between the crack initiation fracture toughness,
K5, and the crack arrest fracture toughness, K“. The characteristics of stick-slip
cracks have been measured and used to determine these properties [Cantwell, 1989].
This method may prove to be valid and valuable in fragmentation data analysis.

As coupon strain is increased, a break in the fiber occurs. If this break
appears at a sufficiently high strain in a fiber with a sufficiently low interfacial shear
strength, a crack at or near the interface will initiate and rapidly propagate some
distance away from the fiber end. The crack will arrest when the strain energy
available is no longer sufficient to create the two fracture surfaces and to produce any
plastic deformation that is required by the matrix deformations associated with
cracking.

Since the matrix behavior is a function of strain rate, with greater brittleness
at higher rates and greater plasticity at lower strain rates, the limit of crack
propagation is greater while it is moving at high speeds than when it is static. When
the crack motion arrests, it therefore remains stationary as coupon strain is increased.
Additional motion occurs only when the strain has increased enough to reinitiate a
stationary crack. This strain is enough to again propagate, and the interface rapidly
fails for some distance until the strain is no longer sufficient to advance a moving
crack. The difference between the static and dynamic materials properties of the
interphase generates this hysteresis which may be quantitated to provide valuable
information on the interphase K, and K”.

While the crack is paused between jumps, creep occurs at the highly strained
crack tip. This plastic deformation leaves behind remanent birefringence patterns that
mark the points at which pauses have occurred. These patterns produce the so-called
"stick-slip” markings that are commonly observed.

The distance travelled in each crack jump is a function of at least four

24
variables. These are: 1) The change in interphase fracture behavior with strain rate.
2) The distance from the break in the fiber to the initial crack tip position. 3)
Whether the crack was initiated by strain energy released by a fiber failure. 4) The
coupon strain at which the jump occured. Some observations relating to these
variables follow.

The distance from the fiber break to the crack tip effects the strain energy
available for crack propagation for at least three reasons. The discontinuity at the
fiber end may serve as a stress concentrator and locally increase the shear stress. For
short fibers that are perfectly bonded, the interface loading goes to zero at the center
of the fiber and reaches a maximum at the ends. The frictional tractions across the
failed interface/interphase load the fiber in tension to some extent, reducing the
stresses at the crack tip. The amount of this shear traction depends on the coefficient
of friction across the failed surface, the normal loading across the failed surface
resulting from matrix thermal or cure shrinkage and the differences in Poisson’s ratio
between the fiber and matrix, and the loading of this surface by strain mismatch
across it. The friction coefficients only describe the maximum possible traction while
the actual traction may be near zero if fiber sliding has accommodated the strains
across the failure surface. This may happen since the fiber ends are not always
gradually loaded, in particular when the fiber snaps after either fiber failure or

interface fracture occur.

2.4.3 RADIAL MATRIX CRACKING

In SFF-188 samfles with strong interfacial adhesion, matrix cracks running
radially outward from the fiber axis are often initiated. Drzal [1983] has suggested
that these cracks occur near sized fibers because of the formation of a brittle
interphase region. This high-modulus, but brittle, region is thought to improve

fiber/matrix adhesion but to change the failure mode from interfacial to transverse

25

matrix cracking, thereby decreasing toughness.

2.4.4 INTERPHASE YIELDING

Plastic deformation of the interphase region sometimes accompanies single
fiber fragmentation with high interfacial shear strength. Interfacial shear strengths
substantially larger than the bulk matrix shear strength have been reported [Netravali,
1989].

Although it has sometimes been stated that the interfacial shear strength can
be no greater than the shear strength of the matrix, because yielding immediately

adjacent to the fiber would take place, this is not a limitation for at least four reasons.

1. The matrix is constrained by the presence of the much stiffer, stronger fiber and

so has material properties different from the bulk material.

2. The composition of the interphase region may differ from the bulk due to

segregation toward the interface or the presence of finishes.

3. The microstructure of the interphase may differ considerably from the bulk
material, especially in the case of the transcrystalline interphases sometimes generated
in semi-crystalline thermoplastics. These oriented interphases may possess much

greater yield strengths in shear than do the spherulitic structures of the bulk material.

4. The extremely small size of the interphase region makes the use of shear strength
data obtained from macro-scale specimens questionable. Whether for brittle fracture
or plastic yielding, the strengths of very small specimens is almost always greater than
for large samples with many more defects to initiate failures present. A change in

failure mode from brittle fracture to plastic yielding may also occur with a change in

26
specimen size. Extensive plastic yielding of material on failure surfaces has been
noted for matrices which undergo brittle failure in large specimens [Hibbs, 1987].
Decreasing the thickness of adhesive joints has been found to increase the extent of

plastic deformation before failure [Stringer, 1985]

2.5 W
Reinforcing fibers do not have a uniquely defined strength, but a statistical

distribution which approximates an exponential function as described in Chapter 3.
This distribution may be fairly narrow, with all fragments failing in a closely defined
stress interval, as with many glass fibers. Carbon fibers, in contrast, fail over a wide
range of stresses. This range is a function of the fiber fragment length, since longer
fragments contain greater numbers of all sizes of flaws and have a larger probability
of containing a large flaw than short fibers.

This length-strength dependence has been described as a semi-log relationship,
with the strength proportional to the logarithm of the fiber length [Phani, 1987].
Other treatments, based upon Poisson-Weibull analyses, have also been proposed
[Phani, 1987], [Asloun, 1989].

The strain energy released by fiber failure can exert a considerable influence
over both the mode and extent of failure in single fiber composites. This influence
is not a simple function of increasing damage with increasing strain energy but may
also depend upon the kind of matrix involved. Since fibers fail over a wide range of
strains, substantially different failure modes can occur within the same specimen,
effecting shear stresses, critical lengths, and measured shear strengths.

Figures 6 and 7 show three breaks in an A84 fiber in the same coupon at two
different coupon strain levels. The two breaks in the top fiber occurred at a low fiber
failure strain while the break in the lower fiber was at a significantly higher strain.

As can be seen in Figure 6, the high failure strain break has initiated and propagated

27

a stick-slip type interfacial crack for a considerable distance while the two lower strain
breaks have debonded much shorter distances. Figure 7 shows the same three breaks
at a higher strain level, approximately 3.0% . The high failure strain break has
continued to debond for greater distances than the two low strain breaks. Clearly, the
strain energy released as a Shock wave from the failing fiber has strongly affected the
ability of the interface to transmit stress. This effect is shown in diagramatic form in
Figure 8, which shows a longer stress transfer length associated with the higher failure
strain breaks causing extensive debonding, lower, frictional, shear tractions, and a
longer final fragment length.

An additional complication arises when different matrices and failure modes
are considered. Observations of birefringence patterns in polycarbonate matrix
specimens that undergo interphase yielding rather than interfacial cracking show a
fiber failure strain energy influence, but of a different sort. At the completion of the
test, the lowest failure strain breaks were seen to have more extensive regions of
remanent birefringence, an indication of more extensive plastic deformation, than
those occurring at higher strains. Birefringent sheaths were approximately twice as
long near the low strain breaks than those occurring at medium or high failure strains.
Apparently, in the absence of interfacial failure, the greater period of time available
for creep causes more extensive plastic yielding of the highly stressed material near
the breaks occurring early in the test. This effect is shown in diagramatic form in
Figure 9. The shear stress loading length is greater for breaks occurring at low

strains, exactly the opposite of the case for interfacial debonding.

 

Figure 6. Fiber failure strain energy effects on interfacial failure.

 

Figure 7. Fiber strain energy effects at higher coupon strain.

29

 

 

 

 

 

 

 

 

 

 

 

II
or
L ________________________
IO
f Break #1
_L, T - _ _ _\ /- ________________
or
L \ /—
“of _ _ _ _____ Break #2 _ _
“ Debond
Of — — — — — — —-
_L. /
L____l l I
Transfer Length 1 Transfer Length 2

Figure 8. Diagram of fiber strain energy effects on Shear stress transfer.

 

“TB-115 XI-DBW

3O

 

 

 

 

 

 

0’1'
Break #1
_L, _____ \ /' ————————————————
IO, .,
___ _______________ Q
_I; '\ /- a
3
3

 

 

 

‘i: “\/ “““ \/"“v

Transfer Length 1 Transfer Length 2

 

Figure 9. Diagram of fiber failure strain effects on interphase yielding.

31

The influence of fiber failure strain energy on birefringence patterns and the
confusion they can cause is also documented in section 5.4.2.8 with 1M6 birefringence
images. Uniformly incremented changes in fiber surface treatment in otherwise
identical systems gave the appearance of producing completely different failure modes
with increasing treatment. By considering the additional variable of fiber failure strain
energy release, the failure modes can be seen to change in a consistent, predictable
way.

Another influence of fiber strengths on SFF tests arises because fiber failure
during the fragmentation test begins at the largest flaws and proceeds to successively
smaller sizes, changing the makeup of the flaw distribution throughout the test. The
strengths of the fiber fragments are therefore a function of the coupon strain level as
well as the fragment length, complicating data analysis. DiBenedetto, et al. have
referred to this process as "proof testing" and have altered the strength distributions

assumed to compensate for this factor [DiBenedetto, 1985].

2.6 EAILURE MQDE INTERACTIQNS

The different kinds of failure occurring within single fiber composites are not
independent, but may occur in either a competing or COOperative fashion. Strain
energy release resulting from radial matrix cracking may act to entirely prevent or
reduce interfacial failure which might otherwise occur. Similarly, the initiation of
interfacial cracks sometimes prevents the formation of radial matrix cracks by

accommodating strains near the fiber ends.

2.7 SFF SPECIMEN FABRICATICN EFFECTS
The process of fabricating SFF specimens is largely accomplished manually.

It is a tedious and time consuming process which requires appropriate safeguards

against fiber-surface contamination and fiber damage. Some considerations and

32

precautions associated with this process are outlined in this section.

2.7.1 FIBER SURFACE CONTAMINATION

Contamination of the fiber surface is the most serious specimen preparation
artifact, and the most difficult to avoid. Even in a clean laboratory environment,
fibers may be contaminated from many sources such as skin oils, RTV silicone molds,
researcher breath, and other surface active contaminants. Sensitive surface analysis
techniques can detect the movement of low molecular weight Species over Significant
distances. Segregation of low molecular weight constituents from the matrix to single
fiber surfaces by free energy driving forces may also result in interphase compositions
which differ from those in a high V, composite where an equilibrium state is not

attained.

2.7.2 FIBER DAMAGE

Mechanical damage to the fibers during layup does not usually present a
problem because the large flaws thus produced do not significantly influence the final
fragment length attained. This value is determined instead by the fiber stress at which
the final fragments no longer fail. Provided that the fibers are not extensively
damaged during handling and layup, the flaws present in these short fragments are not
likely to be changed.

A possible exception to this may result from the difficulty in removing single
fibers from a sized tow. Although sizing protects fibers from processing induced
damage, it makes the separation process substantially more difficult. Thus although
finished fibers in an actual, high volume fraction composite may be slightly stronger
than their unfinished and unprotected counterparts, finished fibers could be weaker in

a single fiber specimen, from the difficulty of separating single fibers.

33

2.7.3 STRESSES INDUCED BY MATRIX CURING AND COOLING

Dimensional changes occur in the matrix during specimen curing and cooling
in thermosets and cooling and crystallization in thermoplastics. These changes can
induce normal stresses across the fiber/ matrix interface which alter the apparent
interfacial Shear strength. Normal compressive stresses are also produced by the
difference between the Poisson’s ratios of the fiber and matrix. These stresses may
be different from those present in high volume fraction composites. Residual stresses
are also developed from contraction of the matrix during cooling from T, following

consolidation or curing.

2.8 MEASURABLE FRAGMENTATIQN TEST PARAMETERS

Valuable information about interfacial toughness, strain rate effects, and failure
mode modification may be obtainable through additional analysis of SFF tests. The
particular parameters which may be measured depend upon the failure mode acting
in the SFF specimen. Specimens exhibiting transverse matrix cracking will not have
interfacial cracks to measure, for instance. The principal advantage of using the
critical fragment length as a summary of SFF behavior derives from its universality.
All single fiber specimens which can be strained to completion have a measurable
critical length, regardless of failure mode. Specimens with transverse matrix cracks
can therefore be directly compared with those undergoing interfacial failures, in spite
of some ”apples and oranges" ambiguity.

A list of some measurable SFF test parameters follows.

1. Coupon strain at which interfacial cracks are initiated near previously existing low

failure strain breaks (without fiber failure strain energy contribution).

2. Coupon strain at which interfacial cracks are initiated, simultaneously with the

34

fiber break (with fiber failure strain energy assistance).

3. Coupon strain at which interphase yielding occurs near previously existing breaks.

4. Coupon strain increment required to restart an arrested interfacial crack.

5. Distance advanced by a previously existing crack during one "stick-slip" jump.

6. Distance advanced by a newly initiated crack near a previous break, (without fiber

failure strain energy).

7. Distance advanced by a newly initiated crack, simultaneously with the fiber break,
(with fiber failure strain energy assistance). This occurs at a much lower coupon
strain than #6, and with less strain energy available for propagation, the distance

traveled is much shorter.

8. L,/D: The critical length to diameter ratio, the most commonly measured

fragmentation test parameter.

9. Failure modes: Observations of the birefringence patterns near fiber breaks
provide valuable information on the Operative failure modes in fragmentation tests.
The ease of these observations is one of the principal advantages of this test over other
interfacial testing methods. Birefringence pattern acquisition is described in the

following section.

An advantage of recording the strain levels at which particular, well defined

failure events occur within the microcomposite is that the experiment is fully

54

ref

35
controlled. A single failure mode is analyzed by a single algorithm, rather than
subjecting an ill-defined and complex mixture to a single treatment. A disadvantage
arises from attempts to compare specimens undergoing different failure modes, an
arena in which the simple L,/ D approach has advantages.

The consistency of the coupon strains at which interphase yielding takes place
near previously existing breaks can be seen in Figures 10-17 These birefringence
images show a set of 8 breaks in the same A84 fiber, each at the same series of
coupon strain levels. All breaks occurred at the same, low fiber failure strain energy,
which was insufficient to initiate interfacial debonding. As can be seen from the
images (and may be more clearly seen in the higher resolution computer screen
images) changes in the birefringence patterns for all 8 breaks occur in an almost
identical manner. The only differences arise from changes due to randomly

occurring, new adjacent breaks.

2.9 STRESS BIREFRINCENCE PATTERN CBSERVATICN AND RECORDINC
The optical birefringence patterns produced by the local shear stresses

surrounding broken single fibers have been used to monitor the progress of the SFF-
188 test and to garner additional information about failure modes. The conditions
under which these patterns are recorded have often been incompletely characterized,
however, reducing their value and occasionally leading to misleading reporting of
experimental data.

As described in the previous section, Figures 10-17 demonstrate that changes
in photoelastic patterns are consistent and reproducible, provided that all of the
relevant experimental variables are controlled, in particular the fiber failure strain and
the coupon strain. As described in section 2.5 and demonstrated in Chapter 5, breaks
occurring at different strain levels can completely alter the appearance of birefringence

patterns, even when the interfaces are very similar.

 

AS4
Extension

E= 1.3%

 

‘ AS4
Extension
8 = 1.5%

Figure 11. Birefringence patterns for 8 breaks in AS4 fiber, 1.5% coupon strain.

37

AS4
Extension

8= 1.8%

 

Figure 12. Birefringence patterns for 8 breaks in AS4 fiber, 1.8% coupon strain.

AS4
Extension

8 = 2.0%

 

Figure 13. Birefringence patterns for 8 breaks in AS4 fiber, 2.0% coupon strain.

38

   

AS4
Extension

8 = 2.3%

 

 

 

AS4
Extension

8 = 2.5%

 

 

 

 

 

 

 

Figure 15. Birefringence patterns for 8 breaks in AS4 fiber, 2.5% coupon strain.

39

  

. AS4
Extension

8 = 2.7%

 

 

 

 

 

AS4
Extension
8 = 3.0%

 

Figure 17. Birefringence patterns for 8 breaks in A84 fiber, 3.0% coupon strain.

40

Properly controlled birefringence experiments should consist of sets of images
at a series of increasing and decreasing coupon Strain levels. Breaks occurring at
different strain levels should be recorded, including, at least, low, medium and high
failure strain breaks. A few breaks of each type should also be documented, to
produce a large enough sample to indicate whether they are consistent or variable.
The lengths of the adjacent fragments should also be recorded, since the stress
conditions are partly determined by the proximity of the next nearest breaks.

Complete, controlled documentation of the stress birefringence for a single
fiber-matrix combination may therefore require that a substantial number of images
be recorded. Digitized computer images are a natural candidate for this task, both
because of low cost and ease of subsequent manipulation and integration with software
analysis. For these reasons most of the images recorded for this work have been
acquired by computer. Birefringence sequence acquisition is described in detail in
section 5.3.3.9.

Although extracting quantitative information directly from the brightness of
birefringence patterns is difficult because the patterns are the consequence of the stress
induced rotation of polarized light integrated through the thickness of the sample,
changes in the patterns can be readily detected qualitatively, and these changes used
to extract quantitative information. Figure 18 Shows a series of birefringent images
at increasing strains and a plot to the right of each that is produced by integrating the
brightness in a raster pattern, with each vertical column of pixels producing a single
point on the graph. When interphase yielding begins to occur, in the fourth image
from the bottom, the integrated brightness graph shows a discontinuity, where before
yielding, the graphs were consistently smoothly varying. This method can be used
to determine both the strain level at which yielding begins, with more reliability and
consistency than human visual interpretation, and the measure its extent. Quantitative

information has been extracted from the birefringence patterns, even though the exact

I..—

41

 

Birefringence sequence and graph of integrated brightness

 

Birefringence Pattern Birefringence Graph
A ”(a—xx
; x "a. [,1 j: .. L .
Column by column integration of the Graph 0f brightness for
brightness of each pixel in the column each column 0f PIXCIS

shows discontinuities
when debonding or
plastic deformation begins.

Figure 18. Rasterized integration of birefringence patterns to detect yielding.

 

42

nature of the stress distribution and length of the light path has not been addresses.

Another quantitative value which may be acquired involves the measurement
of stick-slip advance characteristics. As described in section 2.8, the distances
advanced and strain levels and increments required for advance can be a source of
interfacial fracture toughness information. Figure 5 shows a birefringence sequence
of a stick-slip pattern with the location of each crack arrest denoted by an upside
down ”T”. The consistency of each crack advance distance can be easily seen, with
shorter advances at greater distances from the break due to frictional stresses loading

the fiber end.

2.10 A I I LE FIBER FRA MENTATI N T T ATA A

Fragment measurement has been a tedious and time consuming process.
Alternative methods can substantially improve the rate and accuracy of data
acquisition, as well as facilitating subsequent computer analysis. As part of this
research program, the software and hardware package Fiber’I‘rack [Waterbury, 1991],
a dedicated single fiber data acquisition and analysis system was developed. This
method is described in section 3.3.4. Acquisition rates more than an order of
magnitude faster than previous methods may be routinely obtained.

Acoustic emissions from single fiber breaks have been detected and
characterized by a number of researchers [Netravelli and Sachse, 1989]. Hamstad and
Moore [1986] detected emissions from dry and lubricated tows and were able to
distinguish emissions emitted by single fiber breaks and two or more simultaneous
breaks.

As part of this research program, a simple apparatus was used to identify
emissions from both fiber breaks and subsequent debonding events. These events
were recorded at very low frequencies (20 kHz digitization rate) and were similar in

form but differed in amplitude, depending on whether they were fiber breaks or

43
debondings. Apparently, either type of failure excites a similar resonance mode
within the specimen.

Acoustic emissions can be readily used to both count fiber breaks and reCord
the coupon strain level at which they occur, an important consideration for in situ
fiber strength analysis (Chapter 3). By noting the arrival times of emissions at a pair
of transducers, it is also possible to determine the locations of breaks, and so measure
the lengths of fiber fragments [Netravali, 1989]. This method may prove somewhat
difficult experimentally, however, since the arrival times must be measured with very
high precision to accurately measure fragments only fractions of a millimeter in
length. The accuracy of these measurements is a function of the velocity of sound
within the matrix, itself a function of the modulus and density, the frequency of data
digitization, which determines the limiting accuracy of arrival time measurements, and
the consistency of the acoustic coupling between the transducers and the specimen.

Interfacial failures can be quantitatively measured in both length and separation
by observations of changes in light transmission transverse to the fiber axis. Sargent
and Ashbee [Sargent, 1985] were able to measure gaps as small as 5 nanometers, but
this method relied upon the transparency of glass fibers and is not be applicable to

carbon fiber composites.

2.11 '_- 'l'k-..’ 00! ’tl ' .‘ 0 L-
Fiber-matrix interfacial shear strengths are currently measured by several
methods. Agreement between these methods has been very poor, and research is
underway to improve the understanding of the relationships between these
experimental procedures. Interfacial shear strength tests include the fragmentation
test, the pullout test, indentation and push through tests, and droplet pullout or
microbonding tests. This section outlines some of the fundamental differences and

similarities between these mensuration techniques.

44

Two factors are often overlooked in comparing fragmentation testing with these
methods. Perhaps the most important is the influence of fiber failure strain energy
release on interfacial crack initiation, described in section 2.5. Of the above tests,
only the fragmentation test inherently includes a contribution from this high frequency
loading of the interface. As suggested in sections 2.5 and 5 .4.2.8, this energy can
completely change the appearance of the failure modes. All other current shear
strength measurement techniques derive the energy for interfacial failure without
contributions from fiber failure.

The second fundamental difference among the different shear strength methods
involves the symmetry of the advancing mode H crack during debonding. In a
homogeneous material, the motion of a mode 11 crack may be said to be symmetric,
as can be seen in Figure 19. As the crack advances in one direction, the material
displaces in opposite directions on either side of the crack, each a mirror image of the
other. When the crack advances along the interface between dissimilar materials,
however, the symmetry is broken. As depicted in Figure 20, the material on one side
of the crack displaces in the same direction as the crack advance, while the different
material on the other side of the crack moves in the opposite direction from the crack.
The crack is asymmetric because the materials moving in the same direction as the
crack is different from that moving in the opposite directions.

When there is a significant difference in material properties between the two
materials, as with a low modulus and strength matrix surrounding a high modulus and
strength fiber, crack asymmetry can effect interfacial debonding characteristics, and
measured values of the shear strength. Figure 21 shows four fundamental cases of a
cylindrical mode 11 crack growth through an isotropic plate under different loading
and crack initiation conditions. Although this example assumes an isotropic material,
the symmetry is still broken by the "inside" and ”outside” of the cylindrical crack,

which may also be considered to be the same as the fiber and the matrix.

45

 

 

A
‘

Mode 11 cracks in a homogeneous material. symmetric case.

Figure 19. Symmetric mode H crack in homogeneous material.

 

 

 

 

 

 

 

 

A
‘

Mode [1 cracks along a fiber/ matrix interface. asymmetric case.

Legend: List of vectors

- - -> Crack propagation direction

-> Matrix displacement direction during cracking
.................... > Imposed shear stress

Figure 20. Asymmetry of mode 11 crack between dissimilar materials.

46

The four cases are comprised of all combinations of two loading and two crack
initiation states. Cases A and B involve loading by exerting a tension traction on a
circular region on the right side of the plate. Cases C and D involve loading by
exerting a compression traction on circular regions on the right side. The sites of
crack initiation complete the symmetry set. In cases A and C crack initiation occurs
on the left face with propagation toward the right, while cases B and D initiate on the
right face and initiate toward the left. Crack propagation directions are indicated by
the "C” vectors. The "M" vector in each diagram indicates the direction that the
matrix (outer material) will displace when the crack passes. This is the opposite of
the direction that the material is strained by the different loading conditions.

With the four cases so defined, we can now investigate the crack growth
properties to evaluate whether they tend to grow inward, toward the fiber-matrix
interface or outward, into the matrix region. In case A the crack grows outward,
since inward motion would tend to wedge the "plug" of material and crack growth
would cease. This is intuitively clear, pulling a plug of material out of a plate of
material would never produce a plug tapered in such way that it could not be
removed. For this case where the M and C vectors point in opposite directions then,
the crack growth is outward.

Case B involves the same loading as case A, but with the opposite crack
propagation direction. The plug of material is tapered in the same direction, for the
same reason, it could not be removed if it were tapered in the opposite manner. The
crack tends to meander inward in this case however, where the M and C vectors are
in the same direction.

Case C has loading by a push from the right, with crack initiation from the left
propagating toward the right. The M and C vectors are in the same direction, and the
growth tendency is inward. Case D has the same loading but opposite crack

propagation, the M and C vectors are opposed, and growth tendency is outward.

47

 

 

 

—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I

Outward Inward Inward Outward
_> +< +> —<

Legend: "C" advancing crack vector. "M" matrix displacement vector

Figure 21. Crack growth habits for 4 crack initiation and loading conditions.

48

The two cases B and C with aligned M and C vectors both have tendencies to
grow inwardly, favoring interfacial failure modes, since the crack will tend to either
hug the fiber-matrix interface or meander toward it. Cases A and D have opposed M
and C vectors, both have the ability to move outwardly, away from the fiber-matrix
interface and into the matrix material. Aligned crack propagation and matrix
displacement vectors tend to produce inward growth and interfacial failures, opposed
propagation and displacement vectors tend to produce outward growth and failures in
the interphase or matrix.

With these tendencies established, we can now analyze the different 188 tests
to determine how their symmetries and potential failure characteristics compare.
Figure 22 is a diagram of the symmetry factors for matrix shear strains and
displacements during interfacial crack propagation in a fragmentation test. In step 1
the entire matrix and fiber region is under tension and the interface is unstressed.
Step 2 shows the fiber snapping back after a break, subjecting the interface to Shear
stress and deforming the matrix. Step 3 shows a crack initiating at the fragment ends
and beginning to propagate away from them. The direction of matrix displacement
associated with crack propagation is opposite that of the crack propagation direction.
Step 4 shows the crack continuing to propagate until arrest.

From the preceeding discussion, there is the possibility that this crack can
meander outwardly, away from the interface. This motion will leave voids or gaps
along the fracture surfaces. Migration toward the interface can also occur, but this
motion must compress together the material across the resulting fracture surfaces,
requiring considerable energy. The maximum shear stresses, of course, occur nearest
the interface and tend to continue to confine it there. This discussion considers the
effects of crack symmetry only, and neglects all other mechanics considerations.

Figure 23 shows a diagram of a pullout test with debonding initiating in two

different positions, either at the point where the fiber emerges from the matrix, where

49

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l Portion of fragmentation test specimen prior to fiber fracture

     
   

   

   
 

 

  

III-
IIII‘I‘III‘IIIIII
..::..'...::::::
III'IIIIIII'IIIII'II I”...
IIIIII-III.III-I-l-IIIIIIIIIIIIIII
2 Fiber snaps back after breaking. briefly displacing matrix

Shear

Crack
3 Cracks initiated near fiber

 

shear stress maxima

 

4 Interfacial crack propagating toward fragment centers
Matrix shears in opposite direction from crack movement

Figure 22 Symmetry of interfacial cracking for fragmentation test

50

shear stresses might be expected to be maximum, or at the embedded end of the fiber
where a local stress concentration may occur. The symmetries of the two cases are
different, when the crack initiates at the emergence point the matrix displaces in the
same direction as the propagation and growth will tend to be inward, confined strictly
to the interface. This behavior has been observed in model gelatine matrix composites
as part of this work. When cracking initiates at the embedded end, however, the
matrix displaces in the opposite direction from propagation, and outward growth is
possible.

Figure 24 shows debonding in a droplet pullout test. This is a Similar case to
the ordinary pullout test, with two possible initation cases. The matrix displaces in
alignment with the propagation for the case of initiation near the restraining blades,
and opposite propagation for initiation at the other side of the droplet. Since most
droplet pullout tests use a pair of blades to hold the droplet, there is a substantial and
irregular stress concentration near the blades and that is the most probable initiation
point.

Figure 25 shows debonding of a short, embedded fiber. This case is identical
to the fragmentation case, with the notable exception that there is no contribution from
fiber failure strain energy release. The matrix displaces in the opposite direction
from the crack propagation, with the possibility of outward growth.

Figure 26 shows debonding for the indentation test. The matrix displaces in the
opposite direction from crack propagation, allowing outward crack growth.

These divergent crack growth propensities may also be understood in terms of
the climb of an edge dislocation in a crystalline material. Edge dislocations are
constrained to motion within a glide plane for conservative motions, i.e. those that do
not create or destroy vacancies. Movement out of the glide plane corresponds to a
mode 11 crack growing up or down, it is only possible if vacancies within the crystal,

or voids within the matrix are produced or consumed. Whether voids are produced

51

2 Crack

Matrix h e r Motron

m
n:

  
    
   
 

llllllllJJJ_ll

hlllllllllTTTl/

11
flllllllllllll
lllllllllllllll

 

Matrix
Shear

 

 

   

Crack
Motion

 

 

 

 

 

 

 

 

 

 

 

 

—1I—I
——

 

 

Positive

Debond

Negative

Debond
Matrix Crack
Shear Motion

 

Figure 23. Symmetry of interfacial cracking for pullout test.

52

 

Figure 24. Symmetry of interfacial cracking for droplet pullout test.

53

 

Ma Shear Ma Shear

 

Crack Motion Crack Motion

Ma Shear Ma h

     

Crack Motion Crack Motion

Figure 25 . Symmetry of interfacial cracking for short, embedded fiber.

54

1 * 2 Crack
' Motion
/
I‘- :
P Matrix ShearI .

F‘“ E/ I—T"
I—w‘I _, __I.__-—I
5“ / w-F‘I—I
~~ ’— ##—
'—““‘ / /"'—
~~ / ’4”—
hh" r’ ”'4'“
'——I~ _/ ”—w-
h“ / _C _—
:"“ '4 fl:—

‘ I '_.—Ir—-I
__4 ” ——-—'5'—1
~~ _s “—1—“
I—o—u ,__ ____“__
I"-I _—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 26. Symmetry of interfacial cracking for indentation test.

or consumed is determined by whether the dislocation is positive, an extra half plane
of atoms, or negative, the absence of a half plane of atoms, in relation to the direction
of climb. This approach will be pursued in future work.

One possible effect of the differences in crack propagation symmetries is
changes in the morphology of fracture surfaces and different resulting frictional
coefficients. Coefficients of friction can be directly obtained from pull-out tests
[Piggot, 1986, 1988], but these coefficients may differ from those in SFF tests
because the initial mode of interfacial failure may not be identical.

The mode 11 cracks in SFF tests advance in the opposite direction from the
matrix displacement, while cracks in pull—out tests advance in the same direction if
debonding begins where the fiber enters the matrix, and the opposite direction if
debonding begins at the fiber end. These different modes of interfacial failure may
produce different failure surfaces, with considerable changes in frictional constants

resulting.

55
5.12 RA M ATI T N L I N

The fragmentation test contains a wealth of potentially valuable information
about the properties of the fiber-matrix interface and interphase, and the interaction
of failure modes with all composite constituents. This information has only begun to
be exploited, with numerous recordable and reproducible parameters that have
received little or no attention in the literature. Some of these parameters extract
information with less ambiguity than the critical length approach, since they involve
a single mode of failure, analyzed by a single algorithm. The critical length
approach, however, also has an advantage in that it allows for a single system for
comparing all fragmentation test results.

Fiber failure strain energy release can significantly alter the failure modes and
measured critical lengths in fragmentation tests. This effect has been largely ignored
in the literature, and has clouded the interpretation of data. Other interfacial shear
strength measurement methods do not include a contribution from fiber failure energy
and so are fundamentally different measurements. In addition, these methods involve
cracking with different symmetries, and therefore different potential crack growth

habits and results.

CHAPTER 3

ON THE DETERMINATION OF FIBER STRENGTHS
BY IN-SITU FIBER STRENGTH TESTING
Published as:
ON THE DETERMINATION OF FIBER STRENGTHS BY IN-SITU FIBER
STRENGTH TESTING, M. C. Waterbury and L. T. Drzal, Journal of Composites
Technology and Research, JCTRER, Vol. 13, No. 1, Spring 1991, pp. 22-28.

3.1 m-Sflfu FIBER STRENGTH TEST SYNOPSIS
A method is described and experimental results given which demonstrate the

feasibility of determining fiber strengths at short gage lengths by monitoring the fiber
failure process during the embedded single fiber fragmentation test. A computerized
weakest link fiber model was used to perform data analysis, without making
assumptions about the statistical nature of the flaw distributions. Fiber strength data
at short gage lengths can be directly obtained by this technique without the necessity
for extrapolation from longer specimens. A dependence on specimen fabrication
technique was found, which demonstrates the necessity of careful control of fiber
prestrain. Specially fabricated strain-free specimens tested by this method, the in-situ
fiber strength test (ISFS), generated length-strength data that were in close agreement

with conventional tension test results.

3.2 ISFS INIBQDUQTIQE

The strength of reinforcing fibers is a function of length, since fiber strength
is not uniform, but is determined by a statistical distribution of flaws. In a composite
material, stresses are transferred to the fibers from the matrix, limited by the strength

of the fiber-matrix interface and adjoining regions, and by the matrix modulus. The

56

57
strength of the composite is best related to the strengths of the fiber fragments which
can just be fully loaded through this stress transfer process. These fragments may be
only a fraction of a millimeter in length, making tension testing difficult.

Fiber strengths can also be a function of specimen strain. The fiber fragments
that remain in a strained single fiber fragmentation (SFF) specimen are pieces
produced by the failure of the largest flaws in the fiber. With these flaws effectively
sorted out by the prior failure process, the final fragments are comprised of a
nonrandom sample of material. In contrast, the gage sections of the fibers in tension
tests consist of randomly selected segments, containing flaws of all sizes. Tension
testing of randomly selected fibers will therefore underpredict the strengths of fiber
fragments in the SFF composite.

A number of researchers [Henstenburg, 1989], [Wagner, 1990], including one
of the authors of the current publication (M.C.W.), have independently proposed an
alternative to single fiber tension testing, the in-situ fiber strength test. This method
may surmount these problems by testing fibers that are embedded in a tensile coupon
of a model matrix material. This technique can virtually eliminate gripping and
alignment problems since the fiber is uniformly supported by the matrix material.
Because of this, measurements at short gage lengths can be obtained without the
necessity for extrapolation from longer specimens. While methods are available for
making this extrapolation [Asloun, 1989], direct confirmation by experiment would
place these techniques on a more secure footing. The test also generates flaw
population data in a form that can provide more complete and relevant information
about defects than does the .simple tension test, allowing improvements in process
design and quality control. Since many breaks occur in a single ISFS test coupon,
data acquisition can be orders of magnitude faster than for the simple tension test,
increasing the sample size and thereby enhancing the resolution.

This paper describes the ISFS testing technique and demonstrates that,

58
provided certain essential requirements are met, the results so obtained are

reproducible, consistent, and in agreement with standard tension tests.

3.3 ISFS EXPERIMENLAL ERQQEQQRE

3.3.1 SIN GLE-FIBER FRAGMENTATION TEST

Since the single fiber fragmentation (SFF) test has been extensively described
elsewhere [Drzal, 1980], it will only be briefly reviewed here.

A representation of the approximate fiber stress distribution throughout the test
is shown in Figure 27, which represents the approximate fiber tensile stress
distribution during the course of the single fiber fragmentation test, assuming a
constant shear traction without debonding.

One or more isolated fibers are centrally embedded in a small tensile coupon
of epoxy or other, usually transparent matrix, parallel to the gage section. As the
coupon is raised to a strain level approximately three times greater than the failure
strain of the fiber, the fiber repeatedly fails. This process is limited when the length
of the remaining fragments reaches a critical value, often called the critical length, L,.
This limiting value, along with the strengths of the fiber fragments, forms the basis
of the single fiber fragmentation interfacial shear strength test.

Fiber failure during the single fiber fragmentation test begins at the largest
flaws and proceeds to successively smaller sizes, changing the makeup of the flaw
distribution throughout the test. The strengths of the fiber fragments are therefore a
function of the coupon strain level as well as the fragment length, complicating data

analysis.

59

——___——__—_——_———_—_—K

Polling Length. Lp

/___—_ _—_\/_—__ —_——\

 

are-us xmew

AA/“\A/""\'
AA/\ AAAA

Figure 27. Fragmentation stresses and polling lengths.

l5
E
E/“\/“\/ ““““““ \
t5
l:

3.3.2 IN-SITU FIBER STRENGTH TEST

During the early stages of the single fiber fragmentation test, the fiber failure
process is well defined. The locations of all new breaks observed in this study were
found to be well away from the ends of fiber fragments, where the fiber strain cannot
be uniquely determined, since it may be significantly less than that of the matrix. The
strains at failure within the central region of each fiber fragment, however, can be

accurately monitored, forming the basis for the in-situ fiber strength test.

60

Dial Gage \

    

 

Single Fiber
Fragmentation
Specimen

Transverse
Fiducial Marks

Figure 28. Straining stage for single fiber fragmentation test.

In general, this value is not exactly equal to the matrix strain, since some
stress is likely to exist in the fiber at zero coupon strain. Fibers that are misaligned
or curved may also undergo rotations rather than axial extensions as coupon strain is
increased. Although these effects have a minimal influence on single fiber
fragmentation interfacial shear strength tests since the specimens are strained well past
the completion of fiber fragmentation, they can strongly skew ISFS results.

The requirement of a well defined fiber prestrain precludes the use of the same
specimens for both interfacial shear strength and ISFS measurements, since the
particular cure histories of interfacial shear strength specimens will usually leave some
unknown value of fiber strain. An additional reason for this prohibition is the
possibility that the highly stressed interfacial region may be subject to creep when
strained to the limiting fragment length in a series of steps rather than monotonically.

Final fragment lengths of incrementally strained specimens tend to be longer than

61
those that are smoothly strained.

The in-situ fiber strength test proceeds as follows. Single-fiber composite
specimens are laid up by methods that produce a well-defined prestrain in the fiber.
The specimens are strained (Figure 28), and the fiber fragmentation process is
monitored to count the number of breaks occurring as a function of the measured
coupon strain. These data are combined with data on the length required to transfer
stress to the fiber to determine the number of flaws per unit length of fiber for each
strain increment. Finally, these flaw population data are processed by a computer
program along with the fiber tensile modulus (obtained from manufacturer’s data in
this study) to generate length-strength data that are compatible with those generated

by traditional tension testing. Each of these steps will be described in detail below.

3.3.3 ISFS SPECIMEN FABRICATION

One set of single fiber specimens was laid up in an epoxy matrix, DER
331/MPDA, cured 2 hours at 75 °C followed by 2 hours at 125 °C. The fibers were
affixed to room temperature vulcanizing silicone specimen molds with a hot—melt
thermoplastic glue which flows viscoelastically during solidification, allowing the
fibers to be drawn through the glue and accurately straightened. An additional
attachment with rubber cement maintained this alignment as curing proceeded.

A second set of Specimens was produced with a solvent deposition technique
intended to eliminate, or at least minimize, fiber prestrain. Fibers were laid onto
precut, 0.8 mm thick polycarbonate coupons and secured in place away from the gage
length with hot melt glue. Four layers of a 5% solution of polycarbonate in
methylene chloride were spin coated over the fibers at 5 minute intervals. Specimens
were then held at 75 degrees °C for 24 hours before testing.

Fiber-matrix adhesion for solvent deposition specimens is poor [Bascom,

1987], [Waterbury,1990], imposing a severe limitation on the equivalent fiber gage

62
length which may be tested. The feature of interest for the purposes of this study was

the absence of fiber prestrain.

3.3.4 Data Acquisition

Data acquisition was performed with FiberTrack [Waterbury, 1990] , a software
and hardware system specifically developed to perform both interfacial shear strength
and ISFS fiber fragment length measurements at high speeds. Hardware consisted of
a microstraining stage mounted on a Newport“ translation stage with a digital position
readout, both mounted on a transmitted, polarized light microscope. A custom
interface provided both control signals to activate the translation stage, and concurrent
timing signals to the FiberTrack software running on a Amigao computer (Figure 29).

Measurements proceeded as follows. The initial length between transverse
fiducial marks (Figure 28) on the specimen gage section was measured with the
translation stage. The specimen was then strained in approximate 0.25 % strain
increments, determined with a dial gage and calibration curve. The break positions
were measured after each strain increment. This was accomplished by positioning the
specimen at the first fiducial mark, translating the stage at a constant rate, and
clicking the "mouse" button as each break passed a crosshair in the microscope,
sending a timing signal to the computer. The translation was halted at the second
fiducial mark and the distance traversed was noted from the translation stage readout.

The FiberTrack software then calculated the break positions by interpolating
between the time elapsed for the entire motion and the times of each break passage.
These positions were saved to a diskette and the strain was accurately calculated by
comparing the current and initial gage lengths. In this manner, break positions can
be measured without having to stop the stage motion at each break, providing an order

of magnitude speed improvement over less automated procedures.

63

 

 

 

 

Polarized,
Tran smitted
Light
Microscope

 

 

 

 

Human Operator

Signalling Passage
of Each Fiber

Break Past Reticle

i it

 

 

 

Video Camera Video Digitizer
(Option al) (Option al)

 

 

Compu ter with
FiberTrack
Software and

Mou se

 

 

l

 

 

 

Micro-Strain in g
Specimen Stage

 

 

Controller Interface
Human to Stage
and Computer

 

 

 

l

 

 

Translation
Stage

 

 

ll

 

 

Translation Stage
Controller and
Position Readout

 

 

 

 

 

Data Analysis

1. Generation of
Computer Fiber
Model from Flaw

Population Data

2. Tensile Test
Simulation by Weak
Link Model Computer
Program

3. Strength vs Length
Data at Short Gage
Lengths

‘

 

 

Flaw Population
Measurement

1.Break Positions -.

Analyzed for Numbers
of New Breaks Per
Strain Increment

2. Fiber Polling Length
Calculation by Shear
Stress Transfer
Length Exclusion

3. Fiber Flaw Population:
Calculation, Flaws per
Unit Fiber @ Coupon
Strain Interval

 

 

 

FiberLink, Weakest
Link Model Tensile
Test Simulation
Computer Program

 

 

 

 

InterLink, Single
Fiber Fragmentation
Interfacial Shear
Strength Test

Simulation

 

Figure 29. Block diagram of FiberTrack/FiberLink

 

 

 

Figure 30. Fiber break positions recorded by FiberTrack.

For interfacial shear strength testing, the data were automatically subjected to a

Weibull/Poisson analysis to determine interfacial shear strengths.

3.3.5 ISFS CALCULATIONS

After the positions of all breaks in each strain increment were recorded, the
complete set of "tracks" of break positions was displayed, and the new breaks
appearing in each track located (Figure 30). These breaks were always found to lie
somewhere within the central portions of the fiber fragments, rather than adjacent to
previous breaks where strain is poorly defined.

The new breaks occurring at each strain level were then apportioned among
strain increments of 0.25% by linear interpolation to compensate for the small
deviations between these uniform increments and the actual, slightly non—uniform
steps. Each new break occurring between measured strains of 1.27 and 1.52% strain,
for instance, was allocated as adding 0.92 breaks to the 1.25 to 1.5% group and 0.08
breaks to the 1.5 to 2.0% group. This introduces an error which is small provided

that the initial sampling increments are close to the desired 0.25% steps. Continuous

65
recording of breaks by acoustic emission will eliminate this approximation.

At each stage of the stepped straining procedure, a "polling length," which is
the length of fiber actually available for fiber failure, was calculated (Figure 27).
While the entire gage section is susceptible to breaking at the onset of the test, as
breaks occur, the regions adjacent to them are no longer under conditions of
increasing strain. The polling length at each stage may be approximated by assuming
it to be equal to the initial gage length, L0, minus the number of previous breaks, Nb,
times the critical length, L,.

Polling Length, L, = L0 - (Nb * L,)

This formula may be used with simple acoustic emission data acquisition, since
only the number of breaks and the final critical length are required. A refinement of
this calculation to consider strain level may be desirable, since the transfer length at
lower strains is actually less than the the final critical length. A transfer length which
is proportional to coupon strain could be used as a first order improvement.

The number of flaws per 25 mm in each 0.25% strain increment was then
calculated from the number of new breaks, B, and the polling length, LP, in
millimeters by:

Flaws per 25 mm, F2, = B * 25/11,

These flaws were then averaged for all specimens in each set and plotted at the
end of each strain increment to produce the graphs of flaws/25 mm versus strain
increment.

The fiber tensile modulus was obtained from manufacturer’s data sheets for the

purpose of this feasibility demonstration.

3.3.6 COMPUTER TENSION TEST SIMULATION
A computer link-model fiber was then generated and tested in the following

manner. A 10,000 element link strength array was set up to represent the strength of

66

the weakest pan of each 100 micron link. Each link was initialized with a strength
of 2,000 ksi as a limiting, case. The experimentally determined flaw population data
was then used as a guide to populate the links in this array with the correct numbers
of flaws. This process was performed in the order of strongest to weakest flaws,
since many links have more than one flaw and the link strength is determined by the
weakest flaw present. In the case of fractional numbers of flaws, a flaw was either
assigned, or not assigned, based on the probability of one occurring. Beyond the gage
length range in which test results were valid, the flaw distribution was assumed to
follow the experimentally determined exponential distribution. This is equivalent to
extrapolating to shorter gage lengths for this pilot study. Matrices with sufficiently
high interfacial shear strength are available to make this unecessary in future work.

One meter long fibers, each simulated by 10,000 one hundred micron links
were produced in this manner and tested as follows.

Testing proceeded by starting at many randomly selected locations and
checking for the weakest link occurring within the selected gage length. This link was
taken as the strength of that fiber segment and these values were stored, averaged, and
a standard deviation calculated. In this manner, six, one meter simulated fibers were
produced and tested at various gage lengths to produce the final length-strength data.
This represents a statistical oversampling of the original data since the flaw population

data were obtained by testing about 200 mm of real fiber.

3.3.7 ACOUSTIC EMISSION DETECTION

To explore the possibility of acquiring ISFS data by acoustic emissions, a
simple detection and recording system was developed. A miniature condenser
microphone element was modified by removing the protective, external membrane and
exposing the condenser diaphragm. A drop of gel-type quick-setting epoxy was

applied to the center of this diaphragm and allowed to protrude slightly from the

67

 

 

Amplitude ——>

I I l l I
0.0 .005 .010 .015 .020 .025

Time (Seconds) -—>

 

Figure 31. Acoustic emission from carbon fiber failure.

element to provide an acoustic link to the specimen. The element was then strapped
to the gage section of a specimen with a rubber band.

After preamplification and passage through a band pass filter to eliminate low
frequency components, the output of this element was applied to an audio frequency
digitizer and sent to an Amiga computer equipped with 2.5 megabytes of RAM. In
this manner, a complete acoustic waveform up to 100 seconds in duration, sampled
with eight bits precision at a 20 KHz sampling rate, could be acquired.

An example of a typical fiber break acoustic emission trace appears in Figure
31. The horizontal axis is time while the vertical axis represents sound amplitude
sampled at 1/20000 second intervals. The trace is characterized by a rapid rise time
and a slow decay with a predominant frequency in the range of a few kilohertz. The

initial, much higher frequency shock wave produced by the failing fiber apparently

68
excites this low frequency resonance within the stretched specimen. When replayed
as a sound through an amplifier and speaker at a reduced frequency, the trace
resembles that produced by a plucked string.

3.4 F LT AND DI I N
Two sets of in-situ fiber strength tests were performed as described above,

using six 25 mm fibers in an epoxy matrix and nine 25 mm fibers in solvent deposited
polycarbonate (PC).

The number of flaws per 25 mm, per strain increment for each of the nine
specimens in the PC tests appear in Figure 32. As can be seen, the scatter in this raw
data was substantial, resulting from the small number of breaks in each specimen.
Figure 33 and Table l depict the average number of flaws for the epoxy and PC
matrix specimens. A smooth increase is seen up to about 2.25% coupon strain for the
PC specimens and 2.75% for the epoxy matrix, followed by a drop off as a result of
the limitations imposed by the interfacial shear strength. This drop off occurs later
for the epoxy matrix case with its stronger interface, allowing much shorter gage

lengths to be measured.

Table l. Flaws per 25 mm @ strain increment for AS4 fibers.
Coupon Fiber Epoxy Matrix PC Matrix

 

Strain Stress Fiber Flaws Fiber Flaws
L96) (MPa—mm
1.00 2346 1 .0 0.40

1.25 2932 0.5 0.13

1.50 3519 2.2 0.99

1.75 4105 6.7 3.33

2.00 4692 19.8 6.70

2.25 5278 28.4 12.16

2.50 5865 64.5 12.93

2.75 6451 82.3 13.31

 

69
40

 

Flaws/25 mm —>
t0 CO
C O
r 1

fl
0
1

 

 

 

l l
1.0 1.5 2.0 2.5

Coupon Strain (96) —>

Figure 32. Flaws versus strain increment by specimen in PC.

 

3.0

70

 

80 -
70 -
Epoxy Matrix —I—

60-

Polycarbon ate .
Matrix

50-

40-

30-

20-

104

 

 

 

I l l I l
1.0 1.5 2.0 2.5
Coupon Strain (%) —>

Flaws/ 25 mm ——>

Figure 33. Flaws versus strain for AS4 fibers in PC and epoxy.

3.0

71

 

80—

70-

60-1

50—

40—

30—

20-

10—

 

Flaws/ 25 mm

 

I
I
Epoxy Matrix —I— I
E -. I ’
x t
pram -+- ,
P0115122: : lirxon ate . [I
E ' 1
axis? -<>-- ,’ ,
l I
l I
l I
I
i4,
- /
/ /
/ /
/ /
/ /
;(/ /
/
/ /
I / Q
3 I I l I I
1.5 2.0 2.5

Coupon Strain (%) —->

Figure 33. Flaws versus strain and exponential curves.

 

3.0

72

 

 

 

'\

 

 

 

 

 

ISFS AS4 in PC,

 

 

ISFS AS4 in E]

 

 

 

 

 

 

 

 

 

 

 

6000

 

 

Tensile t6 st. A534 -0-
1000
.l .3 .55 l 2 4 8 25.4 100
Log Scale of Fiber Length (mm) —9.

Figure 34. In-situ and ex-situ fiber strengths.

Table 2. In situ and ex situ AS4 fiber strengths.

 

 

Gage Length Conventional In-Situ Fiber Strength
Tension Test Epoxy Polycarbonate
(m m) (MPa) (MPa) (MPa)

25.4 3215 j; 966 3188 j; 704 2698 j; 518
8.0 3850 i 738 3347 i 725
4.0 4264 i 787 3733 :I: 752
2.0 4720 j; 856 4175 i 773
1.0 5285 :I: 1731 5223 :I: 911 4582 j; 814
0.55 5644 i 994 5693 :I: 945 4996 i 869
0.3 6189 j; 973 5437 i 883

 

73

Figure 34 plots the epoxy and PC specimen data along with exponential
functions which differ only by a constant multiple, or, equivalently for this type of
function, by a constant strain offset. The curves correspond closely, showing that the
test yields an approximate exponential dependence of new breaks per unit length on
coupon strain within the early part of the graph, falling off when the shear traction
imposed limit is reached.

The difference between the epoxy and PC results shows a dependence on
specimen preparation technique, probably as a result of fiber strain produced by
dimensional changes in the matrix. This indicates that specimens for this test must
be produced by a technique that either leaves a negligible or well defined initial strain
in the fiber allowing accurate determination of the strains at failure throughout the
test.

The flaw population data obtained by the ISFS test and processed with the
FiberLink computer model to convert it to the form of strength versus fiber gage
length appear in Figure 35 and Table 2 along with data obtained by conventional fiber
tension testing [Drzal, 1982]. The prestrain free PC matrix ISFS data show a very
close correspondence with the tension test results in both the value of fiber strength
and the slope of strength versus 10g(gage length).

A least squares fit of the strength versus the base ten logarithm of the gage
length (Figure 35), shows an intercept of 5273 MPa at 1 mm gage length for the
conventional tension test results and 5272 MPa for the PC ISFS results. This virtually
identical result is somewhat coincidental since it is less than the natural scatter in the
data. The slopes were also in agreement, -l464 MPa per unit 10g (gage length) for
the tension test and -1555 MP3 for the PC ISFS test, a difference of about 5%.

The epoxy matrix ISFS data is in agreement in slope but shows an offset
corresponding to a pretension of 0.25 % fiber strain at zero coupon strain. The least

squares fit for this data gave an intercept of 4628 MPa at 1 mm length and a slope of

74
-14l3 MPa per log (gage length).

This value is in agreement with experimental results and theoretical predictions
made by others in this laboratory,‘ which suggests that the strain on the fibers in
epoxy-matrix single-fiber fragmentation specimens prepared with this cure schedule
will be approximately 0.2% in tension. This prediction was made based on the
changes in thermal expansivity of the matrix during the cure cycle in relation to when
gelation occurs.

Small tensile strains in single-fiber composites have also been detected by
Raman spectroscopy [Galiotis, 1988, 1990]. Pretension may be an artifact of the
specimen preparation process, which involves aligning the fibers in a silicone mold
and securing them with adhesives. These results contradict the notion that a net

compression is exerted and are under further investigation.

3.5 Owl's' 0; 0 - ll B ' ' \ TH is]! 0 .51 O A~
W

In-situ fiber strength testing offers the potential for significantly enhancing the rate
of tensile strength data acquisition. Each 25 mm of fiber in a strong interface
specimen fails approximately 50 times within the well defined failure portion of the
single fiber fragmentation test, providing the equivalent to 50 fiber tension tests with
a single-fiber specimen. Longer gage length, multiple fiber specimens can produce
hundreds of tensile data points in a single, semiautomated test. This may represent
two orders of magnitude improvement over previous methods. High resolution fiber
tension tests require large numbers of data points since the resolution increases by
only the square root of the number of samples.

Strength data at short gage lengths are required for the analysis of composite
properties and single fiber fragmentation interfacial shear strength tests. A suitable
a. Kalantar, J.K., Drzal, L.T., to be published.

75
matrix for ISFS specimens should have high interfacial shear strength and a high
modulus to facilitate this process. The fiber prestrain must be consistent and must be
calibrated against conventional tension tests or against strain-free specimens prepared

by solvent deposition.

3.6 W

The feasability of determining fiber strengths at short gage lengths by in-situ
fiber strength testing has been demonstrated. Results obtained from single-fiber
fragmentation, in—situ fiber strength testing are in close agreement with those from
short gage length fiber tension tests. The number of fiber flaws per unit length was
found to increase exponentially with increasing strain increment.

The necessity of determining fiber prestrain produced during specimen
fabrication was shown. A computerized weakest link model has been developed to
analyze the experimentally determined fiber flaw distributions and to simulate the

single-fiber fragmentation process.

CHAPTER 4
DETERMINATION OF FIBER VOLUME FRACTIONS

BY OPTICAL NUMERIC VOLUME FRACTION ANALYSIS

Published as: Determination of Fiber Volume Fractions by Optical Numeric Volume
Fraction Analysis, Waterbury, M.C. , Drzal, L.T. , Journal of Reinforced Plastics and

Composites, JRPC, Vol. 8, Nov. 1989, pp. 627-636.

4.1 QNZEA S XNQPSIS

A method for determining the fiber volume fraction in continuous fiber
composites by automatically counting the fiber ends per unit area in digitized
microscope images of representative cross sections has been developed. Since fiber
counts are digital variables, the accuracy of the method is essentially independent of
small variations in microscope focus and specimen surface preparation. In addition
to producing averaged data, the method enables the construction of volume fiaction
variation profiles ranging from the finest possible scales up to full size components.

Results are in agreement with values obtained by acid digestion tests.

4.2 QB VEA INTRODUCTION

Composite volume fraction determinations based on image analysis techniques
have been pursued with the intention of supplanting methods employing matrix
removal by combustion, solvent, or acid digestion [Cilley, 1974] with a cleaner, more

accurate technique which can provide distribution profiles along with averaged data

76

 

[ASTl
fiber. n
the m2

mania

analysi
1987 I
metallo
from It
inheren
light di
Van'atic
differen.
in lllurr,
I
filCIors c
SGCtions
chinge r
fractionS
fiber dia
Sample 0

fiber area

the r6350:

 

77
[ASTM, 1987 A], [ASTM, 1987 B]. An alternative approach is also essential for

fiber/ matrix combinations for which no suitable solvent is available which can remove
the matrix without attacking the fibers, as with high performance thermoplastic
matrices.

Composite volume fractions determined by conventional areal and lineal image
analysis techniques have been shown to be in error by as much as 10—15% [ASTM,
1987 A]. Highly variable results are also commonly produced by the parent
metallographic methods [J ock, 1986] . These errors are unavoidable since they result
from the small size of modern reinforcing fibers (e.g. 5 microns) in relation to the
inherent resolution limitations of light microscopes, one half of the wavelength of the
light divided by the numerical aperture of the lens, approximately .25 microns.
Variations in fiber images also result from rounding of fiber ends during polishing,
differences in polishing action in fiber and matrix rich regions, surface residue, drift
in illumination sources, and focal differences across the image plane.

It was recognized that more accurate values with less susceptibility to these
factors could be obtained by counting large samples of fiber ends emerging from cross
sections of the composite since the number of fibers is a digital value and does not
change with the brightness or apparent area of the fiber images. Absolute volume
fractions may be obtained from these fiber counts without knowledge of individual
fiber diameters because the average cross sectional area of any sufficiently large
sample of fibers rapidly approaches the average for all of the fibers. Although the
fiber areas cannot be measured with sufficient precision by purely optical means for

the reasons previously outlined, approximate values may be obtained from product

digitiz.
since it
clearly
fiber-f;
Contalr.
screen

and ma

dCICI'm;

boxes a:
may be
VlSUaliz;
“umber
lnIOrmat
made mt
Same dig
”16 Void
Void Vol
Small fra

fiber We} I

 

78

specification sheets, and more precise values may be determined from the weight of
the tow and the fiber density [ASTM 1987 B] measured with the same batch of fibers.

An image analysis program to perform this task can be optimized to process
digitized microscope images (Figure 36) containing very large numbers of fibers,
since it only requires enough information to identify the fibers, without attempting to
clearly resolve their sizes. Accurate fiber counts are produced in spite of apparent
fiber-fiber contact and damaged fiber ends (Figure 37). This program produces a file
containing not only the total number of fibers in the image but also their individual
screen coordinates, which may be analyzed for detailed information about the fiber
and matrix volume fraction distributions, or subjected to a Fourier-type analysis to
determine the average spacings between matrix rich regions.

Simple distribution statistics may be obtained by dividing each image into small
boxes and finding the number of fibers in each (Figure 38). Fiber maps (Figure 39)
may be constructed by plotting each fiber with a single white pixel to allow for the
visualization of large regions of composite cross sections. Statistical profiles of the
number of boxes containing a given number of fibers can provide quantitative
information about the incidence of matrix rich regions, allowing comparisons to be
made more reliably (Figure 40). Void volume fractions may be obtained from the
same digitized images by conventional areal analysis with reasonable accuracy since
the void dimensions are generally large with respect to the optical system limitations.
Void volume fractions determined by acid digestion have limited accuracy due to the
small fractions being measured and the strong influence that the matrix density and

fiber weight measurements have on this value.

Fl,

,. 5931.; .

”E ‘ z.
. 15:3 ,

 

Figure 37. Same image with fibers counted and tagged.

truss-rams ’

33,“ “It
-v 3&2}
r

 

Figure 38. Boxes shaded to indicate number of fibers.

The time required for an ONVfA analysis includes that for standard micro-
structure specimen preparation, and approximately 4 minutes per image for
digitization, storage, and image analysis, with most of this being unattended
microcomputer time. In contrast, volume fraction determinations through matrix
removal by solvent or acid digestion involve boiling the composite in toxic cherrricals
for a period of hours followed by washing and drying of the fiber mass prior to

weighing.

 

Figure 39. Fiber map, one white pixel per fiber.

The spatial resolution of this method is extremely fine, an accurate volume
fraction may be determined by a single digitized image with an effective sampling
volume of only about 50 micrograms of material, selected from any point in a
composite cross section. Fiber distribution determinations within the image give
quantitative information on an even finer scale, limited only by the size of the fibers
themselves.

This report describes ONVfA in its current state of development and presents

experimental data which demonstrate the accuracy and resolution of the method.

 

Figure

 

Figure 4

 

82

              

  

«35“.?
“sewage
flaps... an r .21..

A. a.
nan... 5.?

s 5......
. i .34.. ti

     

   

 

Figure 40. Block areal density map, (fibers/box).

   

u> 33

 

Al madam one

Fibers / Grid Box —>

Figure 41. Fiber areal density distribution function.

83
4.3 QNYEA EXPERIMENTAL

ONVfA analysis of unidirectional graphite composite panels was conducted in
the following manner. Panels were sectioned along a plane perpendicular to the fiber
orientation and two or three samples from each were cast in standard acrylic specimen
mounts. The surfaces were then polished with standard composite microstructure
preparation techniques using firm polishing laps, light pressures, and sharp abrasives
to minimize the surface relief between the harder fiber-rich and softer matrix-rich
regions, followed by thorough ultrasonic cleaning to remove particulate residue. Care
was also taken to ensure that the polished surfaces were flat and parallel with the
bottoms of the specimen mounts in order to minimize focusing errors.

Microscope images of the prepared microstructures were then converted to
digital form by a computer with a video digitizer an analog to digital converter which
transforms the compOsite video signal from a video camera into a 320 X 200 pixel or
640 X 400 pixel image with 16 levels of brightness. Typical low resolution images
cover an area of approximately .35 X .25 millimeters and contain from 1500 to 2000
fibers in a screen. The coverage area was determined by digitizing images of a 100
line/ mm reticle along with each set of images.

Fiber volume fractions were directly obtained by multiplying the number of
fibers in each image by the average area of a fiber and dividing by the area of the
counting field without additional calibration factors.

The average cross sectional area of a fiber can be calculated from information
from product data sheets, and can be more precisely determined by weighing sections

of dried tow from the same lot or spool and dividing by the density, the number of

84

fibers in the tow and the length weighed. The fiber area used in this study was
calculated from the tow weight and density data supplied by the fiber manufacturer
for the same lot of fibers used to make the composite plates in the AC series of
specimens.

Void volume fractions were determined by performing conventional areal
image analysis on images for which optical contrast was maintained between the dark
matrix and the darker void regions. The void fraction was taken as the simple ratio
of these darker pixels to those associated with the fiber and matrix. The accuracy of
this method depends upon the size of the voids being large in comparison with the

resolution of the imaging system.

4.4 E IPMENT
The equipment employed in this experiment was as follows:
Amiga 500 Computer
Digi-view video digitizer
Panasonic WV 1410 B/W video camera
Olympus BHT Microscope with reflected light, IC20 20X objective lens, MTV
video camera adapter, 2.5 X photo projection lens

Microstructure specimen mounting and polishing equipment

85
4.5 QNEEA SAMPLE CALCULATIONS

The area within the counting-region was measured as follows. Images of an
Olympus 100 line/mm calibration slide were digitized during the data acquisition
session. At least three measurements of the horizontal and vertical spacings on the
image of this slide were made to determine that 292 pixels = .35 millimeter
horizontally, and 116 pixels = .15 millimeter vertically. The effective region scanned
by the counting software measures 316 X 202 pixels.

.35 mm/292 pixels = 1.199 microns/pixel horizontally

.15 mm/116 pixels = 1.293 microns/pixel vertically

(1.199 microns/pixel) X 316 pixels = .3787 mm/horiz.

(1.293 microns/pixel) X 202 pixels = .2612 mm/vert.

.3787 mm X .2612 mm = .0989 mmz/image
The average fiber cross sectional areas were calculated as follows. From the
Hercules data sheet for lot 708 - 4C:

Density .0636 lb/in3= 1.7605 g/cm3 = .0017605 g/mm3

Weight 47.94 X 10“ lb/in 12K tow = 8.561 X 10“ g/mm

Fiber Weight (8.561 X 10“ g/mm tow)/12,000 = 7.134 X 10'8 g/mm

Area per fiber 7.134 X 10'8 g/mm /.0017605 g/mm3 = 4.052 X 10" mm2

The volume fraction may then be determined from the average number of
fibers counted per image by:

V, = Fibers per image * Area per fiber/Area per image
For the example specimen fibers in 6 images from each of 3 samples from the

same composite plate were counted and averaged. Acid digestion tests were

86

performed on 3 other samples from the same plate.

1807 * 4.052 X 10’5 mm2 /.0989 mm2 = 74.0%

<
:3
ll

vr2 = 1755 * 4.052 x 10—5 mm2 /.O989 mm2 = 71.9%
v,, = 1763 * 4.052 x 10-5 mm2 /.0989 mm2 = 72.2%

Average fiber volume fraction by ONVfA = 72.7 %

The acid digestion fiber volume fractions for three samples from the same plate

measured according to ASTM procedure D317l-76 were:
Vf by acid digestion = 73.0%, 70.4 %, 71.8 %
Average = 71.7 %.

4.6 QNXEA RESULTS AND DISCUSSION

A set of three unidirectional composite plates was fabricated by autoclave
curing from Hercules AS4 fibers in untreated, treated, and treated and sized condition.
Optically determined fiber volumes reported for these specimens, designated AC-l,
AC-2, and AC-3, are averages of six images per specimen with three specimens from
each composite plate for a total of 18 images per plate. Three additional sets of 8
images each were made of the A03 plate as a check on repeatability. A second
group of three plates fabricated by hot pressing and designated HP-l, HP-2, and HP-3
was also analyzed by both methods, with two acid digestion tests performed per plate
and two sets of 12 images each utilized for ONVfA data. The fiber volume fractions
determined by ONVfA and acid digestion appear in Table 3 and are plotted in Figure

44.

Table 3. Volume fractions by ONVfA and Acid Digestion.

87

 

 

 

 

Sample I-IP-l HP—2 HP-3 AC-l AC-2 AC-3
ELEM} % % % % % %
ONVfA #1 65.9 66.3 66.6 74.0 69.6 69.2
ONVfA #2 64.4 65.9 67.3 71.9 68.2 69.1
ONVfA #3 72.2 66.1 68.5
ONVfA #4 67.9
ONVfA #5 67.0
M 57.0
ONVfA Average 65.0 66.1 67 .0 72.7 68.0 67.7
Acid D. #1 67.4 65.5 64.4 73.0 68.4 70.3
Acid D. #2 65.1 64.2 65.1 70.4 67.8 68.7
Acid D. #3 71.8 68.1 69.7
AD Average 66.2 64.8 64.7 71.7 68.1 69.6
Difference -l.2 -1.3 2.2 1.0 0.1 -1.9
(ONVfA-AD)

Low Vf 10.5 5.6 6.9 5.6 4.2 1.8
Regions

(< 75% Ave.)

 

The results are in agreement to within better than 2.5 % , with a standard
deviation of 1.4% between the two methods. The ONVfA results are randomly higher
or lower than the acid digestion values, with a negligible systematic error.

Fiber ”maps" which represent each fiber in a composite cross-section with a
single white pixel were constructed by combining 9 images from each of the
composite specimens and appear in Figures 42 and 43. Fiber distribution functions
for these same images were obtained by dividing the screen into 25 X 30 micron
boxes and determining the number of fibers in each. The results plotted in the graphs

in Figures 42 and 43 quantitatively descibe the visually evident matrix-rich regions of

 

nsERS/Box> FIBERS/Box» FIBERS/Box}

HP 1 HP2 HP3

Figure 42. Fiber maps and distributions for I-IPl, 2, and 3.

these composite specimens. The percentages of boxes which contain fewer than 75 %
of the average number for the composite are listed in Table 3. The largest matrix-
rich regions appear in specimen HP-l which shows a broad distribution function and
low fiber counts in 10.5% of the boxes while the most uniform appearing composite
is specimen AC-3, which shows a narrow distribution function and low fiber counts
in only 1.8% of the boxes. The average volume fractions for these same composites

differ by only 3%.

    

,1

8

FlBERS/BOX> FIBERS/Box» mama/Box»

AC 1 AC2 AC3

BOXES ———>
BOXES —->

Figure 43. Fiber maps and distributions for AC1, 2, and 3.

The principal source of errors in the ONVfA data was probably changes in
image size due to drift in the non-solid state video camera employed for digitizing.
The standard deviation among the calibration image areas was 1.4%, coincidentally
the same as that of the differences between the acid digestion and ONVfA results.
These size errors can be substantially reduced either by using a dimensionally-stable
CCD video camera or by including calibration marks in each image.

Another potential source of error is from systematic variations in the average

fiber areas. Regions with consistently smaller or larger-than-average fibers would

90

yield incorrect volume fractions with this method, but this was not observed during
this study. Fiber areas determined by measurements of fibers from the same spool
or batch used to produce the composite can minimize this error where higher accuracy

is required.

Table 4. Void volume fractions by areal analysis and acid digestion.

 

Sample I-IP-2 HP-3
Void Vf % %
Areal Analysis 4.2 3.5
Acid Digestion #1 4.8 2.8
Acid Digestion #2 5.1 1.8

 

Void volume fractions were determined for specimens HP-2 and HP-3 by areal
analysis of the ONVfA images and by acid digestion and appear in Table 4. Areal
analysis yielded a void volume fraction of 4.2% for HP-2 compared with 4.8 and
5.1% by acid digestion (ave. = 4.9%) and 3.5% for HP-3 compared with 2.8 and
1.8% (ave. = 2.3%) by acid digestion. These results show general agreement but
more data and more precise acid digestion tests are required to document the acuracy

of this method.

91

 

 

 

 

 

 

 

 

 

 

 

 

100
75 ' I I ' . o - .
ll .0 " 0. .- .0 .' ... I I... .
1..
5‘
Z
.9.
8
LE 25
E Legend:
E - ONVfA
g 0 Acid Difiestion
ii: 0
HP-l HP-2 PIP-3 AC-l AC-2 AC -3

Processing and Sample # HP — Hot Pressed AC - AutoClave

Figure 44. Fiber fractions by ONVfA and acid digestion.

4-7 W

ONVfA will be extended to apply it to a variety of fiber/ matrix combinations,
and to off-axis and non-unidirectional composites. Fiber maps produced by the
method will also be integrated with void fraction information obtained by areal
analysis to produce integrated representations of the distributions of fibers, matrix,

and voids.

92
4.8 W

An optical method for the determination of composite volume fractions has
been developed. The accuracy of the method is not influenced by small image
variations because the data is extracted as a digital parameter, the number of fibers.
The method is an absolute technique, which does not require calibration by any other
test, and which provides fiber volume distribution information with unequalled spacial

resolution.

CHAPTER 5

EFFECTS OF OXIDATIVE SURFACE TREATMENTS ON FIBER
SURFACE CHEMISTRY, FIBER-MATRIX ADHESION AND COMPOSITE
MECHANICAL PROPERTIES OF INTERMEDIATE MODULUS
CARBON FIBERS IN DGEBA/MPDA EPOXY

5.1 WIS

Intermediate modulus Hercules 1M6 carbon fibers with different amounts of
electrochemical oxidative surface treatments, and with an epoxy-compatible size were
subjected to an integrated set of surface analysis and mechanical tests to develop
relationships between processing, chemistry, and properties. Surface analyses
included XPS determination of surface oxygen and nitrogen, micro-Wilhelmy
measurements of polar, dispersive, and total surface free energy, and SEM
observation of surface morphology. Mechanical tests included single fiber tension
tests, single fiber fragmentation interfacial shear strength tests, and mode 11 fracture
toughness, short beam shear strength, and transverse flexural strength tests on
unidirection composites fabricated with a DGEBA/MPDA epoxy.

The first increment of surface treatment was found to produce a rapid increase
in surface oxygen, polar surface free energy, interfacial shear strength (ISS),
interlaminar shear strength, mode 11 fracture toughness, and transverse flexural
strength. Additional surface treatment caused surface oxygen, polar surface free
energy and ISS to increase at a lower, linear rate. Interlaminar shear strengths were
found to increase with the first increment of surface treatment, and to remain
approximately constant with additional surface treatment, indicating a transition to a
matrix-dominated failure mode. Mode 11 fracture toughness increased approximately

linearly with ISS, except for the sized fiber, which showed significantly greater

93

94
toughness. Transverse flexural strength results were somewhat variable, and may

have been influenced by artifacts from fiber bridging or volume fraction differences.

5.2 W

A coordinated set of experiments was performed to attempt to gain an
understanding of the nature of the changes in fiber/ matrix adhesion that occur with
increasing surface treatment and with sizing of PAN-based carbon fibers in an epoxy
matrix. These experiments were directed at measuring changes in fiber surface
composition and energetics, determining the influence these changes make in the
behavior of single fiber composites, and investigating the changes in the properties of
actual composite specimens. The tests were performed using Hercules Magnamite“
IMG fibers and are hereafter referred to as the "IM6" program.

Fiber/ matrix adhesion for carbon fibers in thermoset epoxy matrices has been
the object of numerous research efforts in recent years, since adequate adhesion is
understood to be a necessary condition for good composite performance. Some of
these programs have investigated the basic physical and chemical mechanisms of
adhesion, some have explored the influence of specific fiber surface treatments on
adhesion, while others have attempted to develop relationships between different
adhesion levels and composite properties.

One approach to the study of chemical aspects of fiber/ matrix adhesion has
been in terms of acid/base interactions. Schultz, et a1, investigated the adhesion of
an epoxy matrix to untreated, treated, and treated and sized fibers by comparing an
acid/base interaction parameter and surface free energy measurements, with
fragmentation test measurements [Schultz, 1987]. It was claimed that adhesion
correlated well with this specific interaction parameter, as measured by inverse gas
chromatography with acidic and basic probes, but very poorly with the total surface

free energy. These results must be considered in terms of the three types of fibers

95
studied, however. The surface free energy of a sized fiber is that of the sizing, not
of the fiber itself. The formation of an interpenetrating polymer network and of
crosslinks between the size and the matrix make simple surface energy interactions a
questionable physical model. A series of more than two treated but unsized fibers are
also needed to draw valid conclusions on this matter.

Recently, XPS was combined with adsorption studies to quantify the amount
of chemisorption between a similar AS4 fiber and both epoxy and amine functional
groups. Results indicated that the amount of either amine or epoxy chemisorbed was
less than 3% of the surface coverage [Hook, 1990].

A correlation between acid/base character and fiber/ matrix adhesion has also
been demonstrated by Farinato [1990], using continuous flow microcalorimetry. Of
particular interest was the finding that although most probes used were reversibly,
physically adsorbed, primary and secondary amines were found to be irreversibly,
chemically adsorbed. Since amines are present in the MPDA curing agent used in this
study, this suggests a possibility for primary chemical bond formation.

Crosslinking of epoxy resins in the presence of surface oxidized carbon has
been studied by FTIR [Garton, 1988]. Working with carbon black with an extremely
high surface area/weight ratio to maximize the spectra of species near the surface,
increasing oxidative surface treatment was found to increase crosslinking interactions
by the adsorption of the tertiary amines in the catalyst.

Numerous experimental surface coatings and treatments have been tested in
efforts to improve fiber/ matrix interphase characteristics. Electrocopolymerization of
various polymers directly onto fiber surfaces has been shown to produce small
increases in adhesion [Wimolkiatisak, 1989]. While the mechanism of action of epoxy
compatible finishes is usually described as promoting wetting and protecting the fibers
during handling, Drzal, et al, have proposed that it forms a higher modulus, but brittle

interphase that promotes adhesion while reducing toughness [Drzal, 1983].

96

The carbon fiber epoxy matrix interface has recently been reviewed by two
researchers [Wright, 1990], [Hughes, 1991]. Wright summarized results of studies
of alternative polmer fiber coatings, electrodeposition and electropolymerisation
techniques, theoretical analyses, and surface analytical methods. Wright concludes
that the bulk of current evidence suggests that primary covalent bond formation is not
a significant contributor to interfacial adhesion, that fiber surface area is a negligible
factor, and that the removal of a weak fiber surface layer and an increase in polar
surface interactions are the primary adhesion factors.

Hughes critically reviews carbon fiber/epoxy matrix interface research and
composite property influences [Hughes, 1991]. Possible sites of failure within the
fiber, interphase, and matrix are addressed, and the effects of Poisson’s ratio
differences addressed. Work on the internal and surface structure of carbon fibers and
their influence on failure are cited. Hughes concludes that simple conclusions about
optimal fiber surfaces are difficult to draw, due to the numerous relevant factors and
contradictory literature. He does state that adhesion is increased by some degree of
disorder in the fiber surface, by surface oxidation, and by mechanical interlocking,
particularly for high modulus fibers. The effects of sizing are considered highly
variable, probably depending on the fiber and size.

This portion of the current research effort was directed toward an investigation
of the effects of electrochemical surface treatment on the adhesion of intermediate
modulus PAN based carbon fibers to an epoxy matrix, and the resultant influence on
composite properties. The experimental program, results, and interpretation are
described in the following sections. Finally, chapters 6 and 7 investigate adhesion to
amorphous and semicrystalline thermoplastics with linear polymer structures for
comparison with this work on crosslinked, thermoset epoxy. The conclusions section
(chapter 8), will attempt to form an understanding of how the differences in chemistry

and structure influence fiber/ matrix adhesion.

97

5 .3 W

The 1M6 experimental program involved specially treated carbon fibers
obtained through the 'I'I‘CP-TP3 program (The Technical Cooperation Panel,
Technical Panel 3), an international research effort involving teams working in the
United States, United Kingdom, Canada, Australia, and New Zealand. A standard,
DGEBA/MPDA epoxy matrix material was used to allow results to be compared with
other sets of tests performed in this and other laboratories. The fibers were
characterised by several methods and were fabricated into single fiber fragmentation
specimens and high volume fraction unidirectional composite panels which were
subjected to mechanical testing. These materials, their characterization, and the

subsequent experimental program are described in this section.

5.3.1 1M6 EXPERIMENTAL MATERIALS

Hercules Magnamite", 1M6 intermediate modulus polyacrylonitrile based
carbon fibers were produced in a large, single batch, divided into sub-batches and
surface treated to different extents by a proprietary electrochemical oxidation process.
These treatments were defined as ratios of the standard surface treatment, considered
to be 100%, and were 0% (untreated), 20%, 100%, 200%, and 600%. These ratios
were determined by the number of coulombs of charge passed per unit fiber surface
area in the course of the surface treatment compared with that passed for the nominal
100% treatment. An additional batch was given 100% treatment and coated with a
proprietary epoxy—compatible "G" finish. The designations of the six fiber surface
conditions are: Untreated - 0ST, 20% treated - 20ST, 100% treated - lOOST, 200%
treated - 200ST, 600% treated - 6OOST, and 100% treated and coated - lOOGST.

98
Table 5. Properties of 1M6 fibers summarized from Hercules data sheet

 

PropertL U.S. Units SI Units
Tensile Strength 635,00 psi 4,378 MPa
Tensile Modulus 40.4 mpsi 278 GPa
Ultimate Elongation 1.50% 1.50%
Carbon Content 94.0% 94.0%
Density .0627 lb/in.’ 1.73 g/cm3
Filament Shape round round
Tow Twist none none
Tow Cross Sectional Area 4.17 X104 in.2 0.27 mm2
Fiber Cross Sectional Area 3.475X10'8 in.2 2.247 X 10“ mm2
Fiber Diameter 1.05X10“ in. 5.343 microns

 

The properties of 1M6 fibers are summarized in Table 5. The tensile modulus
of 278 GPa (40.4 mpsi) is greater than that of lower modulus fibers such as Hercules“
AS4, used as a standard in other programs in this laboratory due to pyrolysis of the
PAN precursor at higher temperatures and with greater draw ratios. This difference
in processing may be expected to produce a more highly oriented and more
graphitized structure with a greater number of graphitic basal plane sites exposed on
the surface and fewer edge, comer, or disordered non-graphitic carbon sites.

The epoxy matrix material used for all 1M6 series tests was Dow Chemical
Corporation, DER 331 resin, the diglycidyl ether of bisphenol-A, (DBGEBA) cured
With a stroichiometric ratio (14.5 phr) of metaphenylene diamine (MPDA). The

Chemical structures of these epoxy constituents are shown in Figure 45.

99

o
/ \ IH
H2C—CHCH20 (l3: OCH2 CH—CH2 90%
CH

10%

l
H2 c—CHCH 20-©—(|3-©-OCH2
(::0H
0
/ \ I H3 OCH
H2C—CHCH2O I 2
CH 3

DER 331 . diglycidyl ether of bisphenol -A

NI'II2
NH2

meta-phenylene diamine (MPDA)

Figure 45. Chemical structures of epoxy precursors.

100

The cure cycle used for all specimens in the IM6 program, both fragmentation
and full scale composite, was 2 hours at 75 °C followed by 2 hours at 125 °C and
slow cooling to room temperature in the oven or autoclave. Additional details on
processing appear in the sections on specimen fabrication. This cure cycle was chosen
to produce a matrix with identical properties to those of other research programs for
purposes of comparison. The initial tensile modulus of this matrix is 3.6 GPa (525
ksi) and the tensile strength of bulk specimens is 89.6 MPa (13 ksi).

5.3.2 CHARACTERIZATION OF FIBER SURFACE PROPERTIES

Surface properties of the treated IM6 fibers were characterized by X-ray
photoelectron spectroscopy for chemical composition, by micro-Wilhelmy wetting
studies to determine surface energetics, and by scanning electron microscopy to
determine surface morphological characteristics. The details of each of these sets of

experiments are described in the following sections.

5.3.2.1 XPS Surface Composition Analysis

The surface chemical compositions of the five treated, but unsized fibers were
determined by x-ray photoelectron spectrosc0py. Analyses were performed for
surface oxygen, nitrogen, and, by difference, carbon concentrations. Complete sets
of measurements were performed by two different XPS operators, Tad Devilbiss, and
Kevin Hook, using magnesium and aluminum anodes respectively.

X-ray photoelectron spectroscopy exposes a surface to a beam of approximately
monochromatic x-rays in an ultra-high vacuum chamber. Under this welbdefined
excitation energy, surface species are ionized, resulting in the emission of outer shell
electrons. The kinetic energy of the emitted electrons is equal to the difference in
energy between the X-ray photons and the binding energy of these outer electron

orbitals. This kinetic energy is measured by noting their deflection under a magnetic

101

field in a hemispheric energy analyzer. The binding energy is calculated and
compared with those of known species to identify and quantify the composition of
surface species. This information can also be used to deconvolute the bonding state
of the species, since this influences the binding energy.

XPS measurements were performed with a Perkin-Elmer PHI 5400 X-ray
photoelectron spectrometer with two different target anodes used. An Mg K-alpha
standard source was used for the first set of measurements while the second was

performed with a toroidal Al K-alpha monochromatic source.

5.3 .2. 1. 1 Chemical Composition
The chemical composition of the fiber surfaces were determined by comparing

peak areas for emissions from the C1,, 01,, and N ,, electron orbitals.

5.3.2.1.2 Chemical Group Deconvolution

Changes in bonding state exert an influence in the binding energy of all
electrons in a species, allowing information on the molecular state to be extracted
from XPS data. These data were obtained by deconvolution of the Cu peaks. The
C1, peaks allowed the separation of the carbon atom bonding states into graphitic,
phenolic (C-O-H), ketonic (C=O), and carboxylic (O—C=O).

5.3.2.2 Micro-Wilhelmy Surface Energy Measurements

Fabrication of composite materials without voids and with adequate
fiber/ matrix adhesion is only possible if the matrix material properly "wets" the
fibers, that is, the surface tension of the fibers must be less than that of the liquid

phase.

102
75v ' Ysr. : YLV (C05 9)

SPREADING 75v > 731. + 7w
9 = 0
YSV Liquid 9

   
 

 
 
   
  
     
 

st>Ysr
0<0< 9O

 

 

’YSV < ,YSL
90< 0 < 180

NON—WETTIN G

st

Figure 46. Surface tension influence on contact angles.

103

The micro-Wilhelmy balance [Li, 1984], [Hammer, 1980], is designed to
measure the work of adhesion of liquids with different degrees of polarity to solid
fiber surfaces. This work is defined as the energy required per unit area to displace
a liquid from the surface of a solid, substituting a solid-vapor interface for the
previously existing solid-liquid interface.

W. = 7m + 'st - 71.8
where WA is the work of adhesion, 7“, is the Liquid-Vapor surface tension, 'st is the
Solid-Vapor surface tension, and 715 is the Liquid-Solid surface tension.

The value of the contact angle of a liquid on a solid surface, at equilibrium,
is determined by the surface energies of the solid-vapor and liquid—vapor interfaces.
Contact angles of 0 degrees (Figure 46) exist when the liquid spreads over the solid
without limit. Contact angles between 0 and 90 degrees are considered to represent
wetting, while angles from 90 to 180 degrees occur when the liquid does not wet the
solid. At exactly 90 degrees the surface tensions of the liquid-vapor and solid-vapor
interfaces are equal. These relationships for the equilibrium condition are represented
by the Young equation:

7“ = 71.9 + 7”, * COS(0) where 0 is the contact angle.

The Wilhelmy balance determines liquid—solid contact angles by measuring the
force exerted on a solid object with a known perimeter when it is wetted by an
immersion liquid. Figure 47 shows the surface tension, contact angle, and resultant
force involved in this measurement.

Micro-Wilhelmy contact angle measurements were performed to determine the
fiber surface free energy and to resolve it into the polar and dispersive components

[Kaelble, 1974].

Contact

Liquid
Meniscus

Immersion
Liquid

 

 

 

 

Downward force P = YLV COS(O)

Figure 47. Fiber wetting force and contact angle measurement.

This resolution is made possible by assuming that the total free energies of the

solid and liquid phases are equal to the sum of their polar and dispersive components.

'YTL

'YPL + 'YDL
'YTs

7’2. + 7%
With suitable rearrangements and substitutions [Kaelble,l974], [Hammer,
1980] the following expression may be obtained:
[7t(l + 008(0)]/(27°r”’ = 7%” + 7%." (7"t/7°t)"’
A plot of 71 (l + cosO)/'yDL"’ against (will/7”,)" for immersion in two or more liquids

with different polarities should yield a straight line with a slope and intercept equal
to 'YPs and 'YDs-

The micro-Wilhelmy balance system that was designed for this program and

105

the surface energy measurements are described in the following section.
5.3.2.2.1 Micro-Wilhelmy Balance System

A block diagram of the Wilhelmy balance that was designed and constructed
for this program is shown in Figure 48. This system consists of an electrobalance,
computer controlled micro-stepping motor driven linear positioning stage, temperature
controller, A/ D interface card, microcomputer, vibration isolation table, and an
acrylic environmental housing. This system and control software was designed by the
author and assembled by Edward Drown. Software to control the balance, acquire
data, and perform subsequent analyses was written as part of this research program.
The source code for this software, written in MicroSoft QuickBasic° for the control
and acquisition portion, and MicroSoft AmigaBasicO for the analysis portion, appears
in Appendix D. The balance control and data acquisition software uses the
microcomputer to integrate the operations of the positioning stage, electrobalance,
A/ D converter,“ and temperature controller to provide a flexible, programmable
operating environment for contact angle measurements.

The data acquisition sequence was as follows. The electrobalance output was
first calibrated in the following manner. With the electrobalance, computer, A/D
converter and software operating, the system electronics were allowed to stabilize for
several minutes. With nothing on the electro-balance the A/D output was measured
and set as the zero baseline. A 20 milligram weight was then placed on the balance
at the reference weight position, 1/5 of the distance from the fulcrum as the sample
point, and therefore 1/5 as sensitive. This reference provided a calibration for the
balance electronics and A/D convertor, and set up the software to provide an output

calibrated in micrograms. Following calibration the weight was removed.

106

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Com uter Interface
Personal Computer '——> for SIepping Motor
RS-232
interfaced A/D Convertor
Temperature
Controller é
Balance
Electronics
Electrobalance +—‘ Mgcgfgetglg’lw
«- Fiber
I Fluid Filled
Temperature
Controlled
Container

 

 

 

Figure 48. Block diagram of micro-Wilhelmy wetting balance.

107

A set of fibers was mounted on nichrome or nickel mounting hooks with
cyanoacrylate adhesive, taking care not to contaminate the fiber surface away from
the hook and to align the fiber axis accurately with the hook wire. The mounted
fibers were allowed to dry at least 24 hours in a dessicator before measurement.

A mounted fiber was suspended from the loading hook of the electrobalance
and the balance output was set as the zero by the software, prior to immersion in the
liquid. The stage and electrobalance were then lowered by a manual command
through the computer until the fiber end was immersed in the liquid. The fiber was
carefully inspected to insure that it was immersed at a 90 degree angle to the liquid
surface and was not bent, or held out of the liquid by surface tension. This was a
particular problem with the untreated, low polar surface free energy fibers in a polar
liquid with high surface tension (water).

Ensuring that the fibers were accurately orthogonal to the liquid surface was
the most difficult part of the data acquisition sequence, and resulted in the principal

source of error. This is mainly due to the extemely small diameter of the fibers under
investigation, 5.35 microns, and the dependence of bending stiffness on the fourth
power of the radius. For comparison, AS4 fibers with a diameter of approximately
7 microns and a modulus 25% lower have a bending stiffness about 2.25 times
greater, making measurements much easier.

Following immersion and inspection the computer was instructed to perform
the following data acquisition sequence. The fiber was advanced 1.25 mm into the
immersion liquid and 30 seconds were allowed to elapse to stabilize the wetting force.
The load was then measured repeatedly and averaged by the software. After 5
immersion, pause, and load measurement cycles the the contact angles were calculated
from the measured load and the user inputted fiber diameter (perimeter) and the liquid
surface tension. Sets of 5 measurements were repeated until consistent values were

obtained as a further check on fiber/liquid alignment.

108
5.3.2.2.2 Micro—Wilhelmy Experimental Program

Contact angles were measured for sets of fibers with each extent of surface
treatment in distilled water and ethylene glycol. At least six separate fibers were
tested for each contact angle measurement, with multiple immersions and angle
measurements as described above until consistent values were recorded.

Average fiber diameters were used for perimeter calculations rather than
measuring each fiber individually because the small variance in diameter made this
unnecessary while the small diameter of the fibers makes direct optical measurements
inaccurate. Diameter measurements made with a light microscope and Filar eyepiece
produced identical coefficients of variation between measurements on the same or
different fibers. This indicated that the actual variation in fiber diameter was not

measurable by this technique.

5.3.2.3 Fiber Surface and Cross Section Examination

Fiber surfaces were examined by scanning electron microscopy (SEM) on a
JEOL ISM T330 SEM. Fibers were mounted on aluminum stubs with conductive
adhesive and gold sputter coated to a thickness of approximately 100 nm. To improve
contrast for surface morphology observations, fibers were tilted at 60 degrees to the
horizontal plane, (30 degrees to the incident electron beam). Without this tilt angle
the fibers appeared as perfectly smooth cylinders, with no resolvable surface detail.

A minor artifact resulting from electron beam damage to the gold sputter
coating layer during focusing and contrast adjustment was unavoidable. This damage
appears as a faint rectangular region in each image, and does not interfere with the
interpretation of surface morphological characteristics.

Fibers were prepared for cross sectional SEM observation by mounting on
diagonal mounting tabs on aluminum stubs with conductive paint, cutting the fiber

ends with sharp, surgical scissors, and sputter coating with approximately 100 nm of

109
gold. An attempt was made to prepare the fiber ends by breaking the fibers in tension
but the strength of the conductive mounting medium was insufficient. Attaching the
fibers with epoxy, breaking the fibers, and then grounding them with conductive paint

would allow these observations to be made.

5.3.3 IM6 MECHANICAL TESTING

Mechanical testing of IM6 composites consisted of single fiber tension tests,
fragmentation tests, and three sets of macro—scale mechanieal tests on fibers with each
of the six surface treatments. The macro-scale composite tests were performed by Dr.
Madhu Madhucar and were chosen for their sensitivity to interfacial effects and were:
mode II fracture toughness (end-notched flexural specimens), short beam shear
strength, and transverse flexural strength. Mechanical tests that show only a weak
dependence on interfacial strength and toughness, such as axial tensile strength, were
not a part of this study. The experimental procedures for the mechanical testing

program are described in the following sections.

5.3.3.1 Fiber Tensile Strength Tests

Tensile strength data for the series of IM6 fibers was available from other
TTCP participants only for 23 mm gage length fibers. Interpretation of fragmentation
test results requires a knowledge of the fiber strength at much shorter lengths,
comparable to the critical length attained during this test. To allow a meaningful
extrapolation to these lengths, tension tests at 2 mm gage lengths were performed for
two of the fiber types.

At 23 mm gage length, the highest and lowest strength fiber types were the
2OOST and untreated fibers, respectively. These two types were chosen to test at 2
mm gage length with the expectation that this would bracket the range of fiber types

at this shorter length.

110

Testing was performed by A. Ozzelo with an apparatus developed in this
laboratory for short gage length testing of reinforcing fibers, consisting of a fiber
mounting system, a translation stage, a 250 gram micro-load cell, and a chart recorder
for data acquisition.

Fifteen fibers each of the 2008T and untreated fiber types were subjected to
monotonic tension testing. Loads at failure were determined by measuring the
maximum deflection on the chart recorder, converting to millivolts and to grams at
maximum load. Fiber areas were determined by assuming a 5.35 micron diameter
and a circular cross section. Stresses were calculated as engineering stress,
(load/initial area), since the strain was small. The results of testing and details of the
extrapolation method used to approximate tensile strengths at the critical lengths

appear in section 5.4.2.1.

5.3.3.2 Interfacial Shear Strength Tests

Single fiber fragmentation tests, (SFF) were performed to measure the
interfacial shear strengths for each of the fiber treatments. A diagram of a typical
fragmentation test coupon is shown in Figure 49. This technique is described and
analyzed in detail in Chapter 2 and will not be repeated here. Fiber strengths at
critical lengths were determined by short gage length tensile tests and extrapolation
in a manner described in section 2.4.2.1. Fiber diameters were initially measured by
Filar eyepiece, but this method was found to be inaccurate for small diameter fibers
with only a small variation in diameter. For this reason, the average fiber diameter
from the Hercules product data sheet was assumed.

Fragment lengths were measured by two different techniques. Initial
measurements were performed with a Filar eyepiece, calibrated against an Olympus
calibration slide. Following the development of the FiberTrack, fragmentation data

acquisition and analysis system described in section 3.4.4, subsequent tests were

lll

Tensile coupon made One or more isolated fibers
from matrix material

 

 

 

 

 

 

 

 

Fiber repeatedly fragments
within gage length of specimen

 

Figure 49. Single fiber fragmentation test specimen.

performed with this system. Fragmentation test data have been reported in several
forms in the literature, including mean fragment lengths, LC/D aspect ratios, and as
interfacial shear strengths calculated by either a simple shear lag analysis or, with the
additional consideration of the statistical nature of fiber failure, a Poisson-Weibull type
analysis. The relative merits of these approaches are discussed in Chapter 2.

In this investigation, fragment length data were reduced by performing a
Poisson-Weibull analysis to determine the Weibull scale and shape parameters, and
from these an indication of the approximate interfacial shear strength. This method
has the advantage of simplicity, and ease of comparison with other work using an
identical approach. All Weibull and Gamma function calculations were performed
with the FiberTrack system.

5.3.3.2.1 Fragmentation Specimen Fabrication
Fragmentation specimens were fabricated by the following technique. The
outermost layer of each spool of fibers was unwound and discarded, exposing inner

fibers less likely to have been damaged or contaminated during handling and shipping.

112
Segments of tow approximately 25 cm. (10 inches) in length were cutoff and stored
in aluminum foil packets, taking care to handle the segments only at the ends. The
spools of fibers were then repackaged in aluminum foil and stored for later use in the
macro-scale composite specimens.

In a clean work area with intense illumination and minimal air currents, a foil
packet was opened and single fibers withdrawn while taking care prevent
contamination and minimize fiber damage. One end of the tow was teased and spread
until single fibers were accessible and one fiber was seized between the right thumb
and forefinger. This fiber was then pulled out from the tow along the tow axis to
minimize snagging due to lateral forces. When the fiber was pulled nearly free but
still attached to the tow it was grasped at the left end by the left hand and removed
from the tow.

The single fiber was then laid across the end sprues and gage section of a room
temperature vulcanizing silicone mold and released with the right hand. The right
side was secured at the outer edge of the sprue with a drop of hot-melt adhesive which
was then allowed to solidify. The fiber was then drawn straight by a light tension
from the left side and secured at the outer edge of the left spue by a second drop of
hot-melt adhesive. Light tension was maintained as the adhesive solidified, leaving
the fiber straight and accurately aligned with the gage section. This method provides
an advantage over attachment with rubber cement because the hot-melt adhesive flows
viscously until solidified, allowing better fiber positioning. The fiber was further
anchored in place with drops of rubber cement applied at the inner edges of the end
spues to maintain attachment during the rising temperature portion of the cure cycle,
when the hot-melt adhesive melts.

After fibers were mounted in all eight cavities in the mold, the dangling fiber
ends were trimmed off and the mold assembly stored in a dessicator overnight to

allow the rubber cement solvent and surface moisture to evaporate.

113

Resin was prepared in the following manner. A sufficient amount of a
stoichiometric ratio of DGEBA and MPDA (14.5 phr of metaphenylene diamine in the
diglycidyl ether of bisphenol-A) were weighed in disposable laboratory beakers and
placed in a vacuum oven at 75 °C and under a very slight vacuum to initiate
outgassing while avoiding boiling the MPDA. The MPDA was stored in a dark
refrigerator prior to use to minimize degradation. When the MPDA was fully melted
the beakers were removed, thoroughly mixed, and returned to the vacuum oven.
Outgassing then procwded at low vacuum until the resin mixture stopped bubbling,
approximately five minutes.

The mold assemblies were withdrawn from the dessicator and briefly outgassed
in the vacuum chamber to completely dry the surface. The molds were then removed
and placed on a surface tilted approximately 20 degrees to the horizontal. The
resin/ hardener mixture was introduced to the mold cavities by pouring from the
elevated ends. This causes the resin to sweep along the fiber and avoids entrapment
of air bubbles. The filled molds were lowered to horizontal and excess resin was
removed with a dropper from the ends, taking care not to disturb the fibers.

The filled mold assemblies were then placed in the curing oven which had been
previously raised to the initial cure temperature of 75 °C. Following the complete
cure cycle of 2 hours at 75 °C and 2 hours at 125 °C the oven was allowed to slowly

cool overnight and the specimens removed at room temperature.

5.3.3.3 Fabrication of Composite Specimens

High volume fraction unidirectional composite panels were fabricated for
mechanical testing by the following means. Unidirectional prepreg tape was first
fabricated by hot melt prepregging, and then cut, laid up into composite panels, and
consolidated and cured in an autoclave. Tape was produced by passing the fiber tow
through a batch of DGEBA/MPDA held at 52 °C (125 °F) and removing excess resin

114
by passage through a slit die. The impregnated tow was wound onto a mylar film
covered drum at a tension of about one kilogram and a speed of approximately 3
meters per minute. When a single layer tape was complete the mylar film was cut,
removed from the drum and manually laid up to form the unidirectional composites.
A teflon release layer was incorporated at the central plane of the 24 ply laminate
panels for the mode 11 fracture toughness specimens.

Specimens were cured in an autoclave for 2 hours at 75 °C (167 °F) and 2
hours at 125 °C (257 °F) and 0.69 MPa pressure (100 psi). The vacuum bags were
evacuated for 15 minutes at the beginning of the cycle to remove air and dissolved
gasses and then the vacuum was released. Specimens were slowly cooled to room
temperature before removal from the autoclave.

Test specimens in the geometries shown in Figure 50 were cut from the

composite panels by a high-speed diamond impregnated saw with a water cutting fluid.

l 15
50 50

b
(Width = 25 mm)

j:

e w
110

 

 

25

 

 

3.4

 

 

    

 

 

End Notched Flexure Specimen (Mode 11 Fracture Toughness)

(Width = 6.5mm)

   
   
   

10
14.8

Short Beam Shear Strength Specimen

 

 

 

 

 

 

 

e 130 h

 

 

Transverse Flexural Strength Specimen

Figure 50. Mechanical test specimen diagrams.

116

5.3.3.4 Volume Fraction Analysis by ONVfA

The composite plates produced for mechanical properties evaluation were
characterized by three different means. Fiber volume fractions were determined by
Optical Numeric Volume Fraction Analysis, (ONVfA), which was developed as part
of this research effort and is described in detail in chapter 3 was performed by Brian
Rook. The statistical distribution of fibers was determined by the same means to find
the amount of fiber poor regions. Void contents were measured by areal image
analysis.

5.3.3.5 Mode 11 Fracture Toughness Tests

End-notched flexural specimens were produced from the 24 ply, unidirectional
panels with the previously incorporated teflon release strip serving as the crack starter.
These specimens were subjected to three point bending on a closed-loop
servohydraulic actuated MTS mechanical testing machine by Dr. Madhu Madhukar.
Strains were monitored by adhered strain gages and extensometers and recorded with
an IBM P82/30" microcomputer data acquisition system. Maximum specimen

deflections were obtained from the machine crosshead displacement.

5.3.3.5 Transverse Flexural Tests

Three point transverse flexural data were obtained in accordance with ASTM
D-790 specifications. Testing and data acquisition was performed on the MTS testing
machine described in section 5.3.3.4 by Dr. Madhu Madhukar. The specimen

deflection at the midpoint was taken to be equal to the crosshead displacement.

5.3.3.6 Short Beam Shear Tests
Short beam shear strength tests were performed in accordance with ASTM D-

2344 specifications. Testing and data acquisition was performed on the MTS testing

117
machine described in section 5.3.3.4 by Dr. Madhu Madhukar. These specimens are
designed to fail in shear along the central plane rather than by microbuckling or
tensile failure at the top or bottom. This is accomplished by making the specimens
relatively short, since the midplane shear is proportional only to the shear traction,
and is not a funcion of length while the tension and compression stresses increase with

increasing specimen length.

5.3.3.7 SEM Fractography of mode 11 and Transverse Flexure Surfaces

Failure surfaces of end-notched flexural specimens (mode II) and transverse
flexural specimens were examined by scanning electron microscopy. Documentation
was performed by producing raster-scan photographs at specific distances from the
crack-initiaion notch with the built in Polaroid camera and by videotaping the SEM’s
composite video output while traversing stepwise across large regions of the failure
surface. In this manner high resolution photographic images of representative sites
were recorded for publication and interpretation. while large areas of the failure
surfaces were stored on videotape at lower resolution for later observation and

verification of the representative character of the photomicrographs.

5.3.3.8 Birefringence Evolution Sequence Acquisition

Birefringence evolution sequences and animations (BES and BEA) were
produced for each of the IM6 surface treatment and sizing conditions in DER 331 with
14.5 phr MPDA cured under the standard conditions (2 hr at 75 °C and 2 hr. at 125
°C). These sequences consist of sequences of microscope images of the regions
surrounding fiber breaks, viewed under crossed polarizers, and recorded at
incremented coupon strains.

By assembling entire sequences of images for subsequent analysis, this method

provides a more complete picture of the nature of interfacial shear stresses, and of the

118
interfacial failure modes, than do images obtained at a single strain level.

For complete documentation of birefringence patterns, all of the relevant
experimental variables must be recorded or controlled. In addition to the fiber type,
surface treatment, matrix type and cure conditions, other factors may exert both a
quantitative influence on the extent of interfacial failure, and a qualitative influence
on the failure mode. The coupon strain at which the images are obtained is the most
obvious of these factors, and has been reported by some, but not all researchers. The
strain-at-failure of the fiber break at the center of the birefringence pattern also
strongly effects their characteristics, and appears to have been neglected. The lengths
of the fiber fragments adjacent to each break may also play a role in determining the
mode of failure.

In this investigation, the first image in each birefringence sequence was
recorded at approximately the strain-at-failure of the break. This was accomplished
by viewing a large region of the specimen at low magnification while slowly
increasing the coupon strain. When a new break occurred, straining was immediately
halted, the strain recorded, and the sequence acquisition begun.

Acquisition was performed by digitizing the composite video output of a
Panasonic‘D CCD video camera attached to an Olympus‘D microscope with crossed
polarizers. Digitization was accomplished with a DigiView" video A/D convertor
interfaced with an Amiga 500" microcomputer. Images were acquired in a low
resolution mode, 320 X 200 pixels at 16 shades of gray (4 bit gray scale resolution).
While beneath the maximum available resolution of 768 X 480 pixels with 16 shades
of gray, this precision was sufficient to resolve most of the important image details.

Sequences of images at successive strain increments were acquired in the
following manner. The length at zero strain between transverse fiducial marks on the
specimen gage section was determined by noting the distance translated by the

Newport” stage while moving between the marks as compared against an eyepiece

119
reticle. This length was taken as the reference I.0 and used to measure the coupon
strain. The coupon strain was incremented by increasing the displacement of the
straining stage (described in section 3.3.2). This increase was determined by
advancing a predetermined displacement as measured with a machinists’ dial gage.
The actual coupon strain was then determined by measuring the change in the distance
between the transverse fiducial marks.

Each image was centered on a fiber break which occurred at a well defined
fiber failure strain as described previously. The distance from this break to a fiducial
mark was noted to allow subsequent identification. After incrementing and measuring
the coupon strain, the stage was advanced until the break of interest was located, and
the break was accurately centered against a crosshair drawn on the video monitor to
minimize rigid body displacements. The image was then digitized and saved to
diskette.

A series of birefringence images was defined prior to acquisition, including the
measured strain at fiber failure, the intended strain increments during extension and
retraction of the coupon, the strain at maximum extension, and from these values, the
number of images. This series of strain levels was approximated by use of the dial
gage and a previously made calibration graph, and measured more precisely during
acquisition as described previously.

A sequence of digitized birefringence images saved on a diskette was then
loaded as frames in a computer animation and graphics program for subsequent
processing. Each image was then precisely positioned to cancel all remaining rigid
body motion and make the fiber break appear in the same screen location in
subsequent frames. The entire sequence of images was then framed and "grabbed"
as an "animation brush". This brush was saved to disk and used to produce
birefringence evolution animations and the birefringence sequences that appear in

section 5.4.2.8. These sequences were printed out with a laser printer controlled by

120
a desktop publishing program.

During the course of these investigations it has become increasingly clear that
meaningful, representative fragmentation test birefringence patterns can only be
acquired when all of the relevant experimental variables have been controlled or
recorded. More than one break at each of a range of fiber failure strains and coupon
strains may be required to present a complete, representative set of birefringence

patterns. Additional discussion of these variables appears in sections 2.5 and 5.4.2.8.

5.4 W
The results and interpretation for the IM6 experimental program appear in this
section. Where appropriate, comparable data for Hercules AS4 fibers, obtained from

other researchers in this laboratory, are included to indicate trends.

5.4.1 FIBER SURFACE ANALYSIS RESULTS
The results of the fiber surface analyses by XPS and surface morphological

examination by SEM appear in the following sections.

5.4.1.1 . Surface Chemical Composition Results

The XPS surface composition analysis results for IM6 fibers with increasing
oxidative surface treatment appear in Table 6 and are plotted in Figure 51 (surface

oxygen percentage) and Figure 52 (surface nitrogen percentage).
The untreated fibers were found to have a very low surface oxygen percentage,
2.21%. Surface treatment to 20% of the nominal value resulted in significantly
greater surface oxygen, 5.59%, a threefold increase. Surface treatments to 100%,
200% , and 600% of the nominal value further raised oxygen content at a rate that was
closely linear to treatment percentage over the range from 20% to 600%, as can be

Seen in Figure 51. This rate of increase was much lower than for the step from

 

121
untreated to 20%. resulted in 8.26% oxygen. These results were consistent for all
samples, and in good agreement with results from a previous analysis, except for a
small, consistent, shift of approximately 2.25 % which may be attributed to calibration

differences.

Table 6. Surface oxygen, nitrogen, and functional groups on IM6 fibers.
TreatmenL 0% 20% 100% 200% 600%

Oxygen (%) 2.21 5.59 6.85 8.26 15.62
Std. Dev. (%) 0.51 0.72 0.36 0.39 1.34

Nitrogen (%) 1.68 1.85 1.86 1.88 4.77
Std. Dev.(%) 0.44 0.36 0.25 0.26 0.41

Phenolic (%) 1.2 4.4 4.7 4.9 6.5
Ketonic (%) 1.9 2.8 3.1 4.3 8.6
Carboxylic (%) 2.3 2.5 2.5 2.3 3.0

 

Surface nitrogen percentages measured by XPS appear in Table 6 and Figure
52. Nitrogen remained nearly constant at about 1.8% for surface treatments ranging
from 0% to 200% surface treatment, but increased significantly with 600% surface
treatment to 4.77%. These results are also in agreement with those from the previous
analysis, except that an increase was also found to occur between 100% and 200%
surface treatment in that set of tests.

The large increase in oxygen content resulting from 20% surface treatment in
comparison with the smaller rate of increase from 20% to 600% treatment may result
from either or both of a pair of mechanisms. One possible source of this change in
reactivity is the availability of edge and corner sites on the graphitic lattice of the

untreated fibers, as well as bonding sites on more disordered, non-graphitic carbon.

122

 

 

16

 

l2

 

 

 

 

 

 

 

 

 

Oxygen /6 —->
.5
LL
N

 

 

O 20 100 200 600
Fiber Surface Treatment Percentage
Legend: '1' Set 1 with error bars 0 Set 2

Figure 51. Surface oxygen percentage by XPS.

123

 

 

16

 

l2

 

L///‘i

 

b

 

 

 

 

 

 

 

Nitrogen % —>

 

 

U 20 100 200 600
Fiber Surface Treatment Percentage

Legend: -I- Set 1 with error bars 0 Set 2

Figure 52. Surface nitrogen percentage by XPS.

124
Carbon atoms in these configurations are much more susceptible to attack by reactive
species than are the extremely stable graphitic basal plane atoms. The availability of
a greater number of these sites would result in an initial, rapid uptake of oxygen by
the untreated fiber, followed by a slower reaction rate when the most active sites are
filled and the basal plane atoms are all that remains.

A second possible mechanism is the removal of an exterior "skin" during the
early stages of electrochemical oxidation. A ”skin-core" morphology for PAN based
fibers has been reported in the literature [Lee, 1991]. The removal of carbon material
from fibers during the surface treatment process has also been noted [Drzal, 1987].

Since this analysis would require access to information that is proprietary to
Hercules Corporation it was not further addressed in this work. However, based on
the available data, the relatively small amount of treatment required to effect the
change, only 20% of the nominal value, or less, since the slope appears to have
already changed when this lowest treatment level is attained, appears to favor the

depletion of reactive sites model over the skin removal model.

5.4.1.2 Chemical Group Deconvolution Results

Deconvolution of the XPS spectra was performed by Kevin Hook and Javad
Kalantar and the results appear in Table 6 and are plotted in Figure 53. The groups
were designated in three types; phenolic carbon within an aromatic ring structure and
singly bonded to oxygen, ketonic carbon doubly bonded to oxygen, and carboxylic
carbons bonded to two oxygen atoms, one singly and one doubly. The carboxylic
carbon concentration remained approximately constant for all surface treatments at
2.5%, increasing slightly with 600% surface treatment to 3.0%. In contrast, both the
phenolic and ketonic carbon atom concentrations increased with increasing surface

treatment, following the same pattern as the surface oxygen percentage.

125

 

 

 

 

 

 

 

 

 

 

 

 

 

 

W4
' J
./ 9
C—O )
0
0 20 mo 200 600

Fiber Surface Treatment Percentage —>
Legend: I'_'l Ketone Functional Group (%)
O Carboxylic Acid Functional Group (%)
+ Phenolic Functional Group (%)

Figure 53. Surface functional groups versus surface treatment.

10

h

N
Chemical Group % —->

C

126

The untreated fibers were found to contain very low concentrations of phenolic
and ketonic carbon while surface treatment to 20% substantially increased both group
concentrations. Additional treatment between 20% and 600 % increased concentrations
at rates that were very nearly linear with respect to the surface treatment. The rate
of increase of ketonic carbon was approximately 2.8 times faster than that of phenolic
groups. Both increases matched a linear least squares fit with correlation coefficients
greater than .996 over the interval from 20% to 600% surface treatment.

While the increase in functional group percentage was highly linear over the
range from 20% to 600%, this rate was about a factor of 40 lower than that between
0% and 20% surface treatment for the phenolic carbons and a factor of 4 lower for
ketonic carbons. Clearly, the carbon on the virgin fiber surface is much more

susceptible to electrochemical oxidation than that on treated fibers.

5.4.1.3 Micro-Wilhelmy Surface Energy Results

The results of the micro-Wilhelmy surface free energy measurements appear
in Table 7 and are plotted in Figure 54. Results are reported as the total surface free
energy and decomposed into polar and dispersive components.

The polar component of the surface free energy increases significantly with
increasing surface treatment in the increments from 0% to 20% surface treatment and
from 200% to 600%. Negligible change occurred between 20% and 200% surface
treatment. This closely follows the pattern of surface oxygen percentage, as indicated

in Figure 55, which plots polar surface free energy against surface oxygen percentage.

127

 

 

 

40

 

30

 

 

20*

 

 

 

10

 

 

3"" 2+ Surface Free Energy

 

 

 

 

 

 

0% 20% 100%

200%

600%

Fiber Surface Treatment Percentage —>

D Total Surface Free Energy

0 Polar Free Energy
I Dispersive Free Energy

Figure 54. Fiber surface free energy versus surface treatment.

Table 7. Polar, dispersive, and total free energies on IM6 fibers.

 

Wilt 0% 20% 100% 200% 600%
Dispersive Surface 24.0 17.4 20.0 19.1 12.1
Free Energy (mJ/M’)

Polar Surface 14.8 26.1 26.3 25.4 43.0
Free Energy (mJ/Mz)

Total Surface 38.8 43.5 46.3 45.3 55.1

Free Energy (mJ/Mz)

‘

128

Since oxygen is a strongly electronegative species, it tends to withdraw
electrons from carbon when chemical bonds exist between the two, producing a net
electrical dipole. An increase surface oxygen chemisorbed on a carbon substrate
should therefore increase the polar component of the surface free energy, as observed.
The close correlation between surface oxygen and polar free energy plotted in Figure
55 provides support for both experimental results and for the conclusion that the
oxygen is present in chemisorbed, rather than physisorbed form.

The dispersive free energy undergoes little change with increasing surface
treatment, aside from small decreases between 0 and 20% and between 200% and
600% , the same increments that produce large increases in the polar component. This
reduction probably results from the lower lability of electrons in the electronegative
species, oxygen and nitrogen, which are increased substantially in these treatment

intervals, as compared with the more mobile electrons present in graphitic carbon.

50

40

30

to
O

Polar Free Energy —>
'5

O

129

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Surface Oxygen Percentage —>

Figure 55. Polar free energy versus surface oxygen percentage.

/
/
//..o.
///

20 o 3'71”,”

/
/'”
0 2 4 6 8 10 l2 14 16 18

Legend: 0 Fiber Types. Untreated (U) through BOOST (600)

20

130
5.4.1.4 Fiber Surface and Cross Section Examination Results

Fiber surface morphology was observed by scanning electron microscopy. No
significant changes in morphology were detectable by this method for the range of
surface treatments investigated. Faint axial striations were observed for all surface
treatments (Figures 5 6 and 57). The relief of these striations was much shallower
than that of AS4 fibers, as indicated by the much greater difficulty in producing an
image with noticable contrast.

The finish on the lOOGST fibers was observed to be somewhat irregular,
varying in thickness along the length of the fiber. This irregularity was small enough,
and the change occurred over a length of fiber long enough, that it could not be
readily recorded photographically. Magnifications that were low enough to include
a length of fiber with irregularities were too low for the changes to be visible. Higher
magnifications which could resolve the surface properly did not include enough of the
fiber to show any changes. By using high magnifications and translating the stage
parallel to the fiber axis, however, changes in the thickness of the finish were
apparent. Striations were faintly visible on these fibers in regions where the finish
was very thin.

An SEM of the cross section of an IM6 fiber appears in Figures 58 and 59.
A folding pattern that results from the pyrolysis and extension of the PAN precursor
material can be seen. The fact that the fibers are not homogeneous, defect free
structures is also evident. The fiber interior is complex and convoluted, with many
levels of structure from the graphitic mosaic at a scale of tens of Angstroms, through
these folds, a micron or more in extent.

This intrinsic defect structure influences the failure behavior of carbon fibers
and impacts both the fragmentation tests and the performance of macroscale

composites.

15KU #415,886

 

Figure 57. SEM of fiber surface morphology #2.

132

 

Figure 58. SEM of fiber cross section #1.

 

Figure 59. SEM of fiber cross section #2.

133
5.4.2 MECHANICAL TEST RESULTS

The results of the mechanical testing program appear in this section.

5.4.2.1 Fiber Tensile Strength Results

The results of the fiber tensile tests appear in Figure 60, plotted along with
those measured at 23 mm gage lengths by other TI‘CP participants.

Although the untreated and 200% surface treated fibers were chosen for short
gage length testing because they were expected to represent the weakest and strongest,
respectively, values for the complete set of fiber conditions, the measured strengths
were reversed in order. The untreated fibers were found to be slightly, but
consistently, stronger than those with 200% surface treatment at 2 mm gage length,
in contrast to their order at 23 mm. This result also runs counter to the usual
experience that untreated fibers are weaker than those with some degree of surface
treatment, a finding that has been attributed to the removal of a surface layer
containing flaws that initiate failures.

Since the surfaces of the IM6 fibers were found to be considerably smoother
than Hercules AS4 fibers when examined with scanning electron microscopy, the
strength difference may result from the lack of critical sized flaws at sufficiently short
gage lengths. These small differences may also result from spool-to-spool strength
variations, and may have no real significance. Aditional data was not available and
attempts to draw any conclusions on this matter were not pursued.

The requirement for a knowledge of the fiber strengths at short gage lengths
was met with these data by making the following assumptions and extrapolations.
Since the strength was found to be a weak function of surface treatment, and since this
function reversed when moving from long to short gage lengths, this factor was
assumed to be negligible when making the extrapolation to critical length. Instead,

an average value for the strength at both 23 mm and 2 mm gage lengths was

134

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E Extra olated
E Stren ths
8000 2
7000 i \
\_U
200K Experimental Data
6000
\
II
600
5000
II 3
200
--200
4000
II
IOCIICIIST ‘3 U
3000
I \
I90
2000
II
20 i
1000
(U
a.
2
~1 1 2 4 s 23 100
Log Scale of Fiber Length (mm) —-.-
L en : i 1 A I ‘ ‘
eg d U 20 100 200 600 lOOGST

Critical lengths @ surface treatment in epoxy.

Figure 60. Extrapolation of fiber tensile strengths to critical lengths.

135
determined for all the fiber types measured (all types at 23 mm, untreated and
200%ST at 2 mm). These two average values were plotted on a semi-log graph of
the strength versus the log of the gage length (Figure 60). A line between the two
points was extended to the range of the critical lengths and the strength at the
measured critical length for each surface treatment read from the graph. These

strengths are reported in Table 8.

Table 8. Critical lengths, L,/D’s, tensile strengths, and ISS for IM6 fibers.

 

Fiber Critical L,/ D Weibull Strength ISS
Surface Length (D = 5.35) Shape @ Lc

Type (microns) Parameter (MPa) (MPa)
0% 708 132 3.6 7700 37
20% 466 87 2.8 8200 66
100% 413 77 3.3 8300 70
200% 349 65 3.1 8400 86
600% 267 50 3.3 8800 115
lOOGST 348 65 2.9 8500 90

 

5.4.2.2 Fiber Volume Fractions and Distributions
The fiber volume fractions, void volume fractions, and percentages of fiber-
poor regions for the 24 ply, and 12 ply composite panels appear in Table 9 and appear
in Figures 61 and 62. The fiber volume fractions for most panels were found to be
approximately constant, with only minor variations, except for lower fiber fractions
found in the 24 ply lOOGST panel, at 59.3% and the 12 ply 600%ST panel, at 62.6%.
The average volume fractions and standard deviations for the two types of
composite panels for all six fiber types were found to be:
12 ply average = 68.7%, deviation = 3.3%
24 ply average = 68.7%, deviation = 4.7%
The fiber-poor regions, defined as the percentage of 25 micron square regions
Containing less than 75% of the average number of fibers, were also very consistent,

With slightly higher than usual numbers for the 24 ply 600%ST and 12 ply 100%ST

136
panels. These values are still low enough to indicate good quality composites with
uniformly distributed fibers and minimal impact on material properties.

The void volume fractions for all panels were found to be well under 1% for
all cases except the 12 ply 600%ST and lOOGST panels, which were found to have
1.4% and 1.5% void contents respectively.

In summary, ONVfA and areal void analysis suggests that all panels were well
fabricated, with minor defects present in the 12 ply 600%ST and 100GST panels from
voids, and lower than average fiber volume fractions present in the 24 ply lOOGST
and 12 ply 600%ST panels.

Table 9. Fiber and void volume fractions by ONVfA.

Panel Type 0% 20% 100% 200% 600% lOOGST
12 Ply

Fiber V, % 72.1 68.7 72.7 68.0 62.6 68 0
Void V, % 0.3 0.8 0.4 0.4 1.4 l 5
24 Ply

Fiber V, % 72.5 71.9 71.6 70.7 66.2 59.3
Void V, % 0.6 0.4 0.3 0.3 0.1 0.0

 

137

100

 

80

 

 

 

 

 

 

 

 

60 ii. H?—
01 1 1 i l

 

 

 

 

 

Untreated 208T l 008T ZOOST 6008T lOOGST

'I' Fiber Volume Fraction with Standard Deviation
0 Percentage of Fiber- Poor Regions

Figure 61. Fiber volume fractions and distributions for 24 ply laminates.

138
100

 

80

 

 

40

 

 

20 . 3 3, 3 4

Untreated 208T lOOST 2OOST 6008T 1 00C ST

 

 

 

 

 

 

 

 

* Fiber Volume Fraction with Standard Deviation

0 Percentage of Fiber- Poor Regions

Figure 62. Fiber volume fractions and distributions for 12 ply laminates.

 

139
5.4.2.3 Interfacial Shear Strength Results

The results of the single fiber fragmentation interfacial shear strength tests
appear in Table 8 and are plotted in Figures 63 and 64. The untreated fibers showed
very poor adhesion, with an L,/D of 132 and an ISS of 37 MPa. Adhesion improved
substantially with 20% surface treatment. The LC/D ratio decreased to 87, the ISS
increased to 66 MPa.

Surface treatment to 100% of the nominal value further improved adhesion,
but by a smaller amount than for the step from 0% to 20%. The L,/D ratio decreased
to 77 and the ISS increased to 70 MPa. Treatment to 200% again increased adhesion,
with L,/D equal to 65 and ISS of 86 MPa.

Surface treatment to 600% of the nominal value significantly increased
adhesion to 115 MPa. A nearly linear increase in ISS was observed over this large
increment in surface treatment as shown in Figure 63.

The sized fibers, lOOGST, showed an increase in ISS over the 100%ST equally
treated but unsized fibers, giving an ISS approximately equal to that of the 200%
surface treatment.

Figure 64 shows the ISS values of surface treated IM6 fibers along with those
for untreated (AU4), surface treated (A84) and treated and sized (AS4C) carbon
fibers. Although the moduli of the IM6 fibers is about 25% higher than the AS4
fibers, corresponding to greater orientation achieved during fabrication, the ISS values
for the corresponding types are virtually identical. Surface treatment results in
significant increase for both types, and sizing adds another smaller, but still significant

increase.

140

 

120

 

100

 

so
O

r/l/

 

 

Interfacial Shear Strength
8

.5
C

 

20

 

 

 

 

 

MPa —->

 

 

 

0 20 100 200
Fiber Surface Treatment Percentage —->

Legend: 0 Surface Treated
I Surface Treated and Sized

Figure 63. Interfacial shear strengths for IM6 fibers.

141
120

 

 

100

 

 

80

 

60

 

40

I...

   

 

 

 

 

U AU4 20 100 AS4 200 600 100G AS4C
Fiber Surface Treatment (1 M6) or Designation (A4)

Legend: 7
I /

1M6 AU4. AS4. AS4C

 

 

MPa

 

 

 

 

Figure 64. Interfacial shear strengths for IM6 and A4.

142

Surface Oxygen Percentage —--
0 2 4 6 8 10 12 14 16 18 20

 

120 4

/
/. /600:;r
110

 

 

 

 

 

 

 

 

 

100 ’
/
9o /// [A

zoosr i. /1- /
.5 10081‘7J/ 11
3:0 70 ,
1,3 ZOSIT y /0
U) 60 /
/ /
-'= / /
2 50 ,
.e / /
a; / x
g 40 // I /I Uintneated
r /

30 ,

 

 

20 /

/

0 10 20 30 40 50
Polar Surface Free Energy (mJ/ M2) __-

 

(MP3) ——>

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Legend:
I Interfacial Shear Strength versus Polar Surface Free Energy

I Interfacial Shear Strength versus Surface Oxygen Percentage

Figure 65. ISS versus surface oxygen and polar surface free energy.

143

 

120
7%

 

—I—l

100
C):

 

on
C

T

-o
/%

 

 

Interfacial Shear Strength
8

K

 

l \l

 

 

20

 

 

 

 

 

 

 

MPa—>

0 20 100 200 600

Fiber Surface Treatment Percentage _p
Legend: I Interfacial Shear Strength (MPa)

El Ketone Functional Group (%)
O Carboxylic Acid Functional Group (%)
+ Phenolic Functional Group (%)

Figure 66. ISS and functional groups versus surface treatment.

10

N 4)
Chemical Group % —>

C

144

Figure 65 plots the interfacial shear strength for IM6 fibers against the surface
oxygen percentage and polar surface free energy. Both plots are approximately linear,
indicating a close correspondence between the surface treatment, surface oxygen,
surface free energy, and ISS.

Figure 66 shows both the interfacial shear strength and the surface functional
groups plotted against the surface treatment percentage. The similarity in the pattern
of rapid increase in property, or composition, with initial surface treatment increment
followed by a slower rate of increase with additional surface treatment can be clearly

86811.

5.4.2.3.] Birefringence Evolution Sequence Interpretations

Birefringence sequences for each fiber surface treatment condition appear in
Figures 67 - 72. The coupon strain is listed at the right of each image, and the first
image in each sequence was taken at the approximate failure strain of the break. As
described in Chapter 2, the strain-at-failure of fiber breaks can have a significant
impact on failure modes. These images of only one break per fiber surface treatment
can only represent the behavior of the system at that break’s failure strain and may
not be the same as the behavior at lower or higher strains.

The untreated fiber (Figure 67) gave extremely weak birefringence patterns,
indicative of an interfacial failure mode and weak frictional tractions after debonding.
This fiber break occurred at 1.6% coupon strain, which was sufficiently high for the
fiber to undergo interfacial debonding immediately upon failure. These patterns were
significantly less intense than those for AU4, untreated A4 carbon fibers. Debonding
occurs by a stick-slip crack advance, but the distance the crack propagates is very
large compared with the fragment lengths and so this is not always evident.

Surface treatment to 20% (Figure 68) resulted in substantially stronger

birefringence patterns, with interfacial debonding by a stick-slip crack advance.

145

Although it is difficult to see in the printed image, the break was accompanied by the
initiation of a short interfacial crack. This crack advances in increments with
increasing strain, leaving behind very strong stick-slip markings where plastic
deformation occurs at crack arrest points.

The 100%ST fiber break (Figure 69) occurred at only 1.1% coupon strain.
Strain energy was low enough that no interfacial failure occurred at the strain level
of fiber failure for this strongly adhered fiber, with the fiber end displacement
accomodated only by elastic and plastic matrix deformation. Without the fiber failure
strain energy to initiate debonding, increasing coupon strain was not accompanied by
interfacial crack advance, but by further plastic deformation of the matrix. Between
2.3% and 2.34% coupon strain an interfacial, or close to interfacial crack is finally
initiated. This crack propagates a substantial distance in its first (and only) jump since
there is considerable strain energy available at this high coupon strain. The resultant
birefringence patterns appear to be completely different from those for 20%ST and
200%ST specimens, but this difference results from the fiber failure strain difference,
not from a change in fiber surface properties.

The 200%ST sequence (Figure 70) shows a break that happened to occur at
a somewhat higher strain, 2.2% coupon strain, with approximately 4 times the fiber
failure strain energy of the 1.1% break in the 100%ST fiber. Although it is difficult
to see in the printed images, the computer image clearly shows that an interfacial
crack was initiated simultaneously with fiber failure. This crack propagates in jumps
with small increments in strain, again leaving the characteristic stick-slip patterns
behind.

The 600%ST break occurred at 1.5% coupon strain (Figure 71), insufficient
to initiate a crack in this very strongly adhered fiber. Interfacial, or near interfacial
failure eventually occurs at about 3.3 % coupon strain, significantly higher than the

2.34% required to statically (without fiber failure strain energy) initiate a debond in

146

the less strongly bonded 100%ST fiber. The use of coupon strain required to initiate
debonding as a means of characterizing interfacial adhesion is discussed in detail in
Chapter 2. When debonding is initiated, the propagation distance is substantial, as
with the case of the low fiber failure strain 100%ST fiber, because a large amount of
strain energy is available for its advance. Also as with the 100%ST sequence, the
stick-slip patterns are not closely spaced, because of the fiber failure strain energy,
not the fiber surface adhesion level.

The lOOGST birefringence sequence (Figure 72) documents a 1.6% coupon
strain fiber break, a level low enough not to initiate an interfacial crack. What
appears to be a gradual, interphase yielding occurs between 2.3% and 2.4% coupon
strain. This corresponds well to the 2.34% strain required to statically initiate an
interfacial failure in the unsized, 100%ST fiber. Further yielding or possible
interfacial cracking occurs at the 2.6% strain level. Upon release of the coupon strain
the region that appeared to yield at 2.4% is left with a stronger, small diameter sheath
of birefringence than the segment of fiber that appeared to fail interfacially between
2.5% and 2.6% coupon strain, where there is almost no visible remanent
birefringence. This may indicate a change in failure mode along the fragment from
local plastic yielding of the sizing material between 2.3% and 2.5 % coupon strain to
interfacial failure between 2.5 % and 2.6% coupon strain. This sizing is a Heculestm
"G" type size, described by the manufacturer as a toughened epoxy-compatible size.
Interphase yielding may therefore be more likely in these specimens than in the ones
with unsized fibers.

In summary, the predominant failure mode for the untreated and treated but
unsized fibers was by interfacial cracking, with the initiation and propagation
characteristics heavily influenced by the fiber failure strain energy. The sized,
lOOGST fiber also appeared to include some plastic deformation of the interphase
region, along with eventual interfacial failure.

147

e = 1.6% IM6 0%ST
Extension

 

8: 1.7%

 

e=1.8%

 

6: 1.9%

5 'II"'-‘II1' :1 .

I I'll 114‘,» ',

.7 1 , ... ... 1 1 . 1- - . 1
.iiiéim . 1;. 111.5111 11111319111111! 5.011..- ,

.- “I.

“m“ lililiiii’. I N V "' " ": ' I . L ,3 ' : -. ‘ 7. V :l 8111;”. Wei-l”

In

 

a = 2.0%

 

 

ii. ‘1‘ ’ A €=3-0%

e = 1.8% IM6 0% ST
Retraction

111111‘.

l... ... _, e=0.0%

 

Figure 67 . Birefringence sequence for untreated IM6 fiber.

 

 

e = 1.3% IM6 20%ST
Extension

 

 

e=1.7%

l

   

I ”(It
. .1 ‘II' I".I».....'1~.ll.':I:-I'::..I'-TIII .3

 

c=2.1%

e = 2.6%

 

e = 3.0%

 

e = 3.7%

e = 3.0% [MG 20% ST
Retraction

8=2.0%

e: 1.0%

 

 

‘ aitiiliiflmiii.’

   

e = 0.0%

      

Figure 68. Birefringence sequence for 20%ST IM6 fiber.

e: 1.1%

 

. rig-{12...ngtz. . . .
1 ~11 .. .1 w
i .. .1} I .- r., - 3 ‘ 7‘
. . _n . .
,,,t , 2&2: '. 22.2 . _ .‘ .
E
-
\ 1‘ h ":5 7:75-11”: .. . z . . I
u 1 . . . .
. .‘c

1 1:. ‘ ‘ ,
1'. . -. ..
1 . ‘ ' " .
'1 U 1 ‘1 , , - .
ul- 11 "~ . . 1:.
‘ ‘ .. ~~ ~ — .
, I, 1 .' . ._.¢
' . .i
I .

 

1.10.; ..

e = 2.2%

 

c = 2.3%

 

E = 2.8%

e=1.9%

 

’."""7""“‘5 7 ' " ” ' ;-..-::.~..~..»a-qfifiM-zi J. . " t..»i;.:':. , .,,

 

"W“ "1;: e = 1.2%

   

e = 0.0%

 

Figure 69. Birefringence sequence for 100%ST IM6 fiber.

IM6 100%ST
Extension

8 = 2.34%

IM6 100% ST
Retraction

E = 2.2% IM6 200%ST

Extension

8 = 2.5%

e = 2.7%

e = 2.8%

e = 3.0%

t: = 2.6% IM6 200% ST

Retractlon

e = 2.3%

 

8: 1.2%

 

e = 0.5%

 

e = 0.0%

Figure 70. Birefringence sequence for 200%ST IM6 fiber.

 

.3, I: ,

y f” , . 3 3

ng,

 

E = 1.5% IM6 6OOST

Extension

8: 1.7%

e = 2.0%

e = 2.2%

e = 2.5%

e = 3.3% IM6 6OOST

Retraction

e = 3.0%

e=2.0%

 

e: 1.0%

 

 

e = 0.0%

 

 

Figure 71. Birefringence sequence for 600%ST IM6 fiber.

a: 1.6% IM6 lOOGST
Extension

8 = 2.3%

 

e = 2.4%

e = 2.6%

 

 

“fl 8 = 2.2% 1M6 lOOGST
' Retractlon

 

 

 

 

 

e: 1.2%

 

 

E = 0.6%

 

e = 0.0%

 

Figure 72. Birefringence sequence for lOOGST IM6 fiber.

153
5.4.2.4 Mode 11 Fracture Toughness Results

The results of the mode 11 fracture toughness tests appear in Table 10 and are
plotted in Figure 73. The fracture toughness for all fiber types increases consistently
with increasing surface treatment, and also increases substantially with the addition
of the size in the lOOGST fiber composites. The largest increase is seen between the
poorly bonded, untreated fiber and 20% surface treatment, as with the surface oxygen
and interacial shear strength, with smaller but still substantial increases seen for the
other surface treatment increments. The influence of improved fiber-matrix adhesion
on mode 11 fracture toughness appears to reach a limiting value between 200%ST and
600%ST with only a small toughness increase in spite a substantial ISS increase. This
may be attributed to the failure mode moving away from the interface and into the
matrix, at which point the improved interface properties would have no effect.

Also of considerable interest is the significant increase in toughness for the
lOOGST fiber when compared with either the 100%ST unsized fiber or the 600%ST
unsized fiber. The ISS of the lOOGST fibers was lower than that of the 600%ST, but
the birefringence sequence showed interphase yielding that was not operative in the
other surface treatment conditions. Since even a small amount of plastic deformation
consumes far more energy than any interfacial fracture, the birefringence sequence
and mode 11 fracture toughness data give a strong indication that this failure mode

makes a contribution to the performance of the 100GST composite.

154

 

l 20
lOOGST

 

100

 

 

 

 

 

.. i

 

 

 

40

Mode 11 Fracture Toughness

 

[O
C

 

 

 

 

 

 

Eula .

 

 

O

0% 20% 100% 200% 600%
SURFACE TREATMENT (%) ——->

Figure 73. Mode 11 fracture toughness for IM6 composites.

Table 10. Mode 11 fracture toughness for IM6/epoxy composites.
EMTVDC 0% 20% 100% 200% 600% lOOGST
Mode 11 Fracture 15.3 45.7 67.0 78.6 84.6 118.0

Toughness (J/mz)
Std. Dev. (J/mz) 1.3 7.0 12.2 12.4 4.0 47.4

 

fractt
were

100C}

 

failurt

genen

also 1'

__‘—

umeil
compc
in the
betwee-

of whj

5.4.2.5

 

in Fig

PIEdict;
Possibl:
10w Ira
The 2C
ideMice
a mam
f1bets.

600%S-
mefiSUre

C(instant
large d1

155

The differences in standard deviation between the different surface treatments’
fracture toughnesses is also an interesting result. The untreated and 600%ST values
were very consistent, the 20%ST, 100%ST, and 200%ST less consistent, and the
lOOGST was highly variable. The untreated fibers underwent consistent interfacial
failure at very low stresses, absorbing little strain energy in the process, and
generating consistent values for mode 11 toughness. The 600%ST fiber composites
also failed in a consistent manner, since fiber-matrix adhesion was very high, but this
time failure strain energy was determined by the matrix properties. The lOOGST
composites were seen to undergo combined interphase yielding and interfacial failure
in the birefringence sequence. The large difference in strain energy absorption
between these failure modes, and the variation, even within the same fiber fragment,

of which mode was active, may account for this variability.

5.4.2.5 Transverse Flexural Results

The results of the transverse flexural tests appear in Table 11 and are plotted
in Figure 74. Although the mode 11 fracture toughness results followed clear and
predictable patterns, the transverse flexural results are somewhat enigmatic, and were
possibly dominated by an experimental artifact. The untreated fibers displayed a very
low transverse strength, as might be expected from the poor fiber-matrix adhesion.
The 20%ST, 100%ST, and 200%ST fiber composites all showed approximately
identical, higher levels of transverse flexural strength. This indicates a transition to
a matrix-dominated failure mode from the interfacial mode active in the untreated
fibers. A dropoff in both transverse flexural strength and modulus occurred at
600%ST which may be attributed to the lower volume fraction of fibers present, as
measured by ONVfA. With a lower V,, and the resultant lower flexural modulus, a
constant strain to failure would produce the lower measured strength value. A much

large dropoff occurs for the lOOGST fiber composite, with less than half the

156
transverse flexural strength of any of the treated but unsized fiber composites.

A possible complication in the interpretation of the results of this test may be
seen in the SEM fractographs of the transverse flexural specimens, and in the process
of preparing these specimens for observations. The two pieces of the broken flexural
specimens were usually still attached by bridging fibers, which had to be pulled free
to separate and expose the fracture surfaces. The fibers were also seen to be
somewhat imperfectly aligned, as a result of the manual layup process. Although this
would have little influence on mode 11 toughness tests, where failure propagates along
the fibers, any bridging fibers could significantly influence transverse flexural
strengths, since the fibers are very much stronger than the matrix material. The
extent of the impact of this factor may not be fully resolvable, since quantification of

fiber misalignment would be a difficult process and was not undertaken.

157

 

 

 

 

 

 

 

 

 

 

 

 

80
J:
13° 60
U
I:
m I
. +
a u
U
z: 40
U
(D
b
51
5 ii-roocsr
33 20
M
Q.
E
0%20% 100% 200% 600%

SURFACE TREATMENT (%) —->

Figure 74. Transverse flexural strengths for IM6 composites.

Table 11. Transverse flexural strengths and moduli for IM6 composites.

 

Fiber Tvpe 0% 20% 100% 200% 600% lOOGST
Transverse Flexural

Strength (MPa) 23.2 70.7 67.8 68.5 48.8 34.5
Std. Dev. 6.4 9.2 6.2 5.8 6.4 2.8
Transverse Flexural

Modulus (GPa) 8.8 l .3 12.3 12.1 9.4 9.6
Std. Dev. 1.9 0.9 0.6 1.5 1.0 0.5

 

 

5.4.2

in Ta?
low 13
fiber-
fiber

slight‘.

is slig

 

 

indica
interfa
theTEfI

failure

failure
Condi1
COnfir
at ma
Surpri
short

158
5.4.2.6 Interlaminar Shear Strength Results

The results of the short beam shear, interlaminar shear strength tests appear
in Table 12 and are plotted in Figure 75. The untreated fiber composites showed very
low levels of interlaminar shear strength (ILSS), as expected due to the very weak
fiber—matrix adhesion. The surface treated but unsized and surface treated and sized
fiber composites all showed higher, approximately identical ILSS, with the 600%ST
slightly higher than the others. Compared to the large change in ISS, this constancy
is slightly surprising. Upon analysis, however, the consistent ILSS values are an
indication that the failure mode for all of these composites has moved away from the
interface, and is dominated by failure within the matrix material. The ISS values,
therefore, have no impact once the surface treatment is sufficient to achieve this
failure mode change.

Although the fragmentation test specimens commonly underwent interfacial
failures for all fiber types studied, except for the lOOGST fibers, the loading
conditions are somewhat different in the short beam shear test. Rather than being
confined to a cylinder around the perimeter of the fiber, the shear stresses are applied,
at maximum, along a plane passing through the composite midsection. It is not
surprising that failure can be successfully transferred to a plane in the matrix for the
short beam shear specimens, while the locus of failure tends to be confined to the

interfacial region in the fragmentation test specimens.

159

 

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Interlaminar Shear Strength
.5
O

 

[O
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MPa —>

 

0% 20% 100% 200% 600%
SURFACE TREATMENT (%) ——>

Figure 75. Interlaminar shear strengths for IM6 composites.
Table 12. Interlaminar shear strengths for IM6/epoxy composites.
MType 0% 20% 100% 21X)% 600% lOOGST
Interlaminar Shear
Strength (MPa) 29.5 56.3 57.3 54.7 63.1 55.8
Std. Dev. 1.7 3.0 2.6 4.7 8.4 4.0

 

 

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160
5.4.2.7 SEM Fractographic Analysis

Scanning electron micrographs of end-notched flexural (mode 11 fracture) and
transverse flexural specimens for each surface treatment condition appear in Figures
76-87. Mode 11 fractures are shown at 200X (Figures 76-81) and 1000X (Figures 82-
87) while transverse flexural fractures are shown at 500x (Figures 88-93). The mode
II failures occurred in the same direction as the fiber orientation, while the flexural
failures were transverse to the fiber axis.

As can be seen in Figures 76 and 82, axial mode 11 failure of composites
fabricated from untreated fibers yielded fracture surfaces with the fibers almost
completely stripped clean. Almost the only visible matrix material is that constrained
beneath the fibers. Very small regions of "hackles" can also be seen, usually where
the matrix is constrained behind pairs of fibers.

Surface treatment to 20% of the nominal value (Figures 77 and 83) results in
slightly increased matrix retention, some regions of exposed matrix occur while most
portions are bare fiber. Further treatment to 100% results in significant changes in
the fracture surface morphology (Figures 78 and 84). Most of the surface is covered
with hackles and adjacent regions of matrix material, with only the topmost portions
of the fibers exposed. This same morphology was exhibited by the 200% (Figures 79
and 85) and 600% (Figures 80 and 86) surface treated composites.

Composites fabricated with the epoxy—compatible finished fibers, lOOGST seem
to show lower amounts of retained matrix on mode 11 failure surfaces (Figures 81 and
87). A reduced incidence of hackle formation was also evident. The appearance of
a decrease in matrix retention may result from the decrease in hackle numbers, since
these structures are the most visible components of the exposed matrix. Smooth
matrix regions are much more difficult to identify and quantify than structures which

conspicuously differ from the fiber surfaces.

 

Figure 77. 200X SEM, 20% treated mode II fracture.

162

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Figure 78. 200x SEM, 100% treated mode II fracture.

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Figure 79. 200x SEM, 200% treated mode II fracture.

 

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Figure 80. 200X SEM, 600% treated mode 11 fracture.

Figure 81. 200K SEM, 100% GST sized mode II fracture.

15KU XIaOB‘B

 

Figure 83. 1000X SEM, 20% treated mode 11 fracture.

 

Figure 85. 1000X SEM, 200% treated mode II fracture.

 

Figure 87. 1000X SEM, 100% GST sized mode 11 fracture.

 

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167

Artifacts from specimen preparation may be present in the transverse flexural
fractographs because of fiber bridging (Figures 88-93). Specimens were not cleanly
broken into two pieces but remained joined after failure by misaligned fibers. These
pieces were separated by hand, and most of the bridging fibers were removed with as
little disruption of the fracture surface as possible. Final surfaces were mainly
exposed by transverse flexural failure, but with small regions attributable to this
peeling of bridging fibers. Some loosely attached fibers remained, producing charging
phenomena in the SEM.

All transverse flexural specimens appeared to present fiber surfaces completely
stripped free of matrix material, regardless of fiber surface treatment. No hackle

structures were observed anywhere on any transverse flexural surfaces.

168

 

Figure 89. 500x SEM, 20%ST transverse flexural fracture.

 

Figure 90. 500x SEM, 100%ST transverse flexural fracture.

I II

 

Figure 91. 500X SEM, 200%ST transverse flexural fracture.

170

 

 

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Figure 92. 500x SEM, 600%ST transverse flexural fracture.

 

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171
2.5 W

Surface treatment of IM6 fibers produced an increase in chemisorbed surface
oxygen. This increase occurred rapidly for the untreated fibers, and then at a lower,
linear rate as surface treatment continued. This difference is probably attributable to
the availability of reactive, edge, corner, and disordered carbon atom sites on the
untreated fibers, compared with exclusively graphitic basal plane carbon atoms on the
treated fibers.

The interfacial shear strength increased almost linearly with increasing surface
oxygen percentage and with polar surface free energy, rapidly rising with 20% surface
treatment compared to the untreated fiber and then increasing at a lower rate as
surface treatment continued. Although these variables were shown to be closely
correlated, actual causality is much more difficult to establish. It cannot be
conclusively stated that there is a cause and effect relationship based upon these data,
though such a relationship is strongly supported. The addition of the "G" size also
increased the measured values of interfacial shear strength, and caused a change in
failure mode in the fragmentation specimens from entirely interfacial to combined
interfacial and interphase yielding.

The mode 11 fracture toughness increased with increasing fiber surface
treatment and with the addition of the size. Sizing led to a particularly large increase,
probably because of increased plastic deformation of the interphase region. This
increase closely followed that of ISS, except for the sized case, as shown in Figure
94.

Transverse flexural strengths increased with the initial surface treatment
increment and then remained approximately constant with additional treatment.
Artifacts from fiber volume fraction differences, fiber bridging, and the aging of the

size may have influenced the results for the 600%ST and lOOGST fibers.

172

 

120
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100

200 I
80 I

 

 

100 -

 

I20

 

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20 / .0

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0 25 50 75 100 125
Interfacial Shear Strength (MPa)

 

 

 

 

 

 

zeal 9 —> Mode 11 Fracture Toughness

 

Figure 94. Mode II fracture toughness versus ISS.

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173

Interlaminar shear strengths increased with surface treatment compared with
the untreated fibers, but increased at a low rate for all surface treated and treated and
sized fibers. This was probably due to a matrix dominated failure mode with small
interfacial effects. Nevertheless, the plot of ILSS versus ISS shows an approximately
linear relationship, as seen in Figure 95.

The results of the mechanical testing program are summarized in Figure 96,
which shows the interfacial shear strength, interlaminar shear strength, transverse
flexural strength, and mode 11 fracture toughness for the surface treated but unsized
fibers, plotted against surface treatment in each case. In all four cases, the initial
increment of surface treatment increase the strength property substantially. This
probably results from the removal of a weak surface layer from the fiber and a
resultant change in failure mode from within the fiber to the interface or matrix.
Additional surface treatment continues to increase the interfacial shear strength, but
the transverse flexural and interlaminar shear strengths level off, apparently because
the locus of failure has moved to the matrix, away from the interface. Mode 11
fracture toughness continues to increase with additional surface treatment until 200%
surface treatment is reached, then levels off in the increment from 200% to 600%,

again, because the mode of failure no longer involves the fiber/ matrix interface.

174

 

 

 

 

 

 

 

 

 

 

 

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Interfacial Shear Strength (MPa) —>

Figure 95. Interlaminar shear strength versus ISS.

175

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Interfacial Shear Strength Interlaminar Shear Strength

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Transverse Flexural Strength Mode 11 Fracture Toughness

Figure 96. Summary of mechanical test results versus surface treatment.

CHAPTER 6
THE INFLUENCE OF PROCESSING TIME, TEMPERATURE, AND
COMPOSITION ON THE ADHESION OF CARBON FIBERS
TO BISPHENOL-A POLYCARBONATE

6-1 W

Interfacial shear strengths of AS4 and AU4 carbon fibers in pure BPA-
polycarbonate and commercial Lexan 141 polycarbonate were measured with the
single fiber fragmentation test. Specimens were prepared both by matrix deposition
from methylene chloride followed by equilibration at temperatures below T, and by
hot pressing at temperatures above T,, with and without solvent. Stress transfer in
the hot pressed specimens showed substantial improvement over the weakly adhered
solvent deposition specimens. Increasing consolidation time and temperature
improved shear strength in the pure polycarbonate specimens. Lexan 141 matrix
specimens, however, appeared to reach a lower, limiting shear strength which was not
significantly changed by increasing consolidation time, temperature, or pressure, or

by the presence of solvent.

6.2 W

Thermoplastic matrix composites are under intensive investigation in an effort
to exploit potential advantages in toughness, fabrication speed, and environmental
resistance. Optimization of these properties requires that a better understanding of
fiber to thermoplastic matrix adhesion be developed. Amorphous thermoplastics, such
as bisphenol-A polycarbonate, possess much greater fracture toughness than typical
thermoset epoxy matrices, with a notched Izod impact strength of 801 J/m for Lexano
141 [GE, 1988]. This toughness has not yet been fully translated into toughened

composite systems, however, apparently because of problems with interfacial adhesion

176

177
[Parker, 1989], [Parker, 1988], [Bascom, 1987], [Lauke, 1988].

Understanding the mechanisms of adhesion between carbon fibers and
thermoplastic matrices to improve composite performance has been the object of
numerous studies [Kardos, 1973], [Di Landro, 1987], [Peacock, 1986]. While the
thermoset epoxy matrix used in the work described in chapter 5 was applied to the
fibers in the form of highly reactive monomers, dimers, and curing agent and
subsequently polymerized, the polycarbonate thermoplastic investigated in this section
was applied in a much less reactive polymerized form. The possibility of interfacial
adhesion by the formation of primary chemical bonds is therefore considerably
reduced. The microstructures of the matrices was also fundamentally different, with
the epoxy polymerizing to form a three dimensional network of monomers linked by
primary chemical bonds while the polycarbonate consists of an amorphous mass of
linear polymer chains held together by secondary polar and dispersive bonds.

The possibility of fiber nucleation of crystallization introduces an additional
microstructural variable by generating an anisotropic transcrystalline interphase with
mechanical properties significantly different from the bulk matrix. The slow
crystallization rate of polycarbonate allows this factor to be studied in isolation from
other effects. The use of solvents in the pre-pregging steps of thermoplastic composite
fabrication can lead to changes in crystallization and adsorption which can in turn
influence fracture toughness and adhesion.

Along with the usual difficulties with the measurement of interfacial shear
strengths, thermoplastic matrices present problems with specimen fabrication due to
the high melt viscosities characteristic of these systems. These problems neccessitated
the development of special single fiber specimen production methods which allow
testing in both amorphous and semi~crysta1hne thermoplastic materials. This paper
describes these techniques and presents data which characterizes adhesion for this

model amorphous thermoplastic matrix system.

178
6.3 W

Matrices investigated in this section included pure BPA-polycarbonate obtained
from Polysciences Co. with a molecular weight range of 32-36,000, and an injection
molding grade of polycarbonate, Lexan 141 from General Electric Co. which contains
proprietary toughening agents and ultraviolet light stabilizers. Although the exact
composition of the Lexan material is unknown because of its proprietary nature, it was
chosen as one of the polycarbonate models for this investigation because is has been
used as a matrix in a number of composite studies [Parker, 1988], and its mechanical
properties are well characterized and available in product data sheets. These
properties are summarized in Table 13.

The chemical structure of polycarbonate is shown in Figure 97. The
alternation along each monomeric unit between bulky phenyl groups and methyl
groups and the polar acetate, and ether linkages makes crystallization of this structure
difficult. This produces a high entanglement density and an amorphous structure for
kinetic reasons, i.e., the structure is not atactic and so may be crystallized, but the
entanglement prevents crystallization except with extended annealing.

The fibers for this investigation were Hercules AS4 PAN-based carbon fibers,
with the standard electrochemical oxidative surface treatment (type AS4) and without

surface treatment (type AU4).

179

Bisphenol-A Polycarbonate

N

Figure 97 . Chemical structure of BPA-Polycarbonate.

Table 13. Properties of Lexan 141 polycarbonate resin.

 

 

21202213! U.S. Units SI Unit;
Tensile Strength

(yield) 9,000 psi 62 MPa
(ultimate) 10,000 psi 69 MPa
Shear Strength

(yield) 9,000 psi 40 MPa
(ultimate) 10,000 psi 70 MPa
Shear Modulus 1.14 x 10‘ psi 790 MPa
Izod Impact Strength 15 ft—lbs/in 801 J/m
(notched, 1/8" thick)

Coefficient of Thermal

Expansion 3.75 x 10" in/in °F 6.75 x 10" m/m °C
6.4 1 ED R

The experimental procedure for thermoplastic matrix fragmentation specimen

fabrication and testing are described in this section.

6.4.1 HOT PRESSED SPECIMEN PREPARATION
Thermoplastic matrix single fiber fragmentation test specimens were fabricated

by hot pressing fibers between pairs of matrix sheets in the following manner.

180

Preforrn sheets, one half the thickness of the final specimens, were first produced by
hot pressing pelletized material between aluminum foil sheets with the thickness
controlled by a surrounding dam of RTV silicone material. Times and temperatures
for this preliminary step were kept as low as possible to minimize chances of thermal
degradation and the assembly was kept sealed in foil throughout the process to
minimize oxidation. Aluminum foil pressing sheets were used to avoid the use of any
release agents which might cause surface contamination and to allow the foil to be
peeled away from the polycarbonate sheets without deforming them. One, 14 cm
square by .8 mm thick preform sheet was then placed on a .1 mm aluminum sheet
atop an outer aluminum foil sealing sheet and surrounded by a 1.6 mm thick high
temperature RTV silicone frame (Figure 98).

Single, separated fibers were then draped across the sheet and surrounding
gasket. Care was taken to avoid fiber contamination and damage during this layup
process. Repositioning the fibers after placement was avoided since this can lead to
twisting and premature failure. Spacing strips of the same matrix material were
placed on either side of the lower sheet to maintain separation and avoid fiber damage
during the early heating stages before T, was reached. The preform sheets and
silicone gasket were carefully matched in size and thickness to produce minimal
material flow which can produce bent and wavy fibers.

With enough isolated fibers laid in place, a razor knife was used to cut them
into approximate 25 mm segments with minimal disturbance. This reduces fiber
bending during matrix flow and contraction, and instead causes small rigid-body
rotations and displacements which have no effect on final specimen yield. A pair of
thermocouple wires were inserted at one corner of the sheet and insulated from the
foil with teflo'n strips. The upper preform sheet was then laid over the spacer strips,
followed by the top aluminum pressing sheet. The entire assembly was sealed in the

outer aluminum foil and carefully placed between the hot press platens without

181
Upper Aluminum Foil Pressing Sheet

   
 
   
 
 
   
   

Fibers Aligned.

Separated. and
Lower Matrix Cut to 25 mm.

 

 

Spacer
Strips

 

Silicone
Gasket

 

 

Lower Aluminum Foil Prnessig Sheet

Figure 98. Fixture for hot pressing single fiber specimens.

disturbing the fibers, preforms, and gaskets.

Hot pressing then proceeded in the following manner. To ensure uniform
heating, a light load, equal to the upper platen weight was applied during heating.
This load was born by the spacer strips and did not produce fiber damage. A 1 hour
soak at 125 °C was applied to dry the polycarbonate, which is sensitive to hydrolysis
at elevated temperatures [Golovoy, 1989].

Following the 125 °C soak, the temperature was raised at approximately 5
°C/minute. Upon reaching the desired temperature, the load was applied and
maintained throughout the pressing cycle. Cooling was accomplished by the standard
platen water cooling system at approximately 1 °C/second for rapidly cooled
specimens and 1 °C/minute for slow cooling.

Test coupons were die cut from the composite monolayers produced by this

system with fibers aligned with the specimen gage sections.

182

    

Hot Melt
Adhesive

Isolated Fibers

Figure 99. Spin coating fixture for solvent deposition specimen fabrication.

6.4.2. SOLVENT DEPOSITED SPECIMEN FABRICATION

Additional specimens were produced by embedding fibers in Lexan 141
polycarbonate deposited from a methylene chloride solution in the following manner,
adapted from Bascom, et a1 [Bascom, 1987]. Isolated fibers were aligned on pre-cut
polycarbonate coupons and secured with hot melt adhesive at the ends. These
specimens were affixed radially to a disk atop a small centrifuge. A 5% solution of
polycarbonate in methylene chloride was applied along the fiber length and the excess
immediately spun off by briefly starting the centrifuge. This was repeated 4 times at
5 minute intervals to allow evaporation and the specimens were then equilibrated at

the specified temperature for at least 24 hours prior to testing.

6.4.3 DATA ACQUISITION AND ANALYSIS
Fragment lengths were measured and a Poisson-Weibull analysis [Drzal, 1982]
performed by using FiberTrack, [Waterbury, 1991]. Strengths were calculated using

an average fiber diameter of 7.5 microns and a fiber strength of 5865 MPa for both

183
AS4 and AU4 fibers for the fragments in the elevated temperature tests, with a lower

value for the longer lengths in the solvent deposition tests.

6.4.4 BIREFRINGENT IMAGE ACQUISITION
To document the failure characteristics of the failure modes in the
polyearbonate matrix fragmentation specimens, birefringence patterns were acquired

with a cross-polarized transmitted light microscope.

6.5 EQLXCARBQUATE RESULTS AND DISCUSSIQN

Three groups of single fiber fragmentation specimens were fabricated and
tested, two employing Lexan 141 BPA-PC with and without solvent, and one group
with pure polycarbonate with a molecular weight range of 32-36,000. The resultant
fragment length/diameter ratios and interfacial shear strengths calculated from a

Weibull-Poisson analysis appear in Tables 14 and 15 and in Figures 100 and 101.

6.5 .1 SOLVENT PROCESSED SPECIMENS

The results from the first group of solvent deposition specimens (Table 14,
Figure 100) with AS4 fibers in Lexan 141, show adhesion which increases with
increasing equilibration temperature, reaching a limiting value at about 75 °C. With
an ISS of only 27 MPa and LC/D of 113/1, however, this level is inadequate for use
in advanced composites.

The birefringence patterns of a solvent deposited specimen, equilibrated at 75
°C, appears in Figure 102. These patterns show an interfacial failure mode and very
weak bonding as indicated by the weakness of the birefringence and the substantial

crack advance distances in each stick-slip event.

184

Table 14. Matrix type, processing, LC/D’s, and ISS for AS4 in Lexan 141.

 

Spec. Fiber Temp. Time Pres. Cooling L,/ D ISS
Desig. Type ( °C) (min.) (kPa) Method - (MPa)
MeCll AS4 25 1440 (atm) - 173.9 17. 1
MeCl2 AS4 60 1440 (atm) Rapid l 15 .9 26.2
MeCl3 AS4 70 1440 (atm) Rapid 1 12.8 27.3
MeCl4 AS4 230 15 475 Rapid 69.0 53 .7

PCI AS4 230 20 137 Rapid 60.2 53.5
PC2 AS4 230 20 689 Rapid 69.4 52. 1
PC3 AS4 230 20 1379 Rapid 65 .5 54.5
PC4 AS4 230 20 689 Slow 69.1 51.6
PC5 A84 240 20 1370 Rapid 64.5 54.5

 

Specimens with methylene chloride present but hot pressed 15 minutes at 230
°C (MeCl4) showed greatly improved adhesion, with an 188 of 53.7 and LC/D of 69,
comparable to Lexan matrix specimens produced without solvent. The birefringence
patterns for these specimens differ from those processed without solvent with much
greater intensity, indicative of high ISS, and showing stick-slip behavior with much
shorter crack advance distances (Figure 103). The initial presence of solvent did not
appear to interfere with adhesion, provided that sufficient time and temperature were
allowed for the solvent to diffuse away.

Thermogravimetric analysis of polycarbonate deposited from methylene
A chloride and equilibrated at 25, 50, and 75 °C for at least 24 hours showed weight
loss over the temperature range from 25 °C to 150 °C (1") in the 25 and 50 °C
samples but negligible loss in the 75 °C specimens. The small, methylene chloride
molecules are apparently mobile within polycarbonate at this temperature. The ISS
specimens equilibrated at 75 °C were therefore free of methylene chloride, producing
the levelling off of ISS in the temperature range below T,. Without consolidation of
the polymer at a temperature at which the chains themselves are mobile, a porous,
poorly consolidated microstructure existed. This poor microstructure also extends to

the conformation of the polymer chains at the carbon fiber surface.

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185

 

60

 

50

 

40

 

30

20‘

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ISS (MPa)—>

 

34 67891011
Specimen Set Number

 

Legend: Methylene chloride deposited

I With out solvent

Figure 100. Interfacial shear strengths for AS4 in Lexan 141.

CD
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0

MPa —> Interfacial Shear Strength
to .1:-
o o

 

l 2 3 4 5 6 7 l 2 l
AS4 AU4 IM6

Figure 101. Interfacial shear strengths for AS4 in pure polycarbonate.

Dispersive and polar bonding are extremely sensitive to distance and
orientation, with intimate contact required for strong bond formation. With limited
mobility of the polymer chains near the fiber surface this intimate contact cannot
occur.

These results may be summarized as indicating that adequate
fiber/thermoplastic matrix adhesion requires that a sufficiently high temperature be

attained for full relaxation of the polymer chains to occur.

6.5.2 SOLVENT FREE SPECIMENS
The influence of consolidation pressure was investigated with three sets of

specimens, PC1, PC2, and PC3 (Table 15, Figure 100) produced at constant time and

187

temperature with increasing pressure. No significant change in IFSS was observed

for these specimens, with IFSS values of 53.5, 52.1, and 54.5 MPa for pressures of

137, 689, and 1378 MPa respectively. Further work with Lexan matrix specimens

showed no significant ISS changes with any of the variables, however, indicating that

a limiting value of adhesion appears to have been reached for this system. Since this

is a commercial product containing proprietary toughening agents and U.V.

stabilizers, some segregation of these components to the interface with subsequent
weakening may have occurred.

Table 15. Matrix type, processing, Lc/D’s, and ISS for AS4 in PC.

 

Spec. Fiber Temp. Time Pres. Cooling Lc/D ISS
Desig. Type (°C) (min.) (kPa) Method (MPa)
P82 AS4 250 475 Rapid 61.7 58.4
P83 AS4 250 475 Rapid 58.7 62.2
PS6 AS4 250 475 Rapid 55.4 64.2
PS4 AS4 275 475 Rapid 60.5 59.2
PS9 AS4 275 475 Rapid 62.5 57. 1
P85 AS4 300 475 Rapid 52.7 67.8
PSl AS4 275 475 Slow 61.7 57.5
PS7 AU4 250 475 Rapid 71.9 5 1. 3

 

 

 

 

 

 

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188

Consolidation time and temperature were found to have a significant influence
on the pure polycarbonate specimens (Figure 101 and Table 15), with improvements
resulting from increasing both. For specimens pressed 15, 60, and 120 minutes at
250 °C, ISS increased uniformly from 58.4 to 64.2 MPa . The specimens processed
15 and 30 minutes at 275 C showed a slight rwuction from 59.2 to 57.1 MPa, but
this is probably due to experimental scatter. A significant increase over these values
was seen in the set pressed 15 minutes at 300 °C, with an ISS of 67.8 MPa.
Attempts to repeat this test with longer press cycles were unsuccessful because of
gasket failures but this is under continuing investigation. Matrix decomposition and
property changes are problematic at such elevated temperatures and are under
investigation.

These results are in general agreement with those of Brady and Porter [Brady,
1989], who investigated transverse toughness in carbon fiber/ polycarbonate composites
processed with different annealing times and temperatures. As they have pointed out,
the temperatures at which improvements are seen are substantially greater than the
melt crystallization temperature of 265 °C, thereby ruling out transcrystallinity, and
suggesting an adsorption effect as the mechanism of variation.

It is also interesting to note that the minimum processing temperature found
to produce maximum adhesion and elimination of solvent artifacts is approximately
1.2 times the polymer T, (°K). Such processing temperature guidelines have been
proposed based on polymer devolatilization studies [Mossner, 1988].

The untreated fibers AU4 had a lower ISS, 51.3 MPa compared with 58.4
MPa for identically processed AS4 fibers. Surface treatment evidently raises adhesion
levels for this thermoplastic system, but the increase is not as great as that for AU4
and AS4 specimens in an epoxy matrix, which increased from less than 40 MPa to
nearly 70 MPa with surface treatment.

This difference may arise from the formation of primary chemical bonds

189

between the chemisorbed surface oxygen attached to the carbon fiber during surface
treatment and the reactive metaphenylene diamine curing agent. The absence of a
similar reactive moiety in the polycarbonate precludes similar bond formation and
limits adhesion increases to that resulting increases in the much-weaker polar bonds
between the surface oxygen and the oxygen in the polycarbonate chains.

Another possible difference may result from the greater thermal compression
stresses exerted by the therm0plastic on cooling from T, than those produced in the
thermoset cooling from its Tr A greater compression may reduce the tendency for
the weak surface layer in the carbon fiber to fail, producing an ISS of 50 MPa in the
thermoplastic and < 40 MPa in the thermoset even though the locus of failure may be

within the fiber in both cases.

6.5.3 INTERPRETATION OF BIREFRINGENCE PATTERNS

Four general types of birefringence patterns were observed among the different
sets of specimens. Solvent deposited specimens displayed very faint patterns extended
along several hundred microns of fiber (Figure 102), indicative of the weak bonding
in these systems and an interfacial failure mode. Hot pressed and fast cooled Lexan
141 specimens showed interfacial failure by stick-slip cracking in the longer specimen
fragments, particularly in those with methylene chloride present (Figure 103). These
stick-slips were not as sharply defined as those present in epoxy matrix specimens,
probably indicating a greater amount of plastic deformation accompanying the
cracking.

Although the ISS of all Lexan matrix specimens consolidated above T, were
unaffected by time and temperature, one processing variable, cooling rate, did produce
a change in the apparent failure mode. Slowly cooled Lexan matrix specimens
showed evidence of shear band formation at sites some distance away from fiber

breaks. These bands were visible under both polarized and non-polarized transmitted

190
light micrographs, as shown in Figure 104. The bands were never seen near the
breaks, but always appeared some distance away. Apparently, a change in failure
mode with distance from the breaks occurred, probably moving from interfacial to
plastic shear deformation of the matrix.

Patterns in the pure polycarbonate specimens (PS series), were very strong,
showing no evidence of stick-slip behavior or other variations (Figure 105) . The
intensity of these patterns indicates high ISS and a failure mode involving deformation
of the matrix rather than interfacial cracking.

Although no evidence of crystallinity was observed in any of the actual
fragmentation specimens produced under these processing conditions, extended
annealing times (24 hours) for pure polycarbonate caused changes that appear to be
crystallization related (Figure 106). Specially prepared specimens subjected to
extended periods above T: but below the melting temperature developed optically
anisotropic regions in the vicinity of the fiber interphase (Figure 107). From these
observations, however, sufficient time was not available for crystallization to occur
under typical composite processing conditions.

In addition to the failure modes operative in the immediate vicinity of the
fibers in the fragmentation specimens, crazing occurred within the matrix during
testing for both Lexan 141 and pure polycarbonate specimens (Figure 108). The
crazes did not appear to be nucleated by deformation near the fiber, but were

completely independent of the fiber and breaks.

191

     

 

Figure 102. Solvent deposited Lexan matrix birefringence pattern.

 

Figure 103. Fast cooled Lexan matrix birefiingence pattern.

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Figure 105. Pure polycarbonate matrix birefringence pattern.

 

Figure 106. Surface of annealed polycarbonate.

193

 

Figure 107. Possible polycarbonate crystalline sheath around AS4 fiber.

 

Figure 108. Crazed polycarbonate fragmentation specimen.

 

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195
6.6 W

Interfacial shear strengths of carbon fibers in pure polycarbonate were found
to increase with increasing consolidation temperature and time. Specimens produced
by solvent deposition at low temperatures showed much lower ISS while specimens
with solvents present but consolidated at higher temperatures showed good adhesion.
Lexan matrix specimens appeared to reach a limiting ISS, lower than that for pure
polycarbonate, which did not vary significantly with consolidation temperature or
pressure.

Slowly cooled Lexan matrix specimens showed evidence of shear band
formation in both polarized and unpolarized micros00pe observations. Rapidly cooled
Lexan specimens appeared to fail by stick-slip interfacial cracking accompanied by
some matrix deformation. Pure polycarbonate specimens showed intense birefringence
patterns, indicating strong adhesion. Surface treatment increased ISS but to a lesser

extent than for thermoset epoxy matrix specimens.

CHAPTER 7

THE INFLUENCE OF FIBER NU CLEATED CRYSTALLIZATION
ON INTERFACIAL SHEAR STRENGTHS AND FAILURE MODES
OF CARBON FIBERS IN NYLON 6,6

7.1 W

Interfacial shear strengths of carbon fibers in a semicrystalline thermoplastic,
Nylon 6,6, processed at various time, temperature, and pressure schedules were
measured by single fiber fragmentation tests. The effects of processing conditions on
fiber nucleation of crystallization, crystallite morphology, fiber-matrix stress transfer,
and modes of failure were investigated by this technique. PAN-based Hercules AU4,
AS4, and IM6 fibers were investigated. Interfacial shear strengths were calculated
from a two parameter Weibull distribution treatment. Interphase microstructures and
failure modes were evaluated by transmission optical microscopy and confocal

scanning optical microscopy.

7.2 NYLON 6,6 INTRODUCTION

Fiber-matrix adhesion has been shown to play a critical role in composite
performance for a wide variety of systems, ranging from thermoset polymer matrices
through metal matrices, to brittle ceramics. Semicrystalline thermoplastic matrix
composites are currently under intensive investigation in an effort to produce
composites with improved toughness, environmental stability, and high temperature
properties, and which may be rapidly and economically processed. The exploitation
of these desirable properties requires that a full understanding of the nature of fiber-

thermoplastic matrix adhesion be developed.

196

197

An additional variable is introduced for a semicrystalline thermplastic, a
complex interphase microstructure with mechanical properties which may substantially
differ from the bulk material. This microstructure, often called "transcrystallinity",
is generated when the fiber nucleates matrix crystal growth at numerous closely
spaced sites, causing the normal, spherically symmetric growth habit to change to a
radial, cylindrical symmetry, or two dimensional spherulitic structure [Kumamaru,
1983]. While this type of growth is often attained in very low Vf, it is less commonly
observed in actual, high Vf composites [Zeng, 1986].

An extensive body of thermoplastic crystallization research has been performed
on composites fabricated with poly(ether ether ketone) (PEEK) formulations usually
obtained from Imperial Chemical Industries. Since this material is available only in
proprietary compositions containing nucleating agents of an undisclosed nature,
analysis of the literature is not entirely straightforward. The influence of thermal
history on nucleant density has been the object of much of this work. Higher
temperatures and longer durations of melt preheating have been shown to reduce the
nucleant density in the bulk PEEK [Lee and Porter, 1986]. Reduced competition from
nucleants in the matrix tends to increase the growth of the transcrystalline interphase.
Transverse tensile strengths were found to double with increased preheat duration, and
matrix retention on the fracture surfaces was correspondingly increased. For the case
of ICI PEEK, then, the adhesion was found to increase with increasing
transcrystallinity. Another conclusion that can be drawn from this work is that the
nucleation agents in the matrix are more temperature sensitive than is the nucleation
activity of the carbon fiber surface.

The effects of cooling rate on PEEK composites have been investigated to
determine changes in degree of crystallinity and fracture toughness [Lee, 1987 A].
Crystallinity was found to decrease with increasing cooling rate. Axial tensile

strength was unchanged, but both mode I and mode 11 fracture toughness decreased

198

with increasing degree of crystallinity. Further work showed that strengths and
moduli of both the neat matrix and carbon fiber composites increased slightly with
increasing degree of crystallinity while the fracture toughness and fracture energy
decreased [Talbott, Springer, Berglund, 1987]. These properties were found to vary
only with the final degree of crystallinity and not with the nature of the thermal
history required to achieve that degree, i.e. , slow cooling compared with rapid cooling
and subsequent annealing.

The thermal prehistory of PEEK has been shown to involve a number of
processes in addition to the destruction of nucleating agents [Deslandes, 1989]. Chain
scission, chain branching, cross linking and nucleant formation were believed to occur
at different rates and temperatures during preheating above the melt temperatures.

Epitaxial growth of polymers on fibers and fiber-like surfaces has been noted
by a number of researchers, for example, [Tuinstra, 1970], [Kumamaru, 1983 (A) and
(B)]. The general mechanisms involved in polymer nucleation, however, are not fully
understood [Keller, 1977], [Binsbergen, 1977], [Stack, 1986] and the mechanisms
involved in fiber nucleation may, or may not, involve epitaxy.

The embedded fiber fragmentation method for measuring interfacial shear
strengths has been widely used with thermoset matrices because of its well
documented consistency and sensitivity to interfacial properties and the relative ease
of collecting a statistically significant data sample. The application of this valuable
technique has generally depended upon the transparency of the matrix material for
measurement of fragment lengths and observation of failure modes by optical
birefringence. The development of methods to extend fragmentation testing to
translucent semicrystalline materials was therefore made a goal of this research effort.

Observation of fi'agmentation test failure modes was facilitated by the
availability of a new microscopy technique, confocal scanning optical microscopy

(CSOM) which scans both the laser illumination source and the imaging optics to

199
produce an optical micrograph with high resolution and a very high rejection of
interference from out of focal plane sources [Yatchmenoff, 1988] ['Thomason, 1990].
This chapter descibes the results of an investigation of the influence of fiber
nucleated crystallization on the microstructure, shear strength and failure modes of

Nylon 6,6, semicrystalline thermoplastic fragmentation specimens.

7.3 N 2mg §,§ EXPERIMENTAL BROOEDORE

Single fiber specimen fabrication with thermoplastic matrices and fragment
length measurement for the translucent matrix presented special experimental problems
which were addressed. Specimens were die cut from an isolated fiber sandwich which
was produced by hot pressing a layer of aligned and separated single fibers between
sheets of the matrix under an argon atmosphere without the use of solvents.
Translucent matrix specimens were first strained to achieve the limiting fiber
fragment length and then released, sanded and polished to reveal the fibers, and re-
strained to expose breaks and transverse cracks for fragment measurement.

The experimental materials and methods used to study fiber-semicrystalline

thermoplastic matrix adhesion are described in this section.

7.3.1 NYLON 6,6 EXPERIMENTAL MATERIALS

The model semicrystalline thermoplastic matrix chosen for this study was
Nylon 6,6, poly(hexamethyl adipamide), (Figure 109). The choice was based upon
the relative ease of processing compared with high temperature, high performance
polymers such as PEEK and PPS and on the availability of the material without
contamination by proprietary nucleating agents or other additives.

The fibers used include PAN-based Hercules types AU4, (untreated), AS4
(surface treated), and intermediate modulus IM6, (surface treated), which are

described in chapter 4.

200

O 0
II II

N
Nylon 6,6 poly(Hexamethylene adipamide)

Figure 109. Chemical structure of Nylon 6,6 - poly(hexamethyl adipamide).

7.3.2 FABRICATION OF NYLON 6,6 ISS SPECIMENS

Thermoplastic matrix ISS specimens were fabricated by the following
technique, similar to that used for polycarbonate matrices described in section 6.4.1.
Sheets of the neat matrix material .5 mm thick x 14 cm square were produced by hot
pressing between 0.1 mm thick aluminum sheets under an argon atmosphere at a
temperature slightly above Tm to minimize thermal degradation. This thickness of
acetone-washed aluminum pressing foil was selected to allow the foil to be peeled
away from the specimens without causing deformation and to allow pressing to
proceed without the use of a release agent which might cause surface contamination.
Thickness and shape were controlled by the use of 0.5 mm thick RTV silicone strips
which were arranged to form a dam.

After trimming to accurate dimensions, a bottom sheet was placed in the
molding stack shown in Figure 98. Single fibers were draped across the sheet and the
adjacent silicone frame and were straightened, aligned, and arranged in groups of two
or three so that more than one fiber could be included in each specimen. When a
sufficient set of fibers was laid in place they were then cut into segments
approximately 2.5 cm in length with as little disturbance as possible.

A top sheet of matrix was then placed over the fibers and thermocouple,

followed by the upper foil sheet. The aluminum foil was then sealed aroung the

201
assembly, taking care not to disrupt it. The packet was then placed in the hot press
and an argon entry tube was affixed with tape. Following argon purging the press
was heated to the required upper temperature and the desired load applied. Loads
were monitored with an electronic hydraulic pressure transducer which was found to
provide higher resolution than the Bourdon type gage supplied with the system.

Rapid cooling to the isothermal crystallization temperatures was accomplished
by opening the press’ water quenching valves for brief, predetermined periods of
time. Although a precise step profile could not be achieved, the control was sufficient
to allow for rapid cooling to a well defined temperature.

Following consolidation an outline of the specimen was placed over the straight
segments of fibers and guide marks penciled on. Following the guide marks,
specimen preforms were trimmed with scissors to sizes to allow entry into an arbor
press die. Specimens were cut with with the arbor press and a sharp ASTM standard
punch and die set leaving negligible deformation of the matrix within the gage length.
The above procedure has been tested with Nylon 6,6 and BPA-polycarbonate and
found to produce an acceptable yield of fibers which were sufficiently straight and

aligned with the coupon.

7.3.3 NYLON 6,6 FRAGMENTATION TESTING

Interfacial shear strength testing proceeded as follows for the semi-crystalline
nylon 6,6 matrix specimens. The translucence of the matrix precluded direct
observations of fragment lengths through the full specimen thickness. The following
method was therefore used.

Specimens were strained to approximately 6% strain, a level sufficient to
ensure that the limiting fragment length was achieved. The coupons were then
released, removed from the straining stage and sanded to closely approach the fiber

surface. Since the fibers were generally very close to the coupon center, this could

202

generally be achieved by removing nearly half of the coupon thickness. If necessary,
the depth of the fiber beneath the coupon surface was measured periodically by
alternately focusing a microscope on the scattered fiber image and the surface during
the latter stages of this approach. When the fiber was within 20—40 microns of the
coupon surface the specimen was polished and remounted into the straining stage.
Mineral oil was applied as a refractive index matching fluid and a cover slip applied
to further improve image quality.

The specimens were then strained to separate the ends of the fiber fragments,
making the break positions clearly visible and also allowing any matrix cracking to
be observed. The positions of these breaks were recorded and analyzed with a
computer interfaced translation stage utilizing FiberTrack [Waterbury, 1991].

7.4 NYL N R LT AND D1 881 N

Single fiber fragmentation ISS specimens were tested as described. The
processing conditions, Lch ratios, interfacial shear strengths, and microstructure and
failure mode observations are reported in this section and appear in Table 16 and

Figure 110.

7.4.1 NYLON 6,6 ISS RESULTS

The AU4, untreated fibers showed substantially lower ISS, 44.8 and 45.8 MPa
for sets U1 and U2 respectively, than the surface treated AS4 fiber specimens
processed under the same conditions, 72.7 MPa for set N 1. This difference may be
attributed to the removal of a weak surface layer which may allow failure within the
fiber, or to the addition of chemisorbed oxygen which may form polar or hydrogen
bonds with polar groups in the nylon structure. As with the polycarbonate/AU4
specimens, the ISS of untreated fibers in this thermoplastic matrix was higher than

that for AU4 fibers in thermoset epoxy. This effect is discussed in in the conclusions,

203
in the conclusions, chapter 8.

Additional ISS improvements were achieved by slowly cooling at 1 degree
°C/ minute over those rapidly cooled at approximately 1 degree °C/ second. Rapidly
cooled specimens which were preheated at 300 °C to reduce nucleant density showed
slightly reduced ISS compared with those consolidated at 275 °C.

The three sets of specimens consolidated at 382 KPa pressure showed lower
adhesion than those processed at higher pressures, possibly due to inadequate
consolidation and the persistence of a knit line. The best adhesion was shown by the
set which was crystallized isothermally at the relatively low temperature of 225 °C.

Finally, the specimens with IM6, intermediate modulus fibers showed slightly

lower adhesion than the comparable AS4 set.

204

 

 

co
0

G)
O

to
O

 

MPa —> Interfacial Shear Strength
.h
o

 

 

 

 

 

 

Figure 110. Interfacial shear strengths of carbon fibers in Nylon 6,6

Table 16. ISS and Lch of AU4, AS4, and IM6 fibers in Nylon 6,6.

 

Spec. Fiber Fab. Fab. Cooling L/D ISS Crack
Desig. Type Temp. Pres. Method Ratio Diameter
°C 1) (MPa) (microns)

N1 AS4 275 657 Rapid 44.6 72.7 --
N2 AS4 300 657 Rapid 44.7 69.5 --
N3 AS4 275 657 225 36.4 85.8 ~-
N4 AS4 275 657 Slow 36.9 79.9 27
N5 AS4 275 382 245 48. l 65 . 1 27
N6 AS4 300 382 255 43.3 70.5 38
N7 AS4 300 382 250 42.7 70.6 45
U1 AU4 275 657 Rapid 75.7 45.8 13
U2 AU4 275 1313 Rapid 74.6 44.8 --
[Ml IM6 275 657 Rapid 54. 1 66.9 --

 

205

7 .4.2 MICROSTRUCTURE AND FAILURE MODE OBSERVATIONS

Confocal scanning microscope images (Figure 111) revealed the presence of
a transcrystalline sheath surrounding the fibers and extending several fiber diameters
out. This sheath was not uniformly cylindrical, but was itself comprised of discrete
spherulitic structures, spaced more or less closely together depending upon the thermal
history of the melt and on the cooling rate. Lower melt temperatures and faster
cooling rates produced less extensive transcrystalline regions, along with finer

spherulitic textures in the matrix.

 

Figure 111. Four CSOM micrographs of transcrystallinity in Nylon 6,6.

207

Transmission optical micrographs (TOM) of fragmentation test breaks are
shown in Figures 112-116. Matrix cracking at fiber breaks was observed in all
samples.

The improved shear traction transmission of transcrystalline regions result from
different factors. As crystallization proceeds compressive forces may increase due
either to the contraction of the matrix during or after crystallization. These shrinkage
stresses increase adhesion by increasing polar and dispersive interfacial forces and
static and moving frictional coefficients.

Another possible source of enhanced adhesion from transcrystallinity results
from the greater stiffness of the oriented interphase compared with the bulk matrix.
The dependence of shear stress transmission on the ratio of fiber to interphase
modulus was predicted, [Kelley, 1986] and shown experimentally, [Rao, 1990].
Although direct measurements of the stiffness of the transcrystalline interphase are
probably not possible because of the small size, the strongly oriented crystalline
material may be expected to have significantly greater shear modulus than either the
amorphous or spherulitic crystalline forms of the material. Moreover, increasing
interphase thickness will increase the overall stiffness of the local microstructure,
since a thick layer of high shear modulus material has a greater stiffness than a thin
layer surrounded by lower modulus material.

Yet another possible source of improved shear tractions associated with
transcrystallinity arises from the intimate fiber/ matrix contact achieved during the
process of fiber nucleation of matrix crystallization. Strong dispersion bonding forces
may be expected to result from the close fiber/ matrix association resulting from
coherence between the graphitic fiber structure and epitaxially crystallized polymer

chains.

 

Figure 112. TOM of AU4 breaks in Nylon 6,6.

 

dly cooled Nylon 6,6.

in rapi

TOM of AS4 break

Figure 113.

 

 

Figure 114. TOM of AS4 break in Nylon 6,6 slowly cooled from 275 °C

 

Figure 115. TOM of AS4 in Nylon 6,6 cons. @ 275 °C, iso-xtal @ 225 °C.

 

Figure 116. TOM of AS4 in Nylon 6,6 cons. @ 300 °C, iso-xtal @ 245 °C.

213

Epitaxial crystallization has been reported as the mechanism of nucleation of
polymer crystals, [Kumamaru, 1983], [Tuinstra, 1970]. Tuinstra immersed freshly
cleaved graphite basal plane surfaces in a polyethylene solution and found crystal
growth at preferential orientations separated by 60° , strong evidence of true epitaxial
nucleation.

The source of fiber nucleant activity may also arise from a "pseudo-epitaxial"
enhancement of crystallization arising from the conjunction of molecularly flat
graphitic basal planes [Hoffman, 1988] with the polymer melt. The spherulitic
structures in polymer crystals are built up from flat, lamellar crystals [Keller, 1977],
[Keith, 1986] [Stack, 1988]. These lamellae may be significantly stabilized by
association with extremely flat surfaces, in particular in the presence of a corner
between graphite crystals.

As fiber—matrix adhesion increased in moving from AU4 to AS4 fibers and
with different processing conditions, a change occurred in failure mode from
interfacial debonding with small radial matrix cracks to extensive matrix cracking with
minimal debonding (Figures 112-116).

To investigate the relationship between interfacial shear strength and radial
matrix cracking, measurements were made of some representative matrix cracks for
five sets of specimens, reported in Table 16. The ISS is plotted against the average
diameters of these cracks in Figure 117. Although the number of specimen types was
limited, a correlation between higher ISS and greater radial crack diameter can be
seen.

These cracks were more irregular than those in thermoset matrices, apparently
due to the anisotropy of the matrix. The interaction of the transverse matrix cracks
with the anisotropic interphase and matrix regions may be most clearly seen in the

confocal scanning optical microscopy images (CSOM).

 

 

 

 

 

 

 

 

 

 

 

50 a
N4 N6 N7
I I
I
:3
1‘3 U1
(I) I
8
,1: 30
U)
E
8
‘t:
8
E. 20
18
o.
2 o
0 10 20 3O 4O 50
Microns —> Radial Crack Diameter

Figure 117. Interfacial shear strength versus radial crack diameter.

Cracks were initiated at random locations by breaks occurring at defects in the
fiber. These cracks then propagated into the interphase along the preferred failure
planes. For a spherulitic microstructure, this is either between spherulites (inter-
spherulitic) or directly through the center of a spherulite (intra-spherulitic). By
extension from spherulitic structures, the preferred failure plane for a strongly
oriented transcrystalline interphase should be directly radially outward from the fiber.
Examples of these kinds of cracks can be seen in Figures 118 and 119 (interspherulitic
cracks), Figures 120 and 121 (intraspherulitic cracks), and Figure 122 (transcrystalline

crack).

215

 

Figure 118. CSOM of AS4 break initiated interspherulitic crack #1.

 

Writ-*7 rewa- I” ~ , - -~ .
.. u! - - O; A
A - 3...? "f I ‘ ._ La... in:

Figure 119. CSOM of AS4 break initiated interspherulitic crack #2.

 

Figure 120. CSOM of AS4 break initiated intraspherulitic cracks #1.

 

Figure 121. CSOM of AS4 break initiated intraspherulitic cracks #1

217

 

Figure 122. CSOM of A84 break initiated transcrystalline crack #1.

218

ZOOIIZO T'BI

 

 

Figure 124. CSOM optical section of AS4 break in Nylon 6,6, 2: 3.6.

219

 
 
 

   

. 75¢? “7 _ ,. v i
. . - . . .. W'K "".

   

r

zoos-2s T388 Z-Pos - -4.8|0 pa US

Figure 125. CSOM optical section of AS4 break in Nylon 6,6, 2: 4.8.

2003-20 T-Os Z-Pos - -6.IOO VA US

 

Figure 126. CSOM optical section of AS4 break in Nylon 6,6, 2: 6.0.

220

ZOOHIZI TIC!

ZOOHIZI TOO! Z-Pos ' -O.450 90 US

 

Figure 128. CSOM optical section of AS4 break in Nylon 6,6, Z= 8.45

221
7 .4.3 HEATED STAGE MICROSCOPE OBSERVATIONS

Heated stage microscope observations showed that nucleation of crystallization
at the fiber surface slightly preceeded that in the bulk matrix. This nucleation took
place in the absence of any shear deformations, which tend to additionally promote
nucleation and which are likely to occur during processing of high Vf composites due
to flow of the matrix material and thermal contraction of the melt in relation to the
immobile fiber mass.

The fact that crystallization occurs as a result of nucleation at the fiber surface
implies that extremely close contact exists at the fiber/ matrix interface, closer than
that which is likely to occur as a result of the growth of spherulites nucleated within
the matrix eventually impinging upon the fiber. Since both polar and dispersive forces
are strongly affected by distance, this close contact significantly increases adhesion.

Spherulite sizes were measured for specimens preheated at 275 and 300 °C and
isothermally crystallized at 245, 250 and 255 °C on a microscope hot stage as a
measure of the dependence of nucleant density on thermal treatment. Preheating at
300 °C was found to reduce this density by approximately 2 orders of magnitude
compared with the 275 °C preheat. These temperatures were chosen for ISS

specimen fabrication to investigate the influence of this variable.

7.5 NYLON 6,6 CONCLUSIONS

A method for fabricating and interrogating single fiber fragmentation
specimens in semicrystalline thermoplastics has been developed that allows optical
observations of failure modes. Interfacial shear strengths were found to increase with
increases in the development of transcrystallinity at slower cooling rates and in
specimens isothermally crystallized at low temperatures. CSOM observations of the
interaction of fiber failure induced matrix cracks indicate that matrix cracks begin at

random fiber breaks and migrate toward preferred failure planes within the matrix.

CHAPTER 8

CONCLUSIONS

T ON L

The fragmentation test contains a wealth of potentially valuable information
about the properties of the fiber-matrix interface and interphase, and the interaction
of failure modes with all composite constituents. This information has only begun to
be exploited, with numerous recordable and reproducible parameters that have
received little or no attention in the literature. Some of these parameters extract
information with less ambiguity than the critical length approach, since they involve
a single mode of failure, analyzed by a single algorithm. The critical length
approach, however, also has an advantage in that it allows for a single system for
comparing all fragmentation test results.

Fiber failure strain energy release can significantly alter the failure modes and
measured critical lengths in fragmentation tests. This effect has been largely ignored
in the literature, and has clouded the interpretation of data. Other interfacial shear
strength measurement methods do not include a contribution from fiber failure energy
and so are fundamentally different measurements. In addition, these methods involve
cracking with different symmetries, and therefore different potential crack growth

habits and results.

222

223

8. 3 W

The feasability of determining fiber strengths at short gage lengths by in-situ
fiber strength testing has been demonstrated. Results obtained from single-fiber
fragmentation, in-situ fiber strength testing are in close agreement with those from
short gage length fiber tension tests. The number of fiber flaws per unit length was
found to increase exponentially with increasing strain increment.

The necessity of determining fiber prestrain produced during specimen
fabrication was shown. A computerized weakest link model has been developed to
analyze the experimentally determined fiber flaw distributions and to simulate the

single-fiber fragmentation process.

8.4 A NLIN

An optical method for the determination of composite volume fractions has
been developed. The accuracy of the method is not influenced by small image
variations because the data is extracted as a digital parameter, the number of fibers.
The method is an absolute technique, which does not require calibration by any other
test, and which provides fiber volume distribution information with unequalled spacial

resolution.

8.5 W113

Surface treatment of IM6 fibers produced an increase in chemisorbed surface
oxygen. This increase occurred rapidly for the untreated fibers, and then at a lower,
linear rate as surface treatment continued. This difference is probably attributable to
the availability of reactive, edge, corner, and disordered carbon atom sites on the
untreated fibers, compared with exclusively graphitic basal plane carbon atoms on the
treated fibers.

The interfacial shear strength increased almost linearly with increasing surface

224
oxygen percentage and with polar surface free energy, rapidly rising with 20% surface
treatment compared to the untreated fiber and then increasing at a lower rate as
surface treatment continued. Although these variables were shown to be closely
correlated, actual causality is much more difficult to establish. It cannot be
conclusively stated that there is a cause and effect relationship based upon these data,
though such a relationship is strongly supported. The addition of the toughened "G"
size also increased the measured values of interfacial shear strength, and caused a
change in failure mode in the fragmentation specimens from entirely interfacial to
combined interfacial and interphase yielding.

The Mode II fracture toughness increased with increasing fiber surface
treatment and with the addition of the size. Sizing led to a particularly large increase,
probably because of increased plastic deformation of the interphase region. This
increase closely followed that of ISS, except for the sized case.

Transverse flexural strengths were somewhat enigmatic and may have been
influenced by fiber bridging artifacts or differences in fiber volume fraction.

Interlaminar shear strengths increased with surface treatment compared with
the untreated fibers, but increased at a low rate for all surface treated and treated and
sized fibers. This was probably due to a matrix dominated failure mode with small
interfacial effects. Nevertheless, the plot of ILSS versus ISS shows an approximately

linear relationship.

8.6 ARB NATE N L I N

Interfacial shear strengths of carbon fibers in pure polycarbonate were found
to increase with increasing consolidation temperature and time. Specimens produced
by solvent deposition at low temperatures showed much lower ISS while specimens
with solvents present but consolidated at higher temperatures showed good adhesion.

Lexan matrix specimens appeared to reach a limiting ISS which did not vary

225
significantly with consolidation temperature or pressure.

Slowly cooled Lexan matrix specimens showed evidence of shear band
formation in both polarized and unpolarized microscope observations. Rapidly cooled
Lexan specimens appeared to fail by stick-slip interfacial cracking accompanied by
some matrix deformation. Pure polycarbonate specimens showed intense birefringence

patterns, indicating strong adhesion.

8.7 W

A method for fabricating and interrogating single fiber fragmentation
specimens in semicrystalline thermoplastics has been developed that allows optical
observations of failure modes. Interfacial shear strengths were found to increase with
increases in the development of transcrystallinity. CSOM observations of the
interaction of fiber failure induced matrix cracks indicate that matrix cracks begin at
random fiber breaks and migrate toward preferred failure planes within the interphase

and bulk matrix.

ERM P A I MATRIX

The three classes of matrices studied in this investigation, thermoset,
amorphous thermoplastic, and semicrystalline thermoplastic, differ in microstructure,
reactivity of the melt, moduli, and other properties. The pattern of their adhesion to
untreated and surface treated carbon fibers, however, is remarkably similar. The
interfacial shear strength of untreated AU4 and surface treated, AS4 fibers in a
thermoset epoxy, an amorphous thermoplastic, polycarbonate, and a semicrystalline
thermoplastic, Nylon 6,6 are plotted in Figure 129. As can be seen, in all three
matrices the AU4 fiber adhesion is significantly lower than the A84 fiber. Moreover,

the magnitude of the adhesion is approximately the same, with higher values for

226
80

 

8

 

 

 

as
O

N)
O

 

 

   

 

 

MPa —> Interfacial Shear Strength

 

 

 

 

O

 

 

AU4 AS4 AU4 AS4 AU4 AS4
EPOXY POLYCARBONATE NYLON 6.6

Legend: D Untreated. AU4 Treated. AS4

Figure 129. ISS of AU4 and AS4 fibers in thermoset and thermoplastic matrices.

 

227
the Nylon 6,6 AS4 case, and slightly higher values for AU4 in both polycarbonate and
Nylon 6,6 than for epoxy. The similarity implies that a similar failure mechanism is
involved for the AU4 fibers, that of failure within a weak surface layer in the fiber.
The slightly higher values for the thermoplastics may then be attributed to the greater
thermal contraction stresses increasing the normal force and therefore the maximum
shear strength on this weak fiber layer.

The greater ISS of the AS4 fiber in Nylon 6,6 probably results from both the
intimate fiber/ matrix interface contact resulting from fiber nucleation of crystallization
and from the higher stiffness of the oriented transcrystalline interphase. Chemical
bonding at the interface does not appear to play a significant role, as indicated by the

lower ISS of the more reactive thermoset epoxy.

APPENDIX A

SOURCE CODE FOR FIBERTRACK, FRAGMENTATION TEST
DATA ACQUISITION AND ANALYSIS SYSTEM

The following program is the source code listing written compiled AmigaBasic
(Absoft, AC-Basic) for the FiberTrack, fragmentation test data acquisition and analysis
program described in chapter 7. Weibull calculation routines were translated and
adapted from a mainframe Fortran program (author unknown). A list of subroutines
and a brief description of their functions preceeds the actual code. Long code lines
have been reformatted, with leading hyphens attached to the second portions.

Main: Main program loop.

Start: Sets up menu interrupts and "sleeps” here until summoned by a menu call from
the user.

StartupText: Displays copyright information and specifies df 1: drive for all data
diskettes.

ArrayDimensions: Defines all data arrays and allocates space to them.
Initialize: Sets all initial variables, file names, graphics colors, default moduli.
GammaData: Sets up a look-up table of the Gamma function.

InitializeMenu: Initializes the menu selections.

CheckMenu: Arrival point when user makes a menu selection. Finds column and
routes to submenus.

Filemenu: Checks first column of menu items and routes to appropriate subroutine.
Graphics: Checks second column of menu items and routes to appropriate subroutine.
Tracking: Checks third column of menu items and routes to appropriate subroutine.
Calcs: Checks fourth column of menu items and routes to appropriate subroutine.

GammaLoader: Inputs Weibull shape and scale factors from user and performs
Gamma function calculations.

FiberData: Inputs data on fiber diameter, modulus, etc. from user for all calculations.
MatrixData: Inputs data on matrix name, modulus, etc. from user for printouts.

LengthStrength: Simply sets fiber tensile strength at this point, intended to be
upgraded to perform log-linear extrapolation to automatically find strength @ length.

228

229
GammaPlot: Produces a graphical plot of the Gamma function.
Dir: Lists directory of the dfl: drive.

WriteTrack: Writes a file with the positions of all breaks, dial gage reading, strain,
etc.

ReadTrack: Reads files written by WriteTrack.

ReadTracks: Reads a set of tracks with the same root file name and different track
numbers.

PrintLengths: Prints out the fragment lengths, calculated from the break positions.
PrintBreakList: Prints out the break positions in a column format for a set of tracks.
WriteLengths: Writes a file with the fragment lengths, rather than positions.

WriteBreakList: Writes a file with the break positions for a set of tracks in column
format.

WriteBreaks: Writes a file with the break positions, track by track.
ReadBreaks: Reads files written by WriteBreaks.

Tracker: Startup for tracking fiber break positions. Initializes file name, dial gage,
asks if track should be destrained, sets up mouse interrupts.

TimeO: Waits for joystick port input to note translation stage startup time and
direction. Routes to " Loop ".

Loop: Tracking routine loops here as long as the joystick port input is non-zero.
Goes to ”NewBreak" whenever user clicks mouse button, and when joystick port
becomes zero

at the moment the stage is halted. After stage stops prompts the user for the distance
traversed and routes to "ScaleTrack" , "WriteTrack" , and "WeibullLoader".

NewBreak: Records the exact time of each mouse click, calculates the delta time from
translation startup to that time, calculates a break position based on an assumed
velocity that contains the correct sign for the stage motion direction, prints out the
number of breaks, and generates an audio feedback tone to confirm that a break
was recorded.

ScaleTrack: Rescales the track to the actual distance traversed, based on the user
input. Destrains the track if desired.

ZeroTrack: Sets track to zero breaks and all break positions to zero.

ShowFibers: Displays a graphical representation of all break positions for one or
more tracks. Allows user specification of breaks using mouse.

CheckMouse: Checks for mouse clicks and if on lower part of screen scrolls the
break display to the left or right. If on upper part of screen checks to see which track

230

and
break is being selected and stores its index in the DataT() array.

DrawFibers: Performs the actual fiber display graphic output.
ListBreaks: Lists track and break numbers for selected breaks.
Cleanup: Clears the screen.

Quit: Resets menu and stops program operation.

Palet: Initializes screen, window, and pallettes.

WeibullLoader: Loads fragment lengths into Weibull routine. This version always
Weibullizes track 1.

Weibull: Performs Weibull calculations, displays results, calls "LengthStrength' and
"Gamma" routines. '

Gamma: Performs Gamma function calculations based on lookup table and linear
interpolation, prints out results.

FIBERTRACK 1.0 PROGRAM LISTING

’ = = = =Single Fiber Critical Length Test= = = = = = = = = =
’ = = = = =Fiber Break Tracker - Data Input Program

’10/1/1989, Copyright Mark Waterbury
CLEAR ,25000
CLEAR ,70000&

Programloop:

GOSUB ArrayDimensions

GOSUB Initialize ’Sets Graphics and screen constants
GOSUB Palet’ Sets palette, screen, and window
GOSUB StartupText

GOSUB InitializeMenu

Start:
ON MENU GOSUB CheckMenu : MENU ON
Unfinished = -l
WHILE Unfinished
SLEEP ’this program is event driven

StartupText:
CLS
LOCATE 10,1
PRINT ”This program Copyrighted by Mark C. Waterbury
PRINT "10,1,1989 Licensed for use by the
PRINT ”Composite Materials and Structures Center
PRINT ”May not be reproduced or duplicated without the

231

PRINT "written consent of the author.

LOCATE 18,1

PRINT ”Insert formatted data disk in dfl:

PRINT ”All track files will be saved to that disk.
RETURN

ArrayDimensions:
DIM X(30,200)
DIM NBreaks(30), Length(30), NewBreaks(30)
DIM DG(30),Strain(30), TStress(30)
DIM AveStrain(30) ’Ave. of track and the preceeding one
DIM F1$(30)
DIM DataT(200),DataB(200)
DIM Fiber(200),Stress(200)
DIM W(2000), WLog(2000) ’ For Weibull Routine
DIM Gamma (205)

RETURN

Initialize:
WIDTH ”LPT1:",255
Modulus = 34000000& ’modulus set to AS4 default
AS4Mod = 34000000& ’AS4 modulus, psi
IM6Mod = 40400000& IM6 modulus, psi
Pi = 3.14159
Scrx = 640:ScrY = 400
FT% = 160:FB% = FT% + 15
G096 = 2 ’ gap color (integer)
Gap% = 4 ’break gap
fc1% = 6 ’fiber color 1
f02% = 7 ’fiber
Velocity = 200
F1$(0) = "00":F1$(1) = "01":Fl$(2)= "02": F1$(3) ="03"
Fl$(4)= "04": Fl$(5)= "05": F1$(6)= "06": F1$(7) ="07"
F1$(8) = "08": F1$(9) ="09": F1$(10)= "10": F1$(11) ="ll"

F1$(12) = "12": Fl$(l3)= "13":Fl$(14) = "14": F1$(15) ="15"
F1$(16) = "16": F1$(l7)= "17": F1$(18) = "18": F1$(l9) ="19"
F1$(20) = "20": Fl$(21)= "21": F1$(22) = "22":Fl$(23) ="23"
F1$(24) = "24": F1$(25) = "25": Fl$(26)= "26":Fl$(27) ="27"
F1$(28) = "28": F1$(29) = "29":Fl$(30) = "30"

GOSUB GammaData
RETURN
GammaData:

FOR I = 100 TO 200

READ Gamma(l)

NEXT I

DATA 1.00,.99433,.98884,.98355,.97844
DATA .9735,.96874,.96415,.95973,.95546
DATA .95135 , .94740, .94359, .93993 , .93642
DATA .93304, .92980, .92670, .92373 , .92089
DATA .91817,.91558,.91311,.91075,.90852
DATA .90640,.90440,.90250,.90072,.89904
DATA . 89747, . 89600, . 89464 , . 89338 , . 89222

232

DATA .89115,.89018,.88931,.88854,.88785
DATA .88726,.88676,.88636,.88604,.88581
DATA .88566,.88560,.88563,.88575,.88595
DATA .88623,.88659,.88704,.88757,.88818
DATA .88887,.88964,.89049,.89142,.89243
DATA .89352,.89468,.89592,.89724,.89864
DATA .90012,.90167,.90330,.90500,.90678
DATA .90864,.91057,.91258,.91466,.91683
DATA .91906,.92137,.92376,.92623,.92877
DATA .93138,.93408,.93685,.93989,.94261
DATA .94561,.94869,.95184,.95507,.95838
DATA .96177,.96523,.96877,.97240,.97610
DATA .97988,.98374,.98768,.99l71,.99581,1!

FOR I = 101 TO 200

= (I-100)/ 100
Gamma (I-100) = Gamma(I)/N
NEXT I
RETURN

InitializeMenu:
MENU 1,0,1,"File"
MENU 1,1,1,"Write Break File
MENU 1,2,1,"Read Break File"
MENU 1,3,1,"Read Track"
MENU 1,4,1,"Read Set of Tracks"
MENU l,5,l,"Dir"
MENU 1,6,1,"Quit, return to Basic"
MENU 2,0,1,"Calcs"
MENU 2, 1, 1,"Weibull Calcs"
MENU 2,2,1,"Gamma Calcs"
MENU 2,3,1,"Gamma Plot"
MENU 2,4,1,"Fiber Data"
MENU 2,5 ,1,"Matrix Data"
MENU 3,0,1,"Graphs"
MENU 3, 1 , 1 , "Show Fibers"
MENU 3,2,1,"Clear Screen"
MENU 3,3,1,"Write Break List"
MENU 3,4,1,"Write Length List"
MENU 3,5,1,"Print Break List"
MENU 3,6,1,"Print Length List"
MENU 4,0,1,"Tracker"
MENU 4,1,1,"Track Breaks"
MENU 4,2, l , "List Selected Breaks"
RETURN

CheckMenu:

Menuld = MENU(0)

Menultem = MENU(1)

ON MenuId GOSUB Filemenu,Calcs,Graphics,Tracking
RETURN

Filemenu:
ON Menultem GOSUB WriteBreaks,ReadBreaks,ReadTrack,

233

-ReadTracks,Dir,Quit
RETURN

Graphics:

ON Menultem GOSUB ShowFibers,Cleanup,WriteBreakList, WriteLengths,
_PrintBreakList, PrintLengths
RETURN

Tracking:
ON Menultem GOSUB Tracker,ListBreaks
RETURN

Calcs:

ON Menultem GOSUB WeibullLoader,GammaLoader,GammaPlot, FiberData,
_MatrixData

RETURN

GammaLoader:
INPUT "File Name ",Fil$
INPUT "Alpha, Beta (set Alpha = 0 to quit) ",Alpha,Beta
IF Alpha = 0 THEN RETURN
GOSUB Gamma
GOTO GammaLoader
RETURN

FiberData:
CLS
INPUT "Fiber Designation ",FDesig$
INPUT "Fiber Diameter (microns) ",Diameter
INPUT "Fiber Strength @ 25 mm ",StrengthO
INPUT "Fiber Modulus ",Modulus
RETURN

MatrixData:
CLS
INPUT "Matrix Designation",MDesig$
INPUT "Matrix Tensile Strength (psi) ",MTStrength
INPUT "Matrix Shear Strength (psi) ",MSStrength
INPUT "Matrix Tensile Modulus (psi) ",MTModulus
INPUT "Matrix Shear Modulus (psi) ",MSModulus
RETURN

LengthStrength:
Strength = StrengthO

GammaPlot:
PSET (0,10*Gamma(100)),1
FOR I = 0 TO 200
LINE -(1 * 3,10 * Gamma(I)),1
NEXT I
FOR I = 0 TO 200 STEP 25
LINE (1 * 3 ,180)-(I* 3,200),2

234

NEXT I
INPUT "Printout? Y/N ",Pr'S
IF Pr$ < > "Y" THEN GOTO NoPrint
LPRINT "Gamma Function for N = 0 to 2.00 in l/ 100 ths"
LPRINT
FORI = 0TOZOOSTEP5
LPRINT USING " ###.#####";I/100;Gamma(I);Gamma(I+1);
-Gamma(I+2);Gamma(I+3);Gamma(I+4)
NEXT I
NoPrint:
RETURN

Dir:
FILES "dfl:"
RETURN

WriteTrack:
FilTS = Fil$ + F1$(nT)
OPEN FilT$ FOR OUTPUT AS 1
WRITE #1, FilTS
WRITE #1, nT
WRITE #1,DG(nT),Strain(nT)
WRITE #1,NBreaks(nT),Length(n'l‘)
FOR K = 1 TO NBreaks(nT)
WRITE #1, X(nT,K)
NEXT K
CLOSE #1
PRINT "File saved as " ;FilT$
RETURN

ReadTrack:
CLS
INPUT "File name ",Fil$
INPUT "Track ",nT
IFnT = OTHENnT =1
IF nT > NTracks THEN NTracks = nT
FilT$ = "dfl:" + Fil$ + F1$(nT)
OPEN FilT$ FOR INPUT AS 1
INPUT #1, FS
INPUT #1, “IT
INPUT #1,DG(nT),Strain(nT)
INPUT #1 ,NBreaks(nT),Length(nT)
FOR K = 1 TO NBreaks(nT)
INPUT #1, X(nT,K)
NEXT K
CLOSE #1
RETURN

ReadTracks:
CLS
INPUT "Parent File Name ",FilS

235

INPUT "First and Last Tracks ",NFirst,NIast
NTracks = NLast - NFirst + 1
FOR nT = NFirst TO NIast
FilT$ = "dfl:" + Fil$ + F1$(nT)
OPEN FilTS FOR INPUT AS 1
INPUT #1, FS
INPUT #1, Tn
INPUT #1,DG(nT),Strain(nT)
INPUT #1 ,NBreaks(nT),Length(nT)
FOR K = 1 TO NBreaks(nT)
INPUT #1, X(nT,K)
NEXT K

CLOSE #1
NEXT nT
RETURN

PrintLengths:
LOCATE 1,1
LPRINT Fil$
LPRINT NTracks
FORI = 1 TO NTracks-l
LPRINT USING " ##";1;
NEXT I
LPRINT USING " ##";I
FORI=1TONTracks-l
LPRINT USING " ###";DG(I);
NEXT I
LPRINT USING " ###";DG(I)
FOR I = 1 TO NTracks -l
LPRINT USING " ##.####";Strain(I)-l;
NEXT I
LPRINT USING " ##.####";Strain(I)-1 '
FOR J = 1 TO NTracks -l
LPRINT USING " ###";NBreaks(J);
NEXT J
LPRINT USING " ###";NBreaks(J)
MaxBreaks = NBreaks(l)
FOR I = 2 TO NTracks -1
IF NBreaks(I) > MaxBreaks THEN MaxBreaks = NBreaks(I)
NEXT I
FOR I = 2 TO MaxBreaks
FOR J = lTO NTracks -1
IF X(J,I) - X(J,I-1) > 0 THEN
Lx% = (X(J,I)-X(J,I-1))
LPRINT USING " ##1##"; Lx%;
ELSE
LPRINT USING " ####";X(J,I);
END IF
NEXT J
IF X(J,I) - X(J,I-l) > 0 THEN
Lx% = (X(J,I)-X(J,I-1))
LPRINT USING " ####"; Lx%
ELSE

236

LPRINT USING " ####";X(J,I)
END IF
NEXT I
RETURN

PrintBreakList:
LPRINT Fi1$
LPRINT NTracks
FOR I = 1 TO NTracks-l
LPRINT USING " ## ";1;
NEXT I
LPRINT USING " ##";I
FORI=1TONTracks-l
LPRINT USING " ###";DG(I);
NEXT I
LPRINT USING " ###";DGO)
FORI = ITO NTracks -1
LPRINT USING " ##.####";Strain(I)-l;
NEXT I
LPRINT USING " ##.####";Strain(I)-1
FOR J = lTO NTracks -1
LPRINT USING " ### ";NBreaks(J);
NEXT J
LPRINT USING " ###";NBreaks(J)
MaxBreaks = NBreaks(l)
FOR I = 2 TO NTracks -1
IF NBreaks(I) > MaxBreaks THEN MaxBreaks = NBreaks(I)
NEXT I
FOR I = 1 TO MaxBreaks
FOR J = 1 TO NTracks -l
XX% = X(J,I)
LPRINT USING " #####"; XX%;
NEXT J
XX% = X(J,I)
LPRINT USING " #####"; XX%
NEXT I
CLOSE #1
RETURN

WriteLengths:

LOCATE 1,1

INPUT "Save Lengths ",Fil$

Fil$ = "dfl:" + Fil$

OPEN Fil$ FOR OUTPUT AS 1
WRITE #1, F113
WRTTE #1, NTracks
FOR I = 1 TO NTracks-1

PRINT #1, USING " ##";1;
NEXT I
PRINT #1, USING " ##";I

FORI=1TONTracks-l
PRINT #1, USING " ###";DGO);
NEXTI

237

PRINT #1, USING " ###";DG(I)
FORI = 1 TO NTracks -1
PRINT #1, USING " ##.####";Strain(I)-l;
NEXT I
PRINT #1, USING " ##.####";Strain(I)-l
FOR J = 1 TO NTracks -l
PRINT #1, USING " ###";NBreaks(J);
NEXT J
PRINT #1, USING " ###";NBreaks(J)
MaxBreaks = NBreaks( 1)
FOR I = 2 TO NTracks -1
IF NBreaks(I) > MaxBreaks THEN MaxBreaks = NBreaks(I)
NEXT I
FOR I = 2 TO MaxBreaks
FOR J = 1TO NTracks -1
IF X(J,I) - X(J,I-l) > 0 THEN
Lx% = (X(J,I)-X(J,I—1))
PRINT #1, USING " ####"; Lx%;
ELSE
PRINT #1, USING " ### ";X(J,I);
END IF
NEXT J
IF X(J,I) - X(J,I-1) > 0 THEN
Lx% = (X(J,I)-X(J,I-l))
PRINT #1, USING " ####"; Lx%
ELSE
PRINT #1, USING " ####";X(J,I)
END IF
NEXT I
CLOSE #1
RETURN

WriteBreakList:
LOCATE 1,1
INPUT "Save Break List ",Fil$
Fil$ = "dfl:" + Fil$
OPEN Fil$ FOR OUTPUT AS 1
WRITE #1, Fil$
WRITE #1, NTracks
FOR I = 1 TO NTracks-l
PRINT #1, USING " ## ":1;
NEXT I
PRINT #1, USING " ##";I
FORI=1TONTracks-l
PRINT #1, USING " ## ";DG(I);
NEXT I
PRINT #1, USING " ###";DG(I)
FORI = ITO NTracks -1
PRINT #1, USING " ##.####";Strain(I)-l;
NEXT I
PRINT #1, USING " ##.####";Strain(I)-l
FOR J = ITO NTracks -l
PRINT #1, USING " ### ";NBreaks(J);

238

NEXT J
PRINT #1, USING " ###";NBreaks(J)
MaxBreaks = NBreaks(l)
FOR I = 2 TO NTracks -1
IF NBreaks(I) > MaxBreaks THEN MaxBreaks = NBreaks(I)
NEXT 1
FOR I = 1 TO MaxBreaks
FOR J = ITO NTracks -l
XX% = X(J,I)
PRINT #1, USING " #####"; XX%;
NEXT J
XX% = X(J,I)
PRINT #1, USING " #####"; XX%
NEXT I
CLOSE #1
RETURN

WriteBreaks:
LOCATE 1,1
INPUT "Break File Name ",Fil$
Fi1$ = "dfl:” + Fil$
LOCATE 1,1:PRINT " "
OPEN Fil$ FOR OUTPUT AS 1
WRITE #1, NT racks
FOR I = 1 TO NTracks
WRTTE #1,T(I),DG(I),Strain(I)
NEXT I
FOR J = 1 TO NTracks
WRITE #1,NBreaks(J),Length(J)
NEXT J
FOR I = 1 TO NTracks
FOR J = 1 TO NBreaks(I)
WRITE #1,X(I,J)
NEXT J
NEXT 1
CLOSE #1
RETURN

ReadBreaks:
LOCATE 1,1
INPUT "Read Breaks ",Fil$
Fil$ = "dfl:" + Fil$
OPEN Fil$ FOR INPUT AS 1
INPUT #1, NTracks
FOR I = 1 TO NTracks
INPUT #1,Tn,DG(I),Strain(I)
NEXT I
FOR J = 1 TO NTracks
INPUT #1,NBreaks(J),Length(J)
NEXT J
FOR I = 1 TO NTracks
FOR J = 1 TO NBreaks(I)

239

INPUT #1,X(I,J)
NEXT J
NEXT I
CLOSE #1
RETURN

Tracker:
CLS
INPUT "File Name? ",Fil$
INPUT "Track Number (RETURN for single track) " ,nT
IF nT = 0 THEN nT = 1
INPUT "De-Strain Tracks? 1/0 ",DStrain
IF DStrain THEN INPUT "Track Strain? ",Strain(n’I)
PRINT "Set Newport drive to ZERO before starting "
Fil$ = "dfl:" + Fil$
LOCATE 5,1:PRINT "Number of breaks = "
GOSUB ZeroTrack
ON MOUSE GOSUB NewBreakzMOUSE ON

TimeO:
IF STICK(3) = 1 THEN
Tm# = TIMER
V = Velocity
GOTO Loop
END IF
IF STICK(3) = -1 THEN
Tm# = TIMER
-.- —Velocity
GOTO Loop
END IF
GOTO TimeO

Loop:
’ cles through this loop while tracking,
’ gorng to NewBreak on Mouse
WHILE STICK(3) < > 0
LOCATE 13,1:PRINT "Moving":LOCATE 13,1:PRINT " "
WEND
GOSUB NewBreak ’ Records end of track as the last break
CLS
INPUT "Length traversed (microns) ",Length(nT)
IF Length(nT) = 0 THEN RETURN
GOSUB ScaleTrack
GOSUB WriteTrack
GOSUB WeibullLoader
IF NTracks = 0 THEN NTracks = 1
RETURN

NewBreak:
T# = TIMER
DeltaT# = TIMER - Tm#
NBreaks(nT) = NBreaks(nT) + l
X(nT,NBreaks(nT)) = V * DeltaT#

240

LOCATE 5,20:PRINT NBreaks(nT)
SOUND 1024,.3
RETURN

ScaleTrack:

IF X(nT,NBreaks(nT)) = 0 THEN RETURN
Scale = ABS(Length(nT))/ABS(X(nT,NBreaks(nT)))
IF DStrain THEN Scale = Scale /(1 + Strain(nT))
FOR I = 1 TO NBreaks(nT)
X(nT,I) = X(nT,I) * Scale
NEXT I

IF V < 0 THEN

FOR I = 1 TO NBreaks(nT)
X(0,NBreaks(nT)-I+l) = Length(nT) + X(nT,I)
NEXT I

FORI = 1 TO NBreaks(nT)
X(nT,I) = X(0,I)
NEXT I

END IF
RETURN

ZeroTrack:

IF nT = 0 THEN nT = 1
FOR I = 1 TO 200
X(nT,I) = 0
NEXT I

NBreaks(nT) = 0

RETURN

ShowFibers:
N = 0 ’Number of data points
CLS
INPUT "Number Fibers? 1/0 ",PNumb
Shift% = -600
ON MOUSE GOSUB CheckMouse:MOUSE ON
GOSUB DrawFibers
InkL:
Inks = INKEYS
IF Ink$ = "0" THEN XOff% = 0:GOSUB DrawFibers
IF Ink$ = "9" THEN XOff% =Last%* Shift%:GOSUB DrawFibers
IF Ink$ = "1" THEN XOff% = Shift%:GOSUB DrawFibers
IF Ink$ = "2" THEN XOff% = 2 * Shift%:GOSUB DrawFibers
IF Inks = "3" THEN XOff% 3 * Shift%:GOSUB DrawFibers
IF Ink$ = "4" THEN XOff% 4 * Shift%:GOSUB DrawFibers
IF Ink$ = "5" THEN XOff% 5 * Shift%:GOSUB DrawFibers
IF Ink$ = "6" THEN XOff% 6 * Shift%:GOSUB DrawFibers
7
8

IF Ink$ = "7" THEN XOff% * Shift%:GOSUB DrawFibers
IF Ink$ = "8" THEN XOff% - * Shift%:GOSUB DrawFibers
IF Ink$ = "Q" THEN :RETURN
IF Ink$ = "q" THEN :RETURN

241

CheckMouse:

F = MOUSE(O)

Mx% = MOUSE(1):My% = MOUSE(2)

IF My% > 175 THEN
IF Mx% < 160 THEN XOff% = XOff% - Shift% :GOTO MHop
IF Mx% < 320 THEN XOff% = XOff% - Shift%/2 :GOTO MHop
IF Mx% < 480 THEN XOff% = XOff% + Shift%/2 :GOTO MHop

XOff% = XOff% + Shift%

MHop:

GOSUB DrawFibers

END IF

IF My% < 170 THEN

Dt = OzDB = O

N = N + l

Dt = INT(My%l8)

DataT(N) = Dt

FORI = 1 TO NBreaks(Dt)

Lx = X(Dt,I)l 10 + XOff%

IF ABS(Lx + 3 - Mx%) < 3 THEN DB =1

NEXT I

IF DB = 0 THEN DataT(N) = 0:N = N - l :GOTO EndHop

DataB(N) = DB
Ly% = Dt "‘ 8
Lx = X(Dt,DB)/ 10 + XOff%
LINE (Lx,Ly%)—(Lx+6,Ly% +2),4,bf

EndHop:

END IF
RETURN

DrawFibers:
CLS
Last% = INT(-X(1,NBreaks(1))/(Shift%*10))
FOR I = 1 TO NTracks
Ly% = I * 8
LINE (0,Ly%)-(640,Ly% + 2),3,bf
FOR J = 1 TO NBreaks(I)
Lx = X(I,J)/10 + XOff%
IF Lx < 0 THEN GOTO Next]
IF Lx > 640 THEN GOTO Next]
LINE (Lx,Ly%)-(Lx+6,Ly%+2),2,bf
L1 = I
Px% = Lx/8
IF Px% > 39 THEN Px% = 39
IFPx% <1THENPx% =1
IF Lx > 0 AND PNumb THEN LOCATE L1,Px%:PRINT USING "##";J
NextJ: NEXT J
NEXT I
FOR I = 1 TO N
Ly% = DataT(I) * 8
Lx = X(DataT(I),DataB(I))/10 + XOff%
IF Lx < 0 THEN GOTO DataHop
IF Lx > 640 THEN GOTO DataHop

242

LINE (Lx,Ly%)-(Lx+6,Ly% +2),l,bf
DataHop: NEXT I

LINE (0,175)-(640,175),3

FOR I = 0 TO 63

LINE (I*lO,175)-(I*10,170),3

NEXT I

FOR I = 0 TO 6
LINE (I*100,l75)-(I*100+l,165),3 ,bf
NEXT I

LOCATE 23,1:PRINT -XOff%*10;:PRINT " Type O to return";
RETURN

ListBreaks:
CLS
FOR I = 1 TO N
PRINT X(DataT(I),DataB(I))
NEXT I

RETURN

Cleanup:
CLS
RETURN

Quit:
MENU RESET
STOP

Palet:

SCREEN 1,640,200,3,2

WINDOW l,"FiberTrack Single Fiber IFSS/ISFS Data

- Acquisition and Analysis M.C. Waterbury",,0,l

COLOR 3,0
PALETTE 0,0/15,0/15,2/15 :PALETTE 1,0/15,0/15,15/15
PALETTE 2,5/15,4/15,0/15 :PALETTE 3,15/15,15/15,15/15
PALETTE 4,15/15,12/15,0/15 :PALETTE 5,0/15,15/15,0/15
PALETTE 6,0/15,15/15,15/15 :PALETTE 7,2/15,2/15,2/15

RETURN

WeibullLoader:
CLS
N = 0
nT = 1 ’Always does Track 1 in this version
FOR J = 2 TO NBreaks(nT) - l
N = N + 1
W(N) = X(nT,J)-X(nT,J-l)
NEXT J
GOSUB Weibull
RETURN
Weibull:
REM= = = =W(I) must contain the N values to be Weibullized
Sum1# = O

FORI=1TON

243

WLog(I) = LOG(W(I))
Suml# = Suml# + WLog(I)
NEXT I
Suml# = Suml# / N
A = .1
FOR Iteration = 1 TO 100
Sum2# = 0: Sum3# = 0: Sum4# = 0
FOR I = 1 TO N
xA = W(I) " A
Sum2# = Sum2# + xA
Sum3# = Sum3# + xA * WLog(I)
Sum4# = Sum4# + xA * WLog(I) " 2
Gola = WLog(I)
PXE = EXP(A * Gola)
Sum2# = Sum2# + PXE
Sum3# = Sum3# + PXE * Gola
Sum4# = Sum4# + PXE * Gola " 2
NEXT I
F = Sum3# / Sum2# - l / A - Suml#
Fp =(Sum4#*Sum2#-Sum3#*Sum3#)/(Sum2#*Sum2#) + 1/(A*A)
An = A - F / Fp
IF ABS(A - An) < .0001 THEN GOTO Converged
PRINT Iteration, A, An
A = An
NEXT Iteration
PRINT "No Convergence"
RETURN
Converged:
Beta = 0
FOR I = 1 TO N
Beta = Beta + EXP(An * WLog(I))

NEXTI
Beta = (Beta/N)"(l/An)
Alpha = An

PRINT "Alpha = "; Alpha, "Beta = "; Beta
PRINT "Number of Breaks = ";NBreaks(nT)
GOSUB LengthStrength
GOSUB Gamma
RETURN

Gamma:

’Performs linear interpolation using Gamma array values
IF Diameter = 0 THEN Diameter = l

BetaD = Beta/ Diameter

N = l-l/Alpha

N100 = 100 * N

NInt = INT(N100)

NFrac = N 100 - NInt

DeltaGamma = Gamma(NInt + 1) - Gamma(NInt)
GammaN = Gamma(NInt) + DeltaGamma * NFrac
Tau = (Strength/(2 * BetaD)) * GammaN

PRINT Fil$;" ";FDesig$;" in ";MDesig$

PRINT " Alpha Beta Gamma Strength

 

244

- Diameter IFSS"
PRINT USING "#######.## ";Alpha,Beta,GammaN,Strength,
-Diameter,Tau
PrintOut = 0
INPUT "Print out results? (Y/N) ";POS
IF PO$ = "Y" THEN PrintOut = 1
IF PO$ = "y" THEN PrintOut = 1
IF PrintOut = 0 THEN GOTO GammaJump
LPRINT
LPRINT "Number of Breaks = ";NBreaks(nT)
LPRINT F115;" ";FDesig$;" in ";MDesig$
LPRINT " Alpha Beta Gamma Strength
— Diameter IFSS"
LPRINT USING "#######.## ";Alpha,Beta,GammaN,Strength,
-Diameter,Tau
LPRINT
GammaJump:
RETURN

APPENDIX B

SOURCE CODE FOR FIBERLINK, IN SITU FIBER STRENGTH,
FRAGMENTATION TEST DATA ANALYSIS SYSTEM

The following program is the source code listing for the FiberLink, in situ
fiber strength fragmentation test data acquisition and analysis program written in
compiled AmigaBasic (Absoft, AC-Basic) described in chapter 7. Weibull calculation
routines were translated and adapted from a mainframe Fortran program (author
unknown). A list of subroutines and a brief description of their functions preceeds

the actual code. Long code lines have been reformatted, with leading hyphens
attached to the second portions.

Main: Main program loop.

Start: Sets up menu interrupts and " sleeps" here until summoned by a menu call from
the user.

StartupText: Displays copyright information and specifies dfl: drive for all data
diskettes.

ArrayDimensions: Defines all data arrays and allocates space to them.
LinkDims: Defines link-strength related arrays and allocates space to them.

InterLinkDims: Defines fragmentation test simulation related arrays and allocates
space to them.

Initialize: Sets all initial variables, file names, graphics colors, default moduli.
GammaData: Sets up a look-up table of the Gamma function.
InitializeMenu: Initializes the menu selections.

CheckMenu: Arrival point when user makes a menu selection. Finds column and
routes to submenus.

Filemenu: Checks first column of menu items and routes to appropriate subroutine.
Graphics: Checks second column of menu items and routes to appropriate subroutine.
LinkMenu: Checks third column of menu items and routes to appropriate subroutine.

InterLinkMenu: Checks fourth column of menu items and routes to appropriate
subroutine.

GammaLoader: Inputs Weibull shape and scale factors from user and performs
Gamma function calculations.

245

246
ListLinks: Prints out list of the strength assigned to each fiber link.
FiberData: Inputs data on fiber diameter, modulus, etc. from user for all calculations.
MatrixData: Inputs data on matrix name, modulus, etc. from user for printouts.

LengthStrength: Simply sets fiber tensile strength at this point, intended to be
upgraded to perform log-linear extrapolation to automatically find strength @ length

future versions.
GammaPlot: Produces a graphical plot of the Gamma function.
Dir: Lists directory of the dfl: drive.

WriteTrack: Writes a file with the positions of all breaks, dial gage reading, strain,
etc.

ReadTrack: Read files written by WriteTrack.

ReadTracks: Reads a set of tracks with the same root file name and different track
numbers.

PrintLengths: Prints out the fragment lengths, calculated from the break positions.
PrintBreakList: Prints out the break positions in a column format for a set of tracks.
WriteLengths: Writes a file with the fragment lengths, rather than positions.

WriteBreakList: Writes a file with the break positions for a set of tracks in column
format.

WriteBreaks: Writes a file with the break positions, track by track.
ReadBreaks: Reads files written by WriteBreaks.

ShowFibers: Displays a graphical representation of all break positions for one or
more tracks. Allows user specification of breaks using mouse.

CheckMouse: Checks for mouse clicks and if on lower part of screen scrolls the
break display to the left or right. If on upper part of screen checks to see which track
and

break is being selected and stores its index in the DataT() array.

DrawFibers: Performs the actual fiber display graphic output.

Cleanup: Clears the screen.

Quit: Resets menu and stops program operation.

Palet: Initializes screen, window, and pallettes.

BreakNumbers: Reads in experimentally measure data on number of breaks in each
strain interval for AS4 fibers in epoxy and solvent-deposited polycarbonate.

247

FiberModel: Core routine for fiber tensile test simulation. Initializes fiber, then goes
to tensile test.

EditTest: Inputs specifications for tensile test simulation, number of samples, gage
length, etc.

AddFlaws: Generates simulated fiber by adding flaws to links. Begins by initializing
at 2 mpsi then adds correct numbers moving from smallest to largest flaws, (large
flaws written over smaller ones since they control failure strength).

EPMod: Specifies A84 in epoxy matrix data for fiber flaw populations.
PCMod: Specifies AS4 in epoxy matrix data for fiber flaw populations.
UserMod: Allows user-defined fiber flaw population data to be entered.
DrawFlaws: Draws a graphical representation of the fiber flaw distribution.
TensileStart: Entry point for tensile test simulation.

TensileTest: Performs simulated fiber tensile test. Cuts fiber at random point, checks
links for weakest link in specified gage length, averages results.

PrintStrengths: Prints out results of simulated fiber tension test simulation.

SOURCE CODE LISTING FOR FIBERLINK

CLEAR ,4000O&
CLEAR ,150000&
SCREEN 1,640,400,3,4
WINDOW l,"Fiberlink/FiberTrack (C) SFF-ISFS",,0,1

Programloop:

GOSUB ArrayDimensions

GOSUB Initialize ’Sets Graphics and screen constants
GOSUB Palet’ Sets palette, screen, and window
COLOR 2,0 ’Specifies palette for screen outputs
GOSUB StartupText

GOSUB InitializeMenu

GOSUB BreakNumbers

Start: ’Main Program Loop, waits for menu inputs
ON MENU GOSUB CheckMenu : MENU ON
Unfinished = -l
WHILE Unfinished

SLEEP ’this program is event driven
WEND

StartupText:
CLS
LOCATE 10,1
PRINT "This program Copyrighted by Mark C. Waterbury

248

PRINT "FiberLink (C) Fiber Link Length Simulation
Program

PRINT " May not be reproduced or duplicated

PRINT " without the consent of the author.

LOCATE 18,1

PRINT " Insert formatted data disk in dfl:

PRINT "All track files will be saved to that disk.
RETURN

ArrayDimensions:
DIM X(21,500) ’Flaw Position Arrays
DIM NBreaks(21)
DIM Length(21)
DIM NewBreaks(21)
DIM DG(21)
DIM Strain(21)
DIM TStress(21)
DIM AveStrain(2l) ’Ave of each track and preceeding one
DIM F1$(21)
DIM T(21)
DIM DataT(SOO)
DIM DataB(SOO)
DIM Fiber(500)
DIM Stress(500)
DIM W(2000)
DIM WLog(2000) ’ For Weibull Routine
DIM Gamma (205)
LinkDims:
DIM link%( 10000) ’Strength of each fiber link
DIM Strength%(2000) ’Strength of each fiber sample
DIM NBr(21) ’Number of Breaks/25 mm @ (Strain)
DIM NBI(21),NBF(21)’Integral and Fractional Breaks/25 mm
DIM NbrEP(20) ’NBr/25 mm for AS4/Epoxy
DIM NbrPC(20) ’NBr/25 mm for AS4/PolyCarbonate
DIM NFibs(50) ’Numbers of Fibers to test
DIM Sample(50) ’Lengths of Fiber to test
InterLinkDims:
DIM Inter%( 10000) ’Strength of each interface element
DIM BPos%(250) ’New Breaks array
DIM BPost(100)
DIM Transfer%(21)
Initialize:
Modulus = 34000000& ’AS4 default
AS4Mod = 34000000&
IM6Mod = 40400000&
Pi = 3.14159
Scrx = 640:ScrY = 400
FT% = 160:FB% = FT% + 15
60% = 2 ’gap color (integer)
Gap% = 4 ’break gap
fcl% = 6 ’fiber color 1
f02% = 7 ’fiber
Velocity = 200 ’default tracking speed

249

F1$(0) = "00" ’Appended to track file names
F1$(1) = "01": F1$(2)= "02":Fl$(3) = "03":Fl$(4) = "04"
Fl$(5)= "05": F1$(6) = "06": F1$(7)= "07": Fl$(8)= "08"
F1$(9)= "09": F1$(10) ="10": F1$(11) = "11": F1$(12) ="12"
F1$(l3) ="13": F1$(14) =:"14" F1$(15) = "15": F1$(16) ="16"
F1$(17) =:"17" F1$(18) =:"18" F1$(19) = "19": F1$(20) ="20"
F1$(21)= "21"
WIDTH "LPT1:",255 ’Eliminates printer carriage returns
GOSUB GammaData
RETURN

GammaData: ’Loads the gamma function into Gamma(I)
RESTORE

FOR I = 100 TO 200

READ Gamma(I)

NEXT I

DATA 1.00,.99433,.98884,.98355,.97844
DATA .9735,.96874,.96415,.95973,.95546
DATA .95135 , .94740, .94359, .93993, .93642
DATA .93304,.92980,.92670,.92373,.92089
DATA .91817,.91558,.9l3l1,.91075,.90852
DATA . 90640, .90440, .90250, .90072 , . 89904
DATA . 89747, . 89600, . 89464, . 89338 , . 89222
DATA .89115,.89018,.88931,.88854,.88785
DATA .88726,.88676,.88636,.88604,.88581
DATA .88566,.88560,.88563,.88575,.88595
DATA .88623,.88659,.88704,.88757,.88818
DATA .88887,.88964,.89049,.89l42,.89243
DATA . 89352 , . 89468 , . 89592, . 89724, . 89864
DATA .90012,.90167,.90330,.90500,.90678
DATA .90864,.91057,.91258,.91466,.9l683
DATA .91906,.92137,.92376,.92623,.92877
DATA .93138,.93408,.93685,.93989,.94261
DATA .94561,.94869,.95184,.95507,.95838
DATA .96177,.96523,.96877,.97240,.97610
DATA .97988,.98374,.98768,.99l71,.99581,1!
FOR I = 101 TO 200 ’Calculates lower Gammas
= (I-100)/ 100
Gamma (I-100) = Gamma(I)/N
NEXT I
RETURN

InitializeMenu:
MENU 1,0,1,"File"
MENU l,l,l,"Write Break File "
MENU 1,2,1,"Read Break File "
MENU 1,3,1,"Read Track "
MENU 1,4,1,"Read Set of Tracks"
MENU 1,,5 l, "Dir
MENU 1, 6,1,"Quit"
MENU 2,0,1,"Calcs"
MENU 2,1,1, "Weibull Calcs "
MENU 2,2,1,"Gamma Calcs "

250

MENU 2,3,1,"Gamma Plot "
MENU 2,4,1,"Fiber Data "
MENU 2,5,1,"Matrix Data "
MENU 3,0,1,"Graphs"

MENU 3,1,1,"Show Fibers "
MENU 3,2,1,"Clear Screen "
MENU 3,3,1,"Write Break List "
MENU 3,4,1,"Write Length List "
MENU 3,5,1,"Print Break List "
MENU 3,6,1,"Print Length List "
MENU 3,7,1,"Track Breaks "
MENU 3,8,1,"List Selected Breaks "

MENU 4,0,1,"FiberLink"

MENU 4,1,1,"Define Fiber Flaws "
,2,l,"Generate Fiber "
,3,1,"Draw Fiber "
,4,1,"Tensile Test "
,5 , 1 , " Print Fiber Strengths"
,0, l, "InterLink"
,1,l,"InterLink Setup "

MENU 5 ,2,1,"InterLink Simulation "
MENU 5,3,1,"Print Link List "
RETURN

CheckMenu:
MenuId = MENU(O)
Menultem = MENU(1)
ON MenuId GOSUB Filemenu,Ca1cs,Graphics,LinkMenu,
-InterLinkMenu
RETURN

MENU4
MENU4
MENU4
MENU4
MENUS
MENUS

Filemenu:
ON Menultem GOSUB WriteBreaks,ReadBreaks,ReadTrack,
-ReadTracks,Dir,Quit

RETURN

Graphics:
ON Menultem GOSUB ShowFibers,Cleanup,WriteBreakList,
-WriteLengths,PrintBreakList,PrintLengths,Tracker,
-ListBreaks

RETURN

LinkMenu:
ON Menultem GOSUB FiberModel,AddFlaws,DrawFlaws,
-TensileStart,PrintStrengths

RETURN

InterLinkMenu:
ON Menultem GOSUB InterModel,InterLink,ListLinks
RETURN

Calcs:
ON Menultem GOSUB WeibullLoader,GammaLoader,GammaPlot,

251

-FiberData,MatrixData
RETURN

GammaLoader:
INPUT "File Name ",Fil$
INPUT "Alpha, Beta (set Alpha = 0 to quit) ",Alpha,Beta
IF Alpha = 0 THEN RETURN
GOSUB Gamma
GOTO GammaLoader
RETURN

ListLinks:

FOR I = 0 TO NLinks STEP 10
LPRINT link%(I);link%(I+1);link%(I+2);link%(I+3);
-link%(l+4);link%(I+5); 1ink%(I+6);link%(I+7);
-link%(I+8);link%(I+9)

NEXT I
RETURN

FiberData:
CLS
INPUT "Fiber Designation ",FDesig$
INPUT "Fiber Diameter (microns) ",Diameter
INPUT "Fiber Strength @ 25 mm ",StrengthO
INPUT "Fiber Modulus ",Modulus
RETURN

MatrixData:
CLS
INPUT "Matrix Designation",MDesig$
INPUT "Matrix Tensile Strength (psi) ",MTStrength
INPUT "Matrix Shear Strength (psi) ",MSStrength
INPUT "Matrix Tensile Modulus (psi) ",MTModulus
INPUT "Matrix Shear Modulus (psi) ",MSModulus
RETURN

LengthStrength:
Strength = StrengthO
RETURN

GammaPlot:
PSET (0,10*Gamma(100)),1
FOR I = 0 TO 200
LINE -(1 * 3,10 * Gamma(1)),l
NEXT I
FOR I = 0 TO 200 STEP 25
LINE (1 * 3 ,180)-(I* 3,200),2
NEXT I

INPUT "Printout? Y/N ",Pr$

IF Pr$ < > "Y" THEN GOTO NoPrint
LPRINT "Gamma Function for N = 0 to 2.00 in 1/ 100 ths "
LPRINT

FORI = OTOZOOSTEPS

252

LPRINT USING " ###.#####";I/100;Gamma(l);Gamma(I+1);
-Gamma(I+2);Gamma(I+3);Gamma(l+4)
NEXT I

NoPrint:
RETURN

Dir:
FILES "df 1 : "
RETURN

WriteTrack:
FilT$ = Fil$ + F1$(nT)
OPEN FilT$ FOR OUTPUT AS 1
WRITE #1, FilT$
WRITE #1, nT
WRITE #1,DG(nT),Strain(nT)
WRTTE #1,NBreaks(nT),Length(nT)
FOR k = 1 TO NBreaks(nT)
WRITE #1, X(nT,k)
NEXT k
CLOSE #1
PRINT "File saved as ";FilT$
RETURN

ReadTrack:
CLS
INPUT "File name ",Fil$
INPUT "Track ",nT
IFnT = OTHENnT =1
IF nT > NTracks THEN NTracks = nT
FilT$ = ”dfl:" + Fil$ + F1$(nT)
OPEN FilT$ FOR INPUT AS 1
INPUT #1, FS
INPUT #1, TT
INPUT #1,DG(nT),Strain(nT)
INPUT #1,NBreaks(nT),Length(nT)
FOR k = 1 TO NBreaks(nT)
INPUT #1, X(nT,k)
NEXT k
CLOSE #1
RETURN

ReadTracks:
CLS
INPUT "Parent File Name ",Fil$
INPUT "First and Last Tracks ",NFirst,NLast
NTracks = NLast - NFirst + 1
FOR nT = NFirst TO NLast
FilTS = "dfl:" + Fil$ + F1$(nT)
OPEN FilT$ FOR INPUT AS 1
INPUT #1, F$

253

INPUT #1, Tn
INPUT #1,DG(nT),Strain(nT)
INPUT #1 ,NBreaks(nT),Length(nT)
FOR k = 1 TO NBreaks(nT)
INPUT #1, X(nT,k)
NEXT k

CLOSE #1

NEXT nT

RETURN

PrintLengths:
LOCATE 1,1
LPRINT Fil$
LPRINT NTracks
FOR I = 1 TO NTracks-1
LPRINT USING " ##";1;
NEXT I
LPRINT USING " ##";I
FORI=1TONTracks-1
LPRINT USING " ###";DG(I);
NEXT I
LPRINT USING " ###";DG(I)
FOR I = 1 TO NTracks -1
LPRINT USING " ##.####";Strain(I)-1;
NEXT I
LPRINT USING " ##.####";Strain(I)-l
FOR J = lTO NTracks -1
LPRINT USING " ###";NBreaks(J);
NEXT J
LPRINT USING " ###";NBreaks(J)
MaxBreaks = NBreaks(I)
FOR I = 2 TO NTracks -1
IF NBreaks(I) > MaxBreaks THEN MaxBreaks = NBreaks(I)
NEXT I
FOR I = 2 TO MaxBreaks
FOR J = 1 TO NTracks -1
IF X(J,I) - X(J,I-l) > 0 THEN
Lx% = (X(J,I)-X(J,I-l))
LPRINT USING " ####"; Lx%;
ELSE
LPRINT USING " ####";X(J,I);
END IF
NEXT J
IF X(J,I) - X(J,I-l) > 0 THEN
Lx% = (X(J,I)-X(J,I-1))
LPRINT USING " ####"; Lx%
ELSE
LPRINT USING " ####";X(J,I)
END IF
NEXT I
RETURN

PrintBreakList:

254

LPRINT Fil$
LPRINT NTracks
FOR I = 1 TO NTracks—1
LPRINT USING " ## ";I;
NEXT I
LPRINT USING " ##";I
FORI=1TONTracks-1
LPRINT USING " ###";DG(I);
NEXT I
LPRINT USING ” ###";DG(I)
FOR I = 1 TO NTracks -l
LPRINT USING " ##.####";Strain(I)-l;
NEXT I
LPRINT USING " ##.####";Strain(D-1
FOR J = 1 TO NTracks -1
LPRINT USING " ### ";NBreaks(J);
NEXT J
LPRINT USING " ###";NBreaks(J)
MaxBreaks = NBreaks(I)
FOR I = 2 TO NTracks -1
IF NBreaks(I) > MaxBreaks THEN MaxBreaks = NBreaks(I)
NEXT I
FOR I = 1 TO MaxBreaks
FOR J = 1 TO NTracks -1
XX% = X(J,I)
LPRINT USING " #####"; XX%;
NEXT J
XX% = X(J,I)
LPRINT USING " #####"; XX%
NEXT I
CLOSE #1
RETURN

WriteLengths:
LOCATE 1,1
INPUT "Save Lengths ",Fil$
Fil$ = "dfl:" + Fil$
OPEN Fi1$ FOR OUTPUT AS 1
WRITE #1, Fil$
WRITE #1, NTracks
FOR I = 1 TO NTracks-1
PRINT #1, USING " ##";1;
NEXT I
PRINT #1, USING " ##";I
FORI=1TONTracks-l
PRINT #1, USING " ###";DG(I);
NEXT I
PRINT #1, USING " ###";DG(I)
FOR I = 1 TO NTracks -1
PRINT #1, USING " ##.####";Strain(I)-l;
NEXT I
PRINT #1, USING " ##.####";Strain(I)-l
FOR J = ITO NTracks -1

255

PRINT #1, USING " ###";NBreaks(J);
NEXT J
PRINT #1, USING " ###";NBreaks(J)
MaxBreaks = NBreaks(I)
FOR I = 2 TO NTracks -1
IF NBreaks(I) > MaxBreaks THEN MaxBreaks = NBreaks(I)
NEXT I
FOR I = 2 TO MaxBreaks
FOR J = 1 TO NTracks -1
IF X(J,I) - X(J,I-l) > 0 THEN
Lx% = (X(J,I)-X(J,I-1))
PRINT #1, USING " ####"; Lx%;
ELSE
PRINT #1, USING " ####";X(J,I);
END IF
NEXT J
IF X(J,I) - X(J,I-l) > 0 THEN
Lx% = (X(J,I)-X(J,I-l))
PRINT #1, USING " ### "; Lx%
ELSE
PRINT #1, USING " ####";X(J,I)
END IF
NEXT 1
CLOSE #1
RETURN

WriteBreakList:
LOCATE 1,1
INPUT "Save Break List ",Fil$
Fil$ = "dfl:" + Fil$
OPEN Fil$ FOR OUTPUT AS 1
WRTTE #1, F113
WRITE #1, NTracks
FOR I = 1 TO NTracks-l
PRINT #1, USING " ## ";I;
NEXT I
PRINT #1, USING " ##";I
FORI=1TO NTracks -1
PRINT #1, USING " ###";DG(I);
NEXT I
PRINT #1, USING " ###";DG(I)
FOR I = lTO NTracks -1
PRINT #1, USING " ##.####";Strain(I)-1;
NEXT I
PRINT #1, USING " ##.####";Strain(I)-l
FOR J = lTO NTracks -1
PRINT #1, USING " ### ";NBreaks(J);
NEXT J
PRINT #1, USING " ###";NBreaks(J)
MaxBreaks = NBreaks(I)
FOR I = 2 TO NTracks -1
IF NBreaks(I) > MaxBreaks THEN MaxBreaks = NBreaks(I)
NEXT I

256

FOR I = 1 TO MaxBreaks
FOR J = ITO NTracks -l
XX% = X(J,I)
PRINT #1, USING " #####"; XX%;
NEXT J
XX% = X(J,I)
PRINT #1, USING " #####"; XX%
NEXT I
CLOSE #1
RETURN

WriteBreaks:
LOCATE 1,1
INPUT "Break File Name ",FilS
Fil$ = "dfl:" + Fil$
LOCATE 1,1:PRINT " "
OPEN Fil$ FOR OUTPUT AS 1
WRITE #1, NTracks
FOR I = 1 TO NTracks
WRTTE #1,T(I),DG(I),Strain(I)
NEXT I
FOR J = 1 TO NTracks
WRTTE #1,NBreaks(J),Length(J)
NEXT J
FOR I = 1 TO NTracks
FOR J = 1 TO NBreaks(I)
WRITE #1,X(I,J)
NEXT J

NEXT I
CLOSE #1
RETURN

ReadBreaks:
LOCATE 1,1
INPUT "Read Breaks ",Fil$
Fil$ = "dfl:" + Fil$
OPEN Fil$ FOR INPUT AS 1
INPUT #1, NTracks
FOR I = 1 TO NTracks
INPUT #1 ,Tn,DG(I),Strain(I)
NEXT I
FOR J = 1 TO NTracks
INPUT #1 ,NBreaks(J),Length(J)
NEXT J
FOR I = 1 TO NTracks
FOR J = 1 TO NBreaks(I)
INPUT #1,X(I,J)
NEXT J
NEXT I
CLOSE #1
RETURN

257

ShowFibers:
N = 0 ’Number of data points
CLS
INPUT "Number Fibers? 1/0 ",PNumb
Shift% = —600
ON MOUSE GOSUB CheckMouse:MOUSE ON
GOSUB DrawFibers
InkL:
Ink$ = INKEY$
IF Ink$ = "0" THEN XOff% = 0:GOSUB DrawFibers
IF Ink$ = "9" THEN XOff% = Last% * Shift%:GOSUB
DrawFibers
IF InkS = "1" THEN XOff% = Shift%:GOSUB DrawFibers
IF Ink$ = "2" THEN XOff% = 2 * Shift%:GOSUB DrawFibers
IF Ink$ = "3" THEN XOff% 3 * Shift%:GOSUB DrawFibers
IF Ink$ = "4" THEN XOff% 4 * Shift%:GOSUB DrawFibers
IF Ink$ = "5" THEN XOff% 5 * Shift%:GOSUB DrawFibers
IF Ink$ = "6" THEN XOff% — 6 * Shift%:GOSUB DrawFibers
= "7" THEN XOff% = 7 * Shift%:GOSUB DrawFibers
IF Ink$ = "8" THEN XOff% = 8 * Shift%:GOSUB DrawFibers
= "Q" THEN :RETURN
IF Ink$ = "q" THEN :RETURN

CheckMouse:
F = MOUSE(O)
Mx% = MOUSE(1):My% = MOUSE(2)
IF My% > 175 THEN
IF Mx% < 160 THEN XOff% = XOff% - Shift% :GOTO MHop
IF Mx% < 320 THEN XOff% = XOff% - Shift%/2 :GOTO MHop
IF Mx% < 480 THEN XOff% = XOff% + Shift%/2 :GOTO MHop
XOff% = XOff% + Shift%
MHop:

GOSUB DrawFibers
END IF
IF My% < 170 THEN
Dt = 0:DB = 0
N = N + l
Dt = INT(My%lS)
DataT(N) = Dt
FOR I = 1 TO NBreaks(Dt)
Lx = X(Dt,I)l 10 + XOff%
IFABS(Lx +3-Mx%) < 3THENDB =I
NEXT I
IF DB = 0 THEN DataT(N) = 0:N = N - l :GOTO EndHop
DataB(N) = DB
Ly% = Dt * 8
Lx = X(Dt,DB)/10 + XOff%
LINE (Lx,Ly%)-(Lx+ l,Ly% +2),4,bf
EndHop:
END IF
RETURN

258

DrawFibers:
CLS

Last% = INT (-X( 1,NBreaks( 1))/ (Shift%*10))

FORI = 1 TO NTracks

Ly% = I * 8

LINE (0,Ly%)-(640,Ly% + 2),3,bf

FOR J = 1 TO NBreaks(I)
Lx = X(I,J)/10 + XOff%

IF Lx < 0 THEN GOTO Next]

IF Lx > 640 THEN GOTO Next]
LINE (Lx,Ly%)-(Lx+2,Ly% +2),0,bf
L1 = I
Px% = Lx/8
IFPx% > 39THENPx% = 39
IFPx% <1THENPx% =1

IF Lx > 0 AND PNumb THEN LOCATE L1,Px%:PRINT USING

"##";J
Next]: NEXT J
NEXT I
FOR I = 1 TO N

Ly% = DataT(I) * 8

Lx = X(DataT(I),DataB(I))/10 + XOff%

IF Lx < 0 THEN GOTO DataHop

IF Lx > 640 THEN GOTO DataHop

LINE (Lx,Ly%)-(Lx+6,Ly%+2),1,bf
DataHop: NEXT I

LINE (0,175)-(640,175),3

FOR I = 0 TO 63

LINE (I*lO,l75)—(I*10,170),3

NEXT I

FOR I = 0 TO 6
LINE (I*lOO,175)-(I*100+1,165),3 ,bf
NEXT I
LOCATE 23,1:PRINT -XOff%*10;:PRINT "
return";
RETURN

ListBreaks:
CLS
FORI = 1 TO N
PRINT X(DataT(I),DataB(I))
NEXT 1
RETURN

Cleanup:
CLS
RETURN

Quit:
MENU RESET
STOP

Palet:

Typtho

259

PALETTE 0,0/15,0/15,0/15 :PALETTE 1,0/15,0/15,15/15

PALETTE 2,5/15,S/15,5/15 :PALETTE 3,15/15,15/15,15/15

PALETTE 4,6/15,6/15,6/15 :PALETTE 5,15/15,0/15,0/15

PALETTE 6,15/15,0/15,0/15 :PALETTE 7,0/15,15/15,0/15
RETURN

BreakNumbers:

- ’Breaks per 25 mm for Epoxy and PC matrix and AS4
Fibers

NbrPC(O) = 0 :NBrPC100(l) = 0 :NBrPC100(2) = 0
NbrPC(3) = 0 :NbrPC(4) = .4: NbrPC(S) = .13
NbrPC(6) = .99 :NbrPC(7) = 3.33 :NbrPC(8) = 6.2

NbrPC(9) - 12.16 :NbrPC(lO) = 25 :NbrPC(ll) = 50

NbrPC( 12) = 100:NbrPC( 13) =200:NbrPC(l4) =400:NbrPC(15) =800
NbrPC(16)=1600:NbrPC(17) =3200:NbrPC(18) =5000
NbrPC(19)=5000: NbrPC(20) = 5000

NbrEP(l) = 0 :NbrEP(2) = 0:NbrEP(3) = 0:NbrEP(4) = 1
NbrEP(S) = .53:NbrEP(6) = 2.22 : NbrEP(7) = 6.75

NbrEP(8) = 19.95:NbrEP(9) = 28.39:NbrEP(10) = 64.52
NbrEP(l l) = 156:NbrEP(12) = 379:NbrEP(l3) = 918

NbrEP(l4) = 2224: NbrEP(lS) = 5388:NbrEP(16) = 13054
NbrEP(17) = 31630:NbrEP(18) = 76638&: NbrEP(19) = 185689&
NbrEP(20) = 449916&

RETURN

FiberModel:
CLS
RANDOMIZECTIMER/Z)
Flawed = 0
Modulus = 340& ’in .1 mpsi for AS4 for strain in %
INPUT "Model Length in links, 1 < L < 10000 ",NLinks
IF NLinks > 10000 THEN NLinks = 10000
IF NLinks = 0 THEN NLinks = 1000
INPUT "Link Length (microns) ",LinkLength
FiberLength = LinkLength * NLinks
MMpLinlr = LinkLength /1000
LinkC = FiberLength/25000 ’ breaks/NLinks to B.Per 25 mm
INPUT "Epoxy, PC, or User? E/P/U ",EPC$
IF EPCS = "P" THEN GOSUB PCMod
IF EPCS = "E" THEN GOSUB EPMod
IF EPC$ = "U" THEN GOSUB UserMod
GOSUB EditTest
GOSUB AddFlaws
GOSUB TensileTest
RETURN

 

EditTest:
LOCATE 1,1:PRINT " "
LOCATE 1,1:INPUT ”N Lengths ";NLengths
LOCATE 1,1:PRINT " "
LOCATE 1,1:INPUT "Draw Fiber? Y/N ",Flaw$:
LOCATE 1,1:PRINT " "
LOCATE 1,1:INPUT "Draw Breaks? Y/N ",Brk$

260

LOCATE 1,1:PRINT " "
LOCATE 1,1:INPUT "Draw Cuts? Y/N ",CutS
FOR k = 1 TO NLengths
LOCATE 1,1:PRINT " "
LOCATE 1,1:PRINT k;" ";
INPUT "Length, N Fibers ",Sample(k),NFibs(k)
IF NFibs(k) >2000 THEN NFibs(k)=2000 ’Limit of Strength
Dim
NEXT k
RETURN

AddFlaws:
Sammti2%n = 2000:’ Number of flaws/25 mm for limit case
Sat =
FORI = 20 TO 1 STEP -1
IF NBr(I) > Saturation THEN Sat = I
Strain(I) = I * .25
TStress(I) = Modulus * Strain(l)
NEXT I

L0% = Sat * .25 * Modulus
FORI = 1 TO NLinks
link%(I) = L0%

NEXT I

FORI = Sat-l TO 1 STEP -1
NBrks = NBr(I) * LinkC ’number in NLinks from 25 mm
FOR J = 1 TO NBrks
XT = RND * NLinks
1ink%(X'T) = TStress(I)
NEXT J
Fract = NBrks - INT(NBrks)
IF RND < Fract THEN
XT = RND * NLinks
link%(XT) = TStress(I)
END IF
NEXT I
RETURN

EPMod: ’loads epoxy flaws into array
FOR I = 1 TO 20
NBr(I) = NbrEP(I)
NEXT I

RETURN

PCMod: ’loads PC flaws into array
FORI = 1 TO 20
NBr(I) = NbrPC(I)
NEXT I

RETURN

UserMod:
CLS
FOR I = 1 TO 20

261

PRINT I;" strain = ";I * .25;" ";
INPUT "Breaks/25 mm = ",NBr(I)
NEXT I
Check: INPUT "All OK? (Y) ",ChS
IF Ch$ = "Y" THEN RETURN
IF Ch$ = "y" THEN RETURN
GOTO UserMod

DrawFlaws:
CLS
LINE (0,0)-(640,400),3,bf
COLOR 2,0
FibWid = 24
FOR J = 0 TO 15
Is = J * 625
YS = (J +1) * FibWid
FOR I = 1 TO 625
Ix = Is + I
Iy = link%(lx)/85
Ic = 5 + Iy/2
LINE (I,YS)-(I,YS-Iy),0
NEXT I

NEXT]
RETURN

TensileStart:
GOSUB EditTest
GOSUB TensileTest
RETURN

TensileTest:
INPUT "Print Flaw Distribution? (YIN) ",PFD$
IF UCASE$(PFD$) < > "Y" THEN GOTO NoFLawPrints
LPRINT "FiberLink simulated fiber tensile test"
LPRINT "Number of breaks/25 mm"
FOR k = lTO 20 STEP 5
LPRINT "NBr(";k;")=";NBr(k);" NBr(";k+1;")=";
-NBr(k+l);" NBr(";k+2;")=";NBr(k+2);" NBr(";k+3;")=";
-NBr(k+3);" NBr(";k+4;")=";NBr(k+4)
NEXT k
LPRINT "LinkLength = ";LinkLength
LPRINT "Total Length = ";FiberLength
LPRINT "Link constant = ";LinkC
LPRINT "Fiber Modulus = ";Modulus
NoFLawPrints:
FOR k = 1 TO NLengths
IF Flaw$ = "Y" THEN GOSUB DrawFlaws
PRINT Sample(k),NFibs(k)
SSize = Sample(k) * 1000/LinkLength ’Scales to 100
micron
IF SSize = 0 THEN RETURN
Range = NLinks - SSize

262

WeakAve = 0
FOR I = 1 TO NFibs(k)
X] = RND * Range
WeakL = 2000 ’Initial Fiber Strength before flaws
FOR J = 1 TO SSize
IF link%(XJ+J) < WeakL THEN
WeakL = link%(XJ+J)
XJJ = X] + J
END IF
NEXT J
Strength%(I) = WeakL
Is = INT(XJJ/625)
Y8 = FibWid * (1 + 18)
Xf=X]J-625*Is
Xc = X] - 625 * Is
IF Brk$ ="Y"THEN
LINE(Xf- 1 ,YS)-(Xf+ l,YS-link% (X]])/85) ,2,bf
IF Cut$ = "Y" THEN LINE (Xc,YS)-(Xc,YS-20),1
’Cut

WeakAve = WeakAve + WeakL
NEXT I
WeakAve = WeakAve/NFibs(k)
DevSum = 0
FOR I = 1 TO NFibs(k)
DevSum = DevSum + (Wer - Strength%(I))"2
NEXT I
DevSum = DevSum/NFibs(k)
Sthev = SQR(DevSum)
IF EPC$ = "E" THEN LPRINT "AS4/Epoxy ";
IF EPC$ = "P" THEN LPRINT "AS4/PC ";
IF EPCS = "U" THEN LPRINT "User ";
LPRINT NFibs(k);" Fibers ";Sample(k);" mm, Strength = ";
-WeakAve;" Std Deviation = ";Sthev
LOCATE 1,1:PRINT " "
LOCATE 1,1
PRINT NFibs(k);" Fibers ";Sample(k);"mm, Strength = ";
-WeakAve;" Std Dev = ";Sthev;
NEXT k
RETURN

PrintStrengths:
LPRINT "FiberLink Tensile Test Simulation"
LPRINT "Strengths of ";FiberDesig$;" Fibers
LPRINT "Length ";Sample(l);" Strength"; WeakAve
FOR I = 1 TO NFibs(l) STEP 10
FOR J = 0 TO 8
LPRINT USING "#### "; Strength%(I+J);
NEXT J
LPRINT USING "#### "; Strength%(I+9)
NEXT I
RETURN

APPENDIX C

SOURCE CODE FOR OPTICAL NUMERIC VOLUME FRACTION ANALYSIS

The following program is the source code written in compiled Amiga Basic
(AC-Basic) for the optical numeric volume fraction analysis system described in
chapter 5. Image loading and saving routines are adapted and corrected from
Carolynn Scheppner’s (Commodore Business Machines) routines, provided on the
Amiga "Extras" disk. A list of subroutines and a brief description of their
functions preceeds the actual listing. Long lines have been reformatted to fit the page,
with leading hyphens attached to the second portion.

Main: Central routine that routes to all startup routines.

Start: Sets up menu interupts and "sleeps" here until called.

Libs: Loads libraries of pointers to system calls.

ArrayDimensions: Defines arrays and allocates space to them.

Cycle: Routes to GetAddrs which finds screen pallettes and sets up for color cycling.
ScreenSetup: Defines screen and window parameters.

Initialize: Initializes graphics variables, filenames, and defines grid sizes for statistics.
Call: Specifies default image size calibration.

Ca12: Specifies second default image size.

SetCal: Allows user specified image size calibration.

InitializeMenu: Initializes menu selections.

CheckMenu: Checks menu interrupts and routes to each menu.

Filemenu: Checks file menu and routes to selection.

Calcs: Checks calculations menu and routes to selection.

Graph: Checks graph menu and routes to selection.

Batch: Checks Batch menu and routes to selection.

Dist: Checks Statistics menu and routes to selection.

Region: Draws crosshairs and marks starting comer for defining a region within an
image. Passes to "Square" routine when the mouse button is choked and held.

263

264

Square: Defines the ending corner for a box started by "Region" routine then finds
number of fibers in the box, determines volume fraction, and displays it in menu.

Distribution: Counts number of fibers in each box in a grid of small boxes on the
screen.

statsZ: Finds number of boxes with few fibers, finds average fibers/box and standard
deviation. Called by "ReadDist".

Stats: Same as "StatsZ", called during fiber counting.
Histogram: Plots number of boxes vs. fiber/box.

WriteStats: Writes a disk file named "FileName" + ".STA" containing the number
of boxes vs. fibers/box, the average fibers/box, and the standard deviation.

ReadStats: Reads files written by "WriteStats" for concatenation with new data.
ReadDist: Reads files written by "WriteDist" for displaying block maps or
concatenation with new data. Variables K and L designate starting indices for
positioning inputted data into a larger array.

WriteDist: Writes block map data of fibers/box for grids of boxes on screen.

Map: Draws block maps with gray scales proportioned to fibers/box. Uses indices
inputted in "ReadDist".

PrintDist: Prints out distribution data determined by "Stats" routines.

BarGraph: Displays bar graphs in grid boxes with heights proportioned to number
fibers/box.

SmallBar: Same as "BarGraph" except all bars are squeezed to the left of the screen.
BlockGraph: Displays a small block graph with gray scale proportioned to fibers/ box.

Grid: Displays a grid of hollow boxes with outline gray scale proportioned to
fibers/box.

Paletl: Sets colors of each of 32 screen pallettes. Colors in top 16 for easy viewing.
Palet2: Sets colors to gray scale for top 16 pallettes.

AutoCounter: Autmated fiber counting routine. This is the core routine of the
program that identifies fibers, checks to see if they have been counted previously,
assigns their coordinates to arrays in columns, calculates the volume fractions, and
saves the results to disk and the menu.

FiberCounter: A manual fiber counter using the mouse. May be used for correcting
auto counts. May confuse AutoCounter if used during its processing.

Dir0: Displays directory of drive df0:.

265
Dirl: Displays directory of drive (if 1:.

Rad: Displays directory of drive Radz, a recoverable RAM disk used in some
systems.

Brt: Sets brightness threshold for fibers.

Cali: Sets horizontal and vertical calibration data for number of pixels per 100
microns. Converts to microns per pixel and determines overall screen area.

FibArea: Inputs cross-sectional area of average fiber.

Distance: Sets up "MeasureRadius" which measures any dimension on the screen
with a mouseedragged line.

MeasureRadius: Measure dimensions on the screen, converting number of pixes with
horizontal and vertical calibration data to X, Y and total distances. Can be used to
measure fibers for setting counting radius.

FindDiameter: An attempt to automatically measure fiber diameters. Not very
successful so far.

WriteMenu: Writes the counting radius and fiber brightness threshold to a menu.

PalBar: Displays a bar with each of the pallettes in it. Clicking the mouse on these
colors can be an aid to setting the fiber brightness threshold.

BatchRead: Reads in the numbers of fibers in a previously counted batch. Finds
average volume fraction for the batch.

BatchPrint: Prints out the numbers of fibers for each image in a batch and the
average for the whole.

RResults: Reads in the number of fibers/image files written by WResults.
WResults: Writes a file with the number of fibers/image.

BatchGraph: Produces a graph with line heights proportioned to the number of
fibers/image.

Notice: Displays progam information and copyright.

BatchCounter: Counts batches of previously save fiber images. Writes fibers/image,
fiber coordinates, and statistics and map files to disk.

BCalc: Calculates the volume fraction results for a batch of counted images.

VoidCalcs: Calculates the approximate void volume fraction from the fiber volumes
and the composite, fiber, and matrix densities.

BPrint: Prints out the results of a counted batch.

BWrite: Writes a disk file with the results of a counted batch.

266

WriteFibers: Writes the coordinates of the fibers in an image to a disk file named
"FileFibers"

ReadFibers: Reads in the files written by "WriteFibers".
DrawTags: Draws tags on counted fibers after "ReadFibers" .

TagMap: Draws a map of fibers with one white pixel representing each fiber
position, 1/3 scale.

Cleanup: Clears the screen.

Histograph: Performs an areal analysis by determining the number of pixels assigned
to each pallette.

MouseTograph: Momentarily changes the color of all pixels assigned to a given
pallette so that they may be seen.

Diameter: Assigns the position of a fiber to a vertical column array form.

Quit: Closes libraries, ends program.

ReadImage: Interfaces menu with PictureLI subprogram.

GetAddrs: Returns screen addresses and information.

WriteImage: Interfaces menu with PictureSI subprogram.

EnterImageName: Enters save file name for PictureSI.

SUB PictureSI Saves IFF images (C. Scheppner, CBM).

GetScrAddrsSI: Returns information on screen data to the PictureSI subprogram.
SUB PictureLI Loads IFF images (C. Scheppner, CBM)

GetScrAddrsLI: Returns information on screen data to the PictureLI subprogram.
SUB InvertVideo Switches to reverse video for crosshairs.

SUB NormalVideo Returns to normal video after crosshairs.

267
PROGRAM LISTING

’ = = = =Fiber End Counter- Volume Fraction Calculator=
’Copyright l2/3/88, Mark Waterbury

’Optical Numeric Volume Fraction Analysis (ONVfA)
’Fiber volume determination by plotting fiber end

’ positions

GOSUB ScreenSetup

GOSUB Notice

CLEAR ,35000& ’clears basic stack

CLEAR ,120000& ’clears data memory space

DEFINT 1,] ,K,X,Y ’defines these variables as integers Main:
GOSUB Libs ’Initializes Amiga LIBRARYs and FUNCTIONS
GOSUB ArrayDimensions ’Sets sizes of array variables
GOSUB InitializeMenu ’Sets screen menu system

GOSUB Initialize ’Sets Graphics and other constants

Start:
CLS
ON MENU GOSUB CheckMenu : MENU ON
Unfinished = -1
WHILE Unfinished
SLEEP ’ event driven
WEND

Libs:
DECLARE FUNCTION xOpen& LIBRARY
DECLARE FUNCTION xRead& LIBRARY
DECLARE FUNCTION xWrite& LIBRARY
DECLARE FUNCTION AllocMem&0 LIBRARY
LIBRARY "dos.library"
LIBRARY "exec.library"
LIBRARY "graphics.library"

ArrayDimensions:

DIM X(3000),Y(3000) ’X, Y coordinates of fibers

DIM Xc(l20,60),Yc(120,60),Xn(120)

DIM F1$(20),FilName$(20),FileName$(20) ’images (2 disks)
DIM FlName$(10,40)

DIM CMap%(3l) ’Palettes to brightness values 0 to 15

DIM MapC%(3l) ’Brightness to Palettes

DIM Histo(3l) ’Histograph of percent each palette

DIM HistoSum(31),SumHisto(31)

DIM Fibers(10,40) ’Number of fibers in each picture

DIM FibDist(20,20),DistNumb(100) ’Number of fibers/square
DIM DistMap%(15,15,10,5)

DIM RE(31),GR(31),BL(31) ’Color Palettes

DIM BPlaneSI&(5),BPlaneLI&(5) ’For PicLI and PicSI

DIM NFirst(10),NLast(10),Drv$(4) ’Batch numbers and drive
DIM Total(10),NPics(10),Average(10)

DIM AveFibres(10),DComposite(10)

268

DIM NFibres(20)
DIM cTab%(32)
RETURN

Cycle:
GOSUB GetAddrs
RETURN

ScreenSetup:
SMode = 1: Depth = 5: WMode = 16 ’Lo-res, 5 bit planes
ScreenX = 320:ScreenY = 200 ’Screen dimensions in pixels
SCREEN 2,ScreenX,ScreenY,Depth,SMode
WINDOW 2,"",,WMode,2
PALETTE 0,0,0,0

RETURN

Initialize:
GOSUB Paletl
GOSUB Cal2
XEnd = 311: YEnd = 195
XScreen = 312: YScreen = 190
TC% = 16 ’Tag color
VC% = 18 ’Void color
MC% = 17 ’Map color
Ch% = 16
NXGroups = 12 ’sample area groups per 312 X pixels
NYGroups = 10 ’sample area groups per 190 Y pixels
NX = NXGroups/XScreen ’groups per X pixel
NY = NYGroups/YScreen ’ groups per Y pixel
Xn = XScreen/NXGroups ’Pixels per X group
YN = YScreen/NYGroups ’Pixels per Y group
F1$(0) = "0" :F1$(1) = " 1 " :Fl$(2) = "2" :Fl$(3) = "3" :Fl$(4) = "4"
F1$(5) - "5":Fl$(6) = "6":Fl$(7) = "7":Fl$(8) = "8"
F1$(9) "9":Fl$(10) = "10":F1$(ll) = "11":F1$(12) = "12"
F1$(l3) = "l3":Fl$(14) = "14":Fl$(15) = "15":F1$(16)="l6"
F1$(17) ="17":F1$(18)= "18":F1$(19) = "l9":Fl$(20) = "20"
RETURN

Call:
HCalib = 179.33:VCa1ib = 159 ’20X ULWD, 6.7x, CCD
FiberArea = 40.5375 ’AS4 microns squared
DFibers = 1.8: DMatrix = 1.206 ’AS4, DER331/MPDA
Thd% = 11 ’fiber brightness threshold
RadiusY = 11 ’counting diameter
MENU 4,7,2," 20X-6.7X-CCD "
MENU 4,8,1," 20X-3.3X-CCD "
GOSUB SetCal
RETURN

Ca12:
HCalib = 91:VCalib = 78 ’20X ULWD, 3.3x, CCD
FiberArea = 40.5375 ’microns squared for AS4 batch
DFibers = 1.8: DMatrix = 1.206 ’AS4, DER33l/MPDA

269

Thd% = 11 ’fiber brightness threshold
RadiusY = 5.1 ’counting diameter
MENU 4,7,1," 20X-6.7X-CCD "
MENU 4,8,2," 20X-3.3X-CCD "
GOSUB SetCal
RETURN

SetCal:
HCal = lOO/HCalib:VCal = 100/VCalib ’Microns per pixel
ScreenX = 316 * HCal:ScreenY = 202 * VCal

Screenarea = ScreenX * ScreenY ’Area in microns square Calibration
= FiberArea/Screenarea
RETURN
InitializeMenu:

MENU 1,0,1,"File"
MENU l,l,l,"Read image "
MENU 1,2,1,"Read Fiber Coordinates "
MENU l,3,l,"Write Fiber Coordinates"
MENU 1,4,1,"Directory of drive 0 "
MENU l,5,l,"Directory of drive 1 "
MENU 1,6,1,"Write image "
MENU 1,7,1,"Write Image Name "
MENU 1,8,1,"Read Statistics "
MENU 1,9,1,"Write Statistics "
MENU 1,10,l,"Quit"
MENU 2,0,1,"Calcs"
MENU 2,1,1,"Test Count "
MENU 2,2,1,"Batch Count "
MENU 2,3,1,"Manual Count "
MENU 2,4,1,"Calculate Distribution "
MENU 2,5 ,1,"Calculate statistics "
MENU 2,6,1,"Histograph "
MENU 2,7,1,"FIBER AREA CALIBRATION "
MENU 2,8,1,"SCREEN AREA CALIBRATION "
MENU 2,9,1,"FIBER BRIGHTNESS ADJUST "
MENU 2,10,1,"COUNTING RADIUS ADJUST "
MENU 3,0,1,"Graph"
MENU 3,1,1,"me Fiber Tags"
MENU 3,2,1,"Color Palet "
MENU 3,3,1,"Gray Palet "
MENU 3,4,1,"Palette Bar "
MENU 3,5,1,"Clear Screen "
MENU 3,6,1,"[Data Output] "
MENU 4,0,1,"Batch"
MENU 4,1,1,"Read Batch "
MENU 4,2,1,"Graph Batch "
MENU 4,3,1,"Print Batch "
MENU 4,4,1,"Read Distrib "
MENU 4,5,1,"Write Distrib"
MENU 4,6, l , "Print Distrib"
MENU 5,0,1,"Stats"
MENU 5,1,1,"Grid "

270

MENU 5 ,8,1,"Distance"
MENU 5,9,1,"Diameter"
RETURN

CheckMenu:

MenuId = MENU(0)

MenuItem = MENU( 1)

ON MenuId GOSUB Filemenu,Calcs,Graph,Batch,Dist
RETURN

Filemenu:
ON Menultem GOSUB ReadImage,ReadFibers,WriteFibers,Dir0,
_Dirl ,WriteImage,EnterImageName,ReadStats,WriteStats,Quit
RETURN

Calcs:
ON MenuItem GOSUB AutoCounter,BatchCounter,FiberCounter,
_ Distribution,Stats,Histograph,FibArea,Cali,Brt,Rad
RETURN
Graph:
ON MenuItem GOSUB DrawTags, Palet1,Palet2,PalBar,Cleanup
RETURN
Batch:
ON Menultem GOSUB BatchRead , BatchGraph ,BatchPrint,
__ReadDist, WriteDist, PrintDist, Call, Ca12
RETURN
Dist:
ON Menultem GOSUB Grid ,BarGraph , BlockGraph , S mallBar, Map ,
_TagMap,Region,Distance,FindDiameter
RETURN

Region:
MOUSE OFF
InvertVideo
ScX% = 320:ScY% = 200
f % = MOUSE(O)
f% = MOUSE(O)
WHILE MOUSE(O) = 0
f % =MOUSE(0)
CX% =MOUSE(1)
CY% =MOUSE(2)
LINE (0,CY%)-(ScX%,CY%),Ch%
LINE (CX% ,0)-(CX% ,ScY %),Ch %
LINE (0,CY%)-(ScX%,CY%),Ch%
LINE (CX%,O)-(CX%,ScY%),Ch%
WEND
GOSUB Square
RETURN

271

S uare:
% = MOUSE(O)
SX % =MOUSE(3)
SY% =MOUSE(4)
WHILE MOUSE(O) = -1
EX% = MOUSE(S)
EY% = MOUSE(6)
LINE (SX%,SY%)-(EX%,EY%),Ch%,B
LINE (SX%,SY%)-(EX%,EY%),Ch%,B
WEND

NormalVideo
LINE (SX%,SY%)-(EX%,EY%),17,B
dX = (EX%-SX%)
= (EY% - SY%)
BoxArea = dX * dY * HCal * VCal
NBox = 0
FOR I = 1 TO NFibers
IF X(I) > SX% THEN
IF X(I) < EX% THEN
IF Y(I) > SY% THEN
IF Y(I) < EY% THEN
PSET(X(I),Y(I)),17
CIRCLE (X(I), Y(I)1),1,17
NBox = NBox +1
END IF
END IF
END IF
END IF
NEXT I
NFib$ = "NFibers "+STR$(NBox)
MENU 3,7,1,NFib$
VFib = 100 * FiberArea * NBox/BoxArea
VFib$ = "Fiber Vf " + STR$(VFib)
MENU 3,8,1,VFib$
MenuString$ = "dX =" + STR$(dX) + " dY= -" + STR$(dY)
MENU 3,9,1,MenuString$
MenuString$ = "Microns‘2 = " + STR$(BoxArea)
MENU 3,10,1,MenuString$
MOUSE ON
RETURN

Distribution:

MaxFib = 0

FOR I = 0 TO NXGroups - 1
FOR J = 0 TO NYGroups - 1
FibDist(I,J) = 0
NEXT J

NEXT I

FOR I = 1 TO NFibers

IF Y(I) < 6 THEN GOTO NeI

XI = INT(X(I) * NX)

Y1 = INT((Y(I)—6) * NY)

FibDist(XI,YI) = FibDist(XI,YI) + l

272

NeI: NEXTI
FOR J = 0 TO NYGroups - 1
FOR I = 0 TO NXGroups - 1
IF FibDist(I,J) > MaxFib THEN MaxFib = FibDist(I,J)
NEXT 1

NEXT J
SOUND 2000,10
RETURN

statsZ:
MaxFiberSet = 30
FibAlarm = 15
NBelow = 0
Sum = 0
Suqu = 0
NGroups = NXGroups * NYGroups
FOR J = 0 TO NYGroups - 1
FOR I = 0 TO NXGroups - 1
Sum = Sum + DistMap%(I,J,K,l)
DistNumb(DistMap % (1,] ,K,l)) = DistNumb(DistMap % (1,] ,K,l)) + 1
IF DistMap%(I,J,K,l)< = FibAlarm THEN NBelow = NBelow + 1
NEXT I
NEXT J
Ave = Sum/NGroups
FOR J = 0 TO NYGroups - 1
FOR I = 0 TO NXGroups - 1
Suqu = Suqu + (Ave - DistMap%(I,J,K,l)YZ
NEXT I

NEXT J
Suqu = Suqu/NGroups
Deviation = SQR(Suqu)

SOUND 3000,8
GOSUB Histogram
RETURN
Stats:
MaxFiberSet = 30
FibAlarm = 15
NBelow = 0
Sum = 0
Suqu = 0

NGroups = NXGroups * NYGroups
FOR J = 0 TO NYGroups - 1
FOR I = 0 TO NXGroups - 1
Sum = Sum + FibDist(I,J)
DistNumb(FibDist(I,J)) = DistNumb(FibDist(I,J)) + 1
IF FibDist(I,J) < = FibAlarm THEN NBelow = NBelow + 1
NEXT I
NEXT J
Ave = Sum/NGroups
FOR J = 0 TO NYGroups - 1
FOR I = 0 TO NXGroups - 1
Suqu = Suqu + (Ave - FibDist(I,J))“2

273

NEXT I
NEXT J
Suqu = Suqu/NGroups
Deviation = SQR(Suqu)
SOUND 3000,8
GOSUB Histogram
RETURN

Histogram:

BotY = 180
FOR I = 1 TO MaxFiberSet
LINE (1 * 4,BotY)-(I*4+4,BotY-DistNumb(I)),l,bf
NEXT I

RETURN

WriteStats:
StatNameS = Fil$ + ".STA"
OPEN StatName$ FOR OUTPUT AS I
WRITE #1, F115
WRITE #1, MaxFiberSet
WRITE #1, Sum,Ave,Deviation
FOR I = I TO MaxFiberSet
WRITE #1, DistNumb(I)
NEXT I
CLOSE #1
RETURN

ReadStats:
INPUT "Enter Stats Name ",Fil$
StatName$ = Fil$ + ".STA"
OPEN StatName$ FOR INPUT AS 1
INPUT #1, Fil$
INPUT #1, MaxFiberSet
INPUT #1, Sum,Ave,Deviation
FOR I = 1 TO MaxFiberSet
INPUT #1, DistNumb(I)
NEXT I
CLOSE #1
RETURN

ReadDist:
INPUT "Distribution Name (.Map) ",Fil$
INPUT "Enter K, L ",K,1
StatName$ = Fil$ + ".Map"
OPEN StatName$ FOR INPUT AS 1
INPUT #1, VoidFraction
FOR J = 0 TO NYGroups - 1
FOR I = 0 TO NXGroups - 1
INPUT #1,DistMap%(I,J,K,l)
IF DistMap%(I,J,K,l) > MaxFib THEN MaxFib=DistMap%(I,J,K,l)
NEXT 1

NEXT J
CLOSE #1

274

IFK > KMaxTHENKMax = K

IF1> LMax THEN LMax =1
GOSUB statsZ

RETURN

WriteDist:
MapName$ = Fil$ + ".Map"
OPEN MapName$ FOR OUTPUT AS 1
WRITE #1, VoidFraction
FOR J = 0 TO NYGroups - 1
FOR I = 0 TO NXGroups - l
WRITE #1,FibDist(I,J)
NEXT I
NEXT J
CLOSE #1
RETURN

Map:
BlockX = 5:BlockY = 4
FOR K = 1 TO KMax
FORI = 1 TO LMax
IF MaxFib = 0 THEN RETURN
FirstX = (K - 1) * (NXGroups * BlockX + I)
FirstY = 5 + (l - 1) * NYGroups * BlockY
FOR J = 0 TO NYGroups - 1
FOR I = 0 TO NXGroups - l
LeftX = FirstX + I * BlockX
RightX = LeftX + BlockX
TopY = FirstY + J * BlockY
BotY = TopY + BlockY
FD = 16 + 15 * DistMap%(I,J,K,l)lMaxFib
IF FD > 31 THEN FD = 31
LINE(LeftX,TopY)-(RightX,BotY),FD,bf
NEXT I
NEXT J
NEXT 1
NEXT K
RETURN

PrintDist:
LPRINT Fil$
FOR J = 0 TO NYGroups - 1
FOR I = 0 TO NXGroups - l
LPRINT FibDist(I,J);" ";
IF FibDist(I,J) > MaxFib THEN MaxFib = FibDist(I,J)
NEXT I
LPRINT
NEXT J
RETURN

BarGraph:
IF MaxFib = 0 THEN RETURN
LeftX = 0:RightX = 0

275

TopY = 0:BotY = 0
BarWidth = 4
FOR J = 0 TO NYGroups - 1
FOR I = 0 TO NXGroups - 1
LeftX = I * Xn
RightX = LeftX + BarWidth
BotY = 5 + (1+1) * YN
FD = 16 + 15 * FibDist(I,J)/MaxFib
LINE(LeftX,BotY)-(RightX,BotY-FibDist(I,J) +5),FD,bf
NEXT I
NEXT J
RETURN

SmallBar:
IF MaxFib = 0 THEN RETURN
LeftX = 0:RightX = 0
TopY = 0:BotY = 0
BarWidth = 4
FOR J = 0 TO NYGroups - 1
FOR I = 0 TO NXGroups - l
LeftX = I * BarWidth
RightX = LeftX + BarWidth
BotY = 5 + (J+1) * YN
FD = 16 + 15 * FibDist(I,J)/MaxFib
LINE(LeftX,BotY)-(RightX,BotY-FibDist(I,J) +5) ,FD,bf
NEXT I
NEXT J
RETURN

BlockGraph:
IF MaxFib = 0 THEN RETURN
LeftX = 0:RightX = 0
TopY = 5:BotY = 0
FOR J = 0 TO NYGroups - 1
FOR I = 0 TO NXGroups - 1

LeftX=I*6
RightX=LeftX+6
TopY=]*5

BotY = TopY + 5
FD = 16 + 15 * FibDist(I,J)/MaxFib
LINE(LeftX,TopY)-(RightX,BotY),FD,bf
NEXTI
NEXT J

RETURN

Grid:
IF MaxFib = 0 THEN RETURN
LeftX = 0:RightX = 0
TopY = 6:BotY = 0
FOR J = 0 TO NYGroups - 1
BotY = TopY + YN
FOR I = 0 TO NXGroups - 1
RightX = LeftX + Xn

276

FD = 16 + 15 * FibDist(I,J)/MaxFib
LINE(LeftX,TopY)—(RightX-l,BotY-l),FD,B

LeftX = RightX
NEXT 1
LeftX = 0
TopY = BotY
NEXT J
RETURN

Paletl:
PALETTE 16,15/15,0/15,0/15 : PALETTE 17,0/15,0/15,10/15
PALETTE 18,0/15,10/15,0/15 : PALETTE 19,15/15,10/15,0/15
PALETTE 20,0/15,0/15,5/15 : PALETTE 21,12/15,12/15,12/15
PALETTE 22,2/15,0/15,0/15 : PALETTE 23,4/15,0/15,0/15
PALETTE 24,7/15,0/15,0/15 : PALETTE 25,10/15,0/15,0/15
PALETTE 26,15/15,0/15,0/15 : PALETTE 27,15/15,15/15,0/15
PALETTE 28,0/15,15/15,0/15 : PALETTE 29,0/15,15/15,15/15
PALETTE 30,0/15,0/15,15/15:PALE'1'TE 31,15/15,15/15,15/15

RETURN

Palet2:
FOR I = 24 TO 31
Gray = I "‘ 2 - 47
PALETTE I,Gray/ 15 ,Gray/ 15 ,Gray/ 15
NEXT I
RETURN

AutoCounter:
GOSUB FiberCounter
XEnd = 311:YEnd = 195
IF RadiusY = 0 THEN RadiusY = 11
NTh% = RadiusY/3
RadiusX = RadiusY*l.2: RadiusSq = l.44*RadiusY"2
CC% = RadiusX/1.5
FORI = 1 TO XEnd/CC% + l

Xn(I) = 0
NEXT I
NFibers = 0

FOR J = 0 TO YEnd
FOR I = 0 TO XEnd
IF CMap%(POINT(I,J)) < Thd% THEN NThd% = 0:GOTO NexI
NThd% = NThd% + 1
IF NThd% > NTh% THEN
Ix = I/CC% + 1
FORK =Ix-1TOIx+1
IF ABS(I - Xc(K,Xn(K))) > RadiusX THEN GOTO NexK
IF ABS(J - Yc(K,Xn(K))) > RadiusY THEN GOTO NexK
IF (I-Xc(K,Xn(K)))"2 + l.44*(J-Yc(K,Xn(K)))"2 < RadiusSq THEN GOTO NexI

NexK: NEXT K
Xn(Ix) = Xn(Ix) + l
Xc(Ix,Xn(Ix)) = I:Yc(Ix,Xn(Ix)) = J
CIRCLE (I,J),1,16

277

PSET (1,]),16
NThd% = 0
END IF
NexlzNEXT I
NThd% = 0
NEXT J
K = 0
FORI = 1 TO XEnd/CC% + 1
FOR J = 1 TO Xn(I)
K = K + 1
X(K) = Xc(I,J):Y(K) = Yc(I,J)
NEXT J
NEXT I
NFibers = K
VFract = NFibers * Calibration
MenuString$ = "NFibers = " + STR$(NFibers)
MENU 3,7,1,MenuString$
MenuString$ = "Vf = " + LEFT$(STR$(VFract*100),4)
MENU 3,8,1,MenuString$
RETURN

FiberCounter:
ON MOUSE GOSUB CountMousezMOUSE ON
RadiusX = RadiusY * 1.2
RETURN
CountMouse:
f = MOUSE(O)
A = MOUSE(3)
B = MOUSE(4)
IF A < 2 THEN IF B < 2 THEN J = YEnd :RETURN
IF CC% = 0 THEN CC% = RadiusX/1.5
Ix = A/CC% + l
Xn(Ix) = Xn(Ix) + 1
NFibers = NFibers + 1
Xc(Ix,Xn(Ix)) = A:Yc(Ix,Xn(1x)) = B
X(NFibers) = A:Y(NFibers) = B
CIRCLE (A,B),1,17
PSET (A,B),17
NFibS = "NFibers = " +STR$(NFibers)
MENU 3,7,1,NFib$
VFib = 100 * NF ibers * Calibration
VFibS = "Fiber Vf = " + LEFT$(STR$(VFib),4)
MENU 3,8,1,VFib$
RETURN

DirO:
FILES "df0: "
RETURN

Dirl:
FILES "dfl:"
RETURN

278

Rad:
LOCATE 24,1:INPUT "Fiber-pixel radius ",RadiusY
RETURN

Brt:
LOCATE 24,1:INPUT "Brightness threshold",ThdSet% RETURN

Cali:
LastHCalib = HCalib :IastVCalib = VCalib
LOCATE 22,1:PRINT " "

PRINT '0 "

LOCATE 22,1
PRINT "Horizontal =";HCalib;" Vertical =";VCalib
LOCATE 23,1
INPUT "Horizontal, Vertical ",HCalib,VCaIib
IF HCalib = 0 THEN HCalib = LastHCalib
IF VCalib = 0 THEN VCalib = LastVCalib
HCal = lOO/HCalib:VCal = 100/VCalib ’Microns per pixel
ScreenX = 316 * HCal:ScreenY = 202 * VCal
Screenarea = ScreenX * ScreenY ’Area in microns square
Calibration = FiberArea/Screenarea

LOCATE 22,1
PRINT " "
PRINT " "
PRINT " "

RETURN

FibArea:
LastFiberArea = FiberArea
LOCATE 22,1
PRINT " "
PRINT 0. fl
LOCATE 22,1:PRINT "Current fiber area = ";FiberArea
LOCATE 23,1
INPUT "Fiber area (square microns) =",FiberArea
LOCATE 22,1
PRINT " "
PRINT I. ll
IF FiberArea = 0 THEN FiberArea = LastFiberArea
RETURN

Distance:
ON MOUSE GOSUB MeasureRadius
MOUSE ON
FD = 0
RETURN
MeasureRadius:
InvertVideo
f % = MOUSE(O)
SX% =MOUSE(3)
SY% =MOUSE(4)
WHILE MOUSE(O) = -1
EX% = MOUSE(S)

279

EY% = MOUSE(6)
LINE (SX%,SY%)-(EX%,EY%),Ch%
LINE (SX%,SY%)-(EX%,EY%),Ch%
WEND
NormalVideo
dX = EX%-SX%: dY = EY%-SY%
dMX = dX * HCaI
dMY = dY * VCal
Distance = SQR(dMX‘Z + dMY‘2)
IF FD = 0 THEN LINE (SX%,SY%)-(EX%,EY%),Ch%

MenuString$="X pix ="+STR$(dX) + " Y pix =" + STR$(dY)

MENU 3,9,1,MenuString$
MenuString$ = "Microns = " + STR$(Distance)
MENU 3,10,1,MenuString$
RETURN

FindDiameter:
TH% = 8
f = MOUSE(O)
f = MOUSE(O)
MOUSE OFF
InvertVideo
WHILE MOUSE(O) = 0
SX% =MOUSE(I)
SY% =MOUSE(2)
LINE (SX%,SY%)-(SX%+20,SY%),16
LINE (SX%,SY%)-(SX% +20,SY%),I6
WEND
NormalVideo
SX % =MOUSE(3)
SY % =MOUSE(4)
NT% = 0
BAve = 0
FOR I = 0 TO 20
B% = CMap%(POINT(SX% + I,SY%))
IF B% > TH% THEN
NT% = NT% + l
BAve = BAve + B%
PSET (SX% + I,SY%),l9
END IF
IF B% < TH% THEN
IF NT% > 3 THEN
BAve = BAve/NT%
RadiusY = NT%/1.2
Thd% = BAve - 2
GOSUB WriteMenu
END IF
NT% = 0
PSET(SX% +I,SY%),0
END IF
NEXT 1
MOUSE ON
RETURN

280

WriteMenu:

MenuString$ ="Diam ="+STR$(NT%) + " Brt =" + STR$(BAve)
MENU 3,11,1,MenuString$

RETURN

PalBar:
FOR I = 0 TO 31
LINE(I*3,180)-(I*3 +3,178),I,bf
NEXT I

RETURN
BatchRead:

INPUT "Enter first file number ",NFirst(Nb)
INPUT "Enter last file number ",NLast(Nb)
INPUT "File Name with disk ",FileNamel$
NPics(Nb) = NLast(Nb) - NFirst(Nb) +1
FOR I = NFirst(Nb) TO NLast(Nb)
FIName$(Nb,I) = FileNamel$ + F1$(I)
NEXT I
Total = 0
FOR I = NFirst(Nb) TO NLast(Nb)
Fil$ = FIName$(Nb,I)
GOSUB ReadFibers
Fibers(Nb,I) = NFibers
Total(Nb) = Total(Nb) + NFibers
NEXT I
OverAllSum = OverAllSum + Total(Nb)
OverAllNPics = OverAllNPics + NPics(Nb)
OverallAverage = OverAllSum/OverAllNPics
Average(Nb) = Total(Nb)/NPics(Nb)

NBatches = Nb
RETURN

BatchPrint:
PRINT "File Name ";FileName1$
PRINT "Total = ";Total(Nb)
PRINT "Average = ";Average(Nb)
PRINT
FOR J = NFirst(Nb) TO NLast(Nb)
PRINT FlName$(Nb,J);
PRINT USING " #### ";Fibers(Nb,J)
NEXT J
INPUT "Printout desired? ",PO$
IF POS = "Y" OR PO$ = "y" THEN
LPRINT "File Name ";FilNamel$

281

LPRINT "Total = ";Total(Nb)
LPRINT "Average = ";Average(Nb)
LPRINT
FOR J = NFirst(Nb) TO NLast(Nb)
LPRINT FlName$(Nb,J);
LPRINT USING " #### ";Fibers(Nb,J)
NEXT J
END IF
RETURN

RResults:

INPUT " Enter Results Name ",ResultFileS
OPEN ResultFile$ FOR INPUT AS 1
INPUT #1 ,NBatches

SumStart = 0

FOR I = I TO NBatches
FOR J = NFirst(I) TO NLast(I)
INPUT #1 ,FlName$(I,J),Fibers(I,J)
NEXT J
NEXT I
CLOSE #1
RETURN

WResults:

INPUT " Enter Results Name ",ResuItFile$
OPEN ResultFile$ FOR OUTPUT AS 1
WRITE #1,NBatches

SumStart = 0

FOR I = 1 TO NBatches
FOR J = NFirst(I) TO NLast(I)
WRITE #1,FlName$(I,J),Fibers(I,J)
NEXT J
NEXT 1
CLOSE #1
RETURN

BatchGraph:
N =

20
FOR I = I TO NBatches
FOR J = NFirst(I) TO NLast(I)
N = N + l
CIRCLE(N*RX,ZO-Fibers(I,J) *R) , 1 ,I
LINE(N*RX,ZO-Average(1) *R)-((N+ l)*RX,ZO-Average(1) *R) ,1
NEXT J
NEXT I
LINE(0,ZO—0*R)-(300,ZO-0*R), 1
LINE(O,ZO-500*R)-(300,ZO—500*R), 1
LINE(0,ZO-1000*R)—(300,ZO—1000*R), 1
LINE(0,ZO-1500*R)-(300,ZO-1500*R),1

282
RETURN

Notice:

CLS

LOCATE 5,1

PRINT " Optical Numeric Volume
PRINT " Fraction Analysis
PRINT " ONVfA"

PRINT " Licensed for use by the Composite

PRINT " Materials and Structures Center
PRINT " Michigan State University
PRINT " Serial No. 1050

PRINT " Copyright October 13, 1989
PRINT " Mark C. Waterbury
PRINT

PRINT " Version 1.1

RETURN

BatchCounter:

BFIag = 1 ’Indicates that a batch is being counted
INPUT "Number of Batches ",NDrives
INPUT "Printout desired? Y/N ",YN$
Printout = 0
IF YN$ = "Y" THEN Printout = 1
IF YN$ = "y" THEN Printout = 1

FOR D = 1 TO NDrives

INPUT "File Name with drive ",FileName$(D)

INPUT "First and last file numbers ",NFirst(D),NLast(D)
INPUT "Composite density (for voids) ",DComposite(D)
INPUT "Matrix density ",DMat

IF DMat < > 0 THEN DMatrix = DMat

INPUT "Fiber density ",DFib

IF DFib < > 0 THEN DFibers = DFib

NEXT D

FOR D = 1 TO NDrives
FOR I = NFirst(D) TO NLast(D)
FilName$(I) = Drv$(D) + FileName$(D) + F1$(I)
NEXT I
NPic = 0
FOR M = NFirst(D) TO NLast(D)
NPic = NPic + 1
F113 = FilName$(M)
PicNameLI$ = Fil$
PictureLI PicNameLI$
GOSUB GetAddrs
GOSUB Paletl
GOSUB AutoCounter
NFibres(NPic) = NFibers
Vf = NFibers * Calibration
LOCATE 1,1:PRINT F113;" NFibers = ";NFibers
PRINT "Fiber Vf = ";100 * Vf

283

PRINT FilName$(M);" Data being written"
GOSUB Distribution
GOSUB Stats
GOSUB WriteFibers
GOSUB WriteDist
GOSUB WriteStats
NEXT M
NPics = NPic
GOSUB BCalc
GOSUB BWrite
IF Printout THEN GOSUB BPrint
NEXT D
BFIag = 0
RETURN

BCalc:
TotalFibres = 0
FOR NPic = 1 TO NPics
TotalFibres = TotalFibres + NFibres(NPic)
NEXT NPic
AveFibres(D) = TotalFibres/NPics
Vf = AveFibres(D) * Calibration
Vm = (DComposite(D)-Vf * DFibers)/DMatrix
Vv = l - Vf - Vm
VFib = 100 * Vf:Vmatr = 100 * Vm: Vvoid = 100 * Vv
RETURN

VoidCalcs:
Vm = -(Vf * DFibers - DComposite)/DMatrix
Vv = l - Vf - Vm

RETURN

BPrint:
LPRINT "Optical Numeric Volume Fraction Analysis"
LPRINT
LPRINT "Volume fractions for ";FileName$(D);" set. "
LPRINT "Fiber density = " ;DFibers;
LPRINT " Matrix density = ";DMatrix
LPRINT "Composite density = ";DComposite(D)
LPRINT
LPRINT "Fiber area = ";FiberArea

LPRINT "Screen area = ";Screenarea
LPRINT
LPRINT "Image # Fibers Vf"
NPic = 0

FOR I = NFirst(D) TO NLast(D)
NPic = NPic + 1
VfPic = NFibres(NPic) * Calibration
LPRINT USING "####.# ";I;NFibres(NPic);VfPic*100
NEXT I
LPRINT
LPRINT "Average number of fibers = ";AveFibres(D)
LPRINT

284

LPRINT "Fiber Vf = ";:PRINT USING "##.#";VFib

LPRINT "Matrix Vm = ";:PRINT USING "##.#";Vmatr

LPRINT "Void Vv = ";:PRINT USING "##.#";Vvoid
RETURN

BWrite:
Fil$ = Drv$(D) + FileName$(D) + ".res"

OPEN Fil$ FOR OUTPUT AS I

PRINT #1, "Optical Numeric Volume Fraction Analysis"

PRINT #1, "Average volume fractions for ";FileName$(D);" set."
PRINT #1,"Fiber density = ";DFibers;" Matrix density = ";DMatrix
PRINT #1,"Composite density = ";DComposite(D)

PRINT #1, "Fiber area = ";FiberArea

PRINT #1, "Screen area = ";Screenarea
PRINT #1, "Image # Fibers Vt"
NPic = 0

FOR I = NFirst(D) TO NLast(D)

NPic = NPic + l

VfPic = NFibres(NPic) * Calibration
PRINT #I,I,NFibres(NPic),VfPic * 100
NEXT I

PRINT #1, "Average number of fibers = ";AveFibres(D)
PRINT #1, "Fiber volume fraction = ";VFib

PRINT #1, "Matrix volume fraction = ";Vmatr

PRINT #1,"Void volume fraction = ";Vvoid

CLOSE #1

RETURN

WriteFibers:
IF NFibers = 0 THEN PRINT "Fibers not counted ":RETURN
FibFilS = Fil$ + "Fibers"
OPEN FibFi1$ FOR OUTPUT AS 1
WRITE #1,Fil$,Note$
WRITE #1,NFibers
FOR I = 1 TO NFibers
WRITE #1,X(I),Y(I)
NEXT I

CLOSE #1
RETURN

ReadFibers:
FibFil$ = Fil$ + "Fibers"
OPEN FibFil$ FOR INPUT AS 1
INPUT #l,f$,Note$
INPUT #1,NFibers
IF Reader = 1 THEN GOTO Fib]ump
FOR I = 1 TO NFibers
INPUT #1,X(I),Y(I)
NEXT I

Fib]ump: CLOSE #1
RETURN

285

meTags:
FOR I = 1 TO NFibers
CIRCLE(X(I),Y(I)),1,TC%

PSET(X(I),Y(I)),TC%
NEXT I

RETURN

TagMap:
MapScale = 3

Factor = 313/MapScale

YFactor = l98/MapScale

INPUT "File name with drive ",FibFlS

INPUT "First and last file numbers ",FirstFib,LastFib

CLS
FOR M = FirstFib TO LastFib
NY = 0

N = M - FirstFib
NCheckle N >MapScale-l THEN N=N-MapScale:NY=NY+ I:GOTO NCheck
FibFil$ = FibFl$ + F1$(M) + "Fibers"
OPEN FibFil$ FOR INPUT AS 1
INPUT #1, Fil$,Note$
INPUT #1, NFibers
FOR I = 1 TO NFibers
INPUT #1, X(I),Y(I)
NEXT I

CLOSE #1
NShift = N * Factor
NYShift = NY*YFactor
FOR I = 1 TO NFibers
PSET (NShift + X(I)/MapScale,NYShift + Y(I)/MapScale),MC%
NEXT I

NEXT M
RETURN

Cleanup:
CLS
RETURN

Histograph:
MaxHisto = 0
FOR I = 0 TO 15
Histo(I) = 0
NEXT I
XSample = 2:YSample = 2 ’Sample rate for Areal Analysis
FOR J = 0 TO YEnd STEP YSample
FOR I = 0 TO XEnd STEP XSample
Histo(POINT (1,1)) = Histo(POINT (1,]» + 1
NEXT 1
NEXT J
SXa = (XEnd+1)/XSample:SYa = (YEnd+l)/YSample
FOR I = 0 TO 15
Histo(I) = 100 * Histo(I)/(SXa * SYa)
1F Histo(I) > MaxHisto THEN MaxHisto = Histo(I)

286

NEXT 1

Sum = Histo(MapC%(0))
HistoSum(MapC%(0)) = Sum
FORI = 1 TO 15

Sum = Sum + Histo(MapC%(I))
HistoSum(MapC%(I)) = Sum
NEXT 1

Sum = Histo(MapC%(15))
SumHisto(MapC%(15)) = Sum
FOR I = 14 TO 0 STEP -1
Sum = Sum + Histo(MapC%(I))
SumHisto(MapC%(I)) = Sum
NEXT I

LOCATE 1,1

FOR I = 0 TO 15

PRINT USING "## ";I;

PRINT USING " ##.##";Histo(MapC%(I));HistoSum(MapC%(I));
PRINT USING " ##.##";SumHisto(MapC%(I))
LINE(I*10,180)-(I*10+8,ISO-Histo(MapC%(I))),MapC%(I),bf
NEXT 1

INPUT "Type Y for printout ";Y$
IF Y3 = "Y" THEN GOTO Pr
IF Y3 = "y" THEN GOTO Pr
GOTO Nope
Pr:
FOR I = 0 TO 15
LPRINT USING "## ";I;
LPRINT USING "##. ##" ;Histo(MapC % (1));HistoSum(MapC % (1));
_SumHisto(MapC % (1))
NEXT 1

Nope: ON MOUSE GOSUB MouseTograph
MOUSE ON
RETURN

MouseTograph:
f = MOUSE(O)
SX% =MOUSE(3)
SY % =MOUSE(4)
Pal = POINT (SX%,SY%)
PALETTE Pal,0,0,l
FOR I = 1 TO 20000
NEXT 1
PALETTE Pal,CMap%(Pal)/15, CMap%(Pal)/15, CMap%(Pal)/15
RETURN

Diameter:
ND = ND + 1
IF ND > 100 THEN RETURN
Xc(ND,J) = NT%
Yc(0,J) = ND
RETURN

287

Quit:

MENU RESET
LIBRARY CLOSE
STOP

ReadImage:

INPUT "Enter file name ",PicNameLI$
PictureLI PicNameLI$

Fil$ = PicNameLI$

FilMenS = "File Name " + Fil$
GOSUB GetAddrs

GOSUB Paletl

ON MOUSE GOSUB MouseTograph
MOUSE ON

NFibers = 0

RETURN

GetAddrs:
sWindow& = W1NDOW(7)
sScreen& = PEEKL(sWindow& + 46)
sViewPort& = sScreen& + 44
sRastPort& = sScreen& + 84
sCoIorMap& = PEEKL(sViewPort& + 4)
colorTab& = PEEKL(sColorMap& + 4)
sBitMap& = PEEKL(sRastPort& + 4)
schepth% = PEEK(sBitMap& + 5)
nColors% = 2‘schepth%
FOR kk = 0 TO 15
cTab%(kk) = PEEKW(colorTab&+(kk*2))
CMap%(kk) = INT(cTab%(kk)/256)
MapC%(CMap%(kk)) = kk
NEXT
RETURN

WriteImage:
PictureSI WritePicName$
RETURN

EnterImageName:
LOCATE 24,1: INPUT "Image Name ",WritePicName$
RETURN

SUB PictureSI (WritePicNameS) STATIC
SHARED BPlaneSI&()
saveError$ = " "

AvailRam& = FRE(-l)
NeededRam& = ((W/8)*h*(D+1))+5000
IF AvailRam& < NeededRam& THEN

PRINT "Not enough free ram"

GOTO McIeanupSI
END IF
GOSUB GetScrAddrsSI

ccrtDir% = l:ccrtStart% = 1:ccrtEnd% = nColors% - 1

288

ccrtSecs& = 0:ccrtMics& = 2000
cReg% = ccrtStart% :fHandle& = O:mybuf& = 0
FileName$ = WritePicName$ + CHR$(0)
fHandle& = xOpen&(SADD(FileName$),lOO6)
IF fHandle& = 0 THEN
saveError$ = "Can’t open output file"
GOTO ScleanupSI
END IF
C1earPublic& = 65537&
mybufsize& = 120
mybuf& = AllocMem&(mybufsize&,ClearPublic&)
IF mybuf& = 0 THEN
saveError$ = "Can’t alloc buffer"
GOTO ScleanupSI
END IF
cbuf& = mybuf&
GOSUB GetScrAddrsSI

zero& = 0: pad% = 0:aspect% = &HAOB:BMHDsize& = 20
CMAPsize&=(2‘schepth%) * 3:CAMGsize& = 4:CCRTsize& = 14
BODYsize& = (schidth%/8) * scrHeight% * schepth%

FORMsize&=BMHDsize&+CMAPsize&+CAMGsize&+CCRTsize&+
_BODYsize&+44
tt$ = "FORM"

wLen& = xWrite&(fl-Iandle&,SADD(tt$),4)

wLen& = xWrite&(fHandle&,VARPTR(FORMsize&),4)
tt$ = "ILBM"

wLen& = xWrite&(fHandle&,SADD(tt$),4)

IF wLen& < = 0 THEN

saveError$ = "Error writing FORM header"

GOTO ScleanupSI

END IF
tt$ = "BMHD"

wLen& = xWrite&(fI-Iandle&,SADD(tt$),4)
wLen& = xWrite&(fHandle&,VARPTR(BMHDsize&),4)
wLen& = xWrite&(fHandle&,VARPTR(schidth%),2)
wLen& = xWrite&(fI-Iandle&,VARPTR(scrHeight%),2)
wLen& = xWrite&(fHandle&,VARPTR(zero&),4)
temp% = (256 * schepth%)
wLen& = xWrite&(fHandle&,VARPTR(temp%),2)
wLen& = xWrite&(fHandle&,VARPTR(zero&),4)
wLen& = xWrite&(fHandle&,VARPTR(aspect%),2)
wLen& = xWrite&(fHandle&,VARPTR(schidth%),2)
wLen& = xWrite&(fHandle&,VARPTR(scrHeight%),2)
IF wLen& < = 0 THEN

saveError$ = "Error writing BMHD"

GOTO ScleanupSI
END IF
tt$ = "CMAP"
wLen& = xWrite&(fHandle&,SADD(tt$),4)
wLen& = xWrite&(fHandle&,VARPTR(CMAPsize&),4)
FOR kk& = 0 TO nColors% - I

regTemp% = PEEKW(coIorTab& + (2*kk&))

POKE(cbuf&+(kk&*3)),(regTemp% AND &HFOO) / 16

289

POKE(cbuf&+(kk&*3)+ l),(regTemp% AND &HFO)
POKE(cbuf&+(kk&*3)+2),(regTemp% AND &HF) * 16
NEXT
wLen& = xWrite&(fHandle&,cbuf&,CMAPsize&)
IF wLen& < = 0 THEN
saveError$ = "Error writing CMAP"
GOTO ScleanupSI
END IF
tt$ = "CAMG"
wLen& = xWrite&(fHandle&,SADD(tt$),4)
wLen& = xWrite&(fHandle&,VARPTR(CAMGsize&),4)
vaodes& = PEEKW(sViewPort& + 32)
wLen& = xWrite&(fI-Iandle&,VARPTR(vaodes&),4)
IF wLen& < = 0 THEN
saveError$ = "Error writing CAMG"
GOTO ScleanupSI
END IF
tt$ = "CCRT"
wLen& = xWrite&(fIIandle&,SADD(tt$),4)
wLen& = xWrite&(fI-Iandle&,VARPTR(CCRTsize&),4)
wLen& = xWrite&(fHandle&,VARPTR(ccrtDir%),2)
temp% = (256*ccrtStart%) + ccrtEnd%
wLen& = xWrite&(fHandle&,VARPTR(temp%),2)
wLen& = xWrite&(fHandle&,VARPTR(ccrtSecs&),4)
wLen& = xWrite&(fHandle&,VARPTR(ccrtMics&),4)
wLen& = xWrite&(fHandle&,VARPTR(pad%),2)
IF wLen& < = 0 THEN
saveError$ = "Error writing CCRT"
GOT O ScleanupSI
END IF
11$ = "BODY"
wLen& = xWrite&(fl-Iandle&,SADD(tt$),4)
wLen& = xWrite&(fI-Iandle&,VARPTR(BODYsize&),4)
schowBytes% = schidth% / 8
FOR rr& = 0 TO scrHeight% -1
FOR pp& = 0 TO schepth% -1
schow& = BPlaneSI&(pp&)+(rr&*schowBytes%)
wLen& = xWrite&(flIandle&,schow&,schowBytes%)
IF wLen& < = 0 THEN
saveError$ = " Error writing BODY"
GOTO ScleanupSI
END IF
NEXT
NEXT
saveError$ =
ScleanupSI:
IF fHandle& < > 0 THEN CALL xClose&(fHandle&)
IF mybuf& < > 0 THEN CALL FreeMem&(mybuf&,mybufsize&)
EXIT SUB
McIeanupSI:
IF loadErrorS < > "" THEN PRINT loadErrorS
IF saveError$ < > "" THEN PRINT saveError$
EXTT SUB

290

GetScrAddrsSI:
sWindow& = W1NDOW(7)
sScreen& = PEEKL(sWindow& + 46)
sViewPort& = sScreen& + 44
sRastPort& = sScreen& + 84
sCoIorMap& = PEEKL(sViewPort& + 4)
colorTab& = PEEKL(sColorMap& + 4)
sBitMap& = PEEKL(sRastPort& + 4)
schidth% = PEEKW(sScreen& + 12)
scrHeight% = PEEKW(sScreen& + 14)
schepth% = PEEK(sBitMap& + 5)
nColors% = 2‘schepth%
FOR kk& = 0 TO schepth% - 1

BPlaneSI&(kk&) = PEEKL(sBitMap& + 8 + (kk&*4))

NEXT

RETURN
END SUB

SUB PictureLI (PicNameLIS) STATIC
SHARED BPlaneLI&0
CLS
loadError$ = ""
f5 = PicNameLI$
MENU l,ll,0,PicNameLI$
ccrtDir% = 0:ccrtStart% = 0:ccrtEnd% = 0:ccrtSecs& = 0
ccrtMics& = 0: fHandle& =0: mybuf& = 0: foundBMHD& =0
foundCMAP& =0: foundCAMG& =0: foundCCRT& =0: foundBODY& = 0
FileName$ = f$ + CHR$(0)
fHandle& = xOpen&(SADD(FileName$),1005)
IF fHandle& = 0 THEN
loadErrorS = "Can’t open/find pic file"
GOTO LcleanupLI
END IF
ClearPublic& = 65537&
mybufsize& = 360
mybuf& = AllocMem&(mybufsize&,ClearPublic&)
IF mybuf& = 0 THEN
loadError$ = "Can’t alloc buffer"
GOTO LcleanupLI
END IF
inbuf& = mybuf&
cbuf& = mybuf& + 120
cTab& = mybuf& + 240
rtlgen& = xRead&(fHandle&,inbuf&,12)
t = "0'
FOR kk& = 8 TO 11
tt% = PEEK(inbuf& + kk&)
tt$ = 11$ + CHR$(tt%)
NEXT
IF tt$ < > "ILBM" THEN
loadErrorS = "Not standard ILBM pic file"
GOTO LcleanupLI

291

END IF
ChunkLoopLI:
rLen& = xRead&(fHandle&,inbuf&,8)
ifsbenar = PEEKL(inbuf& + 4)
FOR kk& = 0 TO 3
tt% = PEEK(inbuf& + kk&)
11$ = 11$ + CHR$(11%)
NEXT
IF tt$ = "BMHD" THEN ’BitMap header
foundBMHD& = 1
rLen& = xRead&(fHandle&,inbuf&,icLen&)
iWidth% = PEEKW(inbuf&)
iHeight% = PEEKW(inbuf& + 2)
iDepth% = PEEK(inbuf& + 8)
iCompr% = PEEK(inbuf& + 10)
schidth% = PEEKW(inbuf& + 16)
scrHeight% = PEEKW(inbuf& + 18)
iRowBytes% = iWidth% /8
schowBytes% = schidth% / 8
nColors% = 2"(iDepth%)
AvailRam& = FRE(-l)
NeededRam& = ((schidth%/8)*scrHeight%*(iDepth%+1))+5000
IF AvailRam& < NeededRam& THEN
loadError$ = "Not enough free ram"
GOTO LcleanupLI
END IF
kk& = 1
IF schidth% > 320 THEN kk& = kk& + 1
IF scrHeight% > 200 THEN kk& = kk& + 2
GOSUB GetScrAddrsLI
ELSEIF 11$ = "CMAP" THEN
foundCMAP& = l
rLen& = xRead&(fl-Iandle&,cbuf&,icLen&)
FOR kk& = 0 TO nColors% - 1
Red% = PEEK(cbuf&+(kk&*3))
gre% = PEEK(cbuf&+(kk&*3)+1)
blu% = PEEK(cbuf&+(kk&*3)+2)
regTemp% = (Red%*l6)+(gre%)+(blu%/16)
POKEW(cTab&+(2*kk&)),regTemp%
NEXT
ELSEIF tt$ = "CAMG" THEN ’Amiga ViewPort Modes
foundCAMG = 1
rLen& = xRead&(fHandle&,inbuf&,icLen&)
camgModes& = PEEKL(inbuf&)
ELSEIF tt$ = "CCRT" THEN ’Graphicraft color cycle info
foundCCRT& = I
rLen& = xRead&(fI-Iandle&,inbuf&,icLen&)
ccrtDir% = PEEKW(inbuf&)
ccrtStart% = PEEK(inbuf& + 2)
ccrtEnd% = PEEK(inbuf& + 3)
ccrtSecs& = PEEKL(inbuf& + 4)
ccrtMics& = PEEKL(inbuf& + 8)

292

ELSEIF tt$ = "BODY" THEN ’BitMap
foundBODY& = 1
IF iCornpr% = 0 THEN ’no compression
FOR rr& = 0 TO iHeight% -1
FOR pp& = 0 TO iDepth% -l
schow& = BPlaneLI&(pp&)+(rr&*schowBytes%)
rLen& = xRead&(fI-Iandle&,schow&,iRowBytes%)
NEXT pp&
NEXT rr&
ELSEIF iCompr% = 1 THEN ’cmpByteRunl
FOR rr& = 0 TO iHeight% -1
FOR pp& = 0 TO iDepth% -l
schow& = BPlaneLI&(pp&)+(rr&*schowBytes%)
ant% = 0
WHILE (ant% < iRowBytes%)
rLen& = xRead&(fHandle&,inbuf&,l)
inCode% = PEEK(inbuf&)
IF inCode% < 128 THEN
rLen& = xRead&(fHandle&,schow& + ant%, inCode%+l)
ant% = ant% + inCode% + I
ELSEIF inCode% > 128 THEN
rLen& = xRead&(fHandle&,inbuf&,l)
inByte% = PEEK(inbuf&)
FOR kk& = an1% TO an1% + 257 - inCode%
POKE(schow&+kk&),inByte%
NEXT
an1% = ant% + 257 - inCode%
END IF
WEND
NEXT
NEXT
ELSE
loadError$ = "Unknown compression algorithm"
GOT O LcleanupLI
END IF
ELSE
FOR kk& = I TO icLen&
rLen& = xRead&(fHandle&,inbuf&,l)
NEXT
IF (icLen& OR 1) = icLen& THEN
rLen& = xRead&(fI-Iandle&,inbuf&,l)
END IF
END IF
IF foundBMHD& AND foundCMAP& AND foundBODY& THEN
GOT O GoodLoadLI
END IF
IF rLen& > 0 THEN GOTO ChunkLoopLI
IF rLen& < 0 THEN ’Read error
IoadError$ = "Read error"
GOTO LcleanupLI
END IF
IF (foundBMHD&=0) OR (foundBODY&=0) OR (foundCMAP&=0) THEN
IoadError$ = "Needed ILBM chunks not found"

293

GOTO LcleanupLI
END IF
GoodLoadLI:
IoadErrorS = ""
IF foundCMAP& THEN
CALL LoadRGB4&(sViewPort&,cTab&,nColors%)
END IF

LcleanupLI:

IF fHandle& < > 0 THEN CALL xClose&(fHandle&)

IF mybuf& < > 0 THEN CALL FreeMem&(mybuf&,mybufsize&)
EXTT SUB

McleanupLI:

IF loadError$ < > "" THEN PRINT loadErrorS
IF saveError$ < > " " THEN PRINT saveError$
EXIT SUB

GetScrAddrsLI:
sWindow& = W1NDOW(7)
sScreen& = PEEKL(sWindow& + 46)
sViewPort& = sScreen& + 44
sRastPort& = sScreen& + 84
sCoIorMap& = PEEKL(sViewPort& + 4)
colorTab& = PEEKL(sColorMap& + 4)
sBitMap& = PEEKL(sRastPort& + 4)
schidth% = PEEKW(sScreen& + 12)
scrHeight% = PEEKW(sScreen& + 14)
schepth% = PEEK(sBitMap& + 5)
nColors% = 2‘schepth%
FOR kk& = 0 TO schepth% - 1

BPlaneLI&(kk&) = PEEKL(sBitMap& + 8 + (kk& *4))

NEXT

RETURN

END SUB

SUB InvertVideo STATIC
CALL SetDer& (W1NDOW(8),3)
END SUB

SUB NormaIVideo STATIC
CALL SetDer& (W1NDOW(8),1)
END SUB

APPENDIX D

SOURCE CODE FOR WILHELMY WETTING BALANCE
DATA ACQUISITON SYSTEM

The following program is the source code listing for the micro-Wilhelmy
balance control and data acquisition program written in compiled MicroSoft
QuickBasic, and the Wilhelmy data analysis program written in compiled AmigaBasic
(ABSoft AC-Basic), described in chapter 2. The routines for controlling the PC21
Compumotor, Omega A/D conversion card, and the Cole-Farmer temperature
controller were adapted from code provided by the respective manufacturers.

A list of subroutines and a brief description of their functions preceeds the
actual code. Long code lines have been reformatted, with leading hyphens attached
to the second portions.

The first progam listing is for controlling the Wilhelmy balance and acquiring
data, the second for further analysing that data.

Main: Main program loop.
Dims: Defines all data arrays and allocates space to them.

MenuRefresh: Writes a menu line at the bottom of the screen. Typing the first letter
in each word directs the program to that subroutine.

InLoop: The main menu "INKEY" loop. Checks user keyboard entries and directs
program flow to the appropriate subroutine.

DataEntry: Inputs data on the fiber, liquid, temperatures, etc.
StageMove: Moves the stage upward 1/100 inch.

Wilhelmy: Main Wilhelmy routine. Immerses fiber in steps, pauses, records balance
weight then saves data.

FindAverage: Averages several voltages measured from A/D converter in "Logger"
after each immersion increment.

Calculations: Calculates wetting angle from immersion force and fiber perimeter.
ArcCosine: Returns the inverse cosine to the calculations routine.

LogStart: Begins logging force data.

Logger: Accesses the A/D card and logs force data.

ReadVolts: Calls A/D card 100 times to smooth out noise and returns average result.

SetZero: Sets the input with the fiber out of the liquid to zero to cancel the tare
weight of the fiber and hook.

294

295

SetMass: Sets the ratio between the change in mass measured and the change in ND
card output voltage.

LoadCalib: Loads a previously stored A/D card calibration.
PrintData: Prints out mass and angle data.

Initialize: Initializes all constants, sets mnemonic variables to appropriate
CompuMotor command strings.

SetCMD: Concatenates CompuMotor command strings from parts.

Reminders: A list of CompuMotor command strings that may be used by users
wishing to customize code.

Helper: A sarcastic reference to the complete absence of online user help.
DriveParameters: Prints out the current status of the CompuMotor commands.
DriveProgram: Allows the user to edit the Wilhelmy sequence.

FileSave: Saves data to file.

ReadFile: Reads previously saved data for re-analysis with different diameter, etc.
Stoppit: Halts the CompuMotor motion.

Reader: Reads position information from the CompuMotor to the system bus, one
character at a time.

CMDWriter: Sends commands stored in CMD$ to CompuMotor via the
"Transmitter" routine 1 character at a time.

Transmitter: Actually transmits each character sent by the CMDWriter routine.

InitializePC21: Initializes the CompuMotor by sending a command string that
prepares it for further instructions.

ReadStatus: Reads the status of the temperature regulator.

ReadTemp: For Cole Parmer Model 20B with 134 ADC, reads temperatures and
setpoint.

ReadVolt: The general A/ D card reading routine, provided for reading temperatures.

LinearizeE: Converts the A/D card voltages into temperatures for use with type B
thermocouples.

Linearize]: Converts the A/D card voltages into temperatures for use with type J
thermocouples.

296
WILHELMY BALANCE CONTROL AND DATA ACQUISITON SOURCE CODE

REM === WilhelmyBalanceControlProgram =================
= = = Copyright April 10, 1989 Mark Waterbury, for the

REM Composite Materials and Structures Center, Michigan

State University

DEFINT I-K

Main:
GOSUB Dims
GOSUB Initialize
GOSUB InitializePC21:
GOSUB MenuRefresh
GOSUB InLoop

END

Dims:
DIM Mass(20, 100), AveMass(20), Deviation(20), Angle(20), Energy(20)
RETURN

MenuRefresh:
CLS
PRINT "Data entry, Wilhelmy, Save file, Read file, Quit"
PRINT "Zero, Calibrate, Load calibration, Arithmatic"
RETURN

InLoop:
M3 = INKEY$
IF M3 = "W" THEN GOSUB Wilhelmy
IF M3 = "w" THEN GOSUB Wilhelmy
IF M8 = "q" THEN GOSUB Stoppit: END
IF M3 = "Q" THEN GOSUB Stoppit: END
IF M8 = "2" THEN GOSUB SetZero
IF MS = "Z" THEN GOSUB SetZero
IF M$ = "C" THEN GOSUB SetMass
IF M$ = "c" THEN GOSUB SetMass
IF M$ "D" THEN GOSUB DataEntry
IF MS "(1" THEN GOSUB DataEntry
IF M5 = "F" THEN GOSUB FileSave
IF MS = "f" THEN GOSUB FileSave
IF M$ = "R" THEN GOSUB ReadFile
IF M3 = "r" THEN GOSUB ReadFile

IF M$ = "S" THEN GOSUB FileSave
IF M3 = "s" THEN GOSUB FileSave
IF M$ = "L" THEN GOSUB LoadCalib
IF M$ = "1" THEN GOSUB LoadCalib

IF MS = "A" THEN GOSUB Calculations
IF M8 = "8" THEN GOSUB Calculations
M$ = "P" THEN GOSUB PrintData

IF MS = "p" THEN GOSUB PrintData

"M" THEN GOSUB StageMove

"m" THEN GOSUB StageMove

are
5
II II

297
GOTO InLoop
RETURN

DataEntry:
CLS
INPUT "Fiber name ", Fiber$
INPUT "Fiber diameter (microns) ", Diameter
INPUT "Liquid name", Liquid$
INPUT "Liquid Surface Tension (mJ/M‘2) ", Elv
INPUT "Liquid temperature " , Temperature

RETURN

StageMove:
AS = "1": VS = ".5": D8 = "60000" ’Up 1/100 inch
CMD$="MNA"+A$+"V"+V$+"D"+D$+"G
"’Preset move
GOSUB CMDWriter
RETURN

Wilhelmy:
MoBeTime2& = 60 ’Seconds to complete stage moves
J =
Samples = 25
CLS
LINE (0, 200)-(640, 200), 1
LINE (0, 350)-(640, 350), 1
INPUT "Data file name ", Fil$
INPUT "Initial immersion distance (inches ) ", Immersion
IF Immersion > 1 THEN Immersion = 0
MoveTimel& = 60
DS = "-500000"

IF Immersion = 0 THEN DS = "0"

IF Immersion = .1 THEN DS = "-100000"
IF Immersion = .2 THEN DS = "-200000"
IF Immersion = .3 THEN DS = "-300000"
IF Immersion = .4 THEN DS = "400000"
IF Immersion = .5 THEN DS = "-500000"

A3 = "1”: VS = "l"
CMD$ = " MN A" + A8 + " V" + V$ + " D" + D8 + " G "’Preset move
GOSUB LogStart
GOSUB FindAverage
GOSUB CMDWriter
StartTime& = TIMER
Waiter: WHILE (TIMER - StartTime&) < MoveTimel&
GOTO Waiter
WEND
A5 = "1": VS = ".1": D3 = "-20000" ’Down 1/100 inch
CMDS = " MN A" + A5 + " V" + V$ + " D" + D3 + " G "’Preset move
FOR J = 1 TO 15
GOSUB CMDWriter
StartTime& = TIMER
Waiter2: WHILE (TIMER - StartTime&) < MoveTime2&

298

GOTO Waiter2

WEND

GOSUB LogStart

GOSUB FindAverage

NEXT J

AS = "1": VS = ".1": D5 = "60000" ’Up 1/100 inch

CMD$ = " MN A" + A5 + " V" + V$ + " D" + D$ + " G "’Preset move
FOR J = 16 TO 20
GOSUB CMDWriter
StartTime& = TIMER

Waiter3: WHILE (TIMER - StartTime&) < MoveTime2&
GOTO Waiter3

WEND

GOSUB LogStart

GOSUB FindAverage

NEXT J

GOSUB Calculations

CMDS = " S "

GOSUB CMDWriter

TIMER OFF

GOSUB FileSave

GOSUB MenuRefresh
RETURN

FindAverage:
Sum = 0
FOR K = I TO Samples
Sum = Sum + Mass(J, K)
NEXT K
AveMass(J) = Sum / Samples
Sum = 0
FOR K = I TO Samples
Sum = Sum + (AveMass(J) - Mass(J, K)) A 2
NEXT K
Sum = Sum / Samples
Deviation(J) = SQR(Sum)
RETURN

Calculations:

FOR J = 0 TO 20
Force = 9.807 * AveMass(J) / 1000000
Perimeter = Diameter * Pi / 1000000
Evig = Elv / 1000
CosTheta = Force / (Perimeter * Evig)
GOSUB ArcCosine
Angle(J) = 180 * ArcCos / Pi
NEXT J

RETURN

ArcCosine:

IF CosTheta < 0 THEN RETURN

ArcCos = -ATN(CosTheta / SQR(-CosTheta * CosTheta + 1)) + 1.5708
RETURN

299

LogStart:
K = 0
ON TIMER(1) GOSUB Logger
TIMER ON
x = INP(ADC) ’Starts first conversion
WHILE K < Samples + I
WEND
TIMER OFF
RETURN

Logger:

K = K + 1

GOSUB ReadVolts

LOCATE 5, 1

PRINT Count, Coun12, Volts, Mass(J, K)

Graph = Volts * 10000

IFJ < 11 THEN PSET (J * (Samples + 5) + K, 200 -
Graph), 1

IF I > 10 THEN PSET ((J - 11) * (Samples + 5) + K, 350 - Graph), 1
RETURN

ReadVolts:
Sum = 0

FOR N = 1 TO 100
Count = INP(ADC + I)
Count2 = INP(ADC)
Sum = Sum + Count * 256 + Coun12
NEXT N
Ave = Sum / 100
Volts = (Ave - 32768!) * .0001522588# - VoltsO
Mass(J, K) = Volts * VtoMFactor

RETURN
SetZero:
Sum = 0
FOR N = 1 TO 5000
x = INP(ADC)

Count = INP(ADC + 1)
Count2 = INP(ADC)

Sum = Sum + Count * 256 + Count2

NEXT N

Ave = Sum / 5000

VoltsO = (Ave - 32768!) * .0001522588#’Scale in
volts

PRINT VoltsO

RETURN

SetMass:
CLS
PRINT "Remove calibration weight and hook"
INPUT "Hit RETURN when ready to zero", F
GOSUB SetZero
PRINT "Apply calibration weight to pan B"

300

INPUT "Calibration weight (milligrams) ", CalibWeight
INPUT "Hit RETURN when ready to calibrate", F

Sum = 0
FOR N = 1 TO 5000
x = INP(ADC)

Count = INP(ADC + l)
Count2 = INP(ADC)
Sum = Sum + Count * 256 + Coun12
NEXT N
Ave = Sum / 5000
VoltsM = (Ave - 32768!) * .0001522588#’Scale in volts
DeltaV = VoltsM - VoltsO
VtoMFactor = (CalibWeight / 5) / DeltaV
PRINT "Voltage with Calibration Mass = "; VoltsM
PRINT "Volts to Milligrams Factor = "; VtoMFactor
OPEN "Calibrat.ion" FOR OUTPUT AS 1
WRITE #1, Volts0, VoltsM, VtoMFactor
CLOSE #1
RETURN

LoadCalib:
OPEN "Calibrat.ion" FOR INPUT AS 1
INPUT #1, Volts0, VoltsM, VtoMFactor
CLOSE #1
PRINT VoltsO, VoltsM, VtoMFactor
RETURN

PrintData:
LPRINT Fil$
LPRINT "Fiber Liquid E (1v) Diameter
Temperature"
LPRINT Fiber$, Liquid$, Elv, Diameter, Temperature
LPRINT " J Mass (mg) Angle"
FOR J = 1 TO 20
LPRINT USING " ###.#### "; J; AveMass(J), Angle(J)
NEXT J
RETURN

Initialize:
SCREEN ll
WIDTH 80, 60
ADC = 797 ’A/D Converter IBM bus location
Status = ADC - 1 ’Digital Input bus location
Channel = 0 ’Specify ADC channel
OUT ADC, Channel * 16’ Select channel
Pi = 3.14159
Q = 1: REM number of thermometers - 1
6(0) = .8: 6(1) = .8: K(0) = 11.4: K(1) = 11.4’Thermocouple calibrations
Interval = 1 ’Seconds between weight samples
NormalMove$ = " MN "
AltMove$ = " MA "
ConMoveS = " MC "
ImpMs = M L"

301

TDelayS = " T"
EndLoopS = " N "
VelS = " V"

ACC$ = II A"
DestS = " D"

GO$ = n G N
CeaseS = " S "
ReverseS = " H"

AS = ".1": VS = ".2": DS = "50000": HS = "+": LS = "1":TS = "0"
MoveS = AltMoveS: LpMS = LoopMS: TDelS = TDelayS: EndeS = EndLoopS
GOSUB SetCMD
SlowLoopS = CMDS
WilhelmyCMDS = CMDS

vs = ".4"

GOSUB SetCMD

MedLoopS = CMDS

vs = "1”

GOSUB SetCMD
FastLoopS = CMDS
MogeS = NormalMoveS: LpMS = "": TDelS = "": TS = "":EndeS = ""

V = ".1"

GOSUB SetCMD

UpSlowS = CMDS

VS = ".4"
GOSUB SetCMD
UpMedS = CMDS
VS = "l"
GOSUB SetCMD
UpFastS = CMDS
AS = "1": VS = ".1": DS = "-20000"
StepDownS = " MN A" + AS + " V" + VS + " D" + D$ + " G "’Preset move
RETURN

 

SetCMD:

CMDS = MoveS + AccS + AS + VelS + VS + ReverseS + HS +
DestS + DS + LpMS + LS + TDelS + TS + EndeS + GoS
RETURN

Reminders:

REM AS = Acceleration Rev/Sec Sec, VS = Velocity Rev/Sec

REM HS = Direction "+" or "-" DS = Distance/ motor steps 25000/rev

REM LS = Number of Loop moves, TS = Time of delay between loops

REM CMDS=" MC A"+AS+" V"+VS+" H"+HS+" G " ’Continuous move
REM CMDS=" S " ’Stop

REM CMDS=" MN A"+AS+" V"+VS+" D"+HS+DS+" G " ’Preset move
REM CMDS=" MA A"+AS+" V"+VS+" D"+HS+DS+" G " ’Altemating
move

REM CMDS=" MN A"+AS+" V"+VS+" D"+HS+DS+" L"+LS+" G " ’Loop
- Function

R_EM CMDS=CMDS+"T”+TS+" N " ELSE CMDS=CMDS+" N " ’Loop w
delay

RETURN

302

Helper:

CLS

PRINT "The Lord Helps Those That Helps Themselves"
RETURN

DriveParameters:
CLS
PRINT " Daedal Drive Programming"
PRINT
PRINT "Velocity (RPS) = "; VS
PRINT " Acceleration (RPS‘2) = "; AS
PRINT "Distance (25000/Rev) = "; DS

PRINT "Looping ";
IF Looping THEN PRINT ”ON” ELSE PRINT ”OFF”
IF Looping THEN PRINT "Number of Loops = "; LS
IF MoveS = NormalMoveS THEN PRINT "Normal Move Mode"
IF MoveS = AltMoveS THEN PRINT "Alternating Move Mode"
IF MoveS = ConMoveS THEN PRINT "Continuous Move Mode"
PRINT "Direction = "; HS

RETURN

DriveProgram:
CMDLS = CMDS
GOSUB DriveParameters
MoveLS = MoveS: VLS = VS: ALS = AS: DLS = DS: HLS = HS
PRINT "Enter new values or hit RETURN"
PRINT
INPUT "New Velocity " , VS
IF VS = "" THEN VS = VLS
INPUT "Distance (with + or - ", DS
IF DS = "" THEN DS = DLS
INPUT "Acceleration ", AS
IF AS = "" THEN AS = ALS
INPUT "Looping? Y/N ", LPS
LpM$ = H": TDel$ = II": Ende$ = II"
IF LPS = "Y" OR LPS = "y" THEN
INPUT "Number of Loops ", LS
LpMS = LoopMS: TDelS = TDelayS: EndeS = EndLoopS
END IF
GOSUB SetCMD
INPUT "Make this the Wilhelmy Cycle? Y/N ", WilecS
IF WilecS = "Y" THEN WilhelmyCMDS = CMDS
IF WiICycS = "y" THEN WilhelmyCMDS = CMDS
GOSUB MenuRefresh
RETURN

FileSave:
OPEN FilS FOR OUTPUT AS 1
WRITE #1, FilS
WRITE #1 , VoltsO, VoltsM, CalibWeight, VtoMFactor
WRITE #1 , FiberS, LiquidS, Elv, Diameter, Temperature
WRITE #1, Samples

303

FOR J = 0 TO 20
WRITE #1, J, Angle(J), Energy(J), AveMass(J),
Deviation(J)
NEXT J
FOR J = 0 TO 20
FOR I = 1 TO Samples
WRITE #1, Mass(J, 1)
NEXT I
NEXT J
CLOSE #1
RETURN

ReadFile:
INPUT "File Name ", FilS
OPEN FilS FOR INPUT AS 1
INPUT #1, FiIS
INPUT #1, VoltsO, VoltsM, CalibWeight, VtoMFactor
INPUT #1, FiberS, LiquidS, Elv, Diameter, Temperature
INPUT #1, Samples
FOR J = 0 TO 20
INPUT #1, J, Angle(J), Energy(J), AveMass(J),
Deviation(J)
NEXT J
FOR J = 0 TO 20
FOR I = 1 TO Samples
INPUT #1, Mass(J, 1)
NEXT I
NEXT J
CLOSE #1
RETURN

Stoppit:
CMDS = " S "
GOSUB CMDWriter
RETURN

Reader: REM + + + + + + = = = =Transfer from PC21 to IBM bus, 1
character at a time

BYTE = INP(ADDRESS% + 1)

IF MESSAGE AND NOT BYTE THEN RETURN

answer = INP(ADDRESS%)

OUT ADDRESS% + 1, (CONTROL OR RECEIVED)
MessByte: BYTE = INP(ADDRESS% + 1)

IF MESSAGE AND BYTE THEN GOTO MessByte

OUT ADDRESS% + I, (CONTROL AND NOT RECEIVED)
CHARS = CHRS(answer)

answerS = answerS + CHARS

IF CHARS = CHRS(I3) THEN RETURN ELSE GOTO Reader
RETURN

CMDWriter: ’Sends instructions to PC21 1 character at a
time
FOR I = 1 TO LEN(CMDS)

304

CHARS = MIDS(CMDS, I, 1)
GOSUB Transmitter
NEXT 1

CHARS = CHRS(13)

GOSUB Transmitter

RETURN

Transmitter:

BYTE = INP(ADDRESS% + 1)

IF IDBREADY AND NOT BYTE THEN GOTO Transmitter
OUT ADDRESS%, ASC(CHARS)

OUT ADDRESS% + 1, (CONTROL OR IDBREADY)
IDByte: BYTE = INP(ADDRESS% + 1)

IF IDBREADY AND BYTE THEN GOTO IDByte

OUT ADDRESS% + 1, (CONTROL AND NOT IDBREADY)
RETURN

InitializePC2I :
ADDRESS% = 768 ’ PC21 IBM bus address
CONTROL = 96 ’This is the normal state of the Control Byte
STOPPED = 2 ’ (is the motor moving)
CRASH = 4 ’ Control Bit 2
LOADRDY = 4 ’ Status Bit 2
INTACK = 8 ’Control Bit 3
MESSAGE = 8 ’Status Bit 3
IDBREADY = 16 ’Control Bit 4
FAULT = 32 ’Control Bit 5
INTERRUPT = 64 ’ Control Bit 6
RECEIVED = 128 ’ Control Bit 7
OUT ADDRESS% + 1, (CONTROL OR CRASH) ’Control Bit 2 high
OUT ADDRESS% + l, (CONTROL AND NOT CRASH) ’Control Bit 2 low
FOR Y = 1 TO 1000
NEXT ’wait for BMA
OUT ADDRESS% + l, (CONTROL AND NOT FAULT) ’Control Bit 5 low
OUT ADDRESS% + 1, (CONTROL OR FAULT) ’Control Bit 5 high
RETURN

ReadStatus:

IF INP(Status) AND 128 THEN DigInp = I ELSE DigInp = 0
’For digital Input
RETURN

ReadTemp: ’For Cole Parmer Model 203 with 134 ADC
OUT ADC, 0
FOR J = 0 TO NThermometers
FOR N = 0 TO 7
GOSUB ReadVolt
V(N) = V
NEXT N
C = (V(3) - V(0)) / K(J) - 273
FOR N = I TO 7
IF N = 3 THEN GOTO NextN

305

V = (V(N) - V(0)) * (3(1)
GOSUB LinearizeE
LOCATE 10, I
PRINT "Thermometer #"; J, "T.C. #"; N -INT(N/ 3) + INT(N / 6)
PRINT USING "####.#"; T;
NextN: NEXT N
NEXT J
RETURN

ReadVolt:
OUT ADC, J * 16 + N ’Select Channel
x = INP(ADC) ’Start conversion
TOT = 0
AVERAGE = 10 ’Set average larger for smoother data
FOR x = 1 TO AVERAGE
TOT = TOT + INP(ADC + 1) * 256 + INP(ADC)
NEXT x
TOT = TOT / AVERAGE
V = (TOT - 32768!) * .152588
RETURN

LinearizeE:
V = V + C * 6.1

IF V < 366 THEN T = V / 6.1: RETURN

IFV < 836THENT = 60 + (V-366)/6.72: RETURN

IF V < 1487 THEN T = 130 + (V - 836) / 7.223: RETURN
IF V < 2494 THEN T = 220 + (V - 1487) / 7.74: RETURN
IF V < 5633 THEN T = 350 + (V - 2494) / 8.049: RETURN
IF V < 6878 THEN T = 740 + (V - 5633) / 7.785: RETURN

T = 900 + (V - 6878) / 7.6: RETURN

LinearizeJ:
V = V + C * 5.2
IFV < 411 THENT = V/5.2: RETURN
[F V < 2738 THEN T 79 + (V - 411) / 5.527: RETURN
IF V < 3367 THEN T 500 + (V - 2738) / 5.72: RETURN
IF V < 3911 THEN T — 610 + (V - 3367) / 6.05: RETURN
T = 700 + (V - 3911) / 6.33: RETURN

306

The following list describes the functions of the subroutines in the Wilhelmy balance
data analysis program written in AmigaBasic.

Main: Main program loop.

Start: Program "sleeps" here until called by user’s menu interrupt.
Libs: Loads libraries of system calls.

ArrayDimensions: Defines all data arrays and allocates space to them.
ScreenSetup: Sets up screen, window, and pallettes.

Initialize: Initializes all constants.

InitializeMenu: Initializes the menu selections.

CheckMenu: Arrival point when user makes a menu selection. Finds column and
routes to submenus.

Filemenu: Checks first column of menu items and routes to appropriate subroutine.
Calcs: Checks second column of menu items and routes to appropriate subroutine.
Graph: Checks third column of menu items and routes to appropriate subroutine.
NSamples: Inputs the number of samples.

GraphData: Produces a graph of force data.

DataEntry: Inputs data on fiber designation and diameter.

Calculations: Calculates contact angles from force and perimeter.

WriteFile: Writes out data files.

ReadFile: Reads in data files.

Palet: Sets the screen pallettes.

Dir: Diplays the directory of the current directory.

DirO: Displays directory of drive df0:.

Dirl: Displays directory of drive dfl:.

Cleanup: Clears the screen.

FindAverage: Finds average and standard deviation of a set of data points.

Quit: Closes libraries, resets menu, ends program operation.

WriteImage: Saves screen image to disk file.

307

EnterImageName: Inputs file name for saving image of graphed data.
WILHELMY BALANCE DATA ANALYSIS PROGRAM SOURCE CODE

REM = = = Wilhelmy Balance Calculations Program

REM = = = Copyright April 10, 1989 Mark Waterbury, for the
REM Composite Materials and Structures Center

REM Michigan State University

GOSUB ScreenSetup

CLEAR ,25000& ’clears basic stack

CLEAR ,50000& ’clears data memory space

DEFINT 1,] ,k ’defines these variables as integers

Main:

GOSUB Libs ’Initializes Amiga LIBRARYs and FUNCTIONS
GOSUB ArrayDimensions ’Sets sizes of array variables
GOSUB Initialize ’Sets Graphics and other constants

GOSUB InitializeMenu ’Sets screen menu system

Start:
CLS
ON MENU GOSUB CheckMenu : MENU ON
Unfinished = -1
WHILE Unfinished
SLEEP ’ event driven
WEND

Libs:
DECLARE FUNCTION xOpen& LIBRARY
DECLARE FUNCTION xRead& LIBRARY
DECLARE FUNCTION xWrite& LIBRARY
DECLARE FUNCTION AllocMem&O LIBRARY
LIBRARY "dos.library"
LIBRARY "exec.library"
LIBRARY "graphics.library"

ArrayDimensions:
DIM Mass(20, 100), AveMass(20), Deviation(20), Angle(20), Energy(20)
DIM BPlaneSI&(S),BPIaneLI&(5) ’For picture Loader and Saver

DIM cTab%(32)

RETURN

ScreenSetup:
SMode = 4: Depth = 4: WMode = 0
WindowTitleS = " "
ScreenX = 640:ScreenY = 400
SCREEN l,ScreenX,ScreenY,Depth,SMode
WINDOW 1,WindowTitleS, ,WMode, l
RETURN

Initialize:
GOSUB Palet

308

COLOR 10,0
Samples = 10
RETURN

InitializeMenu:
MENU 1,0,1,"File"
MENU l,l,l,"Directory"
MENU 1,2,1,"Directory of drive 0"
MENU 1,3,1,"Directory of drive 1"
MENU 1,4,1,"Read File"
MENU 1,5,1,"Write File
MENU 1,6,1,"Read image"
MENU 1,7,1,"Write image"
MENU 1,8,1,"Write Image Name"
MENU I,9,1,"Quit"
MENU 2,0,1,"Calcs"
MENU 2,1,1,"Number of Samples"
MENU 3,0,1,"Graph"
MENU 3,1,1,"Graph Data"
MENU 3 ,2 , 1, "Palet Reset "
MENU 3,3,1,"Clear Screen"
RETURN

CheckMenu:

MenuId = MENU(0)

Menultem = MENU(1)

ON Menuld GOSUB Filemenu,Calcs,Graph,Batch,Dist
RETURN

Filemenu:
ONMenuItemGOSUBDir
,Dir0,Dirl ,ReadFile,WriteFile,ReadImage,WriteImage,EnterImageName,Quit
RETURN
Calcs:
ON MenuItem GOSUB NSamples,CalcuIations
RETURN
Graph:
ON Menultem GOSUB GraphData,Palet,Cleanup
RETURN

NSamples:
INPUT "Number of samples per set ",Samples
RETURN

GraphData:
LINE (0,200)-(640,200),l
FOR J = 0 TO 20
FOR I = I TO Samples
PSET (J * (Samples + 5) + 1,200 - Mass(J,I) * 500),1
NEXT 1
NEXT J
RETURN

309

DataEntry:
CLS
INPUT "Fiber name ", FiberS
INPUT "Fiber diameter (microns) ", Diameter
INPUT "Liquid name", MatrixS
INPUT "Liquid Surface Tension (mJ/M‘2) ", Elv
INPUT "Liquid temperature " , Temperature

RETURN

Calculations:

FOR J = 0 TO 20
Newtons = 9.807 * AveMass(J) / 100000081
Perimeter# = Diameter * Pi / 1000000&
NEXT J

RETURN

WriteFile:
INPUT "File Name ",FilS
OPEN FiIS FOR OUTPUT AS 1
WRITE #1, F113
WRITE #1, VoltsO, VoltsM, CalibWeight, VtoMFactor
WRITE #1 , FiberS, LiquidS,Elv, Diameter, Temperature
WRITE #1, Samples
FOR J = 0 TO 20
WRITE #1, J, Angle(J), Energy(J), AveMass(J),Deviation(J)
NEXT J
FOR J = 0 TO 20
FOR I = 1 TO Samples
WRITE #1, Mass(J, 1)
NEXT 1
NEXT J
CLOSE #1
RETURN

ReadFile:
INPUT "Change Sign? 1/0 ",ChangeSign
INPUT "File name ",FilS
OPEN FilS FOR INPUT AS 1
INPUT #1, FilS
INPUT #1, VoltsO, VoltsM, CalibWeight, VtoMFactor
INPUT #1 , FiberS, LiquidS, Elv, Diameter, Temperature
INPUT #1, Samples
FOR J = 0 TO 20
INPUT #1, J, Angle(J), Energy(J), AveMass(J),Deviation(J)
NEXT J
FOR J = 0 TO 20
FOR I = 1 TO Samples
INPUT #1, Mass(J, 1)
IF ChangeSign THEN Mass(J,I) = -Mass(J,I)
NEXT 1
NEXT J
CLOSE #1

 

310
RETURN

Palet:
FOR I = 2 TO 9
PALETTE I,I/9,I/9,I/9
NEXT 1
PALETTE 10,1,1/2,0
PALETTE 11 1,0,
PALETTE 12,0,1,
PALETTE 13,1,1,
PALETTE 14,0,1,
PALETTE 15,0,0,
PALETTE 0,1,1,l
PALETTE 1,0,0,0

RETURN

‘

p.001—1—

Dir:
FILES
RETURN

Dir0:
FILES "dfO: "
RETURN

Dirl:
FILES "dfl : "
RETURN

Cleanup:
CLS
RETURN

FindAverage:
Sum = 0
FOR k = 1 TO Samples
Sum = Sum + Mass(J, k)
NEXT k
AveMass(J) = Sum / Samples
Sum = 0
FOR k = 1 TO Samples
Sum = Sum + (AveMass(J) - Mass(J, k)) A 2
NEXT k
Sum = Sum / Samples
Deviation(J) = SQR(Sum)
RETURN

Quit:
MENU RESET
LIBRARY CLOSE
STOP

ReadImage:

311

INPUT "Enter file name ",PicNameLIS
PictureLI PicNameLIS

FilS = PicNameLIS

FilMenS = "File Name " + FilS
GOSUB GetAddrs

GOSUB Paletl

NFibers = 0

RETURN

GetAddrs:
sWindow& = W1NDOW(7)
sScreen& = PEEKL(sWindow& + 46)
sViewPort& = sScreen& + 44
sRastPort& = sScreen& + 84
sCoIorMap& = PEEKL(sViewPort& + 4)
colorTab& = PEEKL(sColorMap& + 4)
sBitMap& = PEEKL(sRastPort& + 4)
schepth% = PEEK(sBitMap& + 5)
nColors% = 2‘schepth%
FOR kk = 0 TO nColors% -1
cTab%(kk) = PEEKW(colorTab&+(kk*2))
CMap%(kk) = 1NT(cTab%(kk)/256)
NEXT

RETURN

WriteImage:
PictureSI WritePicNameS
RETURN

EnterImageName:
LOCATE 24,1: INPUT "Image Name ",WritePicNameS
RETURN

BIBLIOGRAPHY

BIBLIOGRAPHY

Ashbee, K.H.G. , Ashbee, E. , Photoelastic Study of Epoxy Resin/ Graphite Fiber Load
Transfer, J. of Composite Mat., 22, Jul. 1988, pp. 602-615.

Asloun, E1. M., Donnet, J.B., Guilpain, G., Nardin, M., Schultz, J., On the
Estimation of the Tensile Strength of Carbon Fibers at Short Lengths, J. of Materials
Science, 24, 1989, pp. 3504-3510.

ASTM D 3171 - 76, ASTM Standards and Literature References for Composite
Materials, 1987 (A), pp. 169-172.

ASTM E 562 - 83, ASTM Standards and Literature References for Composite
Materials, 1987 (B), pp. 511-517.

Atkinson, C. , On Stress Singularities and Interfaces in Linear Elastic Fracture
Mechanics, Int. J. of Fracture, 13, Dec. 1977, pp. 807-820.

Bailey, J.B., Parvizi, A., On Fibre Debonding Effects and the Mechanism of
Transverse-Ply failure in Cross-Ply Laminates of Glass Fibre/Thermoset Composites,
J. Mat. Science, 16, Jan. 1981, pp. 649-659.

Bascom, W.D. , Boll, D.J., Fuller, B., Phillips, P.J., Fractography of the Interlaminar
Fracture of Carbon-Fibre Epoxy Composites, J. Mater. Sc1., 20, 1985, 3184.

Bascom, W.D., Gweon, S.Y., Fractography and Failure Mechanisms of Carbon
Fiber-Reinforced Composite Materials, in Fractography and Failure Mechanisms of
Polymers and Composites, Elsevier, 1989, pp. 351-385.

Bascom, W.D., Jensen, R.M., Stress Transfer in Single Fiber/Resin Tensile Tests,
J. Adhesion, 19, Jan. 1986, pp. 219-239.

Bascom, W.D., Interfacial Adhesion of Carbon Fibers, NASA CR-178306, Aug.
1987.

Bascom, W.D., NASA Report No. CR-178306, Aug. 1987.

Bascom, W.D., Yon, K-J., Jensen, R.M., Cordner, L., The Adhesion of Carbon
Fibers to Thermoset and Thermoplastic Polymers, J. Adhesion, 34, 1991, pp. 79-98.

Binbergen, F.L. , Natural and Artificial Heterogeneous Nucleation in Polymer
Crystallization, J. of Polymer Science Symposium, 59, 1977, pp. 11-29.

312

313

Brady, R.L., Porter, R.S., Interfacial Crystallization and Adsorption in
Polycarbonate/Carbon Fiber Composites, J. Thermo. Comp. Mat, 2, Jul. 1989, pp.
164-171.

Broutman, L.J. , Measurement of the Fiber-Polymer Matrix Interfacial Strength,
ASTM STP 452, Jan. 1969, pp. 27-41.

Cantwell, W.J., Roulin-Moloney, A.C., Fractography and Failure Mechanisms of
Unfilled and Particulate Filled Epoxy Resins, in Fractograph and Failure Mechanisms
of Polymers and Composites, Elsevier, 1989, 233-290.

Cebe, P. , Hong, S. , Crystallization Behaviour of Poly(ether-ether-ketone), Polymer,
27, Aug. 1986, pp. 1183-1192.

Chai, H., Interlaminar Shear Fracture of Laminated Composites,, Int. J. of Fracture,
43, 1990, pp. 117-131.

Cilley E., Roylance D., Schneider N., Composite Materials, Testing and Design
(Third Conference), ASTM STP 546, 1974, pp. 237-249.

Cooke, T.F., High Performance Fiber Composites With Special Emphasis on the
Interface, J. Polymer Eng., 7, (3), Jan. 1987, pp. 197-254.

Crasto, A.S., Corey, R., Dickinson, J.T., Subramanian, R.V., Eckstein, Y.,
Correlation of Photon and Acoustic Emission with Failure Events in Model
Composites, Comp. Sci. Tech., 30, 1987, pp. 35-58.

Crosby, J .M., Drye, T.R., Fracture Studies of Discontinuous Fiber Reinforced
Thermoplastic Composites, J. Reinforced Plastics, 6, Apr. 1987, pp. 162-169.

Curtin, W.A. , Fiber Fragmentation in a Single-Filament Composite, Physical Review
Lett, (In press).

Curtis, RT. , An Investigation of the Mechanical Properties of Improved Carbon Fibre
Composites Materials, J. of Composite Materials, 21, Dec. 1987, pp. 1118-1144.

Dave, R., Lorenzo, L., A Note on Polymeric Inner-Layered Single Fiber Interfacial
Strength Determination,Polymer Composites, 10, (3), Jun. 1989, pp. 199-201.

Denison, P., Jones, F.R, Watts, J .F ., A Quantification and Investigation of Surface
Micro-porosity in Carbon-Fibres Using Labelling and XPS, Surface Interface
Analysrs, 12, 1988, pp. 455-460.

Deslandes, Y., Day, M., Sabir, N .-F., Suprunchuk, T., Crystallization of Poly(Aryl-
Ether-Ether-Ketone): Effect of Thermal History of the Melt on Crystallization
Kinetics, Polymer Composites, 10, (5), Oct. 1989, pp. 360-366.

Di Landro L. , Pegoraro M. , Carbon Fiber Thermoplastic Matrix Adhesion, J. of
Materials Science, 22, 1987, pp. 1980-1986.

Dilangro, L., Dibenedetto, A.T., Groeger, J ., The Effect of Fiber-Matrix Stress
Transfer on the Strength of Fiber-Reinforced Composite Materials, Polymer
Composites, 9, (3), Jun. 1988, pp. 209-221.

314
DeBenedetto, A.T., Nicolais, L., Plast, 10, (5), 1979, p. 83.

DiBenedetto, Evaluation of Fiber Surface Treatments in Composite Materials, Pure
& Appl. Chem. 57, (11), 1985, pp. 1659-1665.

DiBenedetto A.T, Nicolais L. , Ambrosio L. , Groeger J. , Stress Transfer and Fracture
in Single Fiber/Epoxy Composites, ICCI 1, Jul. 1986, pp. 47-54.

Drzal, L.T., Rich, M.J., Camping, J .D., Park, W.J., Interfacial Shear Strength and
Failure Mechanisms in Graphite Fiber Composites, Reinforced Plastics/Composites
Institute Proc. 1980 (A), Sect. 20-C, pp. 1-7.

Drzal, L. T., Rich, M. J., Camping, J. P., Park, W. J., "A Single Filament
Technique for Determining Interfacial Shear Strength and Failure Mode in Composite
Materials", Procwdings of 1980 Conference, Reinforced Plastics and Composites
Institute, SPI, Paper 20C, 1980 (B).

Drzal, L.T. , Hammer, G.E. , Graphite Fiber Surface Analysis by X-Ray Photoelectron
Spectroscopy an Polar/Dispersive Free Energy Analysrs, Applications of Surface
Science, 4, 1980, pp. 340-355.

Drzal L.T. , Rich, M.J . , Lloyd, P.F. , Adhesion of Graphite Fibers to Epoxy Matrices:
II. The Effect of Fiber Finish, J. Adhesion, 16, Jan. 1983, pp. 133-152.

Drzal, L.T. , Rich, M.J. , Lloyd, P.F. ,Adhesion of Graphite Fibers to Epoxy Matrices:
I. The Role of Fiber Surface Treatment, J. Adhesion, 16, Jan. 1982, pp. 1-30.

Drzal, L.T., Rich, M.J., Progress report, "Improved Materials for Composite and
Adhesive Joints", period 9/1/81 - 8/31/82, Contract # F33615-81-C-5056, Dayton
Research Institute, U. Dayton Report # UDR-TR-82-118.

Farinato, R.S., Kaminski, S.S., Courter, J .L., Acid-Base Character of Carbon Fiber
Surfaces, J. Adh. Sci. Tech., 1990, (in press).

Favre J .P., Perrin J ., Carbon Fibre Adhesion to Organic Matrices, J. Mater. Sci., 7,
Jan. 1972, pp. 1113-1118.

Figueroa, J .C., Schadler, L.S., Campbell, L., Filament Fragmentation Phenomena,
Mat. Res. Soc. Symp. Proc., 170, 1990, pp. 65-70.

Folkes, M.J., Wong, W.K., Determination of Interfacial Shear Strength in Fibre-
Reinforced Thermoplastic Composites, Polymer, 28, Jul. 1987, pp. 1309-1314.

Fraser, W.A., Ancker, F.H., DiBenedetto, A.T., Elbirli, B., Evaluation of Surface
Treatments for Fibers in Composite Materials, Polymer Composites, 4, (4), 1983, pp.
238-248.

Galiotis, C., Melanitis, N ., Batchelder, D.N,Robinson, I.M., Residual Strain
Mapping in Carbon Fibre/PEEK Composites, Composites, I9, (4), July 1988, pp.
321-324.

315

Galiotis, C., Melanitis, N., Tetlow, P. L., and Davies, C. K. L., "Interfacial Shear
Stress Mapping in Model Composites," Technomic Publishing Co., E. Lansing, MI,
Jun. 1990, pp. 276-286.

Garton A., Stevenson W.T., Crosslinking of Epoxy Resins at Interfaces. IV.
Anhydride-Cured Resins at Carbon and Graphite Surfaces, J. of Polym. Sci: Pt. A,
26, Jan. 1981, pp. 541-557.

Gaur, U. , Desio, G. , Miller, B. , Measuring Fiber/ Matrix Adhesion in Thermoplastics
Composites, Plastics Engineering, Oct. 1989, pp. 43-45.

GE, Lexan Polycarbonate Resin Properties Guide, GE Plastics, 1988.

Golovoy, A. , Zinbo, M. , Water Sorption and Hydrolytic Stability of Polycarbonates,
Polymer Eng. and Science, 29, (24), Dec. 1989, pp. 1733-1737.

Griffith, A.A., Phil. Trans. R. 800., A221, 1921, p. 163.
Griffith, A.A., Proc. 1st Int. Congr. Appl. Math., Delft, Holland, 1924, p. 55.

Gutowski, W. , Physico—Chemical Criteria for Maximum Adhesion. Part I:

'2I'3e09retical Concepts and Experimental Evidence, J. Adhesion, 19, Jan. 1985, pp.
-4 .

Hamstad M.A., Moore R.L. , Acoustic Emission from Single and Multiple Kevlar 49
Filament Breaks, J. Comp. Mater., 20, Jan. 1986, pp. 46-66.

Henstenburg, R.B., Phoenix, S.L., Interfacial Shear Strength Studies Using the
Single-Filament-Composite Test. Part II: A Probability Model and Monte Carlo
Simulation, Polymer Composites, 10, (5), Dec 1989, pp. 389-408.

Hibbs, M.F. , Bradley, W.L. , Correlations Between Micromechanical Failure
Processes and the Delamination Toughness of Graphite/Epoxy Systems, ASTM STP
948, 1987, p. 389.

Hinkley, J.A., Bascom, W.D., Allred, R.E., Interlaminar Fracture in Carbon
Fiber/Thermoplastic Composites, Mat. Res. Soc. Symp., 170, Jan. 1990, pp.
351-356.

Hodge, D.J., Middlemiss, B.A, Peacock, J .A., Correlation Between Fibre Surface
Energetics and Fibre-Matrix Adhesion in Carbon Fibre Reinforced PEEK Composite,
Mat. Res. Symp. Proc, 170, Jan. 1990, pp. 327-339.

Hoffman, W.P., Elings V.B., Gurley J .A., Scanning Tunneling Microscopy on
Carbon Fibers, Carbon, 26, Jul. 1988, pp. 754-757.

Hooke, K.J., Agrawal, R.K., Drzal, L.T., J. of Adhesion, 32, 1990, pp. 157-170.

Hsiao, B.S., Chen, E.J.H., Study of Transcrystallization in Polymer Composites,
Mat. Res. Symp. Proc, 170, Jan. 1990, pp. 117-121.

Hughes, J .D.H. , The Carbon Fibre/Epoxy Interface - A Review, Composites Science
and Technology, 41, 1991, pp. 13-45.

316

Ishitani A. , Application of X-Ray PhotoElectron Spectroscopy to Surface Analysis of
Carbon Fiber, Carbon, 19, (4), 1981, pp. 261-275.

Ismail M.K., Structure and Active Surface Area of Carbon Fibers, Carbon, 25, (5),
1987, pp. 653-662.

Jang, B., Lin, C.W., Wang, C.Z., Shih, W.K., Mechanical Properties and
Morphology of Crystalline Polymers and Their Continuous Fiber Composites, J. of
Thermoplastic Composite Materials, 1, Jul. 1988, pp. 242-275.

Jaworske, D.A., Gaier, J.R., Hung, C.C., Banks, B.A., Properties and Potential
App6lications of Brominated P-100 Carbon Fibers, SAMPE Quarterly, 18, (1), Oct.
198 , pp. 9-14.

Jaworske, D.A., Maciag, C., Improving the Interlaminar Shear Strength of Carbon
Fiber-Epoxy Composites Through Carbon Fiber Bromination, Nasa Tech. Mem.
100248, Dec 1987.

J eronimidis, G. ,Parkyn, A.T. , Residual Stresses in Carbon Fibre-Thermoplastic
Matrix Laminates, J. Comp. Mats., 22, May 1988, pp. 401-415.

Jock, C.P. , Quantitative Optical Microscopy Fiber Volume Methods for Composites,
J. Reinf. Plast. and Comps, 5, Apr. 1986, pp. 110-119.

Johannesson, T. , Sjoblom, P, Selden, R. , The Detailed Structure of Delamination
Fracture Surfaces in Graphite/Epoxy laminates, J. Mat. Science, 19, Jan. 1984, pp.
1171-1177.

Kardos J .L., Regulating the Interface in Graphite/Thermoplastic Composites, J.
Adhesion, 5, 1973, pp. 119-138.

Katagiri, G., Ishida, Hid., Ishitani, A.,,Raman Spectra of Graphite Edge Planes,
Carbon, 26, 4, Jan. 1988, pp. 565-571.

Kavanagh, A. , Schlogl R. , The Morphology of Some Natural and Synthetic Graphites,
Carbon, 26, 1, Jan. 1988, pp. 23-32.

Keith H.D., Padden P.J., A Discussion of Spherulitic Crystallization and Spherulitic
Morphology in High Polymers, Polymer, 27, Jan. 1986, pp. 1463-1471.

Keller, A., Polymer Crystallization: A Survey and Salient Current Issues, J. Poly.
Sci. P. Sym,59, Jan 1977, pp. 1-10.

Kelley, A., Tyson, W.R., J. Mech. Phy. Solids, 13, 1965, p. 329.
Kelley, A., Macmillan, N.H., Strong Solids, Clarendon Press, 1986.

Kinloch, A.J., Kodokian, G.K.A., On the Calculation of Dispersion and Polar Force
Components of the Surface Free Energy, J. Adhesion, 34, 1991, pp. 41-44.

Kolle, J .J ., Lin, K.Y., Mueller, A.C., A Micro/Macro Approach to Fracture in
Composites, Polymer Composites, 11, (6), 1990, pp. 314-321.

317

Kumamaru, P., Oono, T., Kajiyama, T., Suehiro, K., Takayanagi, M., Epitaxial
Crystallization of Nylon 6 Cast from Solution on the Surface of Poly(p-phenylene
Terephthalamide Filament, Polymer Composites, 4, (2), Apr. 1983 (A), pp. 135-140.

Kumamaru, F. Oono, T., Kajiyama, T., Takayanagi, M., Interfacial Interaction
between Poly(p-phenylene Terephthalamide) Filament and Nylon 6 Matrix Crystallized
from the Melt, Polymer Composites, 4, (2), April, 1983 (B), pp. 141-148.

Lauke B. , W. Pompe, Relation Between Work of Fracture and Fracture Toughness
of Short-Fibre Reinforced Polymers, Comp. Sci. Tech., 31, Jan. 1988, pp. 25-33.

Lee W.I., Talbott M.F., Springer G.S., Berglund, L.A., Effects of Cooling Rate on
the Crystallinity and Mechanical Properties of Thermoplastic Composites, J. of Reinf.
Plastics and Comps., 6, Jan. 1987, pp. 2-12.

Lee Y. , Porter R.S . , Crystallization of Poly(etheretherketone) (PEEK) in Carbon
Fiber Composites, Polym. Eng. Sci., 26, (9), May 1986, pp. 633-639.

Lee, R.N., Carbon-Fiber Surface Properties, Encyc. of Composites, In Press.

Lhymn, C., Schultz, J .M., Strength and Toughness of Fibre-Reinforced

Thermoplastics: Effect of Temperature and Loading Rate, Composites, 18, (4), Sep
1987, pp. 287-292.

Li S.K., Smith R.P., Neumann A.W. Wilhelmy Technique and Solidification Front
Technique to Study the Wettability of Fibres, J. Adhesion, 17, 1984, pp. 105—122.

Ma, B.T. Schadler, L.S., Laird, C., Figueroa, J.C., Acoustic Emission in Single
Filament Carbon/Polycarbonate and Kevlar/ Polycarbonate Composites Under Tensile
Deformation, Polymer Composites, 11, (4), Aug. 1990, pp. 211-216.

Maekawa, Z., Hamada, H., Yoshioka, 8., Fiber Fragment Distribution in Embedded
Single Filament Test, ICCI 11, Jun. 1988, pp. 553-565.

Mahishi J .M. , An Integrated Michromechanical and Macromechanical Approach to
Fracture Behavior of Fiber-Reinforced Composites, Eng.Fracture Mech. , 25, (2), Jan.
1986, pp. 197-228.

Medellin-Rodrig, Phillips, P.J. , Crystallization and Structure-Mechanical Property
Relations in Poly(Aryl Ether Ether Ketone) [PEEK], Poly. Eng. and Sci., 30, (14),
Jul. 1990, pp. 860-889.

Medrano R.E, Gillis P.P., Weibull Statistics: Tensile and Bending Tests, J. Am.
Ceram. Soc., 70, (10), Oct. 1987, pp. 230-232.

Miller, B. ,Muri, P. ,Rebenfeld, L, A Microbond Method for Determination of the
Shear Strength of a Fiber/Resin Interface, Comp. Sci. Tech., 28, Jan. 1987, pp.
17-32.

Miller, A.G., Wingert, A.L., Fracture Surface Characterization of Commercial
Graphite/Epoxy Systems, Nondestructive Evaluation and Flaw Criticality for
Composite Materials, ASTM STP 696, 1979, pp. 223-273.

318

Moore, G.A. , Applications of Modern Metallographic Techniques, ASTM STP 480,
1970, pp. 3-48.

Morris, G.E. , Determining Fracture Directions and Fracture Origins on Failed
Graphite/Epoxy Surfaces, Nondestructive Evaluation and Flaw Criticality for
Composite Materials, ASTM STP 696, 1979, pp. 274-297.

Mossner, L.S., Grulke, E.A., Effects of Thermodynamic Models on the Predictions
of Free Volume Diffusion Theory for concentrated Polymer Solutions, J. of Applied
Polymer Science, 35, 1988, pp. 923-936.

Narkis, M., Chen, E.J.H., Review of Methods for Characterization of Interfacial
Fiber-Matrix Interactions, Polymer Composites, 9, (4), Aug 1989, pp. 245-251.

Netravali, A.N., Henstenburg, R., Phoenix, S.L.,Schwartz, P., Interfacial Shear
Strength Studies Using the Single-Filament-Composite Test. 1: Experiments on
Graphite Fibers in Epoxy, Polymer Composites, 10, (4), Aug 1989.

Netravali, A.N., Schwartz, P., Phoenix, S.L., Study of Interfaces of High-
Performance Glass Fibers and DGEBA-based Epoxy Resins Using Single-Fiber-
Composite Test, Polymer Composites, 10, (6), Dec 1989, pp. 385-388.

Netravali, A.N., Topoleski, L.T.T., Sachse, W.H., Phoenix, S.L., An Acoustic
Emission Technique for Measuring Fiber Fragment Length Distributions in the Single-
Fiber-Composite Test, 35, 1989, pp. 13-29.

Norita T., J unichi M., Matsuda H., Effect of Surface Treatment of Carbon Fiber on
Mechanical Properties of CFRP, ICCI 1, Jul. 1986, pp. 123-132.

Palley, I., Signorelli, A.J. , New Method for Evaluation of Fiber/Matrix Adhesion,
J. Adhesion, 25, 1988, pp. 161-167.

Parker, D.S., Yee, A.F., Factors Influencing the Mode I Interlaminar Fracture
Toughness of a Rubber Toughened Thermoplastic Matrix Composite, J. Thermo.
Comp. Mat, 2, Jan. 1989, pp. 2-18.

Parker, D.S., Yee, A.F., Toughening of a Thermoplastic Matrix Composite:
Processing Issues, Adv. in Mat. and Process Engineering, 1988, pp. 270-279.

Peacock J. A., Fife B., Nield E., Crick R. A.,Examination of the Morphology of
Aromatic Polymer Composite (AFC-2) Using an Etching Technique, ICCI 1, Jul.
1986, pp. 299-306.

Peacock, J .A., Fife, B., Nield, E., Barlow, C.Y., A Fibre-Matrix Interface Study of
Some Experimental PEEK/Carbon-Fibre Composites, Composite Interfaces, ICCI II,
1986, pp. 143-149.

Penn, L.S., Lee, S.M., Interpretation of Experimental Results in the Single Pull-out
Filament Test, J. of Composites Technology and Research, 11, (1), Spring 1989, pp.
23-30.

Peters, P.W.M., Springer, G.S., Effects of Cure and Sizing on Fiber-Matrix Bond
Strength, J. Comp. Mats., 21, Feb. 1987, pp. 157-171.

319

Phani, K.K., The Strength-Length Relationship for Carbon Fibres, Composites
Science and Technology, 30, 1987, pp. 59-71.

Piggot, M.R. , The Effect of the Interface/Interphase on Fiber Composite Properties,
Polymer Composites, 8, (5), Oct. 1987, pp. 291-297.

Piggott M.R., Sanadi A., Chua P.S., Andison D., Mechanical Interactions in the
Interphasial Region of Fibre Reinforced Thermosets,Composite Interfaces, ICCI I,
1986, pp. 109-121.

Piggott M.R., Expressions Governing Stress-Strain Curves in Short Fibre Reinforced
Polymers, J. Mater. Sci., 13, Jan. 1978, pp. 1709-1716.

Piggott M.R., Dai S.R. , Debonding and Friction at Fibre-Polymer Interfaces. 11:
Macroscopic Model Experiments, Comp. Sci. Tech., 31, Jan. 1 88, pp. 15-24.

Piggott, M.R., Andison, D., The Carbon Fibre-Epoxy Interface, J. Reinf. P. &
Comps, 6, Jul. 1987, pp. 290-302.

Piggott, M.R., Debonding and Friction at Fibre-Polymer Interfaces. 1: Criteria for
Failure and Sliding, Comp. Sci. and Tech., 30, Jan. 1987, pp. 295-306.

Plueddemann, E.P., Adhesion Through Silane Coupling Agents, J. Adhesion, 2, Jul.
1970, pp. 184-201.

Purslow, D. , Matrix Fractography of Fibre-Reinforced Thermoplastics, Part 1. Peel
Failures, Composites, 18, 5, pp. 365-380.

Reedy, E.D., Fiber Stress Concentrations in Kevlar/Epoxy Monolayers, J. of Comp.
Materials, 19, Nov. 1985, pp. 533-543.

Rich, M.J., Drzal, L.T., Interfacial Properties of Some High-Strain Carbon Fibers
in an Epoxy Matrix, J. Reinf. Plas. Comp, 7, Mar. 1988, pp. 145-154.

Rich.-Frand. R. , Naerheim, Y. , Fracture Morphology of Graphite/Epoxy Composites,
J. Comp. Materials, 17, Mar. 1983, pp. 105-113.

Roche, E.J., Lavin, J .G., Parrish, R.G., The Mosaic Nature of the Graphite Sheet
in Pitch-Based Carbon Fibers, Carbon, Sep. 1988, pp. 911-912.

Sanadi A R. , Piggott M.R. , Interfacial Effects in Carbon-Epoxies: Part 2 Strength and
Modulus With Short Random Fibres, J. Mater. Sci., 20, Jan. 1987, pp. 431-437.

Sargent J .P., Ashbee K.H.G., Detection and Measurement of Very Small Interfacial
Gaps in GRP, Composites Science and Technology, 22, 1985, pp. 135-152.

Schadler, L.S., Ma, B.T., Laird, C., Acoustic Emission in Single Filament
Carbon/Polycarbonate and Kevlar/Polycarbonate Composites Under Tensile
Deformation, Polymer Composites, 11, (4), Aug. 1990, pp. 211—216.

Schultz, J ., Lavielle, L., Martin, C., The Role of the Interface in Carbon Fibre-
Epoxy Composites, Adhesion Soc. Proc., 10, Feb. 1987, pp. 513-528.

320

Shih G.C., Ebert E.J., Interface Strength Effects on the Compressive-Flexural/Shear
Failure Mode Transition of Composites subjected to Four-Point Bending, J. Mater.
Sci., 21, Jan. 1986, pp. 3957-3965.

Sideridis, E. , The In-Plane Shear Modulus of Fibre Reinforced Composites as Defined
by the Concept of Interphase, Comp. Sci. and Technology, 31, 1988, pp. 35-53.

Stack G.M., Mandelkem L., On the Crystallization of High Molecular Weight
Normal Hydrocarbons, Macromolecules, 21, Jan. 1988, pp. 510-514.

Stringer, L.G., Comparison of the Shear Stress-Strain Behavior of Some Structural
Adhesives, J. Adhesion, 18, 1985, pp. 185-196.

Takemori, M.T. , Polymer Fatigue Fracture Diagrams: BPA Polycarbonate, Polymer
Eng. and Science, 28, 10, May 1988, pp. 641-647.

Talbott M F., Springer G.S., Berglund, L.A., The Effects of Crystallinity on the
Mechanical Properties of PEEK Polymer and Graphite Fiber Reinforced PEEK, J.
Comp. Mater.,21, Nov. 1987, pp. 1056-1081.

Theocaris P.S.,The Concept and Properties of Mesophase in Composites, Composite
Interfaces, ICCI I, 1986, pp. 329-349.

Theocaris P.S. , Philippi T. , Theoretical Evaluation of the Extent of the Mesophase
in Particulate and Fibrous Composites, J. Rein. Plas. Comp., 4, Jan. 1985, pp.
173-185.

Thomason, J .L. , Knoester, A. , Application of Confocal Scanning Optical Microscopy
to the Study of Fibre-Reinforced Polymer Composites, J. of Mat. Sci. Let., 9, Mar.
1990, pp. 258-262.

Tong Y. , Jasiuk I. , The Effect of Interface on the Mechanical Properties of
Composites, ICCI II, 1988, Composite Interfaces, pp. 757-764.

Tuinstra, F. , Baer, E. , Epitaxial Crystallization of Polyethylene on Graphite, Polymer
Letters, 8, 1970, pp. 861-865.

Underwood, F.M. , Batchelder, D.N, Sharpe, D.J. , The Raman Optomechanical Strain
Gauge Adapted for Use in Carbon Fibre Composite Laminates, pp. 69-73.

Wagner H.D., Steenbakkers L., Microdamage Analysis of Fibrous Composite
Monolayers Under Tensile Stress, J. of Materials Science, 24, 1989.

Wagner, H.D. , Statistical Concepts in the Study of Fracture Properties of Fibres and
Composites, Application of Fracture Mechanics to Composite Materials, Elsevier,
1988.

Wagner, H. D. and Eitan, A. , "Interpretation of the Fragmentation Phenomenon in
Single-Filament Composite Experiments", Journal of Materials Science, 1990, (in
press).

321

Waterbury, M. C. and Drzal, L. T., "Interfacial Shear Strengths of Carbon Fibers in
Bisphenol A Polycarbonate" , ICCI III, Elsevier Science Publishing, New York, May,
1990.

Waterbury, M. C., FiberTrack, Single fiber fragmentation data acquisition and
analysis computer program, Copyright, M. C. Waterbury, 1990.

Weibull, W. , in Proceedings of the Royal Swedish Institute for Engineering Research,
151, 1939.

Weibull, W., A Statistical Distribution Function of Wide Applicability, J. Applied
Mech., 18, 1951, p. 293.

Weinberg, M., Shear Testing of Neat Thermoplastic Resins and Their Unidirectional
Graphite Compsites, Composites, Nov. 1987, pp. 386-392.

Wesson, S.P., Allred, R.E., Acid-Base Properties of Carbon and Graphite Fiber
Surfaces, J. Adhes. Sci. Tech., 4, 4, Jan 1990, pp. 277-301.

Wimolkiatisak A, Bell J.P., Interfacial Shear Strength and Failure Modes of
Interphase-Modified Graphite-Epoxy Composites, Polymer Composites, 10, (3), Jun.
1989, pp. 162-172.

Wright, W.W., The Carbon Fibre/Epoxy Resin Interphase - A Review - Part 11,
Composite Polymers, 3, 1990, pp. 360-401.

Yatchmenoff, B., A New Confocal Scanning Optical Microscope, American
Laboratory, Apr. 1988, pp. 58-66.

Yip, P.W., Lin, 8.8., Effect of Surface Oxygen on Adhesion of Carbon Fiber
Reinforced Composites, Mat. Res. Soc. Symp. Proc., 170, 1990, pp. 339-344.

Zeng H., Kong B., Investigations on the Structure and Properties of the Carbon
Fiber/Nylon-10,10 Composites, Composite Interfaces, ICCI I, 1986, pp. 55-64.

Zhu, Y., Zhou, B., He, 6., Zheng, Z., A Statistical Theory of Composite Materials
Strength, J. of Composite Materials, 23, Mar. 1989, pp. 280-287.

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