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LIBHAHY
THESIS . . .
1;) Macnlgan State
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This is to certify that the
thesis entitled

TECHNIQUES FOR ENHANCING IMPACT TESTING

presented by

Brandon Geoffrey Gulker

has been accepted towards fulfillment
of the requirements for the

MS. degree in Mechanical Engineering

 

 

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/2// 7/2007

Date

 

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5/08 K:IProj/Aoc&Pres/ClRClDateDue.indd

TECHNIQUES FOR ENHANCING IMPACT TESTING
By

Brandon Geoffrey Gulker

A THESIS
Submitted to
Michigan State University
In partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE

Mechanical Engineering

2009

ABSTRACT

TECHNIQUES FOR ENHANCING IMPACT TESTING
By
Brandon Geoffrey Gulker
Impact events occur frequently during the life cycle of most structures.
This thesis presents three enhancements to impact testing. (1) A full-field
displacement measurement technique called Projection Moire was implemented
for impact testing which provided the out-of—plane displacement of plate
specimens during impact loading. This measurement revealed the initiation and
growth of major delamination in the plate. Additionally, the measurements were
compared to measurements made at a single point by a load cell. (2) Since
material properties may be different under dynamic loading than under static
loading, it is desirable to establish an efficient test method to extract the dynamic
material properties. The Virtual Fields Method was explored for use in impact
testing. Simulated plate bending from Finite Element Analysis was used to
determine the ideal test setup. Methods for using the Projection Moire data for
real experiments were then explored and a methodology for future study
proposed. (3) In order to observe the internal damage as a function of time,
translucent specimens were manufactured. Methods for implementing Projection
Moire measurements at the same time as viewing the internal damage were
explored. It was demonstrated that this simultaneous measurement was

possible.

To my parents, who have taught me

more than could be put in writing.

ACKNOWLEDGEMENTS

I am extremely grateful for the assistance and support of my academic
advisor, Dr. Dahsin Liu. Without him, this work would not have been possible.

Additionally, I am grateful for the participation of Dr. Soonsung Hong and
Dr. Alfred Loos in my defense committee.

The financial support from the US. Army TARDEC, Warren, MI was
greatly appreciated.

Finally, I would like to thank my colleagues, past and present, who have
provided assistance both professionally and personally: Guojing Li, Liangkai Ma,

Tao Jia, Anupam Dhyani, Shawn Klann, and Kirit Rosario.

TABLE OF CONTENTS

LIST OF TABLES ................................................................................................ viii
LIST OF FIGURES ............................................................................................... ix
Chapter 1: Introduction .......................................................................................... 1
Abstract ............................................................................................................. 1
1.1 Literature review .......................................................................................... 1
1.2 Motivation .................................................................................................... 6
1.3 Objectives .................................................................................................... 8
1.4 Approaches ................................................................................................. 9
1.5 Organization of thesis ................................................................................ 11
1.6 References ................................................................................................ 13
Chapter 2: Impact testing with Projection Moire .................................................. 14
Abstract ........................................................................................................... 14
2.1 Introduction ................................................................................................ 15
2.2 Methods ..................................................................................................... 18
2.2.1 Drop weight impact tester .................................................................. 18
2.2.2 Projection Moiré theory ...................................................................... 19
2.2.3 Projection Moiré setup ....................................................................... 21
2.2.4 Projection Moiré grating study ............................................................ 24

2.3 Results and discussion .............................................................................. 30
2.3.1 Full-field displacement of the rear surface ........................................ 30
2.3.2 Comparison with the single point method .......................................... 36

2.4 Conclusions ............................................................................................... 41
2.5 Future work ............................................................................................... 42
2.6 References ................................................................................................ 44
Chapter 3: Material properties from impact testing .............................................. 44
Abstract ........................................................................................................... 44
3.1 Introduction ................................................................................................ 44
3.2 Numerical simulation ................................................................................. 48
3.2.1 The Virtual Fields Method ................................................................. 48
3.2.2 Numerical study using simulated data ................................................ 51
3.2.2.1 Alternative boundary conditions .................................................. 53

3.2.2.2 Virtual field selection ................................................................... 56

3.3 Experimental implementation .................................................................... 57
3.3.1 Drop-weight impact testing ................................................................. 57
3.3.2 Data processing ................................................................................. 57
3.3.2.1 Filling in unknown region ............................................................ 58

3.3.2.2 Spacial smoothing ....................................................................... 61

3.3.2.3 Spacial differentiation .................................................................. 63

3.3.2.4 Temporal smoothing and differentiation ...................................... 65

3.3.2.5 Virtual field selection ................................................................... 66

3.4 Results and discussion .............................................................................. 67
3.4.1 Numerical study using manually defined virtual fields ........................ 67
3.4.2 Numerical study using mode shapes as virtual fields ......................... 69
3.4.2.1 The CL-U set of boundary conditions .......................................... 72
3.4.2.2 The CL-4 set of boundary conditions .......................................... 74
3.4.2.3 Refinement for the CL-L set of boundary conditions ................... 75
3.4.3 Experimental implementation ............................................................ 76
3.4.4 Sources of error ................................................................................. 76
3.5 Conclusions ............................................................................................... 77
3.6 Future work ............................................................................................... 79
3.7 References ................................................................................................ 81
Chapter 4: Translucent composites for studying damage progression ................ 77
Abstract ........................................................................................................... 77
4.1 Introduction ................................................................................................ 77
4.2 Methods ..................................................................................................... 78
4.3 Results and discussion .............................................................................. 79
4.3.1 Woven composite with painted sections ............................................ 79
4.3.2 Cross-ply laminate ............................................................................. 88
4.3.2.1 Cross-ply delamination ............................................................... 88
4.3.2.2 Estimation of crack speed ........................................................... 91
4.3.2.3 Projection Moiré with cross-ply laminate ..................................... 94
4.3.3 Woven composite with half painted surface ....................................... 96
4.3.4 Semi—transparent surface ................................................................... 99
4.4 Conclusions ............................................................................................. 104
4.5 Future work ............................................................................................. 105
4.6 References .............................................................................................. 107
Chapter 5: Conclusions and future work ............................................................ 108
5.1 Conclusions ............................................................................................. 108
5.1.1 Impact testing with Projection Moire ................................................. 108
5.1.2 Material properties from impact testing ............................................ 109
5.1.3 Translucent composites for studying damage progression .............. 110
5.2 Future work ............................................................................................. 111
5.2.1 Impact testing with Projection Moire ................................................. 111
5.2.2 Material properties from impact testing ............................................ 112
5.2.3 Translucent composites for studying damage progression .............. 112
Appendix A: Dynamic indentation behavior ....................................................... 114
A1 Abstract .................................................................................................. 114
A2 Introduction ............................................................................................. 1 14
A3 Methods .................................................................................................. 116
A.3.1 Measurement of maximum indentation ............................................ 116
A.3.2 Dynamic indentation ........................................................................ 118

vi

A.3.3 Static indentation ............................................................................. 1 19

A4 Results and discussion ........................................................................... 120
A5 Conclusions ............................................................................................ 124
A6 Future work ............................................................................................ 124
A7 References ............................................................................................. 126
Appendix B: Drop-weight impact tester calibration ............................................ 127
B1 DWIT data acquisition calibration ........................................................... 127
B2 Load cell calibration ................................................................................ 129

vii

LIST OF TABLES

Table 3.1. Bending stiffness results when virtual fields were manually defined.. 68

Table 3.2. Results for numerical study of alternative boundary conditions based
on static loading using simulated data. Four mode shapes ere selected as
virtual fields. Definitions of boundary conditions can be found in Figure 3.1.72

Table 3.3. Comparison of results for the CL-U case using different combinations
of mode shapes ............................................................................................. 74

Table 3.4. Comparison of the results obtained for the CL-L case when the first six
modes are considered and when the first twenty modes are considered ...... 76

Table A1. Fitting constants for the power law curves fit to the indentation data
.................................................................................................................... 122

viii

LIST OF FIGURES
Figure 2.1. Schematic of the DWIT machine. The actual device is shown in
Figure 2.4 ...................................................................................................... 18

Figure 2.2. Schematic showing the general setup for Projection Moire
measurements .............................................................................................. 20

Figure 2.3. Schematic of how the Projection Moire method was applied to the
DWIT test setup. In the setup for this testing, a+b z 750 mm, c+d z 750 mm,
and 6 =- 30° .................................................................................................... 22

Figure 2.4. Projection Moire method applied to the DWIT setup ......................... 23

Figure 2.5. Schematic of the milling steps taken for one notch of the machine
aluminum plate .............................................................................................. 25

Figure 2.6. Image of the calibration plate. Notches were milled from an
aluminum plate at incremental depths. ....................................................... 25

Figure 2.7. Displacement contour and profiles for the projected grating of 0.54
lines/mm ........................................................................................................ 26

Figure 2.8.Displacement contour and profiles for the projected grating of 0.94
lines/mm ........................................................................................................ 27

Figure 2.9. Displacement contour and profiles for the projected grating of 1.08
lines/mm ........................................................................................................ 28

Figure 2.10. Comparison between the prescribed depth from the milling process
and the depth measured from Projection Moiré ............................................ 28

Figure 2.11. Regions for which the displacement should be zero ....................... 29

Figure 2.12. The standard fixture used in the DWIT testing. The specimen was
bolted to ensure clamped boundary conditions were obtained ..................... 31

Figure 2.13 Contours for evenly spaced time steps during the impact event. The
time step between each image is 0.4 ms ...................................................... 32

Figure 2.14. Contour image (left) and displacement profile (right) along the dotted
line through the impact point ......................................................................... 33

Figure 2.15. Profile lines drawn for loading (top) and unloading (bottom) histories.
The time step between each image is 0.33 ms ............................................. 34

Figure 2.16. The force history from the impacting surface and the impact point
displacement from the rear surface. Displacement profile lines are shown for
various times ................................................................................................. 35

Figure 2.17. Comparison of the displacement of the impact surface and rear
surface at the point of impact ........................................................................ 37

Figure 2.18. Displacement of the rear surface at the impact point and the fitted
polynomial ..................................................................................................... 39

Figure 2.19. Comparison of the velocity of the impact surface and rear surface at
the point of impact ......................................................................................... 40

Figure 2.20. Comparison of the acceleration of the impact surface and rear
surface at the point of impact ........................................................................ 40

Figure 3.1. Flowchart outlining the study conducted using the Virtual Fields
Method .......................................................................................................... 52

Figure 3.2. Schematics and notation definition of alternative boundary conditions
explored in the numerical portion of the study ............................................... 54

Figure 3.3. Schematic of how the restrictions on the mirror positioning limited the
portion of the specimen which could be viewed ............................................ 58

Figure 3.4. Regions A and B indicate portions of the specimen which could not
be viewed due to shadows produced by the light projection angle ............... 59

Figure 3.5. Displacement profiles through the impact point for the raw data and
filled regions .................................................................................................. 60

Figure 3.6. Comparison between unsmoothed (left) displacement from Projection
Moire and the smoothed results (right) from the central moving average.....62

Figure 3.7. Displacement profile through the impact point comparing the
unsmoothed and smoothed data for different times. The time step between
lines is 0.33 ms ............................................................................................. 62

Figure 3.8. Curvature fields for a typical time step for the CL-L boundary
conditions ...................................................................................................... 63

Figure 3.9. Profile through the impact point for kx ............................................... 64

Figure 3.10. Profile through the impact point for ky ............................................. 64
Figure 3.11. Profile through the impact point for ks ............................................. 64
Figure 3.12. Example of acceleration fields for the CL-L plate ............................ 66

Figure 3.13. Comparison of the degree of symmetry present in each of the simply
supported boundary conditions. The dotted lines represent lines of
symmetry ....................................................................................................... 69

Figure 3.14. The first six mode shapes for the CL-L case. The specimen
orientation is the same as Figure 3.6 ............................................................ 71

Figure 3.15. The first six mode shapes for the CL-U case. The specimen
orientation is the same as Figure 3.6 ............................................................ 73

Figure 4.1. Woven composite specimen with four regions of different degrees of
transparency. The dotted line shows the portion of the specimen which is
visible in Figures 4.2 and 4.3 ........................................................................ 81

Figure 4.2. Typical image during delamination growth (left) and outline of the
delamination shape (right). Only region outlined in Figure 4.1 is shown. The
grid pattern of the delamination corresponds to the weaving geometry of the
layers. The + indicates the impact point ........................................................ 82

Figure 4.3. Delamination growth in the area outlined in Figure 4.1. Images are
0.14 ms apart. ............................................................................................. 83

Figure 4.4. Sample image showing the portion of the specimen for which fiber
breakage is developing. The fiber breakage is outlined with a dotted line. The

glare is outlined with a solid line ................................................................... 84
Figure 4.5. Projection Moire results for Region 2 ................................................ 86
Figure 4.6. Projection Moiré results for Region 3 ................................................ 86
Figure 4.7. Projection Moiré results for Region 4 ................................................ 87

Figure 4.8. The unprocessed image of the specimen (left), and the Projection
Moire results for each region (right) .............................................................. 87

xi

Figure 4.9. Modification of the contrast of the high speed camera image in order
to make delamination more visible ................................................................ 89

Figure 4.10. Outline of the delamination area which is visible in image (solid line)
and the assumed delamination due to symmetry (dotted line) ...................... 90

Figure 4.11. High speed camera images in the area of delamination for the
period of delamination growth. Time between frames is 0.14 ms ................ 90

Figure 4.12. Comparison between the force history and the high speed camera
images showing delamination ....................................................................... 91

Figure 4.13 Comparison between the force history and the estimated crack
speed of the primary direction of delamination .............................................. 92

Figure 4.14. Length of each arm of the delamination in the rear layer of the
laminate as a function of time ....................................................................... 93

Figure 4.15. Projection Moire results for the transparent cross-ply laminate. Time
between frames is 0.57 ms ........................................................................... 94

Figure 4.16. Schematic of how angle of light projection causes one side of the
specimen to be darker than the other ........................................................... 95

Figure 4.17. Woven translucent specimen with half of the rear surface painted
white .............................................................................................................. 97

Figure 4.18. Projection Moire and delamination outlines for the woven composite
with half of the surface painted white. Images are 2.86 ms apart ................ 99

Figure 4.19. Projection Moire results for the translucent composite with two coats
of semi-transparent paint ............................................................................ 101

Figure 4.20. Delamination growth in the woven composite with two coats of semi
transparent paint. Time steps between the images was 1.43 ms ............... 102

Figure 4.21. Projection Moire results for the woven specimen with one coat of
semi-transparent paint. Images are 0.57 ms apart ..................................... 103

Figure 4.22. Delamination growth in the woven composite with one coat of semi
transparent paint. Time steps between the images was 1.43 ms ............... 104

xii

Figure A.1. Image of the impactor (left) and definition of geometry symbols
(right) ........................................................................................................... 117

Figure A.2. Image of the specimen after indentation ......................................... 117

Figure A.3. Schematic of the DWIT machine (left) and the actual device (right).

.................................................................................................................... 118
Figure A.4. Schematic of the static setup (left) and picture of the actual device

(right) ........................................................................................................... 119
Figure A.5. Indentation results with power law fitted curves (n = 1.5) ............... 120
Figure A.6. Indentation results with power law fitted curves (n is variable) ....... 121

Figure A]. Comparison between the fitting curves shown in Figures A5 and A6.
.................................................................................................................... 122

Figure 8.1. Schematic of the data acquisition system ....................................... 127

xiii

C

CDJ>6

KEY TO SYMBOLS AND ABBREVIATIONS

Indentation
Acceleration

Strain

Grating projection angle
Density

Stress

Poisson's Ratio

Phase

Background intensity
Background modulation
Clamped

Marker paint diameter

- Bending stiffness

Drop-weight impact tester
Young's Modulus

Body force
Carrier frequency

Fourier Transform Profilometry
Camera position

Curvature

Power Law fitting constant

Specimen length

xiv

Power Law fitting constant
Correlation

Impactor radius

Surface

Simply supported

Traction

Displacement

Energy

Vdume

Out-of—plane displacement

XV

Chapter 1: Introduction
Abstract

A major difficulty in using composite materials in real structures is their
performance under impact loads. A wide variety of real loading scenarios are
under dynamic conditions, and the damage process under these scenarios is still
not well understood. Several techniques have been established to objectively
characterize a materials impact performance and to compare different materials.
However, these studies have primarily been based on analyzing the data
obtained from a load cell. Load cell data is a measurement of only a single point
of the specimen. Some studies have utilized high speed camera technology to
observe the surface response. This thesis explores techniques which can be
used to enhance impact study. Full-field displacement was implemented for
impact testing. A methodology for obtaining material properties from this data
was established. Additionally, translucent glass/epoxy composite materials were

used to observe the internal damage progression during impact loading.

1.1 Literature review

Composite materials provide an advantage over conventional materials
such as metals in that their stiffness to weight ratios are much higher. For this
reason, they have become popular in applications where weight reduction is a
priority, such as in the aerospace industry. In spite of their advantages,

composites have a disadvantage in that they are not as well understood. The

damage processes present within the material are quite complex. This is
especially true for dynamic loading conditions.

There are a wide variety of dynamic loads that present themselves in the
life-cycle of any product. For an airplane, for example, impact loads range from
the relatively low velocities of a repair tool being dropped onto a panel to the
relatively high velocities of a collision with a bird. Each impact event has the
potential damage the composite material and thus degrade its performance.

In order to properly design a structure using composite materials and take
into consideration these and other loading scenarios, it is necessary to properly
understand the damage process occurring within the composite structure. For
this reason, a number of experimental studies have been carried out. A
considerable amount of work has been done in an attempt to properly
characterize the impact performance of various composite structures.

A large number of studies have been conducted concerning the behavior
of composite materials under impact loading. Reviews of the research can be
found in several locations such as the book by Abrate [1 .1] and the paper by
Richardson and Wiseheard [1 .2]. Several techniques have been developed to
assist in the characterization and comparison of different composite materials.

Basic methods for comparing the performance of various composite
materials under impact loading involve impacting several different materials using
the same impacting mass and velocity. Their force-time and force-deflection
plots can be compared and any differences can indicate a materials

performance. In addition to comparing the curves, several quantities can be

calculated and compared. For example, the energy absorbed by the composite
(absorbed energy), the force at which a Change in stiffness was observed (critical
force), deflection at which a change in stiffness was observed (critical deflection),
the maximum deflection, and the maximum force have all been used in the
comparison of composite materials [1 .2].

Pilchak et al. [1.3] used this approach in comparing laminated composite
materials with angles of 0-90 degrees between layers. In addition, different
methods of stitching layers together were compared. With this method it was
possible to establish that, in general, small angles provided a higher degree of
impact resistance than large angles. Additionally, it was found that stitching
layers together increased the impact resistance.

Rosario [1 .4] compared different methods of weaving layers together by
comparing the absorbed energy, the force history, and images obtained from a
high speed camera. He was able characterize the strengths and weaknesses of
different weaving methods and identify which composite structure provided the
highest impact resistance. By comparing these results with the high speed
camera images, the highest impact resistance was identified as being due to the
high degree of fiber straining in the rear layer of the composite. The composites
with the highest impact resistance had a plateau in the force history at the peak
force. This plateau corresponded to images where the rear layer had a
significant degree of delamination. The delamination of the rear layer could be

seen to the naked eye whereas the internal delamination was not visible. This

study established the importance of the rear layer in designing composite
materials for impact resistance.

More advanced techniques for comparing composite materials have also
been established. Liu [1 .5] developed the energy profiling method. In this
method, different composite specimens of the same material and orientation are
impacted with incrementally increasing amounts of energy. The amount of
energy absorbed by the composite (absorbed energy) is plotted versus the
incident kinetic energy of the impacting mass (impact energy) for the entire set of
data. Also, the load-deflection plots for each specimen are then plotted on the
same graph to create a portrait of the materials impact resistance and damage
progression. This energy profiling method was used to identify key impact
performance parameters of composite plates such as the penetration and
perforation thresholds as well as the range of penetration process. Dominant
damage modes were also identified for different ranges of impact energy. The
dominant damage modes, were cited as indentation, matrix cracking/crushing,
delamination, lamina splitting, bending fractures, and fiber breakage. This tool
provided a method with which to compare two composite materials.

Feraboli and Kedward [1 .6] developed another method to compare
composite materials. In their study, several quantities were defined from the
data. One was the coefficient of restitution which is the ratio of the exit to impact
velocity of the impacting mass. It was observed that when this quantity was
plotted as a function of the kinetic energy of the impacting mass, several kinks

were present in the plot. These kinks divided the behavior at different impact

energies into different regions. At what impact energy these kinks were present
provided a gage of the material's impact damage resistance. Plotting the total
contact duration as a function of the impacting energy confirmed the significance
of these regions. A second impact was performed on the damaged specimens in
order to asses and compare the residual performance of the materials. This
technique could be advantageous in comparing multiple material configurations.
In a later paper [1.7], the same authors used this method to compare the results
from tests with square fixtures to tests with circular fixtures. It was found that
there was no significant variation between the results with the various fixtures.

Delamination is the primary damage mode which introduces a degradation
in the material stiffness. Several studies have been conducted in which the
initiation of delamination was investigated. Many researchers have observed an
point in the loading portion of the force-time curve for which major oscillations
initiate [1.7, 1.8, 1.9]. This oscillation has been attributed to an initiation of
delamination. Since it was not possible to observe the delamination initiation and
growth within the composite, this served as the only means of identifying the
delamination. Schoeppner and Abrate [1.8] theorized that the oscillations after
delamination and initiation were due to crack initiation, arrest, reload, and
propagation cycles. They could not, however, observe the phenomenon directly.

In addition to the study of damage processes, it has been observed that
composite materials can exhibit a strain-rate dependence. For some materials,
the material properties under dynamic loading may be different than those at

static loading. Lee and Liu [1.10] demonstrated that glass/epoxy composite

material present different behavior when loaded statically versus dynamically.
This was shown by performing static and dynamic indentation tests on thick
glass/epoxy laminates by supporting them rigidly at the base. It was observed
that, for the same peak force, the maximum indentation for the static loading was
higher than that of the dynamic loading. Gulker [1.11] also observed a difference
between the static and dynamic response during dynamic indentation. However,
it was observed that the response for all of the dynamic testing was the same,
regardless of impact velocity (impact velocities ranging from 0.94 m/s to 2.64 m/s
were explored). This suggests that properties governing dynamic response differ
from those governing static response. However, there is very little, if any,
variation in properties as the impact velocity is changed within a small range. A

discussion of this subject can be found in Appendix A of this thesis.

1.2 Motivation

The previous work has largely focused on analyzing data obtained from a
load cell at the point of impact. Although this has been useful, it is limited by the
fact that the measurements are only recorded at a single point. With this
approach, conclusions concerning the materials response beyond this point can
only be made indirectly. Since a large amount of the damage processes occur
beyond the impact point, studies could be greatly enhanced by making
measurements of the full specimen.

Some work has been done to include the observations from a high speed
camera. This provides a means of observing the response of the rear surface of

the specimen during the impact event. Since the plates under analysis are thin

relative to the other dimensions, observing a single surface is an acceptable
choice. Even though the surface behavior can be observed with this technique,
not measurements are directly taken here. The study would be greatly enhanced
if some objective values for the strains or displacements were obtained.

From the previous techniques, a useful area to focus future study is in the
implementation of a means of measuring the rear surface. There have been
some dynamic studies using full-field measurements (see Chapter 2 for a
discussion), but more work needs to be done to establish a reliable methodology.
The present work implements Projection Moire to measure the out-of—plane
displacements of the rear surface of the specimen. It is then possible to
objectively discuss the material response during the impact loading.

Once the full-field displacements are obtained, it is desirable to use this
data to obtain the material properties of the specimen. It has already been
established that the dynamic material properties may differ from the static
properties. Chapter 3 of this thesis focuses on this subject. A technique called
the Virtual Fields Method is explored and a methodology for implementing this
technique in drop-weight impact tests is established.

Although the full-field displacement measurements provide a significant
addition to the impact testing, it is still only possible to measure a single surface's
behavior. Since much of the damage is inside of the composite, in order to be
able to fully characterize the damage process, it is necessary to observe how this
internal damage progresses. This would be possible if the specimen were

translucent. With glass/epoxy composites, it is possible to make the specimen

translucent if the index of refraction of the fiber and the matrix are similar.
Chapter 4 of this thesis explores the use of translucent specimens in impact
testing. The specimen was viewed with a high speed camera and the evolution
of the internal damage was observed. To enhance this study, techniques for
simultaneously implementing Projection Moiré along with the translucent

specimen were explored.

1.3 Objectives

The simplicity of the drop-weight impact tester has led to its frequent use
in impact studies as demonstrated in the literature review. Since it is a test that
is performed frequently, it is desirable that experimental techniques be developed
that maximize the amount of information that can be obtained from this setup.
Most studies in the literature investigate measurements only at a single point, the
impact point. It would be advantageous to make measurements over the entire
surface of the impacted plate. One of the objectives of this thesis was to identify
and implement a full-field measurement technique to measure the plate
response. It was also desired that the rear surface measurements made here be
compared to the single point measurements on the impacting surface.

Once the full-field response was obtained, it was desired to use this
information as thoroughly as possible. Since delamination causes a localized
change in bending stiffness, it should present a discontinuity in the slope of the
out-of-plane displacement. For this reason, it should be possible to observe the

initiation and growth of major delamination within the specimen by observing the

change in the specimen displacement. One of the goals of this thesis was to
identify this trend.

An additional way to use the full-field data is to obtain the bending
stiffnesses of the plate. A method exists (the Virtual Fields Method discussed in
Chapter 3) for identifying material properties from the full field response of the
specimen. Identifying an acceptable methodology for implementing this method
was an objective of this thesis.

In addition to exploring the surface response of the specimen, it was
desired to observe the internal damage growth. This could be done through the
use of translucent composites, as discussed in Chapter 4. It was desired to
measure the surface response and the internal damage growth simultaneously.
The objective was to implement a technique which allowed for both

measurements.

1.4 Approaches

Projection Moire was chosen to be the full-field measurement method to
be used in this study. In this technique, a grating is projected onto the specimen
surface, and the out-of—plane displacement can be obtained from the shift in the
projected grating as the specimen deforms. Contour plots for all time were
compared and displacement profiles along a line through the point of impact
were drawn in order to identify trends. This made it possible to identify the
localized change in bending stiffness due to major delamination, and thus identify

its initiation and growth.

In the attempt to identify methods for finding the bending stiffnesses from
the impact test, it was desired that alternative sets of boundary conditions to the
standard set (Clamped on four edges) be explored. The response for different
boundary conditions is reliant on different bending stiffnesses. In order to
accurately identify each property, it is necessary that the response be dependent
on each of them. For this reason, it is possible that the optimum set of boundary
conditions is different from those typically used. In order to explore different
cases, a finite element model was built using Abaqus to simulate the deflection
which would be present in static testing of these plates. It was assumed that the
trends present in this test would be similar to the elastic portion of the impact
response. The technique of using simulated data instead of experimental data
allowed for an efficient exploration of many different combinations of boundary
conditions. The optimal boundary conditions were identified and the
implementation of this technique for real experiments was explored.

In order to measure both the internal damage and the out-of-plane
displacement, it was necessary that the translucent composites reflect enough
light back to the camera so that the projected grating can be accurately captured.
Several techniques were explored. One technique was to coat half of the
specimen with matte white paint to obtain a completely opaque half and a
translucent half. Since the material and boundary conditions were symmetric,
the behavior of each half could be assumed to be representative of the other half.
In order to measure both quantities for the full-field, a balance between

transparency and opacity was obtained by coating the surface of the translucent

10

specimen with semi-transparent paint. Both woven and laminated composites
were investigated. It was possible to obtain an estimate of the crack speed by

recording the amount of growth between frames of the high speed camera.

1.5 Organization of thesis

In Chapter 2 of this thesis, the implementation of full-field methods is
explored. First, a literature review of several alternative techniques is presented,
and the reason for choosing Projection Moire is presented. A summary of the
theory behind the method is presented and the experimental implementation is
outlined. An accuracy study was implemented to validate the experimental
setup. Results for plate impact tests are then presented. The observations
concerning the initiation and growth of major delamination are presented. The
displacement, velocity, and acceleration at the impact point for the rear and
impact surfaces is presented and compared.

Chapter 3 of the thesis explores the implementation of the Virtual Fields
Method in impact testing. A brief summary of the theory is presented and a
review of its past applications is conducted. The techniques used in the present
work are then explained. The results from the simulated data obtained from finite
element analysis are then presented, and the ideal setup for future testing is
identified. The implementation of this method for real experiments is explored
and developed. Reasons for the poor experimental results are discussed, and a
more rigorous technique for extending the method to impact testing is proposed.

Chapter 4 of this thesis explores the use of translucent composites for

observing the internal damage growth during the impact event. The methods for

11

measuring the damage growth and the out-of—plane displacement simultaneously
are presented. Contour plots of the displacement are presented along with the
delamination growth. The delamination growth is also compared to the force
history. An estimation of the crack speed with time is then presented.

Chapter 5 of this thesis summarizes the conclusions made from the
previous work. It also presents an outline of the future work that should be

conducted.

12

1.6 References

[1.1] Abrate, 8. Impact on Composite Structures. 1998, New York, NY:
Cambridge University Press.

[1.2] Richardson, M.O.W., and Wisheart, M.J., “Review of low-velocity impact
properties of composite materials” Composites: Part A, Vol. 27A, 1996, pp. 1123-
1131.

[1.3] Pilchak, A.L., Uchiyama, T., and Liu, D. “Low-Velocity Impact Response of
Small-Angle Laminated Composites,” AIAA Journal. Vol. 44, 2006, pp. 3080-
3087.

[1.4] Rosario, K, “Quasi-three—dimensional woven composites,” Master's Thesis,
Michigan State University, East Lansing, MI, 2008.

[1 .5] Liu, D, “Characterization of Impact Properties and Damage Process of
Glass/Epoxy Composite Laminates,” Journal of Composite Materials, Vol. 38,
2004, 1425-1442.

[1.6] Feraboli, P, and Kedward, KT “Enhanced Evaluation of the Low-Velocity
Impact Response of Composite Plates,” AIAA Journal, Vol 42, 2004, 2143-2152.

[1.7] Feraboli, P, and Kedward, KT, “A new composite structure impact
performance assessment program,” Composites Science and Technology, 2006,
Vol 66, 1336-1347.

[1.8] Schoeppner, GA, and Abrate, S “Delamination threshold loads for low
velocity impact on composite laminates,” Composites: Part A, Vol 31, 2000, 903-
915.

[1.9] Belingardi, G, and Vadori, R, “Low velocity impact tests of laminate glass—
flber—epoxy matrix composite material plates,” International Journal of Impact
Engineering, 2002, Vol 27, 213-229.

[1.10] Lee, C-Y, and Liu, D “Effect of impact velocity on the indentation of thick
composite laminate,” Experimental Techniques, 2008.

[1.11] Gulker, B, “Experimental Methods for Impact of Composite Materials,”
2009, Proceedings of the SEM Annual Conference, Paper no. 575.

13

Chapter 2: Impact testing with Projection Moiré

Abstract

There have been a large number of studies conducted for impact testing
of materials. Most of the analysis done in the past has been focused on using
the force measurement from a load cell. Calculating the displacement from this
measurement requires the data to be integrated twice with respect to time. Since
this is an indirect approach, it is desirable to establish a way to directly measure
the displacement during the impact event. Additionally, if it is possible to
measure the displacement of the entire surface rather than just a single point, it
should be possible to better characterize the damage process in materials.

There are a range of full-field displacement measurement methods. Projection
Moiré was selected as the full-field displacement measurement method to be
used for this study. It was selected due to several factors: quality of results in the
literature, simplicity of its setup, and availability of a program to process the
images. The method has been applied to impact testing of laminated composite
materials using a drop-weight impact tester (DWIT). The displacement of the
rear surface was plotted and the delamination initiation and propagation was
visible in the results. The Projection Moire results were then compared to the
single point measurements of the impacting surface using a load cell. Good

correlation was seen between the measurements of the two surfaces.

14

2.1 Introduction

There are several works in the literature concerning the application of
optical methods to dynamic measurements. Kokidko et al. [2.1] used the
Shadow Moire method to study the deformation of a composite specimen under
ballistic loading. Chai et al. [2.2] also used the Shadow Moire method but for
low-velocity compression studies of composite materials. An advantage of the
Shadow Moire’ method is that it is very well established and easy to implement.
Unfortunately, however, the test setup requires the placement of a reference
grating very near the specimen (typically less than 15 mm away). This would
result in the destruction of a grating any time the maximum displacement was as
large or greater than this gap. This would both be cost prohibitive as well as
make it impossible to study the displacement history after the grating was
destroyed.

One of the most common optical methods found in the literature is Digital
Image Correlation (DIC). A review of the method has been presented by Sutton
et al. [2.3]. In this method, a pattern is placed on the specimen and the
deformation of that pattern is recorded and related to the displacement. Reu et
al. [2.4] used the method to measure the rear surface deformation of a steel plate
during impact testing. Tiwari et al. [2.5] studied the deformation of an aluminum
plate under explosive loading. This method is beneficial because both the in-
plane and out-of—plane deformations can be directly measured. A disadvantage

of this method, however, is that it requires the use of two cameras to record out-

15

of-plane deformation. This increases the cost of implementation and the
complexity of the experimental setup.

Fourier Transform Profilometry (FTP) is a method similar to Projection
Moire in that a grating system is also projected onto the specimen. A review of
the method has been written by Su and Chen [2.6]. The difference is in the way
this information is processed. In FTP, the displacement calculation can be
extracted from a single image rather than several phase shifted images. This
advantage has led several researchers to pursue it for dynamic studies. Zhang
et al. [2.7] used the method to study the rotation of fan blades. Su et al. [2.8]
used it to study the topography of the surface of a can of paint while it was being
stirred. Zhang and Su [2.9] studied a drum vibration using FTP. Paepegem et
al. [2.10] used FTP to study the out-of—plane deformation of a composite panel
subjected to a bird strike. For the study of the deformation during bird strike, the
resulting displacement contours were very noisy. The method needs further
refinement to increase its usefulness.

Projection Moire using phase shifting has also been used for dynamic
studies. Since phase shifting in its traditional form requires actual physical
shifting of a grating and recording several images, it has been limited in its
application to static studies. If a grating has to be physically shifted and several
images recorded, these images cannot be at exactly the same time. This
severely limits the speed at which this method can be implemented. Pan and
Huang [2.11] introduce a method in which several phase shifted gratings are

embedded in a single image by using a different color for each phase shift. The

16

individual phase shifts could later be extracted digitally. A disadvantage of this
method is that it would be sensitive to the color of the image and the light
intensity distribution on the object's surface. Additionally, many high speed
cameras on the market currently are black and white only, thus eliminating this
as an Option.

Chan and Bryanston-Cross [2.12] showed how Projection Moire methods
involving phase stepping were less computationally intensive than FTP. They
also introduced a phase estimating method which was faster than FTP by about
ten times for high resolution images and four times for low resolution images.
Since it is desired to implement an optical displacement measurement method in
dynamic testing using a high speed camera, there may be several hundred
images to process. The increase in computational efficiency is quite attractive
for this reason. Heredia and Patterson refined the Projection Moiré method and
made it much more user friendly by developing the JOSHUA software package to
automate the displacement calculation from a reference and object image [2.13].
This software package used a similar phase estimating approach as Chan and
Bryanston-Cross' method [2.12]. In their study, the method and software were
validated by running a series of tests on numerically simulated data and images
of static objects. Heredia and Patterson [2.13] studied the accuracy of the
method by experimentally measuring cone shapes and inclined plates.
Measurements for these tests were reported to be within 1% of the measurement

range.

17

2.2 Methods

2. 2.1 Drop weight impact tester

The device used in this study to create the dynamic loading was the
Dynatup drop-weight impact tester, model 8250. In this setup, a freely falling
weight falls through some prescribed distance and impacts the specimen. The
drop height determines the velocity at which the impact event will occur. The
various components of this device are shown in the figure below. The actual

device is shown in Figure 2.4.

   
  

 

 
  

 

Velocity
flag Load cell
" Impactor
Specimen\ Anti-rebound
Optical_\~ switches
sensor _ Anti-rebound
Fixture brake

Figure 2.1. Schematic of the DWIT machine. The actual device is shown
in Figure 2.4.

The impactor used in this study had a hemispherical nose with a diameter
of 12.7 mm (0.5 in). The rebound brake is used in this device to prevent the

impactor from impacting the specimen more than one time. If the mass rebounds

18

from the specimen, the brake is activated and prevents any additional impact
events. The optical sensor serves two purposes. The first is to trigger the data
acquisition system and the second is to record the initial velocity. The initial
velocity is calculated based on two flags which pass through the sensor
immediately prior to impact of the specimen. The load cell and optical sensor are
connected to the data acquisition system. The DWIT data acquisition system
was calibrated at the beginning of this study. The procedure can be found in

Appendix A of this thesis.

2.2.2 Projection Moiré theory

Projection Moiré measurements were used In this study to measure full
field out-of—plane displacements. In this method, a system of lines (grating) is
projected at some angle, 9, onto the object to be measured. Typically, the object
is viewed normal to the specimen. An image is captured before and after
deformation. From these images, it is possible to extract the phase data which is
directly related to the out-of-plane displacement. By subtracting the phase of the
reference image from the deformed image, the phase difference is obtained. The
phase difference is related to the deformation between the two frames. The
basic principles of the method are presented in this section. A comprehensive
discussion of the method can be found in the literature such as the paper by

Heredia and Patterson [2.13].

19

Physical
~t/grating

   

 

 

 

 

 

‘ \ \ ‘_J

9 ~ 30° \ t "

:I —————————— i - -{
Camera Object Reference

; surface plane
f4 - - _,__, >4
h z 1 m I

Figure 2.2. Schematic showing the general setup for Projection Moire
measurements.

From the above test setup, the intensity of the recorded image can be
expressed by the following equation.

‘ I

I(x,y)=A(x,y)+B(x,y)Cos(2nf0x+<D(x,y)J (2.1)
A and 8 represent the background intensity and modulation. The term fO is

called the carrier frequency which is related to the grating pitch. (D is the phase
and A49 is the difference between the deformed and undeformed phase which is
related to displacement of the specimen. The phase, CD, is obtained by obtaining
several intensity maps and solving the system of equations for the phase. The
additional intensity maps are found by virtually shifting the grating as discussed
in [2.13]. Since phase is a discontinuous quantity, it must be unwrapped to
obtain a continuous quantity in space.

If the phase for the deformed object and a flat reference object are both
obtained, then the subtraction of these two terms provides the displacement of

the deformed object. If the grating and the camera are sufficiently far away from

20

the object (infinite optics assumption), the displacement is related to the phase

by the following equation.

_ D
W_ 2ntan9A¢ (2'2)

 

In the above equation, w is the out-of—plane displacement, p is the pitch of the
projected grating, and 6 is the angle between the viewing axis and the projection
axis. The infinite optics assumption can be used as long as the distance from the
camera to the object surface, h, is at least one order of magnitude larger than the
object being studied. In this study, the Specimen was 75 mm along the edge, so
the distance must be at least 750 mm.

A program called JOSHUA has been developed by Heredia and Patterson
to perform the above Projection Moire calculations for a pair of images [2.13].

This study has made extensive use of this tool (JOSHUA version 1.12.2).

2. 2.3 Projection Moiré setup

For the DWIT (discussed in Chapter 2 of this thesis), Projection Moire was

implemented as Shown in the following schematic.

21

K Physical grating

 

Specimen
holder

Specimen

   

 

Mirror 1

Mirror 2

Figure 2.3. Schematic of how the Projection Moiré method was applied to
the DWIT test setup. In the setup for this testing, a+b z 750 mm, c+d z
750 mm, and 6 = 30°.
The Specimen is positioned such that the fiber direction of the rear layer is
perpendicular to the direction of the projected grating lines. This ensures that

matrix cracking will not be confused with the grating lines. The actual DWIT

machine and the Projection Moiré components are presented in the following

figure.

22

 

Figure 2.4. Projection Moiré method applied to the DWIT setup

The images were recorded with a Phantom v12 high speed camera from
Vision Research. The speed of the images was 7000-15000 frames/sec
depending on the test. Considering that an average impact event for this loading
scenario lasts about 10 ms, this frame rate provided an adequate number of data
points. Since the light sensitivity of high speed cameras decreases as the frame
rate increases, the rear surface of the Specimen was coated with a white matte
paint to maximize the amount of light reflected to the camera, and therefore
maximize the frame rate which could be used in the experiments. Additionally,

all of the fixture components were painted with a black matte paint to prevent any

23

undesired reflections from contaminating the image. The acquired images were

then processed using JOSHUA 1.12.2 to determine the out-of—plane deformation.

2. 2.4 Projection Moiré grating study

It is known from Heredia's study [2.13] that the accuracy of the Projection
Moiré method increases as the Size of the projected grating decreases.
However, the minimum projected grating allowed for using this method is limited
by the resolution of the camera. If the grating is too fine, then there will not be
enough pixels to properly represent each grating line.

In order to determine the appropriate grating Size for use with the
Projection Moire system, a test object was developed with carefully machined
notches. A pair of notches was milled into a 0.5 in thick aluminum plate. Along
these notches, the depth of the milling increased in steps incrementally. Initially,
the depth was such that the mill barely scratched the surface. This was defined
as the zero reference for the rest of the steps. When the mill had traveled
laterally for 10.16 mm (0.4 in), the milling depth was increased by 0.025 mm
(0.001 in). This was repeated until the edge of the plate was reached. The
process was then repeated for the second notch. The schematic of the stepping

increments is Shown below.

24

 

H,“ , L _, .2 ,i L L L L
95.25mm $i
(3.75in)

0.0254 mm
(0 001 In)

Figure 2.5. Schematic of the milling steps taken for one notch of the
machine aluminum plate.

The actual machined plate is shown in the following image.

10.16 mm

(0.4 in)
,, ,,_ Li H

 

 

95.25mm
(3.75 in)

Figure 2.6. Image of the calibration plate. Notches were milled from an
aluminum plate at incremental depths.

As shown in Figure 2.2, the camera was positioned about 750 mm from

the test object and the projection angle, 9 was about 30°. Three different
physical gratings were used. They were 10, 20 and 30 lines/mm Ronchi Rulings

purchased from Edmund Optics. The lens system used to focus the physical

25

gratings onto the specimen also magnified the gratings so that they covered the
entire surface of the specimen. The sizes of the projected gratings on the
specimen plane were 0.54, 0.94, and 1.08 lines/mm, respectively. The increment
between the second and third gratings was smaller Since increasing it any further
resulted in the camera not being able to distinguish between lines. The
resolution of the camera during this test was 1024 x 1280 pixels. As a result of
the camera resolution, each pair of lines of the projected grating was represented
by 11.74, 6.91, and 5.82 pixels, respectively. These values were calculated by
counting the number of grating lines in the image and then dividing that number
by the resolution of the image. The Projection Moiré results for each grating are

shown below. Profiles are shown for each step in the notches.

 

\WWWW

“CE.

I
.l
l

J
j
,3
i

WMJLWMAM

”AIM—‘4‘!» v,

 

Figure 2.7. Displacement contour and profiles for the projected grating of
0.54 lines/mm.

26

 

I I I I I I

Figure 2.8.Displacement contour and profiles for the projected grating of
0.94 lines/mm.

(I I (I

I I

(I

I

 

 

Iii§§§

._E

Figure 2.9. Displacement contour and profiles for the projected grating of
1.08 lines/mm.

The depth of each step was plotted for each grating and is Shown in the following

 

figure.
|
E l
E I
2' 1 —Reference
0_ j I 0.54 lines/mm
g l A 0.94 lines/mm
t l O 1.08 lines/mm
.C
a I
‘1’ l
O l

O :77 T 'l" T T TE "TI ' “f -7— —— ,, it
0 0.1 0.2 0.3 0.4 0.5
Depth from milling machine, mm

Figure 2.10. Comparison between the prescribed depth from the milling
process and the depth measured from Projection Moire.

The largest deviation from the prescribed depth for any of the measurements in
the graph above was 0.103 mm. The mean deviation for the 0.54, 0.94, and 1.08
lines/mm data sets was 0.049, 0.044, and 0.052 mm, respectively. The accuracy
of the milling machine was 0.025 mm (0.001 inch), so some of this deviation can
be attributed to machining errors. At the location of the dashed line, it is seen
that the Projection Moiré results all exhibit a bend. It is believed that this bend is
due to the completion of the first notch and the initiation of the second notch.

The results for 0.54 and 0.94 lines/mm are closer to the prescribed depth than
that of the 1.08 lines/mm case indicating that once the projected grating becomes

too fine, accuracy decreases.

28

An increase in the amount of noise present is seen as the grating

becomes too fine. To quantify this effect, the standard deviation of the calculated

displacement in the flat regions of the plate was calculated.

Region 1

 

Region 3

Figure 2.11. Regions for which the displacement should be zero.

Table 2.1. Comparison of the standard deviation of the displacement
measured from Projection Moiré which Should have zero values.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Standard Deviation

Physical grating: 10 lines/mm Region 1 0.0389
Projected grating: 11.74 px/line-pair Region 2 0.0313
Region 3 0.0302

All regions 0.0324

Physical grating: 20 lines/mm Region 1 0.0199
Projected grating: 6.91 px/line-pair Region 2 0.0189
Region 3 0.0236

All regions 0.0214

Physical grating: 30 lines/mm Region 1 0.0423
Projected grating: 5.82 px/line-pair Region 2 0.0529
Region 3 0.0842

All regions 0.0765

 

 

 

From the above study, the deviation was the lowest when there were 6.91 pixels

per line-pair. It was concluded that this case should be used in subsequent tests

as the minimum for the combination of grating density and camera resolution.

Selection of the grating frequency depends on the camera resolution for a given

29

test. If a finer grating density is desired, then a higher camera resolution will be

required in order to satisfy this requirement.

2.3 Results and discussion

2. 3. 1 Full-field displacement of the rear surface

A square 125 mm x125 mm composite laminate which was clamped along
all four edges such that a Specimen testing area 75 mm x 75 mm was visible.
Clamping was applied by two clearance holes in the specimen on each edge
outside of the testing area. Two steel plates sandwiched the composite
Specimen by bolting the assembly together through these clearance holes as

shown in Figure 2.8.

 

Figure 2.12. The standard fixture used in the DWIT testing. The specimen
was bolted to ensure clamped boundary conditions were obtained.

The specimen was impacted at the center of this region. The impacting mass fell
from a height of 320 mm with a mass of 5.16 kg. The force history was recorded

by the load cell and the rear surface deflection was recorded by the Projection

30

Moiré system at a frame rate of 15,000 frames/sec. The time duration between
each frame of the high speed camera was 0.067 ms. The total impact duration
for this test was approximately 7 ms, so the impact event was represented by
about 100 images. Below, 18 evenly spaced images are shown to represent the
deformation history. The full frame rate of the camera was not used in this figure
since there were so many frames. The time step between each frame shown in

this figure iS 0.4 ms.

 

 

 

   

Figure 2.13 Contours for evenly spaced time steps during the impact
event. The time step between each image is 0.4 ms.

Profile lines through the impact point are dawn as shown below.

31

 

70“ T

 

 

 

 

60- a
sol ~
E
E
c“ 40' -(
.9
It”:
8 _ .
g 30
20’ 7
10’ ‘
0 1 2 3 4

Displacement, mm

Figure 2.14. Contour image (left) and displacement profile (right) along the
dotted line through the impact point.

Curves similar to the ones in the figure above were drawn for different time steps
to show how the displacement changes with time. This was done for both the

loading and unloading histories.

32

 

Time, ms
-0.08
-—0.41
-— 0.74
—-1.08
— 1.41
—- 1.74
—2.41
— 2.74
— 3.08

Displacement, mm

 

 

 

 

—- 3.08
— 3.41
—— 3.74
—4.08
—4.41
— 4.74
— 5.08
— 5.41
— 5.74
— 6.08
— 6.41
y-position, mm —- 6.74

Displacement, mm

 

 

 

Figure 2.15. Profile lines drawn for loading (top) and unloading (bottom)
histories. The time step between each image is 0.33 ms.

It is seen that deformations early in the loading history is such that the
profile looks very much like a triangle. At some point, however, the triangular
region stops growing for a period of time and a small protruded region develops.
After this turning point in the deformation behavior, both the triangular and
protruded regions continue to grow for the remainder of the loading history.

Upon unloading, the protruded region stops growing any further and both regions

33

decrease in their degree of deformation. There is some amount of permanent

deformation in the protruded region due to delamination.

The profiles through the impact point are compared with the force history

in the plot below.

 

,a/ ~"\_‘\~ '1 _ \‘ //.' N \
/ 5 "-, 7A 6 A
E 4.7" // T“ \ ,5..’."-"/ -\\
u“ /' \‘ 4 z
[x c 3 /./ \ x
/" \. ° \ 3 —
r" ..... fig 2 \ 8
O .. \ I.
2 - / \ 2 LE
% 1 / \
._. / \ 1
D “ ------ WEE/\www
0 O

 

 

 

M/mriilo 1 2 3 4 5 6 7
Time, ms
Displacement ,, Force

Figure 2.16. The force history from the impacting surface and the impact
point displacement from the rear surface. Displacement profile lines are
Shown for various times.

It is seen in this image how the delamination grows compared to the force
history. The initiation of major delamination is seen as a disturbance in the force-
time curve. Also, once the maximum force has been reached, the size of the
delaminated region ceases to grow any further.

It is seen from the above discussion that the material response to impact
loading is more fully understood when the Projection Moiré measurements are
included in the study. Since the damage process is one of the major criteria

when comparing two or more composite structures, this tool could be utilized in

34

future work in order to more objectively and fully compare them. The Significance
of this method is further demonstrated when Rosario‘s [2.14] results are taken
into consideration. In his study, the rear layer was identified as one of the
primary factors in determining how much energy was absorbed by a composite
plate under impact loading. If a similar study were conducted using Projection

Moire measurements, the materials could be better Characterized and compared.

2.3.2 Comparison with the single point method

The results from the Projection Moire from the rear surface at the point of
impact were compared with the measurements of the load cell from the impacting
surface at the location of impact. The load cell provides a measurement of force
which can be related to the acceleration by Newton's Second Law if the
impacting mass is rigid. Integration of this data provides the velocity, and a
second integration provides the displacement. The rear surface and the

impacting surface displacements are compared in the following figure.

35

—- Impact surface
— Rear surface

Displacement, mm

 

Time, ms

Figure 2.17. Comparison of the displacement of the impact surface and.
rear surface at the point of impact.

There is a difference in the magnitude between the impact surface an the rear
surface. The peaks differ by a magnitude of 0.94 mm, and the final displacement
differs by a magnitude of 0.78 mm. Neither of the surface displacements return
to zero due to permanent damage that occurs during the impact event. The
impact surface suffers from some permanent amount of indentation from the
impactor. The rear surface suffers from delamination. A study of the dynamic
and static indentation performance of a 25.4 mm (1 in) thick composite plate
rigidly supported on its rear face was conducted previously [2.15]. The peak
force was related to the maximum indentation during the loading. It is known that
in the present test, the maximum force was 5 kN. In the case of the 25.4 mm
thick composite, this corresponded to a maximum indentation of about 0.25 mm.
Although the thickness and the stacking sequence of the composite in this test is
different from that of the previous work, it expected that the indentation for the

present case is at least in the same order of magnitude as before. Indentation

36

would would take place on the impact surface only, so this would account for
some of the difference between the values. Since the measurements were taken
on opposite surfaces of the specimen, and it is known that indentation will create
a difference between the results for each measurement, it was concluded that

the results were acceptable.

Since the rear surface displacement history is known, it is possible to
calculate the velocity and acceleration histories by differentiating the data. Since
differentiation is sensitive to noise, it was necessary to first smooth the data with
respect to time. A polynomial was fit to the displacement history from Projection
Moire by the Least Squares Method. Selecting a low degree polynomial provides
a poorer fit to the data, but is more smooth. Selecting a high degree polynomial
provides a more accurate representation of the original curve, but is less smooth
Since the original curve contains noise. In order to obtain an acceptable fit, a
balance must be found between these two extremes. From past experience, a
fifth order polynomial was selected. The displacement history at the impact point
of the rear surface with the corresponding polynomial fit is Shown in the following

figure.

37

E ,1 ~ .
E 3 / ‘ \
E" l -’ \
Q) I

2 I ,
0E, ‘ _, ’ \, - PolynomIal fit
8 l \_ —-Rear surface
6. 1 q \
.‘L’ .’ ‘\
D i'

0 r'

O 1 2 3 4 5 6 7
Time, ms

Figure 2.18. Displacement of the rear surface at the impact point and the
fitted polynomial.

It is seen in this figure that the displacement trend is captured well by the fifth
order polynomial fit. Also, the fitted curve does not contain the noise oscillations
present in the original curve. Differentiation of this curve Should give good

results for velocity and acceleration of the rear surface.

The velocities from the first differentiation of the rear surface displacement
and the first integration of the impact surface acceleration are compared in the

following figure.

38

— Impact surface
-— Rear surface

Velocity m/s

 

Time, ms

Figure 2.19. Comparison of the velocity of the impact surface and rear
surface at the point of impact.

The rear surface acceleration from two time derivatives of the Projection Moiré
data and the impact surface acceleration obtained from Newton's Second Law
and the assumption of a rigid impacting mass are compared in the following

figure.

1500
1000
500

0
—- Impact surface
-500 , -— Rear surface

Acceleration, m/S/s

-1000

-1500 '
0 1 2 3 4 5 6 7

Time, ms

Figure 2.20. Comparison of the acceleration of the impact surface and
rear surface at the point of impact.

39

It is seen in the above figures that both the velocity and acceleration histories of
the impact and rear surfaces are reasonably close to each other. It was noted
that the impact surface acceleration was never positive. This was due to the fact
that this acceleration was obtained from a load cell which could only measure

compressive forces.

The results for displacement, velocity, and acceleration for the rear and
impact surfaces were all within a reasonable range of each other considering that
the two measurements took place on two different surfaces of the Specimen. It
can be concluded that both techniques give reasonable values for determining
each quantity. In order to more fully quantify the reasons for the differences
between the quantities, an indentation study on a thinner Specimen Should be

performed with the rear surface unsupported.

2.4 Conclusions

It has been established in this study that Projection Moire is an acceptable
measurement tool for measuring displacement during plate impact testing. The
work done by other researchers has streamlined its implementation, and allows
for an efficient measurement system.

The full-field displacement provided by the rear surface measurements
give a comprehensive evaluation of the specimen. Through observation of these
results, it is possible to observe the initiation and growth of major delamination.
This was due to the fact that delamination causes a localized degradation of the

bending stiffness, and thus a discontinuity in the slope of displacement. The

40

observations are enhanced by plotting the displacement profile along lines
through the impact point. Major delamination is distinguished by a protruded
region which forms during the loading portion of the force curve, and grows to its
maximum value at the peak force.

The results from the Projection Moire measurement of the rear surface
were compared to the load cell measurements of a single point on the impact
surface. The results were quite close to each other considering that the
measurements were taken on opposite surfaces in the structure. Since it was
known that indentation on the impact surface would cause the results from each
surface to be distinct, it was concluded that both techniques give an adequate

measurement of the structure's response.

2.5 Future work

The addition of the Projection Moire' setup to the impact of composite
plates provides a valuable means for quantifying the rear surface specimen
response. Past studies [2.14] have Shown the importance of the rear layer in the
energy absorbing properties of a composite plate. Future work Should use this
setup to quantify the performance of different structures by measuring the full-
field displacement. Such a study Should provide a more thorough understanding
of the individual plate's performance and thus a better comparison of alternative
materials.

It has been shown in this chapter that the measurements by the load cell
on the impact surface and the measurements by Projection Moire of the rear

surface both give reasonable results. Differences between the displacements

41

has been primarily attributed to the indentation on the impact surface.
Indentation tests were conducted on different specimens and a different set of
boundary conditions than was used in the impact tests presented in this Chapter,
however. In order to more fully compare the impact and rear surfaces,
indentation tests Should be performed using the same Specimen as used in this

Chapter and with the same boundary conditions.

42

2.6 References

[2.1] Kokidko, D, Gee, L, Chou, SC, and Chiang, FP, “Method for measuring
transient out-of—plane deformation during impact,” International Journal of Impact
Engineering, 1996, Vol. 19, 127-133.

[2.2] Chai, H, Knauss, WG, and Babcock, CD. “Observation of damage growth in
compressively loaded laminates,” Experimental Mechanics, 1983, Vol. 23, 329-
337.

[2.3] Sutton, MA, MCNiell, SR, Helm, JD, and Chao, YJ, “Advances in 2-D and 3-
D computer vision for Shape and deformation measurements,” In:
Photomechanics, Topics in Applied Physics, Vol. 77, ed. By PK Rastogi, D
lnaudi, Elseiver:Oxford, 2000.

[2.4] Reu, PL, VanGoethem, DJ, and Cordova, TE, “Measurement of steel plate
perforation tests with digital image correlation," Proceedings of the SEM Annual
Conference, 2009, Paper no. 144.

[2.5] Tiwari, V, Sutton, MA, Shultis, G, McNeill, SR, Xu, Shaowen, Deng,
Xiaomin, Fourney, L, and Bretall, D, “Measuring Full-field Transient Plate
Deformation Using High Speed Imaging Systems and 3D DIC,” Proceedings of
the SEM Annual Conference 2009, Paper no. 206.

[2.6] Su, X, Chen, W, “Fourier transform profilometry: a review,” 2001, Optics
and Lasers in Engineering, Vol. 35, 263-284.

[2.7] Zhang, Q, Su, X, Cao, Y, Li, Y, Xiang, L, Chen, W, “Optical 3-D Shape and
deformation measurement of rotating blaeds using stroboscopic structured
illumination,” Optical Engineering, 2005, Vol. 44, 113601.1-7

[2.8] Su, X, Chen, W, Zhang, Q, Chao, Y, “Dynamic 3-Dd shape measurement
method based on FTP,” Optics and Lasers in Engineering, 2001, Vol 36, 49-64.

[2.10] Paepegem, WV, Shulev, A, Moentjens, A, Harizanova, J, Degrieck, J, and
Sainov, V, “Use of projection Moire for measuring the instantaneous out-of—plane
deflections of composite plates subject to bird strike,” Optics and Lasers in
Engineering, 2008, Vol. 46, 527-534.

[2.9] Zhang, Q, Su, X, “High-speed optical measurement for the drumhead
vibration," Optics Express, 2005, Vol. 13, 3110-3116.

43

[2.11] Pan, J, and Huang, PS, “Color phase-shifting technique for three
dimensional Shape measurement,” Optical Engineering, 2006, Vol. 45, 013602-1
- 013602-9.

[2.12] Chan, PH, Bryanston-Cross, PJ, “Spatial phase stepping method of fringe—
patterna analysis,” Optics and Lasers in Engineering, 1995, Vol. 23, 343-354

[2.13] Heredia, M., and Patterson, E.A., “Location and Shape Measurement
Using a Portable Fringe Projection System,” Experimental Mechanics, 2005, Vol.
45, 197-204.

[2.14] Rosario, K, “Quasi-three-dimensional woven composites,” Master's Thesis,
Michigan State University, East Lansing, MI, 2008

[2.15] Gulker, B, “Experimental Methods for Impact of Composite Materials,”
2009, Proceedings of the SEM Annual Conference, Paper no. 575.

44

Chapter 3: Material properties from impact testing

Abstract

One of the ultimate goals in any material testing is to identify its material
properties. If the material is anisotropic, it would require several tests in order to
identify each of the material properties. The matter is further complicated when
dynamic properties are desired. Since some materials have strain rate ,
dependent material properties, it is desired to establish test methods that will
work under dynamic loading. There are methods available which require only
one test and will function under dynamic loading. One such method is the Virtual
Fields Method. In this study, this method has been applied to plate specimens
through the use of numerically simulated data. This Simulation allowed for the
determination of the best set of boundary conditions for real experiments.
Although experimental values for bending stiffness were not found, the general
procedure for data processing in experimental implementation is presented. A
rigorous study for how to implement this method for real experiments is then

proposed.

3.1 Introduction

There are several alternatives available when determining the properties
of a material. Traditional tests such as tensile tests can be employed, but require
several different testing configurations to fully characterize materials.

The situation becomes more challenging when trying to describe the

dynamic material properties if the material of interest is anisotropic. There has

45

been some work in this field such as with the Split Hopkinson Pressure Bar which
can characterize a material, but only with respect to one direction and one strain
rate per test. Researchers have also modified drop-weight impact testing
equipment for dynamic testing of steel bars [3.1]. Any of these methods would
again require the completion of several tests in order to fully characterize the
material. There would be additional concerns surrounding the strain rate at
which the tests were being conducted. To complete this properly, it would be
required that each individual test would have the same strain rate.

In order to move away from the requirement of several individual tests for
multiple material properties, researchers have proposed solutions which utilize
the full field material response (i.e. displacement, strain, etc.). If the complete
material response is known, it is possible to extract many, if not all, material
properties from a single test. One such method is the Virtual Fields Method
developed by Grédiac and his colleagues [3.2]. In this method, surface strains or
displacements are measured as well as the forces acting on the specimen. From
these measurements, the material properties can be identified by a series of
calculations.

There have been several studies on different test setup conditions using
the Virtual Fields Method. Examples of in-plane problems are the most common.
For example, static testing has been successful for the following geometries:
double notched shear Specimen, compression of a thick composite ring, and
bending/Shear loading of a rectangular Specimen [3.2]. In this test, a thick cross

section of a filament-wound tube was compressed in one direction. A grid

46

method was used to measure the displacement on each Side of the ring. Since
the ring was axis-symmetric, only a section of the ring was measured. The
various stiffnesses of the structure were then obtained.

Dynamic in-plane testing has been completed for the tensile loading of a
notched composite Specimen [3.3]. In this test, a quasi-isotropic composite
laminate was tested in a tensile Split Hopkinson Pressure Bar. The Hopkinson
Bar was used as a loading mechanism, only. The in-plane displacements were
measured using the grid method. Several of the frames of the high Speed
camera did not have high enough acceleration values, so could not be used in
the material property calculation. The results for the Elastic Modulus was about
50% higher than the expected value, and for Poisson's Ratio it was about 10%
lower than expected. The low quality of the measurements was deemed to be
the reason for the large amount of error. For the Projection Moire measurements
used in the present work, see Chapter 2 for a discussion of the method's
accuracy.

There are fewer cases of out-of-plane problems available in the literature,
but there are a couple of useful studies available. Grédiac et al. [3.4] studied the
bending of a thin anisotropic plate simply supported at 3 of the 4 comers
(denoted as SS-3PT in this thesis). In this study, however, the displacement
data was not obtained from real test. Rather, the data was simulated using a
finite element model. The effect of noisy data was simulated by modifying the
curvature values. Two types of noise were simulated. First, the coordinates of

the displacement were shifted to Simulate an error in setting up a camera. Shifts

47

of 1% and 5% were considered. Errors in identifying the bending stiffnesses
ranged from 0.23 — 10.17% and 1.81 — 129.66%, respectively. Second, uniform
random noise was added to the curvature. Random noise of 5% of the maximum
curvature was added to each image. Errors in identifying the bending stiffnesses
ranged from 0.00 — 31.33 %. It should be noted that if the Simulated noise were
added to the displacement data instead of the curvature data, it likely that the
amount of error would increase. This is because differentiation magnifies the
effects of noise.

Grédiac also studied anisotropic plates with free-free boundary conditions
under vibration [3.5]. This test, however, required vibration of the specimen at
several frequencies to determine all of the bending stiffnesses. In this approach,
a plate was excited at its center. The vibration response was simulated using
Finite Element Analysis. Steel plates and carbon/epoxy laminates were tested.
Each test showed results close to the predicted values. The predicted values
were based on static material properties, however. Data was obtained by
simulating the experiment in a finite element model. A later study on the same
configuration implemented the method for real experiments using deflectometry
to measure the slope fields [3.2]. This measurement method provided the
advantage of measuring the slopes instead of the displacements. Since the
slope data was known, only one differentiation was required to obtain the
curvature fields. The specimen was a polycarbonate plate. The extracted elastic
modulus showed 4% error from the value obtained from a cantilever beam test.

The extracted Poisson's Ratio was not compared to any reference value.

48

In the initial applications of the method, the virtual fields were selected
manually. Some intuition was used in order to obtain fields which were useful.
As the method matured, more sophisticated methods were developed. The so-
called special virtual fields were defined such that the equations were guaranteed
to be independent by uncoupling the equations [3.6]. Since the equations were
uncoupled, each bending stiffness could be determined from only one equation.
Fields that match this definition are called “special virtual fields." A polynomial
expansion iS taken to be the general form of the virtual fields. This method,
however, requires exploring thousands of possible virtual fields in order to find
the ones which provide the highest degree of independence. This increases the
computation time.

Avril et al. [3.7] later refined this method by developing the special field
which would provide the least sensitivity to noise. It was assumed that the noise
in the measurements were random. The requirement that the virtual fields be
“Special” is maintained, however all of the possible special virtual fields are
compared using optimization theory to obtain the ones which posses the least

sensitivity to noise.

3.2 Numerical simulation

3. 2. 1 The Virtual Fields Method

The fundamental theory of the Virtual Fields Method is centered around
the Principle of Virtual Work. It will be briefly summarized here. The Principle of

Virtual Work is stated as follows [3.2].

49

—fv a:e*dV+ij rurdS+jV f-u*dV=fvpyu*dV (3.1)

In this equation, 0 is the stress, a is the strain, T is the traction, u is the

displacement, f is the body force, p is the density, y is the acceleration, V is the
volume, and Sf is the portion of the surface that the traction is acting on. Any

place that has a superscript *- indicates a virtual field. According to the
principle, this equation is valid for any arbitrary virtual field as long as the virtual
field is kinematically admissible (satisfies the boundary conditions).

If it is assumed that the material behavior follows Classical Plate Theory

and is orthotropic, the equation can be rewritten as follows.

 

DXX Is, kaXdS+Dyijfkykde+nyij(kx ky+kykx dS
,l. 62 u* (3.2)
Wssjskkd8+ jsfrutdS— jvpg—W—tzu dV

In this equation, the D's represent the bending stiffnesses, and the KS represent

the plate curvatures as described by Classical Plate Theory, e.g. [3.8].

2
—5w, —aw_k 25w

8 _ axay

 

 

 

a:
II
1:
II
II

(3.3)

If the actual loading, T, and material response is known and the virtual fields,
k" 'S and. u* 's, are prescribed, then the only unknowns are the bending
stiffnesses. Since there are multiple unknown bending stiffnesses in a given
problem, the same number of equations must be generated as the number of
unknowns. Different equations can be obtained by applying different virtual

fields. This is the fundamental idea behind the Virtual Fields Method.

50

For the case of an orthotropic plate, four equations have to be generated.

Once they are identified, solving for the bending stiffnesses is simply a matrix

algebra problem.

 

'oooo

 

XX

YY
xy

SS

 

 

 

 

 

riskx 18:1 fsky kj'ds1sfs
Skxk: st fsky 1;st sfs X y
fskx k*3ds fsky 13:3de
‘fskxijdS [Skykf/Ads [S X y

[Sf T-uy‘1dS—va

9&2
[SfT-u dS—fvp

 

l

k k*’1+k k*’1
x y y x
k k*'2+k k*’2

S k k*’3+k W3
x y y x

[SfT.u*'3dS—fvp

[SfT-ut'4dS—fvp

dS

 

dS

 

yx
dS

 

k k*'4+k k*'4)dS
y x

azw Mdv

—U
at2
82W U’* 2
atzu

 

dV

2
——a 3““de
at

2
—5 :u*’4dv
at

 

This equation can be expressed symbolically as follows.

AD=B

D=A“1B

J'Sksk:,ds1

ale, 2
Sksks’ d8

fsks k: 3dS

are,4
f8 ksks dS

 

J

(3.4)

(3.5a)

(3.5b)

If the matrix A is independent, then the vector D should be comprised of the plate

bending stiffnesses.

Prior to implementing this method for real experiments, it was desired that

the method be explored using numerically simulated data. This was done for two

primary reasons. First, it confirmed that the method was valid for the desired

loading configuration. Second, it provided a tool for comparing alternative

51

boundary conditions. This allowed for the determination of the best experimental

setup available.

3. 2.2 Numerical study using simulated data

It has been seen in the literature [3.4] that the SS-3PT boundary condition
(as defined in Figure 3.1) provides good results for obtaining the bending
stiffnesses. This, however, is not a realistic boundary condition for impact
testing. Since the ultimate goal of this study is to apply the Virtual Fields Method
to plate impact testing, an effective set of boundary conditions must be identified.
Traditionally, the boundary conditions which have been used in drop weight
testing is such that all four edges of a plate specimen are clamped. This is much
more repeatable than trying to implement some sort of simply supported
condition.

In this study, several boundary conditions were studied as well as two
different methods for defining the virtual fields. The following flowchart outlines

the procedure for evaluating each case.

52

 

Displacement
from FEA
l

 

 

 

 

 

 

 

 

 

Manually defined Mode shapes as
virtual fields virtual fields
[ Obtain D Identify set of mode shapes which
are non-zero at loading point

 

 

highest determinant of A

T
L ObtainD ]

Fdentify set of mode shapes withj

 

 

 

 

 

Compare results and select best boundary
conditions and best virtual fields

 

 

Implement selected boundary
conditions in real experiment

 

Figure 3.1. Flowchart outlining the study conducted using the Virtual
Fields Method.

The displacements obtained from F EA were for static loading. Although the
displacement in impact testing would be different in some ways, the overall
trends in the displacement should be similar for the elastic portion of the impact
event. For this reason, it was assumed that the set of boundary conditions

identified from the static, numerical study could be extended to impact testing.

53

3.2.2.1 Alternative boundary conditions

Since it is feasible for real experiments, the clamped boundary condition
was explored to understand its usefulness. For completeness, simply supported
boundary conditions were also explored as well as various combinations of
supported edges. The image below outlines the various boundary conditions
explored in this study as well as introduces the notation used to describe them.
In this image, the solid triangles (A) represent a simply supported boundary

condition and the hash marks ( .50) represent a clamped boundary condition.

54

 

 

 

 

 

 

""'[U

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

- ' A - - A A
SS-3PT SS-4PT SS-L
41;! u - 4L14vr 'l'y'
' u
’ I
’ I
F I
' -
uriiilu :rillf "r-‘IT
SS-Il SS-U 53-4
, ' gm» ,_ Q§\‘.\R\\‘:~§§k\\‘5§
9;r:<
x N
\ \
\ \
Q. \‘ l
\\\\\V\\V kaR \\\\\\\\\W\\\‘. \\\\\\\\\\\\\\
CL-L CL-ll CL-U
\\\\x\\m:\\\\\: \ l
§ § Vt
-\ \
g x
Q is
(V:
§ (ff:
s
' .x\\\\\\\\‘<§:\r >x
CL-4

Figure 3.2. Schematics and notation definition of alternative boundary
conditions explored in the numerical portion of the study.

A numerical study was performed to to demonstrate the method and
identify an effective experimental setup. Sor simplicity, a static finite element
model was built using Abaqus CAE in order to determine the static bending
response of each case. Once the best setup was determined by the numerical
study, that set of boundary conditions could be applied to real tests with
confidence. The finite element mesh used in this study was composed of

100x100 square shell elements (S4R in Abaqus). The material was defined as a

55

single orthotropic layer with material properties of E11 = 40 GPa, E 22 = 10

GPa, G12 = 4 GPa, and "’12 = 0.3. Since the material properties had to be an

input to Abaqus, the exact bending stiffnesses could be calculated using
Classical Laminate Theory [3.8]. Since the model was for a single layer, the

bending stiffnesses can be calculated as follows.

_1 L 3 3
DU—50U(zL—2L_1) (3.7)

In the formula above, 2 is the through thickness direction with zero defined at the
middle of the plate (with respect to its thickness), L is the layer number, n is the

number of layers (in this example n=1), and Q is defined as follows.

 

 

 

 

' l
_,,
E1 E12 0
11 11
—v
11 22
1
0 O —
G12
c.2=s-1 (3.9)

In the above equations, 1 and 2 are defined as the fiber and matrix directions of
the laminae, respectively. E, G, and v are Young's Modulus, shear modulus, and
Poisson's Ratio of the laminae, respectively. The bending stiffnesses resulting

from the prescribed material properties were as follows.

56

D =O.85 N-m
XX

D =3.41 N-m
yy

D =O.26 N.m
W
D =0.33 N -m
38
The results from the Virtual Fields Method could then be compared to these

reference values.

3.2.2.2 Virtual field selection

In order to solve the system of equations developed by applying different
virtual fields, it is necessary that the equations be independent. The
independence of these equations is related to the independence of the defined
virtual fields. As a first step , the virtual fields were defined manually. It is
difficult, however, to successfully define these fields manually while obtaining
independence. For this reason, it is desired that an objective means of defining
independent virtual fields is desired. In order to refine the field selection, the free
vibration mode shapes were selected as the virtual fields. These mode shapes
were obtained using the same finite element model as used for the displacement
calculation. Several mode shapes were obtained and various combinations of
four of them were explored. In most of the cases explored here, the first six
mode shapes were obtained. The results for each set of boundary conditions
and for each field selection technique were compared in order to determine the

best configuration for the real experiments.

57

3.3 Experimental implementation

An outline of the general procedure which should be followed in
implementing the Virtual Fields Method for plate impact testing is outlined below.
Tests were run, and calculations made on the obtained data. However, first
attempts at extracting the material properties from this test were unsuccessful, as
will be discussed in the subsequent sections. The likely reasons for the errors
are discussed in the Results and Discussion section. Additionally, a thorough
proposal for future study is presented. Future work should use the methods and

results used in this chapter as a starting point to refine the procedure.

3. 3. 1 Drop-weight impact testing

Impact testing was carried out on the drop-weight impact tester (DWIT).
Projection Moire measurements were used to obtain the full field out-of-plane
displacement data. Details of the setup and procedure can be found in Chapter
2 of this thesis. Since the goal is to find the elastic material properties, care must
be taken to ensure that the time step used to obtain the bending stiffnesses is
such that damage has not initiated. The results of Chapter 2 concerning the

protruded region should be taken into consideration in the present study.

3. 3.2 Data processing

Implementing the method for real test data, as opposed to simulated data,
introduces additional complications. In the experiment, the full field out-of-plane

displacement is obtained. It is the curvature data, however, that is desired.

58

Since the plate is thin, as long as the deformation is elastic, Classical Plate
Theory can be used to calculate the plate curvatures as outlined in Equation

(3.3).

3.3.2.1 Filling in unknown region

Due to the configuration of the fixture and the angle of the light projection,
there was a portion of the specimen which was not illuminated during the test.

This was due to the position of Mirror 2, as shown in the following schematic.

\I/ .

—-— LI htsource
/'\ g i) Dark region
+ <7 i 7

I i! i 4%) Specimen edge

\§ ‘//Mirror 1
4 T J

Mirror 2 fix

 

 

 

 

 

 

 

Figure 3.3. Schematic of how the restrictions on the mirror positioning
limited the portion of the specimen which could be viewed.

In order to be able to illuminate the entire specimen while still maintaining the
desired projection angle, Mirror 2 should be shifted in the positive x direction.
However, the dimensions of Mirror 1 did not allow for this. Future work should

include refining the mirror dimensions and positions.

The following displacement plot from the experiment shows the result of

this in the experimental data (Regions A and B).

59

 

 

Figure 3.4. Regions A and B indicate portions of the specimen which

could not be viewed due to shadows produced by the light projection

angle.
Future testing should involve refinement of the testing fixture to allow for the
complete specimen to be viewed. This could be done by optimizing the mirror
dimensions and locations. For the present study, however, these regions were
filled according to an assumed displacement field. Since the displacement in
Regions A and B is known to be near zero due to the clamped boundary
condition, this should not effect the results significantly. Since the Virtual Fields
Method requires the full-field response, we assume displacements in these

regions to be

wi=aix2 (3.10)

in region A where iindicates the row number and a is such that the displacement
is continuous between the known and unknown regions. This function was

chosen due to its consistency with the slope of the actual displacement in the

60

measured portion of the specimen, as shown in Figure 3.5. For region B, the

displacement pattern is assumed in a similar way.
wi=bix2y2 (3.11)
In this equation, b is such that the displacement is continuous across each

region. It was also observed that the slopes between the two regions is

consistent (Figure 3.5).

Profiles for several time steps were drawn through region A at the impact
point to show how the assumed shape of the unknown region compares with the
portion of the specimen which was visible. These profiles are shown in the

following image for several early time steps.

4 ___ _ _. _ _. ._ . .. _ _ __. .-.._ _. . , ..,V..-... . .-_.__._ . _q
E 3 :33:er $31" ”_,WJM"“’M Time, ms
E“ 7 ’/f —0.00
‘g 2 " J — 0.33
GE) 1 I / *“TW‘ —— 0.67
t6 / — 1.00
3 0. /" V —1.33
C) - 1.67

 

 

 

 

I
A
l

0 1O 20 30 4O 50 60 7O 80
Position, mm

Figure 3.5. Displacement profiles through the impact point for the raw data
and filled regions.

Although the method of filling the unknown regions is not ideal, it allows
for the use of the current test setup without modification. It is acceptable for this
testing since the displacements in the unknown region are near zero due to their

proximity to the boundary. Future testing and refinement of the experimental

61

procedure should include refinement of the test setup to eliminate this issue from

the analysis.

3.3.2.2 Spacial smoothing

Since differentiation is sensitive to noise, the displacement data must be
smoothed in order to ensure that the curvature calculations are useful. There are
a variety of methods available for data smoothing, each suited to specific
situations. In this study, there are no sudden changes in slope of the data as
long as the deformation under investigation is prior to the damage initiation. For
this reason, a simple central moving average approach is used. In this method,
the value at each pixel (point of data in an image) is smoothed by taking the
average of the pixels in the region around that pixel. This calculation is
performed for each pixel with respect to the original image. The size of the
region is defined by the user. Smaller regions are more true to the original
image, but less smooth. Several region sizes were explored. It was found that a
square region with sides lengths of 30 pixels (15 pixels in each direction) was the
best for this study since it smoothed the data adequately for differentiation as
well as matched the original data. Since there are many frames of data to be
analyzed when the high speed camera is used, the computational efficiency of
this method is beneficial. A comparison between the raw and smoothed data is

shown below for a typical time step.

62

 

 

Nw-bU'ICDNOJ

_L

 

0
Figure 3.6. Comparison between unsmoothed (left) displacement from
Projection Moiré and the smoothed results (right) from the central moving
average.

In order to ensure that all of the relevant features of the data are captured, a

profile through the impact point is drawn for each frame of displacement up to

delamination initiation. The impact point is chosen because it is the point where

the slope is the steepest. It is assumed here that delamination is the first

damage mode to have a significant effect on the material properties of the plate.

4
|
E 3 ._ ‘a— ““““
E , "" ..
+7 /’ -~2-“"-‘."‘
ac, 2 , ,v' ,,’ Unsmoothed
- I ./ .— ,"
E ,2 I ..a" — —Smoothed
a.) i / I" ,l’ .1
8 I I y" ‘-__.,——"""
E. 1 [II/2” r'”"
_U) I I r/ ,’7’
6 I 42’,’ -_-
éafid" """""""""""""" q-
’u’ __.”
o—-.~“E:—- ______ _._———-‘—— —————— F
0 10 20 3O 40 50 60 70 80
Position, mm

Figure 3.7. Displacement profile through the impact point comparing the
unsmoothed and smoothed data for different times. The time step
between lines is 0.33 ms.

63

3.3.2.3 Spacial differentiation

Once the smoothed data was obtained, the derivatives were taken. As
seen in Equation (3.3), two derivatives are required to obtain the curvatures.
After the first derivative is taken, the data must be smoothed again before the
second derivative is taken. In this study, the same smoothing method was used

at each step. Curvature results for a typical time (t = 1.33 ms) step are shown

below.

Curvature, 1/m

 

Figure 3.8. Curvature fields for a typical time step for the CL-L boundary
conditions

It is seen that the results for kx and ky both vary in a similar way between the

clamped and free edges. The results for ks show results which are nearly

symmetric with respect to the diagonal which is what was expected. Profile lines

through the impact point along the diagonal for each curvature field are shown in

the following figures.

64

 

Curvature, 1/m

0 20 40 60 80 100 120
Position,mm

Figure 3.9. Profile through the impact point for kx

 

Curvature, 1/m

o 20 4o 60 80 100 120
Position,mm

Figure 3.10. Profile through the impact point for ky

Curvature, 1/m
o m 4:. a 00

I
N

o 20 4o 60 80 100 120
Position, mm

Figure 3.11. Profile through the impact point for kg

The figures above show the high degree of noise which is present in the

curvature results. The plot for kS showed less noise due to the fact that

calculating kS involves differentiation in two directions. This has somewhat of a

65

smoothing effect. If two derivatives are taken in the same direction, the amount

of noise present in the results is much greater, as seen in the plots for kx and

ky. Due to the noise, it is difficult to identify exactly what the trend is in each of

the curvature results.

3.3.2.4 Temporal smoothing and differentiation

In addition to differentiation required for the calculation of curvatures, it is
also necessary to perform differentiation with respect to time in order to calculate
the accelerations. In order to do this, it is necessary for the data to be smooth
with respect to time. The methods for smoothing and differentiating this data
were presented in Chapter 2 of this thesis. In the previous discussion, only the
point of impact was considered. For the current discussion, however, the full
field acceleration is required. In order to obtain this, the procedure discussed in
Chapter 2 was implemented for every data point (every pixel of the set of
images). The following figure shows an acceleration field for the CL-L (two
adjacent edges clamped) test configuration at a typical time step using the

described approach.

66

m/s/s

' 4200

-1600

 

 

 

Figure 3.12. Example of acceleration fields for the CL-L plate.

3.3.2.5 Virtual field selection

The method of applying the mode shapes as the virtual fields was
investigated for use in experimental implementation. One difference here,
however, is that the specimen material properties are not known prior to testing.
Therefore, the exact material properties cannot be input to Abaqus in determining
the mode shapes. This is not a problem, however, since the virtual fields may be
arbitrary. Therefore, the results should be independent of the material properties
used in determining the mode shapes. In order to maintain consistency, generic
material properties for glass/epoxy laminates were input to the Abaqus model.

This ensures that the mode shapes obtained are for an orthotropic material.

67

3.4 Results and discussion

3.4. 1 Numerical study using manually defined virtual fields

Abaqus was used to simulate static testing of thin orthotropic plates with
various boundary conditions. The first approach used was to manually define the
virtual fields. These fields were selected by taking equations which were known
to satisfy the boundary conditions. For example, for the case of a plate simply
supported at each of its for corners, 88-4, the following equations were used.

w*’ 12x31x—L23y3ly—Ll3

TT T!
I" IV)

w*,3=(exy_1)(elX-Ll(y—'Ll_1)

1)
Ly

w*' 2=sin sin

 

 

 

(3.6)

w*’4=x55x—Ll53in

 

For different boundary conditions, the equations were modified so as to match
the boundary conditions for a given problem. Although these equations may not
guarantee independence of the matrix to be inverted, they serve as a starting
point for utilizing the Virtual Fields Method. The results are shown in the table

below.

68

Table 3.1. Bending stiffness results when virtual fields were manually
defined.

 

 

if 7T '7 7 7 i 7 7" 7 7» T
T i, _T DX¥j Pyy T 7ny77 95.5 A errxxT erry_y errxy i errss TT
TReference 705857577341 7‘ 9.7276 71 93377 .

SS-3P7TT 0.85 1-37.11 70.33 7 07.337 07.730 -8 69T7 27 ‘56 7 -1.270

3374137 70877 I 34371 0.26 T 0.30 242 0.7476 1.45 7Tf 7-97. 51 T
T ssL 0791 35417025 025 6.64 , 3.66 |-254 7 2-598
; 88-" 0.97 I 3.37 i 0.56 0.12 13.75 -1.07 l 1270 ‘ -6397T

SS-U 5 0.4122 3.75 1.05 0.30 -126 10.03 311 T -.1071
T 3547 OBZI344T109T'6'05 17.87 0.88 T 7315 -1715T
, CL7-7L 7 2.747 , 6.05 15.05 2.67 7189 7 777507757847T 700
. 7 CL-ll [ 2.27 ‘7 4.67 l -2873 141 166 I36 98 -110899 42092
TcL-u7 7 2.03 74.54 ‘ -338 17678 7 7 1739 T7333 -132208 507308T
77 CL-4 772.678 L581 j72739477,-11799 72174 ,770.7 3797 935795 -359927

Since the finite element model was for laminated composite materials, the
Reference values were determined using Equations (3.7-9).

There are a few observations to be made based on this table. First, it is
seen that the results for the clamped boundary conditions are fail, whereas a
large portion of the simply supported boundary conditions provide favorable
results. This is likely due to the difficulty in defining the virtual fields manually as
the boundary conditions become more restrictive. This is reasonable since it is
known that for in-plane testing, the contribution of the different stress
components will influence the identifiability of the different material properties
[3.2].

An additional observation is made when comparing the bending stiffness
results to the degree of symmetry present in the boundary conditions. The
simply supported cases are explored here since they are the only ones which
gave favorable results. The boundary conditions are shown below with lines

drawn for the various lines of symmetry.

69

 

 

 

-. ”:4 .........

 

 

 

 

W'""‘

 

 

 

 

 

' SS-3PT ' SS-4PT

‘IVVVV‘V """

 

 

 

 

 

 

 

 

"II'
"""'

 

 

HALTAI "f‘l'

SS-ll SS-U 88.4

Figure 3.13. Comparison of the degree of symmetry present in each of the
simply supported boundary conditions. The dotted lines represent lines of
symmetry.

The single exception to this observation is the SS-4PT boundary condition. This

can be explained, however, by the lesser degree of restrictiveness of this case

when compared to the cases of support along an entire edge.

3.4.2 Numerical study using mode shapes as virtual fields

In order to define a more robust method for defining the virtual fields, the
mode shapes of each boundary condition were used as the virtual fields. Since
several mode shapes were determined, there were a variety of combinations that
are possible for the selection of four virtual fields. As a starting point, the first six
mode shapes were explored as possible virtual fields.

It was determined that the best results were obtained when the
displacement of the virtual field was non-zero at the location of loading. If the
displacement is zero, then the right hand side of the equation goes to zero. The

resulting bending stiffnesses in this case are not meaningful. There was one

70

observed exception to this trend (the CL-U case) which will be discussed later in
this section.

As an example of the method, the mode shapes for the CL-L condition are
shown below. For each mode shape, it was observed that the displacement at
the center of the plate was non-zero. Therefore, any combination of them should
work, provided that matrix A is independent. In order to rank the various possible
combinations of mode shapes, matrix A was assembled and the determinant was
calculated. The combination which provided the highest determinant of matrix A
was taken to solve for the bending stiffnesses. The combination with the highest
determinant for matrix A was chosen since a high determinant suggests that the

equations which make up matrix A are independent.

Mode 2

Mode 1

        

             

Mode 4 Mode 5 ' Mode 6

Figure 3.14. The first six mode shapes for the CL-L case. The specimen
orientation is the same as Figure 3.6.

71

The same procedure was followed for each of the remaining boundary

conditions. The results are summarized in the table below.

Table 3.2. Results for numerical study of alternative boundary conditions
based on static loading using simulated data. Four mode shapes ere
selected as virtual fields. Definitions of boundary conditions can be found

 

 

 

in Figure 3.1.
7777 47 7T 7 7 I
T Dx7x T Dyy T ny7 T Dss
Reference 0. 85I 737. 41 T 70. 26 170737737
337 -3P7T T086 I 3.67 0 T033
7 ss7-4P7T 2. 21 T39. 76 T7 -0. 2 T 78.72737
S-L T 0 85T 3. 43T 0. 27 0537‘

 

 

 

err Ierr
xx, ny

 

T7778 83-" T225T664 471.927 87.43
T 63-6 T 0.89 3.45 0.29 0.31
T758477 T7072T 1.774T 73 T—1.65
T 671.1 7T091 3.73 023 T03
‘7 (EL-7| 2.38T175 T 10.69 T3567
T 7CL7-u7 T107 4.02 T7-1.7 0.947
T777 1.3 77 27257 T 4.56 T-1g42 6319777

‘ - I

20.46 T 5.763
1597 T 106617
70.273 70.475
7163 T9468
74.14 71.2717
-7616T 1751
6.3 T938
7179 T456177
25 87 T 134

54637137985 T

164 T 33. 59 T-f19422577T1:89591 10

 

 

errx7y T err 3T
_ * l "f ,
7L71017T-1.32 T
7 -178 7-257687I
6.237 7-0747
747579 7 72428 71
13 877 -5. 857
2254] 5975

-8.29 I -10.83

 

-766

 

182 T

In dynamic testing, the general shape of the deflection is the same as for the

static case. All of the symmetry conditions are dictated by the boundary

conditions and the location of loading. For this reason, it is believed that the set

of boundary conditions which is determined to be the best in the numerical

simulation is also the best for impact testing.

3.4.2.1 The CL-U set of boundary conditions

It was stated in the previous section that the CL-U case proved an

exception to the trend that the virtual field should be non-zero at the location of

loading. When the mode shapes with non-zero values at the load location were

72

 

selected (modes 1, 2, 3, and 6), the results were unfavorable. This is seen in
row 2 of Table 3.3. However, when modes 1, 2, 4, and 5 were used, row 3 of
Table 3.3, the bending stiffness results were quite good. Note that modes 4 and
5 have zero values at the loading point. The first six mode shapes are plotted

below.

Mode 1 Mode 2 Mode 3

    

Mode 4 Mode 5 Mode 6

Figure 3.15. The first six mode shapes for the CL-U case. The specimen
orientation is the same as Figure 3.6.

The results for the highest determinant case, the non-zero case, and the “best”
results are shown below. The “best" results were determined by examining all
combinations of the six mode shapes and identifying the option which possessed
the smallest total error, row 4 of Table 3.3. It is seen that all cases possess a
high degree of error, but the expectation was that the smallest error should be
when the mode shapes with the non-zero values at the load point were used.

This, however, was not the case.

73

Table 3. 3. Comparison of results for the CL-U case using different
combinations of mode shapes

 

 

 

 

 

 

 

 

__ " — T ’l
[ Dxx [ Dyy ny Dss errxx erryy errxy errss
T--- --_i- ....... r_____ J . m.— --flwt—u ,_._‘_22__,*.____ L——
_1” 7 Reference 0.85 l 3.414026 093 2'” :_ g if if I
Non-zero at load; , l
_ Modes1 2 3 6 1.07 l 4.02 -1.705 0.94 25.87 17.94 -766 182

 

  
 

 

_———~—{ __fi. -———< _ _ .._, 0___ _ .

 

' T - *- l—- ~_‘~l——+~ if“ _._,
Highest det;
Modes1 3 5 §+0 6.8 3.33 l 2.16 l-O. 33 20.51 -2.27 742 -199

——-— __.. --_!_-_.._____- fl ___,_ _ _ _ _,
“Best” results 1 l
l 4. Moldes1 2; 4 _51 0.52 l 3.69 0.51 ”0.39 -39.16 8.18 97'46l17'76'

,m- . _,i___ __,,_.___. __._.__ ._ u

 

 

 

 

 

 

 

 

___L

It seems as though this must be due to the restrictiveness of the boundary
conditions. Since the CL-U case is one of the most restrictive, based on the
number of restricted edges and type of boundary conditions, it follows that it
should be one of the most difficult to properly identify an appropriate set of virtual
fields. This boundary condition, therefore, should be avoided in the experimental

implementation of the method.

3.4.2.2 The CL-4 set of boundary conditions

The most frequently used configuration for impact testing in past studies
has been one in which each edge of the specimen is clamped. This was due to
the fact that clamped boundary conditions are easiest to obtain in real
experiments. Additionally, the symmetry of the problem made it relatively easy to
analyze compared with alternative boundary conditions. It is found in this study,
however, that the CL-4 set of boundary conditions produces unfavorable results

when implementing the VFM.

74

It has been demonstrated in the previous sections that increasing the
restrictiveness (based on number and type of boundary conditions) of the
boundaries reduced the accuracy with which the bending stiffnesses could be
identified. Also, increasing the amount of symmetry in the specimen decreased
the quality of the results. Since the CL-4 is both the most restrictive (four
clamped edges) and has the highest degree of symmetry, it does not give
favorable results for the bending stiffnesses. Although CL—4 has been used
extensively in past studies, it is not a good candidate for the determination of

plate bending stiffnesses.

3.4.2.3 Refinement for the CL-L set of boundary conditions

From the above study, it is concluded that the most appropriate set of
boundary conditions for further study is the CL-L condition. From past
experience, it is known that clamped boundary conditions are the only practical
choice for real experiments, and the L configuration has proven to be the most
favorable for the implementation of the Virtual Fields Method.

Since the CL-L boundary condition has been selected as the setup of
choice for future use, it was desired to determine how this technique could be
enhanced by considering additional mode shapes. The number of mode shapes
considered was expanded to the first twenty. Again, the combination of four
mode shapes which provided the highest determinant of matrix A was taken as
the best solution. It was found that the highest determinant was found when
mode shapes 3, 4, 10, and 11 were used as the virtual fields. The table below

compares the results.

75

Table 3.4. Comparison of the results obtained for the CL-L case when the
first six modes are considered and when the first twenty modes are
considered.
, .-r _ .._- __--.- ee- _fi. __._m_..
L -.__ loxx -. ny - PXJ_- Pss
' Reference 0.85 3.41 f 0.26 0.33

._________.. ”__...— ‘d # 7* A V #4

l MmggesLG 0.89 @517 13.68: 0.42 4254

 

 

 

 

_gee __.7 , ..__ _. . .1

USiHQEDQQES 1-20 -990 22373.2 923“ 0-30 , ..-

 

 

 

 

 

 

 

 

3.4.3 Experimental implementation

3.4.4 Sources of error

The results of the experiments study did not provide useful values for the
bending stiffnesses. As different combinations of mode shapes were selected as
the virtual fields, there was significant scatter in bending stiffness results. For
this reason, it was concluded that substantial work was still needed.

Among the sources of error was the amount of noise present in the
curvature plots. This can be seen by observing Figures 3.8-11. In this set of
images, there is a great deal of oscillation in the resulting values. The noise
present in the curvature results is more severe than was present in the
displacement data from which it was calculated. This is due to the fact that
differentiation magnifies the effects of noise. Future work should focus both on
further reducing the amount of noise in the original image as well as on better
smoothing techniques. It should be noted that the noise did not negatively effect
the acceleration calculation as much as the curvature calculation. This can be

seen by examining the comparison of the impact and rear surfaces in Chapter 2

76

of this thesis. Apparently, the smoothing technique used for the acceleration
calculation was more effective.

An additional source of error in this test is the section of the specimen
which could not be viewed by the high speed camera as shown in Figure 3.3. In
order to properly implement the proposed method, the fixture should be refined
by optimizing the position and size of the mirrors such that the entire specimen is

illuminated.

3.5 Conclusions

The method of using mode shapes as virtual fields was found to perform
better than the method of manually selecting functions to use as virtual fields. In
part, this was due to the fact that, by selecting mode shapes as the virtual fields,
it is guaranteed that the fields were independent. Additionally, it provided a more
objective method for virtual field selection than semi-arbitrarily manual fields. In
the numerical study of alternative boundary conditions, it was found that the
method of selecting mode shapes provided results which were consistently more
accurate than the method of manually defining the virtual fields. Finally, the
mode shapes method allowed for the identification of bending stiffnesses in the
case of clamped boundary conditions, whereas the method of selecting the
virtual fields manually failed for each of the clamped cases. Since clamped
cases are more practical to implement in real experiments than simply supported,
the method of selecting mode shapes as virtual fields is the better choice.

It was found that the CL-L set of boundary conditions provided the best

results for applying the Virtual Fields Method for the current loading scenario.

77

The selection of this case was a result of finding a balance between the following
contributing factors.

1. The best results are obtained when the boundary conditions are less
restrictive. For example, better results are obtained with simply supported
than with clamped boundary conditions.

2. The selected set of boundary conditions must be selected such that each
bending stiffness influences the plate response significantly enough. For
example, The CL-L configuration performs better than the CL-4
configuration since CL-4 is not sensitive to twisting.

3. The selected set of boundary conditions must be practical for experimental
implementation. For example, clamped edges can be implemented simply
and consistently in experiments whereas simply supported edges cannot.
Although the numerical study was based on static loading, it is thought

that the configuration should also be the best configuration for dynamic loading.

This conclusion is due to the fact

3.6 Future work

The methodology presented in this chapter for implementing the Virtual
Fields Method needs further refinement. It was seen that the curvature fields
contained a large amount of noise. Further study needs to be conducted to
reduce this. Future work should focus on reducing the noise in the displacement
data as well as on alternative techniques to smooth the data before
differentiation. In addition to the data processing, the fixture design needs to be

refined. Presently, the entire specimen is not illuminated by the grating

78

 

projection system. The fixture needs to be refined in order to obtain the optimum
size and location of the mirrors for the prescribed projection angle.

In order to apply the Virtual Fields Method to impact testing, it is proposed
that several intermediate studies be carried out. First, experiment should be run
for static loading cases. This should validate the findings of the numerical
approach used in this thesis study. Upon completion of the static case, quasi-
static simulation and testing should be conducted. This should then be followed
by impact simulation and testing. Each of the simulations should resemble the

numerical method used in this thesis.

By conducting this incremental study, the problem would become more
complex at each step. For example, the static testing results would not include
acceleration calculations. Potential sources of error may be identified and
corrected in each stage of the study. Therefore, the procedure could be refined

step-by-step before finally implementing the impact test.

In addition to being a useful study for refining the method, it would provide
valuable insight into the influence of strain-rate on the materials. If the same
specimen was used for each of the three loading cases, then the material
properties extracted at each stage should provide a portrait of the material's

performance under different loading rates.

79

 

3.7 References

[3.1] Shin, H.-S., Lee, H.-M., and Kim, M.-S., “Impact tensile behaviors of 9%
nickel steel at low temperature,” International Journal of Impact Engineering,
2000, Vol. 24, 571-581.

[3.2] Grediac, M, Pierron, F, Avril, S, and Toussaint, E, “The Virtual Fields
Method for Extracting Constitutive Parameters From Full-Field Measurements: A
Review,” Strain, 2006, Vol. 42, 233-253.

[3.3] Moulart, R, Pierron, F, Hallett, SR, and Winsom, MR, “Full-field strain
measurements at high rate on notched composites tested with a tensile

Hopkinson bar,” 2009, Proceedings of the SEM Annual Conference, Paper no.
176.

[3.4] Grediac, M, Toussaint, E, and Pierron, F, “Special virtual fields for the direct
determination f material parameters with the virtual fields method. 3. —
Application to the bending rigidities of anisotropic plates,” International Journal of
Solids and Structures, 2003, Vol. 40, 2401 -241 9

[3.5] Grediac, M, and Paris, PA, “Direct Identification of Elastic Constants of
Anisotropic Plates By Modal Analysis: Thoeretical and Numerical Aspects,”
Journal of Sound and Vibration, 1996, Vol. 195, 401-415.

[3.6] Grediac, M, Toussaint, E, and Pierron, F, “Special virtual fields for the direct
determination f material parameters with the virtual fields method. 1. — Principle
and definition,” international Journal of Solids and Structures, 2002, Vol. 39,
2691-2705.

[3.7] Avril, S, Grédiac, M, and Pierron, “Sensitivity of the virtual fields method to
noisy data,” Computational Mechanics, 2004, Vol. 34, 439-452.

[3.8] Daniel, I, and lshai, 0. Engineering Mechanics of Composite Materials. New
York: Oxford University Press, 2006.

80

Chapter 4: Translucent composites for studying damage
progression

Abstract

Translucent glass/epoxy specimens can be made by using fiber and
matrix with a similar index of refraction. This technique was used to make
specimens for impact testing. Since the specimen was transparent enough, it
was possible to see the delamination growth within the specimen during the
impact event by using a high speed camera. This information could then be
compared to the force history. Since delamination can be observed as a function
of time, it was possible to estimate the crack speed between images.
Additionally, methods for implementing the Projection Moire method at the same
time as observing the delamination were explored. Partially painted specimens
and semi-transparent paint were used. It was found that both measurements can
be implemented at the same time effectively, but it is difficult to obtain the correct
balance between transparency and opacity. This problem may be easier to solve

over time as high speed camera light sensitivity continues to improve.

4.1 Introduction

In addition to the deflection and force measurements which have been
established in the previous chapters, it would be greatly beneficial to measure
the damage progression within the composite material during the impact event.
Takeda et al [4.1] conducted a study in which light was transmitted through the

specimen during ballistic loading. The light allowed for the observation of the

81

total delaminated region which was recorded by a high speed camera. Since the
specimen was not transparent, however, the study was limited. As the specimen
thickness increases, the amount of light which can be passed through the
specimen decreases, and the visibility of the delamination diminishes.

This would be greatly enhanced if the degree of transparency was
increased. It is possible to make glass/epoxy composites which are very close to
transparent if the index of refraction of the fiber and matrix is very close, if not
identical. Details about how this can be achieved in VARTM manufacturing of
composite materials can be found in the work by Dhyani [4.2].

In addition to observing the damage evolution within the composite, it
would be beneficial to perform Projection Moire measurements simultaneously in
order to more fully quantify the material's behavior. In order to obtain this, it is
necessary to find a balance between complete transparency which is good for
observing internal damage and complete opaqueness which is good for

Projection Moiré measurements.

4.2 Methods

The method for impacting these specimens was the same as outlined in
Section 2.2 of this thesis. The specimens were made with sufficient
transparency by the same procedure as used by Dhyani [4.2]. Two types of
specimens were tested — woven composites and cross-ply laminated
composites. The woven composites were manufactured by stacking several 0/90

plain-weave layers together. The laminated composites were manufactured by

82

aligning yarns to make individual single-direction layers. These layers were then
stacked together to create a cross-ply laminate.

The optimal setup for observing the internal damage is a completely
transparent specimen. In contrast, the optimal setup for Projection Moiré
measurements is a fully opaque in order to reflect the maximum amount of light
possible. In order to reach a compromise, two techniques were used. One
approach utilized the symmetry of the material and the boundary conditions. Half

of the specimen was coated in matte white paint and the other half was left

-' Fifi _‘MM‘JE

 

r;

unmodified. In the other approach, a semi-transparent white paint (Plaid
Pearlcote) was used to coat the rear surface. Since the coating was only semi-
transparent instead of matte white, not as much light was reflected from the
surface. This reduced the maximum frame rate which could be used by the high
speed camera while still recording an image. Additionally, the semi-transparent
paint used in this study had a glossy finish. This produced undesired glare in the
images. In order to remove this glossy finish, the painted surface was lightly
sanded with 600 grit sand paper. The rules established in Chapter 2 regarding

system setup and grating size were maintained in this study.

4.3 Results and discussion

4. 3.1 Woven composite with painted sections

A woven composite specimen was manufactured to use in the
development of the test method. It was known that a balance must be found

between transparency and opacity. For this reason, the testing area of this

83

woven composite was divided into four regions. Region 1 had no paint, Region 2
had a single coat of semi-transparent paint, Region 3 had two coats of semi-
transparent paint, and Region 4 had the same opaque, matte, white paint as
used in Chapter 2 of this thesis. The impact location was approximately at the
intersection of these four regions. The different regions are shown in the image
below with a grating projected onto the specimen. The area outlined with a
dotted line is the portion of the specimen which is visible in Figures 4.2 and 4.3.

The high speed camera was set to 7,000 frames/sec in this image since this is

“new“ - " ' Inga

the frame rate which will be used during testing.

84

Region 1 Region 2

Delamination area

Center ofspecimen

Region 4 Region 3

 

Figure 4.1. Woven composite specimen with four regions of different
degrees of transparency. The dotted line shows the portion of the
specimen which is visible in Figures 4.2 and 4.3.

One of the deformed images from the test on the above specimen is
shown below outlining the delamination region to make it stand out. The impact
point is noted as the + symbol in the image on the left. The impact point is at the
center of the plate, however, the painted regions do not intersect exactly at the

center of the plate.

85

 

Figure 4.2. Typical image during delamination growth (left) and outline of

the delamination shape (right). Only region outlined in Figure 4.1 is

shown. The grid pattern of the delamination corresponds to the weaving

geometry of the layers. The + indicates the impact point.
The symmetry of the delamination pattern in the image above could by utilized in
future studies by painting one half of the specimen in matte white paint and
leaving the other completely transparent. This would provide half of the
specimen which was ideal for Projection Moiré and half that was ideal for
identifying the delamination. It could then be assumed that the delamination was
symmetric over this line since the lay up was orthotropic. Of course, it would be
better not to have to make this assumption at all. For this reason, the method of

simultaneously measuring the full field of both delamination and displacement

through the use of semi-transparent paint was used in this thesis.

In order to show the delamination evolution and how Regions 1—3
performed relative to each other, a sequence of images during delamination

growth are shown below.

86

 

Figure 4.3. Delamination growth in the area outlined in Figure 4.1.
Images are 0.14 ms apart.

The delamination is clearly visible in both Regions 1 and 2. It is still visible
in Region 3, but to a lesser degree. Some of the difficulty in identifying the
delamination area in Region 3, however, is due to the glare (an effect of the
glossy paint) in that portion of the image. This effect is outlined with a solid line

in the following figure. This problem was improved in subsequent testing by

87

lightly sanding the painted surface to remove the glossy effect of the paint. In the
final five frames of the set of images shown above, fiber breakage can be seen.
The region of fiber breakage is outlined with a dotted line for a sample image in

the figure below.

 

Figure 4.4. Sample image showing the portion of the specimen for which
fiber breakage is developing. The fiber breakage is outlined with a dotted
line. The glare is outlined with a solid line.

Once fiber breakage occurs, it is seen that the projected grating lines are no
longer distinguishable in this portion of the specimen due to the blurring. The

blurring could be caused by one of the following. First, the velocity of that portion

88

of the image could have been too high for the specified frame rate (7,000
frames/sec) of the camera to accurately capture. Since increased deformation
causes the projected grating lines to move quickly, this could explain the blurring.
Second, the out-of—plane displacement at that point could have been such that it
was too far from the plane of focus for the camera. A higher camera frame rate
could solve the first issue. The second issue could be solved by ensuring that
the maximum displacement of the image was such that the camera would always

be in focus.

 

Since the projected grating was visible on Regions 2-4, it was possible to
calculate the out-of-plane displacement by the Projection Moire method
discussed in Chapter 2 of this thesis. The results are shown in the images

below.

89

 

Figure 4.5. Projection Moiré results for Region 2.

 

 

   

Figure 4.6. Projection Moire results for Region 3.

90

 

Figure 4.7. Projection Moire results for Region 4.

 

Figure 4.8. The unprocessed image of the specimen (left), and the
Projection Moiré results for each region (right).

91

It is seen that the Projection Moire results for early displacements work
fine for all three regions. However, Regions 2 and 3 have problems for later
frames, whereas Region 4 provides good results for all time. There are several
factors that create problems. First, the glare near the loading point makes it
difficult to identify the grating lines. Second, as fiber breakage develops, the
grating lines are blurred. In order to solve this problem, future tests should be at
an impact velocity such that fiber breakage is minimal or does not occur at all.
Or, if fiber breakage does occur, develop techniques that allow for image

recording at higher frame rates, such as 15,000 frames/sec as used in Chapter 2.

4.3.2 Cross-ply laminate

4.3.2.1 Cross-ply delamination

A [04/904/04 ] translucent laminate with a thin layer of semi-transparent

paint was impacted from a height of 320 mm. Only a thin coat was used in order
to maximize the amount of delamination visible. Since delamination was the
primary feature of this test to be measured, this was deemed acceptable. The
Projection Moire setup was implemented based on these images, but data
processing revealed that not enough light was transmitted back to the camera to
accurately calculate the out-of—plane displacement. The specimen still gave
valuable insight into the delamination evolution within the specimen. In order to
make the delamination more visible, the image contrast and brightness was
adjusted. An example comparing the raw Image to the adjusted image is shown

below.

92

 

 

Figure 4.9. Modification of the contrast of the high speed camera image in
order to make delamination more visible.

It is seen in the image that the delamination at each interface matched the
peanut shape deformation found in the literature [4.3]. For the frame in the
image above, an outline was drawn around each of these delamination regions.
Solid lines indicate where the delamination is clearly seen. Dotted lines indicate
an assumption made about the delamination shape based on the symmetry of

the specimen and boundary conditions.

93

 

Figure 4.10. Outline of the delamination area which is visible in image
(solid line) and the assumed delamination clue to symmetry (dotted line).

The delamination region is shown for the period of delamination growth in the

following set of image.

I Fill‘il “i i' 'l: ‘ ‘ . V ’l
‘Iillllllllll - . I, II llllllll

"“‘lllillllll ‘* "‘IllIllllll

 

Figure 4.11. High speed camera images in the area of delamination for
the period of delamination growth. Time between frames is 0.14 ms.

The corresponding force curve is shown in the figure below. The delamination

area from the high speed camera is also shown.

94

u
,-
e
u
n
,-
u
o
c
-
.9
1
I“‘
,-
.e
a
e
u
,.
,-
e
e
.v

  

77W

Time, ms

 

Figure 4.12. Comparison between the force history and the high speed
camera images showing delamination.

4.3.2.2 Estimation of crack speed

Since the delamination growth between frames is visible, and the time
step between frames is known, it is possible to calculate the average crack
speed between two frames. Takeda was able to do this in a previous study [4.4],
but the use of transparent composites should greatly simplify the process.

The crack is growing in many directions simultaneously, but the primary
direction of growth is along the fiber direction of the bottom layer of the interface.
For the rear layer, the crack speed has been calculated for each of the “arms” of
the delamination. The average crack Speed for both arms of the delamination

was found to be 5.84 m/s.

95

 

-- Force history

0 Crack speed,
left arm

El Crack speed,
right arm

- - Average crack
speed

 

Crack speed, m/s

 

Figure 4.13 Comparison between the force history and the estimated
crack speed of the primary direction of delamination.

The accuracy of the crack speed calculation is dependent on several
factors. First, the camera resolution. Since it is only possible to determine if the
delamination has propagated in discrete steps (pixels), it is not possible to
determine the exact position of the crack tip. Second, the frame rate of the
camera. Again, the time steps between frames are discrete values prescribed by
the frame rate of the camera. This study identifies the pixel number at the crack
tip and determines the crack speed by comparing this to the pixel number of the
crack tip in the previous image. This means that each pixel of delamination
growth between images corresponds to the following crack speed.

0.13 mm * 7,000
pixel sec

 

=0.91m/s/pixel

For example, if the crack grew by 2 pixels, that would be a crack speed of 1.82
m/s. The calculation of the crack speed could be more accurately performed if a

higher frame rate were used for the testing.

96

The length of each arm of delamination is plotted in the following image as
a function of time. Note that, for the right arm, the delamination reached the
edge of the imaged area before arresting. Shadows are cast on the specimen
due to the thickness of the fixture, so the image edge is not the boundary edge.
The delamination likely propagated further as was the case with the left arm.
However, it is not possible to determine the arrest point from this test. In future
testing, the experimental setup should be such that the entire delamination

region is within the imaging area.

 

 

30r
25*

N
O
1

- - Left arm length
— Right arm length

_s
01

 

 

Length, mm
9. a

 

 

O
oq__
_3
N4
00
A

Time, ms
Figure 4.14. Length of each arm of the delamination in the rear layer of
the laminate as a function of time.
There is a wide range of possible testing that could be performed in future
work with this method. For example:
. Delamination resistance for different material configurations.
. The effect of the number of interfaces on the delamination initiation and
propagation.

. The effect of strain rate on the delamination initiation and propagation

97

4.3.2.3 Projection Moiré with cross-ply laminate

In addition to the study of the delamination growth, the Projection Moiré
method was applied to this specimen. The results for this analysis are

summarized in the following figure. The frames in this image are 14 ms apart.

 

Figure 4.15. Projection Moire results for the transparent cross-ply
laminate. Time between frames is 0.57 ms.

98

Although the overall results of this image are not good, several useful
observations can be made. First, The cross-ply laminate was initially more
transparent than the woven composite from the initial study. This made it difficult
to accurately reproduce the degree of translucency from the previous woven
laminate. The same painting procedure as was used in Region 2 of the cross-ply
laminate was implemented for the entire surface of the cross-ply laminate.
However, the end result was more transparency for the laminate due to the
difference in the transparency of the two plates prior to painting.

Second, It is seen that the primary portion of the image that fails to
produce usable results is the left side of the image. This can be explained by
taking into consideration the angle at which light is projected onto the specimen.

The figure below demonstrates this.

'4

Light source —>|

Darker f" Brighter
side side

/

Figure 4.16. Schematic of how angle of light projection causes one side of
the specimen to be darker than the other.

It is seen in this image that half of the deformed specimen will receive less light
to reflect back to the camera than the other half. The darker half corresponds to
the left side of the images in Figure 4.15 where the Projection Moire results are

the worst. In future testing, either more light must be projected onto the

99

specimen, a higher degree of light reflected back by decreasing the transparency
of the specimen, or a camera with a higher sensitivity to light must be used.

‘ Third, it is noted that the second region of the specimen that has a high
degree of error is around the impact point. This corresponds to the increased
velocity of this region as the fibers begin to break as discussed in the section
about woven composites. This could be solved in future testing either by using a
higher frame rate for the camera or by ensuring that the impact velocity was such
that this phenomenon was avoided.

Being able to measure both the delamination and the deformation
simultaneously presents an advantage. It allows for a correlation between the
damage degree and the structural response. Since delamination changes the
stiffness of the composite, it would be possible to objectively quantify the degree
by comparing the out-of-plane displacement and the delamination size.

Subsequent tests refined the method for achieving this.

4.3.3 Woven composite with half painted surface

In order to further explore the simultaneous implementation of translucent
specimens and Projection Moire’ measurements, additional cross-ply specimens
were created. These new specimens were 2.25 mm thick consisting of woven
cross-ply layers. The initial height for the impacting mass during the testing of
these specimens was 150 mm. The frame rate of the high speed camera was
held at 7,000 frames/sec as with the other tests in this chapter; The surface of
one of these specimens was divided into two regions. One region was painted in

the matte white paint used previously while the other region was left unpainted.

100

This provided half of the specimen with the ideal conditions for observing internal
damage while the other region was the ideal condition for Projection Moiré
measurements. Since the material and boundary conditions were symmetric
across the boundary of these two regions, the behavior of the composite should
be the same in each region. Symmetry could then be used to determine the full-
field displacement and the full field internal damage. The specimen with the

separate regions and the projected grating are shown in the following figure.

 

Figure 4.17. Woven translucent specimen with half of the rear surface
painted white.

An additional light source was focused on the impacting surface of the
specimen. The purpose of this light source was to increase the amount of light
traveling through the translucent section of the plate. Since the Projection Morie
section was fully opaque, the addition of this light source should not negatively

effect the displacement calculation.

101

The out-of—plane displacement for the white section is plotted together with
the damage progression in the figure below. The delamination in this specimen
was less than for the previous specimens since the thickness of the composite
was smaller. Due to the thin nature of the plate, fiber breakage took place earlier
in the impact history and delamination arrested earlier. As the fiber breakage
begins to occur, the quality of the Projection Moire results in the area of fiber
breakage decreases. This can be seen in the starting in the second image of the
figure below. It is seen in the figure that both the delamination and the

displacement can both be known through using this technique.

102

 

mm

 

 

Figure 4.18. Projection Moire and delamination outlines for the woven
composite with half of the surface painted white. Images are 2.86 ms
apart.

4.3.4 Semi-transparent surface

There are conceivable testing conditions in which the boundaries or the
material is not symmetric. The CL-L case from Chapter 3 of this thesis is an

example such a case. Although a line of symmetry exists along the diagonal for

103

the boundary conditions, this is not a line of symmetry for the material. In order
to perform a study in which both the damage and the displacement were desired
for the full field, it would be necessary to be able to directly measure both
quantities over the entires surface. It would not be useful to simply paint half of
the specimen as was done in the previous section since symmetry would not
allow one to make conclusions about the full-field. For this reason, it is desirable
to further refine the method of measuring both simultaneously for the entire

surface using semi-transparent paint.

Additional specimens like those in the above section were used to refine
the method for identifying both internal damage and displacement for the full-
field. One specimen was painted with two coats of the semi-transparent paint
and lightly sanded to remove the glossy finish. The results of the Projection
Moire calculation are shown in the following image. It is seen int his figure that
the overall trend in displacement is quite clear. There are some regions,
however, that have noticeable errors. These errors appear in the darker side of
the image and around the fiber breakage zone as previously identified. The
number of regions in which errors occur, however, is drastically reduced in this

test as compared with the cross-ply laminate.

104

 

 

 

 

 

 

Figure 4.19. Projection Moire results for the translucent composite with
two coats of semi-transparent paint.

The next step in analyzing this specimen Is to determine if the growth in
delamination can be seen through the painted surface. The following images
show the evolution of the delamination. In this image, the brightness and
contrast of the image were adjusted to make the delamination pattern visible in
the document. Although there are portions of the delamination which are clearly

visible, other portions of the specimen are more difficult to observe. Still, an

105

outline of the delamination can be drawn with a reasonable degree of confidence.

Dotted lines are used instead of solid lines to indicate a degree of uncertainty in

identifying the delamination area.

 

Figure 4.20. Delamination growth in the woven composite with two coats
of semi transparent paint. Time steps between the images was 1.43 ms.

Since it was desired to obtain the delamination area with a higher degree
of certainty, a specimen was tested in which only one coat of semi-transparent
paint was applied to the surface. The DWIT setup parameters were the same as
those as for the previous specimen. Since there was less paint on the surface,
less light was reflected back to the camera. Therefor, it was expected that the
Projection Moiré results would be of a slightly lower quality that those for the

specimen with two coats.

106

The following image shows the out-of-plane displacement for the

specimen with one coat of semi-transparent paint.

 

 

 

 

Figure 4.21. Projection Moiré results for the woven specimen with one
coat of semi-transparent paint. Images are 0.57 ms apart.

It is seen that there are slightly more errors due to the illumination intensity than
there were for the case of the specimen with two coats of semi-transparent paint.
However, the overall results are quite good. The trend in each individual image

is clear, and the trend with respect to time matches the expected results.

107

Again, the region where delamination took place was inspected to see the

growth with time.

 

Figure 4.22. Delamination growth in the woven composite with one coat of
semi transparent paint. Time steps between the images was 1.43 ms.

4.4 Conclusions

It is seen from this study that the observation of delamination growth is
greatly enhanced through the use of translucent composite materials. With this
approach, it is possible to determine not only the final delamination area, but the
progress of delamination throughout the impact event.

Additionally, it is possible to perform Projection Moire measurements at
the same time as observing the internal damage. There are two techniques

which can be used. First, if the boundary conditions and material are both

108

symmetric, half of the specimen can be painted white while the remaining half is
left uncoated. If the setup is symmetric, the behavior can be mirrored over the
boundary between the painted and unpainted surface.

The second approach is to use a semi-transparent paint to coat the entire
rear surface of the specimen. Using this technique requires some effort to
determine an acceptable compromise between transparency and translucency.
If the specimen is too transparent, the Projection Moire measurements will not
work, and if the specimen is too opaque, the delamination will not be visible. If
an acceptable compromise is reached, both the displacement and internal

damage can be measured accurately.

4.5 Future work

It has been demonstrated here that the internal damage of a specimen
during an impact event can be measured with the use of translucent composites.
Since one of the primary concerns when comparing different composite
structures is their resistance to delamination, it would be beneficial to compare
different composites (stacking sequence, weave geometry, etc.) by measuring
the delamination with respect to time.

It was seen during the use of semi-transparent paint that, while the overall
Projection Moire results were good, there was still some portions of the specimen
which contained errors. In order to further refine the method, these errors should
be eliminated. The reason for these errors was primarily due to the darkness of
the image. There are several factors which could improve these results. First,

increase the amount of light reflected from the specimen back to the camera. A

109

considerable amount of refinement has already been presented for this factor in
this thesis. The second contributing factor is the amount of light provided by the
light source. Increasing the amount of projected light would increase the
brightness of the recorded image. This could be done by optimizing the grating
projection system. Several of the components could be refined including the light
source, lens selection, and component location. The third factor is the light
sensitivity of the camera. High speed camera light sensitivity decreases with
increasing frame rate due to the decrease in exposure time. As high speed

camera technology continues to improve, this problem should be alleviated.

110

 

4.6 References

[4.1] Takeda, N, Sierakowski, RL, Ross, CA, and Malvern, LE, “Delamination-
crack propagation in ballistically impacted glass/epoxy composite laminates,”
1982, Experimental Mechanics, Vol. 22, 19-25.

[4.2] Dhyani, A, “VARTM Process With Some Modifications,” Master's Thesis,
Michigan State University, East Lansing, MI, 2008.

[4.3] Liu, D. “Impact-Induced Delamination - A View of Bending Stiffness
Mismatch,” Journal of Composite Materials, Vol. 22, 1988, pp. 674-692.

[4. 4] Rosario, K, “Quasi- three- dimensional woven composites, Master's Thesis,
Michigan State University, East Lansing, MI, 2008.

 

111

Chapter 5: Conclusions and future work

5.1 Conclusions

5. 1. 1 Impact testing with Projection Moiré

It has been established in this study that Projection Moiré is an acceptable
measurement tool for measuring displacement during plate impact testing. The
work done by other researchers has streamlined its implementation, and allows
for an efficient measurement system.

The full-field displacement provided by the rear surface measurements
give a comprehensive evaluation of the specimen. Through observation of these
results, it is possible to observe the initiation and growth of major delamination.
This was due to the fact that delamination causes a localized degradation of the
bending stiffness, and thus a discontinuity in the slope of displacement. The
observations are enhanced by plotting the displacement profile along lines
through the impact point. Major delamination is distinguished by a protruded
region which forms during the loading portion of the force curve, and grows to its
maximum value at the peak force.

The results from the Projection Moire measurement of the rear surface
were compared to the load cell measurements of a single point on the impact
surface. The results were quite close to each other considering that the
measurements were taken on opposite surfaces in the structure. Since it was

known that indentation on the impact surface would cause the results from each

112

surface to be distinct, it was concluded that both techniques give an adequate

measurement of the structure's response.

5. 1.2 Material properties from impact testing

The method of using mode shapes as virtual fields was found to perform
better than the method of manually selecting functions to use as virtual fields.
Since the mode shapes provide independent virtual displacements, they provide
useful fields to use in application.

It was found that the CL-L set of boundary conditions provided the best
results for applying the Virtual Fields Method for the current loading scenario.
The selection of this case was a result of finding a balance between the following
contributing factors.

1. The best results are obtained when the boundary conditions are less
restrictive. For example, better results are obtained with simply supported
than with clamped boundary conditions.

2. The selected set of boundary conditions must be selected such that each
bending stiffness influences the plate response significantly enough. For
example, The CL-L configuration performs better than the CL-4
configuration.

3. The selected set of boundary conditions must be practical for experimental
implementation. For example, clamped edges can be implemented simply

and consistently in experiments whereas simply supported edges cannot.

113

Although the numerical study was based on static loading, it is thought
that the configuration should also be the best configuration for dynamic loading.

This conclusion is due to the fact

5. 1.3 Translucent composites for studying damage progression

It is seen from this study that the observation of delamination growth is
greatly enhanced through the use of translucent composite materials. With this
approach, it is possible to determine not only the final delamination area, but the
progress of delamination throughout the impact event.

Additionally, it is possible to perform Projection Moire measurements at
the same time as observing the internal damage. There are two techniques
which can be used. First, if the boundary conditions and material are both
symmetric, half of the specimen can be painted white while the remaining half is
left uncoated. If the setup is symmetric, the behavior can be mirrored over the
boundary between the painted and unpainted surface.

The second approach is to use a semi-transparent paint to coat the entire
rear surface of the specimen. Using this techinque requires some effort to
determine an acceptable compromise between transparency and translucency.
If the specimen is too transparent, the Projection Moiré measurements will not
work, and if the specimen is too opaque, the delamination will not be visible. If
an acceptable compromise is reached, both the displacement and internal

damage can be measured accurately.

114

 

5.2 Future work

5. 2. 1 Impact testing with Projection Moire’

The addition of the Projection Moiré setup to the impact of composite
plates provides a valuable means for quantifying the rear surface specimen
response. Past studies [1 .4] have shown the importance of the rear layer in the
energy absorbing properties of a composite plate. Future work should use this
setup to quantify the performance of different structures by measuring the full-
field displacement. Such a study should provide a more thorough understanding
of the individual plate's performance and thus a better comparison of alternative
materials.

It has been shown in this chapter that the measurements by the load cell
on the impact surface and the measurements by Projection Moire of the rear
surface both give reasonable results. Differences between the displacements
has been primarily attributed to the indentation on the impact surface.
Indentation tests were conducted on different specimens and a different set of
boundary conditions than was used in the impact tests presented in this chapter,
however. In order to more fully compare the impact and rear surfaces,
indentation tests should be performed using the same specimen as used in this

chapter and with the same boundary conditions.

5. 2.2 Material properties from impact testing

The methodology presented in this chapter for implementing the Virtual

Fields Method needs further refinement. It was seen that the curvature fields

115

 

contained a large amount of noise. Further study needs to be conducted to
reduce this. Future work should focus on reducing the noise in the displacement
data as well as on alternative techniques to smooth the data before
differentiation. In addition to the data processing, the fixture design needs to be
refined. Presently, the entire specimen is not illuminated by the grating
projection system. The fixture needs to be refined in order to obtain the optimum
size and location of the mirrors for the prescribed projection angle.

In order to implement the Virtual Fields Method for impact testing, a set of
intermediate steps has been proposed in this thesis. Steps include static testing,
quasi-static simulation/testing, and dynamic simulation/testing. If this procedure
is followed, each source of error should be eliminated systematically. In addition
to refining the methodology, final result would allow for the comparison of

material properties at various strain rates.

5. 2.3 Translucent composites for studying damage progression

It has been demonstrated here that the internal damage of a specimen
during an impact event can be measured with the use of translucent composites.
Since one of the primary concerns when comparing different composite
structures is their resistance to delamination, it would be beneficial to compare
different composites (stacking sequence, weave geometry, etc.) by measuring
the delamination with respect to time.

It was seen during the use of semi-transparent paint that, while the overall
Projection Moire results were good, there was still some portions of the specimen

which contained errors. In order to further refine the method, these errors should

116

i;

be eliminated. The reason for these errors was primarily due to the darkness of
the image. There are several factors which could improve these results. First,
increase the amount of light reflected from the specimen back to the camera. A
considerable amount of refinement has already been presented for this factor in
this thesis. The second contributing factor is the amount of light provided by the
light source. Increasing the amount of projected light would increase the
brightness of the recorded image. This could be done by optimizing the grating
projection system. Several of the components could be refined including the light
source, lens selection, and component location. The third factor is the light
sensitivity of the camera. High speed camera light sensitivity decreases with
increasing frame rate due to the decrease in exposure time. As high speed

camera technology continues to improve, this problem should be alleviated.

 

117

Appendix A: Dynamic indentation behavior
Abstract

Static indentation laws have been established in the literature. It is
possible, however, that the properties governing the material's behavior are
different for dynamic loading cases. In order to fully characterize a material, it is
necessary to establish a dynamic indentation law. The present study establishes
such a law. It was found that the form of the governing equation was the same
as for static loading, however, the fitting constants were different. In addition to
identifying dynamic behavior, indentation testing reveals information concerning
the damage process during impact tests. Since indentation is one of the damage
modes present in plate impact testing, quantifying its contribution to the damage
process would provide insight into the process as a whole. In the present study,
the indentation law and testing results were used to obtain the amount of energy

which was absorbed by the material due to the indentation process.

A.1 Introduction

Work with concerning the energy absorbing properties of composite
materials has been a subject of investigation by several researchers. Liu [A.1]
showed which damage modes were important to the energy absorption and the
time period for which each mode was dominant. It was shown that indentation

indentation was dominant at early stages of the impact event.

The indentation law for static loading is well established. Yang and Sun

[A.2] showed that a power law relationship with an exponent of n = 1.5 accurately

118

modeled the force-indentation relationship for glass/epoxy laminates under static

loading. This relationship was valid only for the loading process.

F=chn (A1)
In this equation, F is the force, a is the indentation, and K is a fitting constant.
Tan and Sun [A.3] presented an equation to predict the value of K based on

material properties and the system configuration.

R1/2

 

K=§ 2
+

Ei E22

 

In this equation, R is the radius of the impactor, vi and Ei are Poisson’s Ratio

and Young’s Modulus of the impactor, respectively, and E 22 is the transverse

Young’s Modulus of the composite plate. The indentation law resulting from
these equations has been widely used in dynamic studies for years although it
has only been proven valid for static loading rates. Lee and Liu [A.4] showed in
their experiments that there is a strain rate effect in the force-indentation
relationship, thus proving that the static indentation properties cannot be used for

dynamic analysis.

A.2 Methods

A.2. 1 Measurement of maximum indentation

Since it is not feasible to measure the displacement history during the

impact event, the maximum indentation was recorded by the use of marker paint

119

on the specimen as demonstrated by Lee and Liu [A.4]. A mark was left on the
impactor after impact had occurred. The maximum displacement can be
calculated from the radius of paint left on the hemispheric impactor. In the
following equation, a is the amount of indentation, d is the diameter of marker

paint measured on the impactor, and R is the radius of the impactor.

In order for this measurement technique to be valid, the impactor head must be

a=R (A.3)

 

 

hemispheric in shape. The impactor is shown in the following figure. It is seen

that the shape can be considered the correct shape.

 

 

 

 

 

Figure A.1. Image of the impactor (left) and definition of geometry symbols
(right).

An image of the specimen after impact is shown In the following figure. It is seen
how the paint transfers from the specimen surface to the impactor in the
indentation zone. For consistency, the same indentation measurement was used

in dynamic and static indentation tests.

120

 

Figure A.2. Image of the specimen after indentation.

The specimen used was a 25.4 mm (1 in) thick cross-ply glass/epoxy
laminate manufactured from 3M. Each indentation location was greater than or
equal to twice the impact diameter from any previous impact location and the

edge of the specimen.

A.2.2 Dynamic indentation

The device used in this study to create the dynamic loading was the
Dynatup drop-weight impact tester, model 8250, as discussed in Chapter 2 of
this thesis. The only difference in this case is that the standard fixture was
replaced by a 76 mm (3 inch) thick steel block. This was to ensure that the rear
support of the specimen was completely rigid. In order to determine the effect of
velocity on the indentation relationship, several impact velocities were chosen for
the study. For each velocity, a range of impacting masses was used. The
largest weight used for a given velocity was dictated by the capacity of the load

cell.

121

 
  

Crosshead

Velocity l

 

 

      

flag ‘ e—Load cell
~Impactor
1
Anti-rebound
Specimen\ switches
Optical Anti-rebound
sensor brake
Fixture "

Figure A.3. Schematic of the DWIT machine (left) and the actual device
(right).

A.2.3 Static indentation

In order to ensure consistency between the static and dynamic
measurements, it was desired that the both set of tests be conducted on the
same machine with the same measurement devices. In order to achieve this, the
DWIT was modified to allow for static loading. A frame was build around the
crosshead, as shown in the following figure. A hydraulic press was then placed
between the frame and the crosshead to apply the load. Springs were attached
to prevent the crosshead from loading the specimen prematurely. Indentation

measurements were made with the same method as used in dynamic testing.

122

  
 
   
 
  
  

Spnng

Hydraulic
press

Crosshead

 

Figure A.4. Schematic of the static setup (left) and picture of the actual
device (right).

A.3 Results and discussion

The force-indentation relationship from the dynamic indentation tests was

plotted along with static indentation data from Lee and Liu’s study [A.4]. The

static data was updated to reflect a more accurate system calibration. A power

law curve was fit to both the static and the dynamic data.

As expected, a strain rate effect was seen in the data. Power law

relationships were fit to the data. Two plots are presented in below. For Figure

A.5, the exponent, n, of Equation (A.1) was held constant at-1.5. In Figure A.6, n

was allowed to vary as part of the fitting process. In each plot, curves were fit to

123

each data set individually as well as a curve fit to all three dynamic data sets

together. The constants for each fit curve are presented in Table A1

 

2T W

 

 

20::
E 154
05
8 .
.9 ,/ I>
a 10 . ,/
a) /
CL ’5'

5~ ,uv/

l/’
/'/Ӥ
0 I -- —r— -
O 0.2 0.4 0.6

Indentation, mm

 

I> Static
O 0.94 m/s
l 1.49 m/s
A 2.63 m/s
- - Static fit
— 0.94 m/s fit
—1.49 m/s fit
— - 2.63 m/s fit

 

Figure A.5. Indentation results with power law fitted curves (n = 1.5).

 

 

 

 

25 ~—- - a
20‘ {,7 D Static
4“ o 0.94 m/s
5 15~ D, I 1.49 m/s
8' / A 2.63 m/s
“5 /. D --Statrc fit
an 10 ' — 0.94 m/s fit
(0 / P/
o . ’/ —1.49 m/s fit
CL 7/ /l>
// / ---2.63 m/s fit
5 2 / /D‘ I
/ /' I
/,,_.; I
// '
O f l I #1
0 0.2 0.4 0.6 0.8

Indentation, mm

Figure A.6. Indentation results with power law fitted curves (n is variable).

124

It was found that the correlation coefficients for each of the curves were
quite high. The fitting curves are compared graphically in Figure A.7. Since all of
the dynamic curves with an exponent of n = 1.5 were nearly overlapping; only the

curve fit to all of the data was used in Figure A]. This was done to make the

plot easier to read.

25 .-— — ._ _.. __ _ _ ____- __- __-
/
201 I
372 15~ —A
93“ —E
‘5 "E
x 10W --.
8 ' -—H
0- ---I
5 —J

 

 

 

 

 

   

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Indentation, mm

Figure A]. Comparison between the fitting curves shown in Figures A5
and A6.

125

Table A1. Fitting constants for the power law curves fit to the indentation
data

 

 

 

 

 

 

 

 

 

 

Test Static 0.94 mls 1.49 mls 2.63 mls All dynamic

ID A B c o E

K 25.8 35.5 36.2 35.5 35.9
n 1.5 1.5 1.5 1.5 1.5
,2 0.97 0.98 0.95 0.96 0.99
ID F G H r J

K 25.9 32.5 39.7 34.2 36.7
n 1.51 1.40 1.68 1.41 1.54
,2 0.97 0.98 0.97 0.96 0.99

 

 

 

 

 

 

 

 

The high degree of correlation between the fitted lines and the indentation
data justifies the use of the power law in modeling the material behavior. The

correlation coefficient for each of the fitting curves is quite high, as seen in Table

A1 Since the r2 values for the case of n = 1.5 are so close to those for when n
is allowed to vary, the power law with the 1.5 exponent can be accepted as the

appropriate indentation law for dynamic studies.

It is seen that there is substantial deviation from the static indentation law
for impact loading rates. There is not noticeable variation within the impact data
for the range of impact loading rates applied in this study, however. Within this
range, strain rate effects can be assumed negligible. The use of the static
indentation law for dynamic analysis would be in error. If a dynamic study is to
be conducted, the researcher must first establish the dynamic indentation law to

be used.

126

With the force-indentation relationship known, it is now possible to
calculate the amount of energy absorbed during the indentation process. Since
absorbed energy is simply the integral of force with respect to displacement, the

energy of the loading process can be calculated as

b .
u=jkande=—k— bn+1—a"+1l (A.4)
a n+1

where K is determined from the appropriate dynamic indentation law. This
calculation is made possible by the assumption that the load cell is rigid. For the

case of n = 1.5, the loading energy is described as follows.

b .
u=jka1-5da=0.4klb1-5—a1-5 (A5)
a

A.4 Conclusions

The indentation law is dependent on the loading rate of the system. Use
of static indentation laws cannot be considered valid for analysis of dynamic
events. As a result, using Equation (A2) to predict the value of K would provide
an incorrect value for a dynamic case. A study must be performed for a given
configuration in order to determine the appropriate indentation law coefficient to
be used. For small changes in impact velocity, there is not a noticeable change
in the indentation law, however. If the dynamic indentation law is known for a
material, it is possible to calculate the amount of energy absorbed by the

indentation loading process.

127

A.5 Future work

The present work has established the dynamic indentation behavior for a
range of velocities from 0.94 — 2.63 m/s. It was observed that, within this range,
the response did not change significantly. In order to better understand the effect
of strain-rate on the material's response, future work should investigate a larger
range of impact velocities.

It is now known how specimen geometry such as stacking sequence,
weaving geometry, and thickness effect the dynamic indentation response.
Future work should investigate these factors in order to know more fully how the
indentation law can be applied.

Additionally, only the peak indentation could be measured in this test. In
order to have a more complete characterization of the indentation response, the
complete loading and unloading history is required. Future work should include a

study which obtains each of these quantities.

128

A.6 References

[A.1] Liu, D., “Characterization of Impact Properties and Damage Process of
Glass/Epoxy Composite Laminates,” Journal of Composite Materials, Vol. 38,
2004,pp.1425,1442.

[A.2] Yang, SH. and Sun, C.T., “Indentation law for composite laminates,”
Composite Materials: Testing & Design (6th Conference), ASTM STP 787,
Daniel, IM, Philidelphia, PA: American Society for Testing and Materials, 1981,
425-449.

[A.3] Tan, TM, and Sun, C.T., “Use of Statical Indentation Laws on the Impact
Analysis of Composite Laminated Plates,” Journal of Applied Mechanics, Vol. 52,
1985,pp.6,12.

[A.4] Lee, C.-Y., and Liu, D., “Effect of impact velocity on the indentation of thick
composite laminate,” Experimental Techniques. 2008, pp. 1, 6.

129

Appendix B: Drop-weight impact tester calibration

B.1 DWIT data acquisition calibration

The data acquisition system for the force measurement consists of the
following components: load cell, amplifier, signal conditioning unit, input
impedance, computer with data acquisition card, and digital oscilloscope
software. The system is shown schematically below. In this system, (the Signal
conditioning (ie. amplification, excitation) was performed by the Ectron 778 unit.

The recorded data has units of volts and will be multiplied by a calibration factor

 

to obtain force. This procedure will be discussed later.

 

 

 

 

 

 

 

 

 

:l
A—_/:\
Input
impedance ° |
[ ] .— Computer with data
Load cell . Amplifier and acquisition card and
srgnal conditioner digital oscilloscope

Figure 8.1. Schematic of the data acquisition system.

In order to be able to trust the results from the Dynatup machine, it is
important that the data acquisition system be calibrated prior to each study
performed. The first step in calibrating the system is to verify that each
component is in proper working condition. The simplest components to check
are the cables. A multi-meter was used to check the resistance between pins —
they should be less than 1 0 each. It was determined that all of the resistances

were in the expected range.

130

It is; known that the load cell should be provided with an excitation of 5V.
The voltage across the excitation of the amplifier was measured and determined
to be 5 V exactly, so no adjustments were needed. This voltage was measured
statically, however. It is possible that there is some fluctuation in the voltage
when the Wheatstone bridge is under dynamic loading. In order to verify the
results obtained in the setup above, excitation was supplied by a power supply
instead of the Ectron unit. The power supply was of a much better quality, so the
results could be more readily trusted. It was found that the results from the two
excitation sources matched quite well. Therefor, the Ectron unit can be trusted to
provide the correct excitation.

In order to ensure that gain of the amplifier was being applied correctly
and that the measurement in the digital oscilloscope was correct, a series of
known voltages were applied to the input of the Ectron unit. The measured
voltage on digital oscilloscope was found to be the correct amplification of the
supplied signal, so the measurement system was operating correctly.

The data acquisition card's clock was checked by comparing it to a
satellite-synchronized clock over the course of 30 minutes. Data acquisition was
initiated and the time of initiation was recorded according to the satellite clock.
The time history recorded by the data acquisition card was found to vary less

than 1% from the satellite clock, so the error was deemed acceptable.

32 Load cell calibration

The load cell was calibrated by placing a series of static weights onto the

specimen. The measurement range of the load cell was 22 kN (5000 lbs). Since

131

 

it would not be safe to apply this high of a loading, loads of 0 - 3.9 kN (0 - 877
lbs) were applied incrementally. The maximum force was determined by the
amount of dead weights available. At each increase of load, the output voltage
was recorded on the oscilloscope. A gain of 10 was used during the calibration
since that is the gain that would be used in the impact testing. The calibration
factor to convert the unamplified voltage to units of force was found to be 40.7

kNN (9156 lb/V).

132

73

 

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