FAILURE OF GRAPHITE/EPOXY INDUCED BY DELAMINATION
by
JOHN CHARLES BREWER
S.B. MASSACHUSETTS INSTITUTE OF TECHNOLOGY (1983)
S.M. MASSACHUSETTS INSTITUTE OF TECHNOLOGY (1985)
SUBMITTED TO THE DEPARTMENT OF AERONAUTICS
AND ASTRONAUTICS IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
MAY 1988
@
Massachusetts
Institute
of Technology
1988
.-
Signature of Author
Dep
tment of Aefronauticsand Astronautics
May 19, 1988
Certified by
*I
-
_
I,
P/¶ essor Paul A. Lagace
VF Thesis Supervisor
Department of Aeronautics and Astronautics
Certified by
-- - --
I.V
7;1f-Erofessor
Jmes W. Mar
(J
Department
Thesis Supervisor
of Ae onautics and Astronautics
Certified by
D
Dr. John F. Mandell
Thesis Supervisor
Department of Materials Science and Engineering
a .,
!
Accepted by
t
-
ProferSor
Harold Y. Wachmain
Chairman, Department Graduate Committee
MAY2
Xt288
j WITH
I
. N
M.I.T
LRAR$1i
A@.me
FAILURE OF GRAPHITE/EPOXY INDUCED BY DELAMINATION
by
JOHN CHARLES BREWER
Submitted to the Department of Aeronautics and Astronautics on
of the requirements for
May 19, 1988 in partial fulfillment
the Degree of Doctor of Philosophy
in Aeronautics and Astronautics.
ABSTRACT
The progression of delamination damage in graphite/epoxy
investigated.
Delamination initiation of
laminates
was
specimens with fabric and unidirectional plies was explored.
high
thermally- and
sequences
yielded
The lamination
The
normal
stresses.
mechanically-induced interlaminar
Quadratic Delamination Criterion was shown to accurately
correlate the initiation when thermally-induced stresses were
included. In the remaining experiments, delamination size was
monitored with dye penetrant-enhanced x-radiography after each
test
to
load.
a predetermined
[±153]
specimens
and
Specimen width was varied
failure
stress
was
found
to
for
be
of specimen width.
Lamination sequence and
indepeRdent
and
effective ply thickness were varied using [±15n/0
[0n/±15n]
specimens (n=1,2,3,5,8). No critical delamiRation
size
wag
found
for
any
specimen
type.
In
all
cases,
initiation was a necessary prerequisite to
delamination
delamination growth. Final failure was controlled by in-plane
sublaminates.
strength considerations of the delaminated
Constraints of intact sublaminates on damaged sublaminates can
growth and final failure.
affect delamination
placing
the
primarily warp fibers (200)
critical
delamination
The
effect
or fill fibers (700)
interface
of
fabric
of
at
[+20 ]
laminates was studied.
There were discernable effects Fo
interface character on delamination growth and final failure.
[0 /±15 ] specimens with implanted delaminations and angle
ply sp is
demonstrated that delaminations strongly interact
A strain
with damage in neighboring plies such as splits.
energy release rate analysis was modified to include several
aspects of the three-dimensional nature of observed damage as
dimensions.
effects
of
finite
specimen
well as the
Nonetheless, the model was unable to yield a constant value of
strain energy
would
be
release
expected.
rate, as calculated
from
the
data,
the details of sublaminate constraint and the interaction
the delamination and angle ply split is warranted.
Thesis Supervisor:
Title:
as
A full three-dimensional model including
of
Professor Paul A. Lagace
Associate Professor
Astronautics
of
Aeronautics
and
3
ACKNOWLEDGEMENTS
Completing
thesis
a
such
as
this
the
requires
understanding and assistance of a great many people. I cannot
hope to name all the individuals who have assisted me along
the
way, but I would
as many as
document.
possible
like to express my gratitude
without
doubling
the
publicly
length
of
to
this
The first group which must be given credit is my doctoral
thesis committee. It was chaired by my hard working friend
Paul
Lagace.
today
could not and would not be in this position
I
without
Paul's
help
and
encouragement.
Professor
James W. Mar has been an inspiration to me and the rest of the
Dr. John F. Mandell
laboratory.
We are all grateful to him.
of the Materials Science and Engineering
invaluable with his observations and input.
I
like
would
to
acknowledge
the
Department
contribution
was
of the
faculty and staff of the Department of Aeronautics and
Advanced
Astronautics and the Technology Laboratory for
Composites.
Most especially, I owe a debt of gratitude to Al
Supple who encouraged me over the years and mediated my
disputes with inanimate objects. I would also like to thank
Professor John Dugundji, Ping, Carl, Bonnie, Al Shaw, and all
the rest.
There
is
no room to recognize
the more than one hundred
TELAC members I have worked with over the last 8 years, but I
do appreciate their help. A special thanks goes out to those
who have helped me with my graduate work, including Mary,
Rich, Gail, and Doug.
The hundreds
of
tests in the
ear-splitting racket of the testing room would have been
intolerable without them. I know the Gods of Graphite will
I would also like to thank Pierre Minguet
watch over them.
for his help with the finite element model and Christos
Kassapoglou
for
teaching
me the intracacies
of interlaminar
stresses.
made
The people I have lived with during my time at MIT have
life much more bearable.
I would like to thank the
members
of
J Entry
at
MacGregor
House,
the
Conner 5 over the past three years, and,
resident and non-resident members of MIE.
residents
of
of course, the
I know am truly blessed to have a wonderful family like
mine.
I have met many people with unpleasant home lives. I
want to express my appreciation to my parents, brothers,
sisters, nieces, and nephews for being the type that people
envy. I would also like to acknowledge all my in-laws for
being supportive during this effort.
4
I could not conclude these acknowledgements without
my
recognizing the two most important people in my life:
wife, Katy, and my daughter, Maggie. I know their sacrifices
have been great during the terrible last months of thesis
I will make it up to them soon. They have been
writing.
wonderful
and I love them for it.
When I mention my daughter, I know it is no
she
has
had
serious medical problems.
secret
that
I would like to take
this opportunity to express my sincerest appreciation to
everyone who showed concern (and especially those who gave
their blood) during her hospitalizations. I must also thank
the
staff
of
the Children's
Hospital
Medical Center
and the
In
Harvard Community Health Plan for their outstanding work.
particular, the efforts of Dr. Herbert "Herbie the Heart
Jonas, Dr. Mary VanderVelde,
Dr. Richard
Doctor"
Cohn,
made a very long
Dr. Judy Becker, and Mary Czezot, R.N.
ordeal bearable for Katy and me and have helped Maggie to
become the relatively healthy normal child she is today. With
this
kind
of care, I have no doubt that she will grow strong
It is for this that I am
and tall and live a long, full life.
most grateful.
This work was performed in the Technology Laboratory for
Advanced Composites (TELAC) of the Department of Aeronautics
and
Astronautics
at
the
Massachusetts
Institute of
Technology. This work was sponsored by the Boeing Aircraft
Company under contract number BMAC PO AA0045 and the United
States Air Force Office of Scientific Research under grant
number AFOSR-85-0206.
6
DEDICATION
To my dear wife, Katy
7
TABLE OF CONTENTS
CHAPTER
F'AGE
1
INTRODUCTION
22
2
SUMMARY OF PREVIOUS WORK
27
2.1
Interlaminar Stresses and Delamination
27
2.2
Delamination Initiation
31
2.2.1
Initial Qualitative Approaches
32
2.2.2
Strain Energy Release Rate Approa hes 33
2.2.3
Average Stress Approaches
3
4
5
40
2.3
Delamination Growth
46
2.4
Delamination Failure
50
APPROACH TO PRESENT WORK
53
3.1
Overview
53
3.2
Interlaminar Normal Stress and Delamination
Initiation
54
3.3
Delamination Growth and Final Failure
64
3.4
Analysis of Delamination Growth
81
GENERAL SPECIMEN MANUFACTURING PROCEDURES
83
4.1
Preparation
83
4.2
The Cure
85
4.3
Machining and Measuring
89
4.4
Loading Tabs
92
4.5
Instrumentation
96
and Layup
DELAMINATION INITIATION EXPERIMENTS
97
5.1
Edge Replication
97
5.2
General Testing Procedures
1.00
5.3
Load Drop Testing
I .02
8
TABLE OF CONTENTS (Continued)
CHAPTER
6
PAGE
5.4
Results
103
5.5
Discussion
107
DELAMINATION GROWTH AND FINAL FAILURE
EXPERIMENTS
6.1
112
Specialized Specimen Manufacturing
Procedures
112
6.1.1
Specimens of Nonstandard Width
112
6.1.2
Fabric Specimens
113
6.1.3
Specimens With Implanted
Delaminations and Angle Ply Splits
114
X-Radiography
119
6.2
Dye Penetrant-Enhanced
6.3
Incremental Load Testing
122
6.4
Results
124
6.5
6.4.1
Specimens of Nonstandard Width
124
6.4.2
[±15n/0n]s
131
6.4.3
Fabric Specimens
145
6.4.4
Specimens With Implanted
Delaminations and Angle Ply Splits
151
and [0n/±15n]s
Specimens
Discussion
163
6.5.1
Specimens of Nonstandard Width
163
6.5.2
[±15n/0n]s and [0n/±15n]s Specimens
166
6.5.3
Fabric Specimens
176
6.5.4
Specimens With Implanted
Delaminations and Angle Ply Splits
177
9
TABLE OF CONTENTS (Continued)
CHAPTER
7
8
9
PAGE
ANALYSIS OF GROWTH PHENOMENON
180
7.1
Existing Models of Growth Phenomenon
180
7.1.1 O'Brien's Method
180
7.1.2 Virtual Crack Closure
181
7.2
Finite Element Method
182
7.3
Geometrically Integrated Finite Element
Method
191
7.4
Effects of Finite Specimen Size
199
7.5
Results
214
7.6
Discussion
215
SUMMARY OF PRESENT WORK
233
8.1
Delamination Initiation
233
8.2
Delamination Growth and Final Failure
235
CONCLUSIONS AND RECOMMENDATIONS
240
REFERENCES
244
DATA TABLES
249
APPENDIX TO DATA TABLES: SPECIMEN NOMENCLATURE
255
APPENDIX A: DELAMINATION GROWTH DATA FOR [±153]5 SPECIMENS
OF NONSTANDARD WIDTH
258
APPENDIX B: DELAMINATION GROWTH DATA FOR [±15n/0n]
SPECIMENS
260
APPENDIX C: DELAMINATION GROWTH DATA FOR [0n/±15n]
SPECIMENS
262
APPENDIX D: GROWTH-TO-TAB STRESSES FOR [+15n0 1] AND
[0n/+15n] SPECIMENS
264
APPENDIX E: DELAMINATION GROWTH DATA FOR [±20F]s FABRIC
SPECIMENS
265
10
TABLE OF CONTENTS (Continued)
PAGE
CHAPTER
APPENDIX
F: DELAMINATION AND ANGLE PLY SPLIT FORMATION DATA
SPECIMENS WITH IMPLANTED
FOR [0 /+15
DELAMINATIOASS
APPENDIX
G: GROWTH OF THE DELAMINATION TO THE END OF THE
IMPLANTED ANGLE PLY SPLIT IN [0 /+15 I
SPECIMENS WITH IMPLANTED DELAMINATIONSSAND
ANGLE PLY SPLITS
APPENDIX
APPENDIX
APPENDIX
267
H: SIZING OF THE ELEMENTS IN THE. FINITE ELEMENT
I:
MESH
268
STRAIN ENERGY RELEASE RATE CALCULATIONS FOR
[±1 5 3]s SPECIMENS OF NONSTANDARD WIDTH
273
J: STRAIN ENERGY RELEASE RATE CALCULATIONS FOR
[±15n/0n
APPENDIX
266
s
SPECIMENS
274
K: STRAIN ENERGY RELEASE RATE CALCULATIONS FOR
[0n/+15n
s
SPECIMENS
275
11
LIST OF FIGURES
FIGURE
2.1
2.2
PAGE
GEOMETRY FOR THE PROBLEM OF A LAMINATED PLATE
UNDER UNIAXIAL LOAD
28
SCHEMATIC OF THE STRAIN ENERGY RELEASE RATE
CURVE AND THE CRACK GROWTH RESISTANCE CURVE AT
"POP-IN" OF THE DELAMINATION INITIATION
36
2.3
SCHEMATIC OF THE DELAMINATION RESISTANCE CURVE AS
APPROXIMATED BY A CRITICAL VALUE OF STRAIN ENERGY
RELEASE RATE
47
2.4
SCHEMATIC OF THE STRAIN ENERGY RELEASE RATE
CURVES AT VARIOUS POINTS DURING STABLE AND
UNSTABLE DELAMINATION GROWTH
49
MECHANICALLY-INDUCED INTERLAMINAR NORMAL STRESS
FOR [O / F]
[ U10/'F]S AND [OU5/OF/OU]S
58
3.1
SPECIMENS
3.2
THERMALLY-INDUCED INTERLAMINAR NORMAL STRESS FOR
[SPo/0
SPEIMEN
3.3
3.4
3.5
3.6
3.7
3.8
4.1
4.2
4.3
'
[ U10/OF]'
AND [U/OF/OU]s
STANDARD TELAC TEST SPECIMEN
EFFECT OF PLY THICKNESS
61
61
62
ON THE INTERLAMINAR
STRESS STATE
68
EFFECT OF PLY THICKNESS ON THE STRAIN ENERGY
RELEASE RATE
70
SCHEMATIC OF 5-HARNESS SATIN WEAVE FABRIC
GRAPHITE/EPOXY
74
SCHEMATIC OF OBSERVED DELAMINATION DAMAGE
77
SCHEMATIC OF SPECIMENS WITH IMPLANTED
DELAMINATIONS
79
CONFIGURATION OF THE CURE PLATE FOR CURING OF
GRAPHITE/EPOXY LAMINATES
86
SCHEMATIC
ASSEMBLY
88
OF THE CROSS-SECTION
OF THE CURE
CURE CYCLE FOR AS4/3501-6 UNIDIRECTIONAL
GRAPHITE/EPOXY AND AW370-5H/3501-6 WOVEN
GRAPHITE/EPOXY FABRIC
90
12
LIST OF FIGURES (Continued)
FIGURE
4.4
5.1
PAGE
LOCATION OF MEASUREMENT POINTS ON A STANDARD
TELAC SPECIMEN
POSITION OF REPLICATING TAPE DURING APPLICATION
OF ACETONE
5.2
91
99
MICROGRAPH OF EDGE REPLICATING SHOWING
DELAMINATION INITIATION IN A [ ou/OF]S
SPECIMEN
105
5.3
THERMAL AND MECHANICAL COMPONENTS OF INTERLAMINAR
NORMAL STRESS AT DELAMINATION INITIATION AT THE
] s SPECIMEN
MIDPLANE OF A [0 5U/0F
108
6.1
NOMINAL POSITION OF THE TEFLON FILM AT THE
+15°/-15o INTERFACES WHEN CONSTRUCTING A
[0 /+15 ] SPECIMEN WITH AN IMPLANTED
DEZAMINATfON
116
NOMINAL POSITION OF THE TEFLON FILM AT THE
+15°/-15° INTERFACES AND WITHIN THE [-15;]
SUBLAMINATE WHEN CONSTRUCTING A [0 /+153i
SPECIMEN WITH AN IMPLANTED DELAMINATION AD
ANGLE PLY SPLIT
118
6.2
6.3
LOCATION OF THE STRAIN GAGE ON A SPECIMEN WITH AN
IMPLANTED DELAMINATION
120
6.4
TYPICAL STRESS-STRAIN GRAPH FOR A [+15 3]s
SPECIMEN
6.5
X-RADIOGRAPHS
OF TYPICAL DELAMINATIONS
126
IN [+1 5 31 s
SPECIMENS
129
6.6
PEELING AND UNLOADING OF A [+153]1SUBLAMINATE IN
A [±15 3]s SPECIMEN
130
6.7
TYPICAL STRESS-STRAIN GRAPH FOR A [15n/0n]
SPECIMEN
6.8
6.9
6.10
s
TYPICAL STRESS-STRAIN GRAPH FOR A [On/+15nlS
SPECIMEN
X-RADIOGRAPH OF A [15/0]
133
134
SPECIMEN AFTER
FAILURE
138
PHOTOGRAPH OF FAILURE MODES OF [+15n/0]s
SPECIMENS
140
.
13
LIST OF FIGURES (Continued)
FIGURE
6.11
6.12
PAGE
X-RADIOGRAPH
FAILURE
SCHEMATIC
OF A [0/±151] SPECIMEN
AFTER
141
OF THE "SHEAR OUT" OF THE [-1
5 2n]s
142
SUBLAMINATE IN A [0n/+15n]s SPECIMEN
6.13
6.14
6.15
6.16
PHOTOGRAPH OF FAILURE MODES OF [0n/±+15n]
s
SPECIMENS
143
TYPICAL STRESS-STRAIN GRAPH FOR A [+2 0 F ] S
SPECIMEN
147
X-RADIOGRAPH OF TYPICAL DELAMINATIONS IN
[+±20F] SPECIMENS WITH FILL FACES AT THE
+20°/-20° INTERFACE
152
X-RADIOGRAPH
OF TYPICAL DELAMINATIONS
IN [±20
]F S
SPECIMENS WITH WARP FACES AT THE +20o/-20°
6.17
6.18
6.19
INTERFACE
153
TYPICAL STRESS-STRAIN GRAPH FOR A [0 /+15 ]
SPECIMEN WITH AN IMPLANTED DELAMINATION SAO*ING
THE "FORMATION POINT" OF THE DELAMINATION
156
X-RADIOGRAPH OF A [0 /+15 ] SPECIMEN WITH AN
IMPLANTED DELAMINATION AN
HE ASSOCIATED
SPONTANEOUSLY FORMED ANGLE PLY SPLIT
158
X-RADIOGRAPH OF A [0 /15 ] SPECIMEN WITH AN
IMPLANTED DELAMINATI8N SH8WfNG LIMITED EXTENSION
OF THE DELAMINATION
6.20
6.21
FRONT
161
X-RADIOGRAPH OF A [0 /+15 i SPECIMEN WITH AN
IMPLANTED DELAMINATIN ANA ANGLE PLY SPLIT
SHOWING DELAMINATION GROWTH TO THE END OF THE
IMPLANTED ANGLE PLY SPLIT
162
EXPERIMENTAL VALUES AND ANALYTICAL CURVES FOR
DELAMINATION INITIATION, GROWTH, AND FINAL
FAILURE OF [±15n/0 n]
6.22
7.1
SPECIMENS
170
EXPERIMENTAL VALUES AND ANALYTICAL CURVES FOR
DELAMINATION INITIATION, GROWTH, AND FINAL
FAILURE OF [0n/±15n]s SPECIMENS
172
FINITE ELEMENT MESH USED FOR A SIX PLY LAMINATE
185
14
LIST OF FIGURES (Continued)
FIGURE
7.2
7.3
7.4
7.5
PAGE
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
DELAMINATION INTRUSION FOR A [+15 ] SPECIMEN
USING A TWO-DIMENSIONAL FINITE ELeMeNT MODEL
187
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
DELAMINATION INTRUSION FOR A [+15/0] SPECIMEN
USING A TWO-DIMENSIONAL FINITE ELEMEnT MODEL
188
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
DELAMINATION INTRUSION FOR A [0/+15] SPECIMEN
USING A TWO-DIMENSIONAL FINITE ELEMENT MODEL
189
DISPLACEMENTS
OF THE DELAMINATION
SURFACE FOR
[0 /+15
SPECIMENS AS DETERMINED BY THE
FINITE ELEMENT METHOD
7.6
SCHEMATIC
MODEL OF THE DELAMINATION
IN THE
ANALYSIS
7.7
7.8
190
196
MODIFIED FINITE ELEMENT MESH USED FOR A SIX PLY
LAMINATE WHICH ACCOUNTS FOR A PORTION OF A PLY TO
BE UNLOADED
198
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
DELAMINATION INTRUSION FOR A [15
SPECIMEN
WITH A PARTIALLY UNLOADED [+153] UgLAMINATE
USING A TWO-DIMENSIONAL FINITE ELEMENT MODEL
200
7.9
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
DELAMINATION INTRUSION FOR A [±15/01 SPECIMEN
WITH A PARTIALLY UNLOADED [+15] SUBLAMINATE USING
A TWO-DIMENSIONAL FINITE ELEMENT MODEL
201
7.10
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
DELAMINATION INTRUSION FOR A [0/+15] SPECIMEN
WITH A PARTIALLY UNLOADED [-15] SUBLAMINATE USING
A TWO-DIMENSIONAL FINITE ELEMENT MODEL
202
7.11
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
DELAMINATION INTRUSION FOR A [15
SPECIMEN
USING A GEOMETRICALLY INTEGRATED IAITE ELEMENT
MODEL
7.12
203
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
DELAMINATION INTRUSION FOR A [±15/0] SPECIMEN
USING A GEOMETRICALLY INTEGRATED FINITE ELEMENT
MODEL
204
15
LIST OF FIGURES (Continued)
FIGURE
7.13
7.14
7.15
7.16
PAGE
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
DELAMINATION INTRUSION FOR A [0/+15] SPECIMEN
USING A GEOMETRICALLY INTEGRATED FINITE ELEMENT
MODEL
205
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
SPECIMENS OF
DELAMINATION INTRUSION FOR [+15
NONSTANDARD WIDTH USING A GEOMETRICALLY
INTEGRATED FINITE ELEMENT MODEL INCLUDING THE
EFFECTS OF FINITE SPECIMEN DIMENSIONS
210
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
SPECIMENS
DELAMINATION INTRUSION FOR [+15 /0
USING A GEOMETRICALLY INTEGRATED FNTE
ELEMENT
MODEL INCLUDING THE EFFECTS OF FINITE SPECIMEN
DIMENSIONS
211
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
DELAMINATION INTRUSION FOR [0 /+15 ] SPECIMENS
USING A GEOMETRICALLY INTEGRATED FNTTE ELEMENT
MODEL INCLUDING THE EFFECTS OF FINITE SPECIMEN
DIMENSIONS
212
7.17
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE RATE
AS A FUNCTION OF DELAMINATION INTRUSION FOR
216
[±1 5 3]s SPECIMENS USING O'BRIEN'S METHOD
7.18
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE RATE
AS A FUNCTION OF DELAMINATION INTRUSION FOR
[+15 ] SPECIMENS USING A TWO-DIMENSIONAL FINITE
ELEMAN~ MODEL
217
7.19
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE RATE
AS A FUNCTION OF DELAMINATION INTRUSION FOR
[+15
SPECIMENS USING A GEOMETRICALLY
INTEgRaTED FINITE ELEMENT MODEL
218
7.20
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE RATE
AS A FUNCTION OF DELAMINATION INTRUSION FOR
[+15
SPECIMENS USING A GEOMETRICALLY
INTERRTED FINITE ELEMENT MODEL INCLUDING THE
EFFECTS OF FINITE SPECIMEN DIMENSIONS
219
7.21
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE RATE
AS A FUNCTION OF DELAMINATION INTRUSION FOR
[±15n/0n]s SPECIMENS
USING O'BRIEN'S METHOD
220
n ns~~~~~~~~~~~2
16
LIST OF FIGURES (Continued)
FIGURE
PAGE
7.22
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE RATE
AS A FUNCTION OF DELAMINATION INTRUSION FOR
[+15 /0 ] SPECIMENS USING A TWO-DIMENSIONAL
FINITE ELEMENT MODEL
221
7.23
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE RATE
AS A FUNCTION OF DELAMINATION INTRUSION FOR
[+15 /0
SPECIMENS USING A GEOMETRICALLY
INTE8RA EB FINITE ELEMENT MODEL
222
7.24
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE RATE
AS A FUNCTION OF DELAMINATION INTRUSION FOR
[+15 /0 ] SPECIMENS USING A GEOMETRICALLY
INTEBRA EB FINITE ELEMENT MODEL INCLUDING THE
EFFECTS OF FINITE SPECIMEN DIMENSIONS
223
7.25
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE RATE
AS A FUNCTION OF DELAMINATION INTRUSION FOR
[0n/+15n] SPECIMENS USING O'BRIEN'S METHOD
224
7.26
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE RATE
AS A FUNCTION OF DELAMINATION INTRUSION FOR
[O /+15
SPECIMENS USING A TWO-DIMENSIONAL
FIMITE ELEMENT MODEL
225
7.27
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE RATE
AS A FUNCTION OF DELAMINATION INTRUSION FOR
[0O/+15 ] SPECIMENS USING A GEOMETRICALLY
INEGRA EB FINITE ELEMENT MODEL
226
7.28
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE RATE
AS A FUNCTION OF DELAMINATION INTRUSION FOR
[0 /+15
SPECIMENS USING A GEOMETRICALLY
INtEGRAtEB FINITE ELEMENT MODEL INCLUDING THE
EFFECTS OF FINITE SPECIMEN DIMENSIONS
227
7.29
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE RATE
AS A FUNCTION OF DELAMINATION INTRUSION FOR A
[0 /+15
SPECIMEN USING A GEOMETRICALLY
IN4EGRA4EB FINITE ELEMENT MODEL INCLUDING THE
EFFECTS OF FINITE SPECIMEN DIMENSIONS
230
17
LIST OF TABLES
TABLE
3.1
PAGE
MATERIAL PARAMETERS OF HERCULES AS4/3501-6
UNIDIRECTIONAL GRAPHITE/EPOXY AND HERCULES
AW370-5H/3501-6 FABRIC GRAPHITE/EPOXY
59
3.2
TEST MATRIX FOR DELAMINATION INITIATION SPECIMENS 63
3.3
5 3]
TEST MATRIX FOR [±+1
s SPECIMENS OF
NONSTANDARD WIDTHS
3.4
TEST
MATRIX
FOR
[±+15 /0
]
AND
[0 /15
66
n]
SPECIMENS WITH DIFFEREN~ EFFECTIVE PLY
THICKNESSES
72
3.5
TEST MATRIX FOR [±20F]s FABRIC SPECIMENS
76
3.6
TEST MATRIX FOR [+15 /0 3] SPECIMENS WITH
IMPLANTED DELAMINATI NS AAD ANGLE PLY SPLITS
80
4.1
NOMINAL AND MEASURED LAMINATE THICKNESSES
93
4.2
NOMINAL LAMINATE AND LOADING TAB THICKNESSES
94
5.1
PREDICTED VERSUS ACTUAL INITIATION STRESS AND
CALCULATED INTERLAMINAR NORMAL STRENGTH
109
AVERAGE MODULUS, FAILURE STRESS, AND FAILURE
STRAIN FOR NONSTANDARD WIDTH [±+153]
s SPECIMENS
127
AVERAGE FIRST GROWTH STRESS RANGE, MAXIMUM
INTRUSION, AND DELAMINATION AREA BEFORE FAILURE
FOR NONSTANDARD WIDTH [±+153] SPECIMENS
132
AVERAGE MODULUS, FAILURE STRESS, AND FAILURE
STRAIN FOR [+15n/0n]s AND [0n/+15n]s
SPECIMENS
135
AVERAGE FIRST GROWTH STRESS RANGE, MAXIMUM
INTRUSION, AND DELAMINATION AREA BEFORE FAILURE
FOR (±15n/0n] AND [0n/+15n1s SPECIMENS
137
6.1
6.2
6.3
6.4
6.5
AVERAGE
GROWTH-TO-TAB
AND [n/±15n]
6.6
6.7
s
STRESSES
FOR [±15 /0n]
SPECIMENS
AVERAGE MODULUS, FAILURE STRESS, AND FAILURE
STRAIN FOR [±20F]s FABRIC SPECIMENS
s
146
149
STRENGTH PARAMETERS FOR HERCULES AW370-5H/3501-6
FABRIC GRAPHITE/EPOXY
150
18
LIST OF TABLES (Continued)
PAGE
TABLE
6.8
MODULUS AND FAILURE DATA FOR [0 /+15
SPECIMENS WITH IMPLANTED DELAMIAATIOS
6.9
DELAMINATION AND ANGLE PLY SPLIT FORMATION DATA
FOR [0 /+15
]
155
SPECIMENS WITH IMPLANTED
DELAMIAATIONS s
159
6.10
STRENGTH PARAMETERS FOR HERCULES AS4/3501-6
UNIDIRECTIONAL GRAPHITE/EPOXY
164
6.11
STRAIN ENERGY RELEASE RATE AT AVERAGE
GROWTH-TO-TAB STRESSES FOR [±15n/0n]s AND
[0n/+15n]s SPECIMENS
173
H.1
FINITE ELEMENT MODEL WIDTHS FOR VARIOUS
DELAMINATION
H.2
SIZES
POSITION OF BOUNDARIES OF FINITE ELEMENTS
ACROSS MODEL WIDTH
270
271
19
NOMENCLATURE
a
delamination length in a two-dimensional analysis
Adel
area of delaminated region
b
specimen test section halfwidth
E
modulus
Elam
Eloc
longitudinal
specimen
modulus of the completely laminated
local longitudinal
modulus
of
a
differentially
thin cross-section of the specimen
E
weighted average longitudinal modulus
sublaminates of a delaminated specimen
F
coefficient in a general tensor criterion
G
strain energy release rate
G
strain energy release rate determined from the
two-dimensional finite element analysis
GPa
Gigapascal (= 109 Pascals)
1
specimen test section halflength
mm
millimeter
MPa
Megapascal (= 106 Pascals)
n
normalized effective ply thickness
psia
pounds per square inch of absolute pressure
psig
pounds per square inch of gage pressure (pressure
above atmospheric)
S
in-plane
shear
strength
of
of
the
the unidirectional
composite
T
temperature
t
laminate thickness
tply
ply thickness
u, v, w
displacements
respectively
in the x 1 , x 2, and
x3
directions,
20
U
internal energy
U
internal energy per unit length
x
distance
edge
x
avg
from a reference
point, such as the free
averaging dimension in the Quadratic Delamination
Criterion
yt
in-plane transverse strength
Zc
compressive interlaminar normal strength
zt
tensile interlaminar normal strength
Z
interlaminar
shear strength
for alz
Z s2
interlaminar
shear strength
for a2z
coefficient of thermal expansion
ratio
of
the
local strain level to the average
strain level over the specimen length
6
total longitudinal
section
c
strain level
c
average strain level over the specimen length
pstrain
microstrain (microinch/inch of strain)
a
stress
a
component of stress averaged over a distance xavg
displacement
from the free edge
0a
far-field stress
a
lamination angle
°C
degrees Celsius
SUBSCRIPTS
c
critical value for delamination
del
delaminated
F
fabric graphite/epoxy composite
for
the
test
21
I
mode I (opening) component
II
mode II (sliding) component
III
mode III (tearing) component
lam
laminated
loc
local
L,
1
longitudinal
T,
2
transverse
0
or 90°
direction
direction
unidirectional graphite/epoxy composite
U
z,
or
3
through-the-thickness
direction
SUPERSCRIPTS
c
only compressive values considered
t
only tensile values considered
22
CHAPTER
1
INTRODUCTION
composite
Advanced
advances
in
materials
Although
presently
high,
material
these
significant
All aspects of
engineering possible.
aerospace
the industry have found applications for
materials.
made
have
light,
these
processing
and
stiff
costs
are
often offset by reduced material
are
waste and life cycle fuel savings.
One
which
aircraft
to fly non-stop around the
enterprise
composites
advanced
This experimental craft was able
is the Voyager.
extensively
This
employs
world
demonstrated
without
to
aerial
the world
refueling.
the potential
of
advanced composites as structural materials.
An
example
aircraft
is
the
of
the
use
Beechcraft
of
composites
Starship
1.
in
production
This fuel efficient
business jet recently became the first aircraft with a primary
structure
composed
structural
certification
Administration.
beginning
entirely of advanced composites to obtain
The
from
the
Federal
Aviation
certification of the Starship marks the
composites
in
Voyager and the Starship would
not
of an era when the use
of
advanced
aircraft structural design will be routine.
The
success
of
the
have been possible without the groundbreaking
composites on other aircraft.
application
of
The Boeing 757 and 767 aircraft
were designed primarily for fuel efficiency and as
such
advanced composites extensively in secondary structures.
used
23
Advanced
composites have many uses in military aircraft.
They offer ease of fabrication of the
necessary
for
reducing
radar
complex
configurations
cross-section.
The potential
weight savings allows the designer to increase range, payload,
and/or maneuverability.
Only the weight savings from advanced
composites makes the AV-8B vertical takeoff and landing (VTOL)
fighter possible in its present configuration.
The
inherent anisotropy of fibrous composites gives them
the potential to be "tailored" in useful ways.
the
ambitious
use
of
aeroelastic
An example
tailoring
Grumman/DARPA
X-29 forward swept wing aircraft.
the lamination
angles of the plies
wings
can
be
swept
forward
in
the
while
is
of
the
By adjusting
wing
skins,
inhibiting
the
aeroelastic
instabilities such as divergence.
Advanced
composites
are
important
in
the
field
astronautics.
In an industry where launch costs are
in
of
thousands
dollars
per
pound,
structural weight with functioning
valuable.
the ability
electronics
of
measured
to replace
is
extremely
The material and fabrication costs are essentially
negligible.
The
largest
composites
in
a
examples
spacecraft
of
an
application
are the payload
of
advanced
bay doors
on the
space shuttle orbiter.
Another example is the filament
solid
rocket
case
These
cases
counterparts
case).
booster
have
far
(32200 kg
designed
less
versus
mass
wound
for the space shuttle.
than
46000 kg
their
for
D6ac
each
steel
booster
Although the Challenger disaster has put plans to
use
24
filament
wound
cases
polar orbit on space
on hold, they could be used to achieve
shuttle
launches
from
Vandenburg
Air
Force Base or to significantly increase payload to orbit.
Despite recent progress, advanced composites still have a
great deal of untapped
safety
potential.
factors are quite high.
the Starship
secondary
At
present,
the
design
Even the primary structure of
is more lightly loaded than some of the composite
structures
on
researchers
learn
composites,
engineers
more
the
larger
about
the
can
more
commercial
complex
confidently
jets.
As
behavior
use
of
them to a
fuller extent.
An
issue
understanding
of
utmost
importance
of all possible
to date is delamination.
"plies"
of
out-of-plane
composite
direction
engineers
failure modes.
puzzling
the
to
even
from
when
the
One of the most
In this mode,
separate
is
the layers or
each other in the
the
loading
is
in-plane [e.g. 1].j Delamination has been determined to result
from the
out-of-plane
layer [2).
plates [e.g. 3].
free
of
arises
These
edges,
in
an
thin
interply
multi-directional
stresses
cutouts,
matrix
immediate
loss
of
composite
are significant in regions
and
delamination has initiated, it can
causing
a
This failure results from a full three-dimensional
state of stress that
near
failure
ply
dropoffs.
propagate
strength
across
Once
a
a
part
and stiffness
and,
often, failure.
The primary
damage
objective
of this work is
to
determine
the
sequence which leads to "premature" failure of general
25
graphite/epoxy
laminates
Investigations
in
the
either delamination
Wang
and
this
thesis,
literature
initiation
Crossman
of delamination:
induced
by
have generally focused on
[e.g. 4]
[6] recognized
delamination.
or
growth
that there are three phases
initiation, growth, and final
each
phase
[e.g. 5].
will
be
failure.
investigated
In
both
experimentally and analytically.
A
which
of
secondary
objective
can correlate
the
various
is
to develop analytical models
data and serve as a basis
damage
stages.
Such models
preliminary design process by allowing
larger
numbers
propensity
prediction
can aid in the
designers
to
compare
candidate laminates on the basis of their
to fail via delamination.
Chapter
regarding
growth,
of
for
2 of this thesis
interlaminar
and
final
is a review
stresses,
failure
in
of
the
delamination
laminated
literature
initiation,
composites.
The
approach taken to achieve the objectives of this investigation
are
discussed
in
Chapter 3.
The
procedures are detailed in Chapter 4.
general
manufacturing
A series of experiments
undertaken to investigate delamination initiation in laminates
dominated by thermally-induced
are
described
undertaken
to
in
Chapter 5.
growth
observed
are
Four
sets
normal
of
stresses
experiments
ascertain the stages of damage progression and
evaluate their interaction are
Chapter 7,
interlaminar
modifications
proposed
damage.
in
The
to
discussed
in
Chapter 6.
In
existing models of delamination
order
to
better
investigation
is
approximate
summarized
the
in
26
Chapter
8.
The
results
is
ascertained and the applicability of the analytical
model
is
evaluated.
work
The
significance
relevant
of the experimental
conclusions
of
this
are
summarized in Chapter 9 along with recommendations for further
research
into
the
subject
of
the
ultimate
strength
composite laminates prone to delamination failure.
of
27
CHAPTER
2
SUMMARY OF PREVIOUS WORK
A
great
deal of research has been conducted on advanced
composite materials.
deals
with
reviewed.
three
In this chapter,
out-of-plane
or
of
literature
which
"interlaminar" stresses will be
Subsequently, literature
phases
the
delamination
of
concerning
each
of
the
graphite/epoxy composites
(initiation, growth, and final failure) will be discussed.
2.1 Interlaminar Stresses and Delamination
Researchers have investigated
composites
delamination
for some time. /Delamination
of
advanced
has been determined
to
result from the out-of-plane failure of a thin interply matrix
layer
[2].)' Interlaminar
initiation of this damage.
and
stresses
are
responsible
for the
These stresses have high gradients
are significant only in regions near free edges, notches,
and ply dropoffs.
Classical Laminated Plate Theory [e.g. 7]
describes
the
behavior of a laminated set of plies or "laminate" by imposing
continuity
thickness.
of
coefficient
orientation
strain
throughout
the
laminate
For reference, the coordinate system used in
investigation
properties
in-plane
is
of
a
depicted
ply
in
Figure 2.1.
(e.g. modulus,
The
Poisson's
this
elastic
ratio,
of mutual influence) are functions of the angular
of its fibers.
Hence, there will in general be
a
28
- I
lI·
I
12
I
T
I
Ot
..Ad
(i)
i.. - 11
FIGURE
2.1
b-
GEOMETRY FOR THE PROBLEM
UNDER UNIAXIAL LOAD
OF A LAMINATED PLATE
29
mismatch
between the elastic properties of neighboring plies.
The effect
of the difference
each
has
ply
a 1 2).
its
For example,
all
own
in
elastic
properties
is
in-plane stress state (all,
if the Poisson's
that
2 2,
and
ratio is not identical
in
plies, the Classical Laminated Plate Theory solution will
predict non-zero transverse stress (a2 2 ) that will
ply
to
ply
for the case of uniaxial loading.
vary
This solution
will satisfy the stress-free boundary conditions at
edge
of
a
specimen
from
only in an average sense.
the
free
The boundary
conditions and equilibrium requirements will result in a
three-dimensional
full
state of stress in the region near the free
edge.
The calculation of
important
elements
used.
[e.g. 8,9]
topic.
and
stresses
has
been
an
Numerical methods such as finite
finite
difference
[10]
have
been
Early analytical approaches focused on one component at
a time.
for
research
interlaminar
Pagano and Pipes
interlaminar
normal
[11] derived a
stress
(azz)
rough
approximation
by assuming a stress
distribution and enforcing force and moment equilibrium at the
free edge.
Puppo and Evensen
[12] calculated
the interlaminar
shear stress alz by modeling the interlaminar matrix layers as
isotropic
Fourier
shear
series
derivative
of
layers.
Pipes
approach.
They
displacement
and Pagano [13] attempted a
found,
however,
that
the
with respect to location through
the thickness diverged with the addition of
terms.
Hsu
and
Herakovich [14] used a perturbation solution and obtained good
agreement with finite difference solutions.
They
also
found
30
some instabilities
in azz and a dependence
of the distribution
shape on specimen width and applied strain.
Pagano and Soni [15]
parts
contain
recognized
They
believed
sophisticated approach.
specialized
actual
a substantial number of layers.
finite element model would be
unwieldy.
that
to
the
computationally
the
problem
composite
An associated
intensive
and
would require a more
They developed a
variational
method
interlaminar stress problem.
The method
divides
the part into "global" and "local" domains.
The local
domain
is
the region of interest.
is in the global domain.
domain
are
smeared
The remainder
Most characteristics
together.
The
of
approach
of the part
the
is
global
akin
to
the evaluation
of
substructuring in the general finite element method.
Kassapoglou
and Lagace
[16] approached
interlaminar stresses by assuming stress
satisfied
integral
the
boundary
equilibrium.
conditions
distributions
and
which
differential
and
The complementary energy of the system
is evaluated symbolically and made
stationary.
When
actual
stresses and elastic parameters are considered, the parameters
needed to describe the interlaminar stress
be
solved
for iteratively.
distributions
This method was shown to require
far less computational effort than the finite
while
showing
literature.
the solution
conditions
some special
excellent
Any
agreement
significant
in the literature
or equilibrium.
cases
[17]
and
can
with
element
solutions
method
in
the
differences could be traced to
not
satisfying
the
boundary
The method has been evaluated for
extended
to
thermally-induced
31
loading
[18].
Wang
and Choi [19] have suggested
singularity
at the free edge
singularity,
however,
of
may
that there is a stress
composite
ply
properties
properties
may
theoretical
may
have
break
to
existence
This
only be important over regions so
small that the underlying assumptions of
of
laminates.
down
be
of
smeared
and
homogeneity
fiber
considered
and
matrix
explicitly.
The
the singularity may therefore have
only limited practical importance.
There are
stresses. ' The
several
does
not
in
evaluating
interlaminar
method of Kassapoglou and Lagace will be used
in this investigation
It
options
because
include
it is
efficient
a singularity
and
accurate.
in its present
this does not appear to be an important
factor in the
form, but
present
investigation.
2.2 Delamination Initiation
The
interlaminar
initiating
knowledge
of
stress
delamination.'
initiation
materials
the
approach.
how
to
in
incorporate
has been a subject of debate.
been
and
instrumental
stress state into the prediction
basic methodologies have
approach
is
Nonetheless,
of the interlaminar
delamination
state
explored:
strain
the
energy
mechanics
release
Two
of
rate
32
2.2.1 Initial Qualitative Approaches
Early
attempts to correlate delamination initiation with
the interlaminar stress state
Pipes
et
al. [3]
have
no
mismatch
Classical
of
Laminated
transverse
stress
calculations
stress
studied
[e.g. 17]
(azz)
were
[±e]s laminates.
Poisson's
Plate
ratio
Theory
show
delamination
in
these
These laminates
from
ply
the
[±e2 ] s
("alternating")
these laminates
are the
interlaminar
shear
was
primarily
laminates.
the
layer
thickness
stresses.
laminates
normal
responsible
Herakovich [20] also
laminates
The
mismatch.
with
He
[(+±)2]s
and
the
resulting
magnitude
of
at the interfaces of
greater in the clustered laminates.
clustered
stress
The essential differences between
interlaminar shear stresses az
is
no
The conclusion reached was that
("clustered")
laminates.
ply.
predicts
interlaminar
investigated laminates containing no Poisson's
compared
to
Interlaminar
that
is negligible.
qualitative.
therefore
(a2 2 ).
the interlaminar shear stress alz
for
essentially
failed
at
the
interest
Herakovich found that
significantly
lower
stresses.
This indicates earlier delamination initiation.
concluded
that
"the
differences
are explained analytically
through consideration of the influence of layer
the magnitude
Rodini
approach
by
of the interlaminar
and
Eisenmann [1]
He
thickness
on
shear stress."
attempted
a
quantitative
trying to correlate delamination with the volume
integral of the interlaminar normal stress (azz).
They
only
33
integrated
over
that volume
edge and the point where
the
propensity
for
of the laminate
azz changed sign.
delamination
between
They proposed
azz.
solution
of Pagano and Pipes
They used
[11] to determine
This approach predicts that delamination strength
strong function of specimen length.
correlation of analysis
and
that
could be determined with a
Weibull distribution of the value of this integral.
the approximate
the free
is
a
They achieved "reasonable
tests"
although
they
did
not
specifically test the effect of specimen length.
Lagace
[21]
of integrating
propensity
over the entire volume, however,
of various
the integral
changed
also considered the effect of azz
interfaces
to delaminate
he
rated
the
on the basis
of azz from the free edge to the point
sign.
Instead
where
Specimen length was not considered.
of
it
Specimen
thickness was only accounted for indirectly in that it changed
the
distribution
of a
on each interface.
higher tensile values of this integral was a
of a greater propensity
These
early
however,
in
approaches
was
the
indication
often achieved good qualitative
individual
general
good
that
for delamination.
agreement with the data generated for the
conditions
He believed
enough
special
references.
to
be
used
cases
None
of
and
them,
in all cases for
general laminates.
2.2.2 Strain Energy Release Rate Approaches
K
Delaminations
can be
regarded
as
interlaminar
cracks.-
34
This
prompted
some researchers to look at delamination onset
and growth in terms of fracture mechanics methodologies.
most
popular
approach
is
Rybicki et al. [5] reasoned
growth
in
isotropic
delamination
release
per
of
unit
strain
energy release rate.
that methods developed
metals
laminated
rate approach
the
could
The
be
for
extended
composites.
The
to
strain
can be applied in terms
of
crack
the
energy
energy
area of crack growth available from released strain
energy (strain energy release rate curves) and the energy
unit
the
per
area needed to create the new surface area (delamination
resistance curve or "R-curve").
Rybicki et al. [5] determined the strain energy
released
during incremental crack growth using a two-dimensional finite
element model of a laminate cross-section.
change
in
energy,
they
released
crack tip, and reevaluated the
could
approximate
the
change
To
evaluate
the
an additional node at the
finite
element
model.
They
in energy by closing the node
with the nodal forces observed when that node was closed.
energy
was
the
integral of the product of virtual force and
virtual displacement.
method.
The
This is
the
"virtual
crack
closure"
Data they obtained suggested that "the strain energy
release rate appears to warrant further investigation as a way
of predicting initiation" of delamination in composites.
Wang
and
Crossman
[6] engaged in further work with the
strain energy release rate
closure
method.
components
of
They
force
approach
specifically
and
and
the
noted
displacement
virtual
that
could
the
crack
three
be integrated
35
mode II (sliding),
to obtain the mode I (opening),
separately
and mode III (tearing) contributions to strain energy
rate.
They
exist.
They approximated
the
assumed
crack
initial
that
a
small
the R-curve as starting
size
and rising quickly
to an asymptotic
The strain
a slight hump for a small delamination
strain
was
level
at
analysis
curve
the
zero
from their finite element
rate
contained
at
release
for all larger crack sizes.
obtained
crack does
energy
value
they
interlaminar
release
such
size.
When
the
that this hump approximated
R-curve as illustrated in Figure 2.2, the conditions were said
to
be
for "pop-in" of a delamination
acceptable
They obtained data for some
with
n
from
ranging
They
cases.
one half to eight
tested
(n
that transverse
to
in
cracks
two.
delamination
For
value.
laminates
showed
all
the
90 °
layer
thinner
the fact
appeared
laminates,
thicker
strain
Their
good
the
before
for laminates with n greater than or
initiation
predicted
They found
or equal to three) despite
initiation
delamination
equal
than
less
[±25/90n]s
[22,23].
good correlation for delamination initiation for
laminates
initiation.
was
results
the
observed
significantly below the
for
some
agreement [24].
quasi-isotropic
Their
analysis for
these cases led them to believe that pop-in delaminations
on the order of one to three ply thicknesses
Kim
and
laminates.
They
are
in size.
Hong [25] applied this methodology to angle ply
They obtained
determined
that
good
mode III
failure of angle ply laminates.
agreement
dominates
with
the
their
data.
interlaminar
This is not surprising
given
36
DELAMINATION
SIZE AFTER
"POP-IN"
PREVIOUSLY
STABLE
DELAMINATION
SIZE
ILU
en
-
/
I/
1
_
_
_
CD
z-J
z
LUJ
LU
H
--
RESISTANCE CURVE
---
STRAIN
ENERGY REILEASE RATE
(f)
DELAMINATION SIZE
FIGURE
2.2
SCHEMATIC OF THE STRAIN ENERGY RELEASE RATE CURVE
AND THE CRACK GROWTH RESISTANCE CURVE AT "POP-IN"
OF THE DELAMINATION INITIATION
37
the
that
value
selection
to
respect
with
changes
this
of
of
a
geometry assumes nothing
position,
including
He calculated the energy
regions
delaminated
approach
He used a rule of mixtures
the
of
modulus
He
in
terms
of
the
modulus, the laminate dimensions, and the strain
longitudinal
level.
and
energy release rate.
longitudinal
delamination width and strain level.
in the laminated
an
as strips along the free edge
the delaminations
The
strain
the
for
obtaining
of
method
O'Brien [26] derived a simpler
specimen.
angle
are zero [17].
ply laminates
approximate
and
azz
shear stress a2z at the free edge of virgin
interlaminar
modeled
stress
normal
interlaminar
predicted
delaminated
region
to
from
calculate
the moduli
the
of the
He obtained the following expression for strain
sublaminates.
energy release rate:
G = 2(Elam- E(2.1)
= strain energy release rate
where: G
t
= laminate
C
=
thickness
strain level
Elam = modulus of the laminated region
= weighted average modulus of delaminated region.
E
The
factor
available
therefore,
is
t
embodies
the general principle
proportional
the
ply
to
thickness.
the
laminate
The factor c2
that the energy
thickness
and,
shows that the
38
available
level.
for
energy
is proportional
to the square of the strain
O'Brien concedes that this equation only gives a value
total energy released.
An approach such as virtual crack
closure is necessary to determine the relative contribution of
the
various
modes.
He
includes no provisions for any more
general delamination geometry and makes no attempt to
account
for the effects of the interlaminar stress boundary region.
O'Brien's
initiation
critical
equation
in a laminate
value
delamination
of
can
be
applied to the delamination
if it is assumed
strain
initiation.
energy
that
release
there
rate,
is
one
Gc,
for
In cases in which the effective ply
thickness is varied by stacking
plies
of
the
same
angular
orientation
together, it predicts that initiation stress will
be inversely
proportional
ply
thickness.
He
root of the
effective
was able to get reasonable agreement for
his data for delamination
specimens.
to the square
initiation
of
[+45n/-45n/0n/90n]s
He concluded that this method was "sufficient" for
the purposes of preliminary design.
In a subsequent
utility
of
a
paper, O'Brien
width
tapered
specimen with a [±30/±30/90/90]
to
measure
compared
double cantilever beam (WTDCB)
"edge delamination
specimen"
and
the
the
edge
delamination
delamination
specimen
GI,
in
the
edge
crack closure method.
using
initiation onset strain.
They determined the mode I component of strain energy
rate,
the
the critical value of strain energy release rate.
They computed G c for
equation 2.1
et al. [27]
delamination
They found it was
release
case using the virtual
significantly
lower
39
value,
GIC,
determined
data and that data
from
both
the
than
specimen
critical
to
necessary
of
types
are
tests
"interlaminar fracture
material's
a
quantify
the WTDCB
from
toughness".
[28] then attempted
O'Brien
to
contribution
mode I
to
strain
quantify
energy
rate on the
release
critical value of total strain energy release rate.
rate remained constant while the mode I
He
loading,
the criterion
a
reach
of
varied.
systems under static
was
for onset of delamination
GI
that
Further experiments by O'Brien et
that "toughened"
when
GI
contribution
resin
brittle
value.
critical
al. [29] indicated
values
for
that
concluded
He varied
so that the total strain energy release
sequences
lamination
of
effect
the
mode I
the
resins had lower
critical
constituted
contributions
a
smaller percentage of total strain energy release rate.
The strain energy
sound
events
principle:
feasible.
energetically
can
only
is
they
if
occur
equation
assume
likely
laminate.
O'Brien
not
simplified
be the case for a delamination
if G c
is taken to be a function
contribution to the strain energy release rate.
this
requires
This nullifies
are
the
geometry and a constant
This will
in a general
Additionally, data can only be correlated with
equation
a
Nonetheless, the proposed forms have
strain level with respect to longitudinal position.
most
on
based
Both the virtual crack closure method and
some problems.
O'Brien
release rate approach
the
of the mode I
At
present,
finite element modeling and a large data base.
the
benefits
gained
from
having
a
simple
40
approach.
the papers dealing with strain energy release rate as
Of
a
Wang
initiation [5,6,22-29], only
preexisting
or
predicting
for
method
delaminations
delamination
correlating
and
Crossman [6]
mention
Nonetheless,
in their derivation.
fracture mechanics methodologies are derived in terms of crack
tip
The
fields.
stress
virtual crack closure results show
for
such
question
the
that the strain energy release rate approaches zero
proper
If no crack of sufficient
initiation.
delamination
orientation
necessary
Broek
criterion
initiate
some
via
this
sufficient
need
delamination
Hence,
is a
not
be
have
may
a
to
other mechanism before fracture mechanics
Once the delamination has initiated,
delamination
size
It
for crack extension.
methodologies can apply.
however,
crack
about
[30] has stated, "The energy criterion
criterion."
sufficient
and
size
exists at the free edge, then there may not
be sufficient concentration of stresses to bring
extension.
to
methodologies
mechanics
fracture
of
applicability
into
brings
This
delaminations.
small
for
may
fracture
itself
mechanics
serve as a crack of
methodologies
to
apply.
2.2.3 Average Stress Mechanics of Materials Approaches
Wang and Choi [19] suggested
singularity
at the free edge.
the existence
Although
of
a
stress
the region over which
this effect is important may be extremely small in most cases,
41
a
singularity
straightforward
brings
into
mechanics
question
the
applicability
of materials approaches.
edge is an example of a small region of high stress
stress
gradients.
concentration
a
In
one
The free
and
high
sense,
it is akin to the stress
at the edge of a hole.
In the case of a hole in
composite specimen, data suggests the stress at the edge of
the hole far exceeds the in-plane
To
of
deal
with
this effect
strength
in holes, Whitney
introduced the "average stress" concept.
theoretical
longitudinal
edge of the hole.
of
stress (11)
the
laminate.
and Nuismer
They
[31]
averaged
over a distance
the
from the
The general equation for an average
stress
is:
Xavg
--v1{ij dx
(2.2)
all X ~avg
0
where: aij
= stress component
aij
= average stress component
x
= distance
from a reference edge
xavg = averaging dimension.
They
predicted
failure
when
this stress reached a critical
value.
In
an
analagous
interlaminar
strength
observed.
shear
parameters
Kim
and
fashion,
the
theoretical
values
of
and normal stresses far exceed reasonable
before
Soni
4]
delamination
thus
attempted
initiation
to
is
correlate
42
delamination
initiation with an average value of interlaminar
normal stress.
They averaged the stress over one nominal
ply
thickness and approximated the interlaminar normal strength by
the transverse strength of the unidirectional composite.
resulting
The
criterion was therefore that delamination initiates
when:
=t
-
zz
(2.3)
where: yt = in-plane transverse strength of the unidirectional
composite.
They
only
considered
capable
of
tensile
initiating
interlaminar
delamination.
demonstrated that the theoretical value
of
normal
stress
Their
results
the
interlaminar
normal stress far exceeded the estimated strength.
In a subsequent
the
effect
averaged
of
this
the
investigation,
interlaminar
Kim and Soni [32] analyzed
shear
stress
alz.
They
shear component over one nominal ply thickness
and estimated the interlaminar shear strength as the
in-plane
shear strength of the unidirectional composite.
The resulting
criterion was that delamination initiates
the
when
absolute
magnitude of the average interlaminar shear stress reached the
estimated shear strength:
ilzl
where:
=
S
S = in-plane
composite.
(2.4)
shear
strength
of
the
unidirectional
43
Reasonable agreement was obtained.
They did not discuss which
interlaminar stress component was more
important
or
how
to
choose between the two criteria they proposed.
Kim and Soni [33] then proposed a general criterion which
included the effects of all
interlaminar
stress
components.
The criterion stated that delamination would initiate when:
-2
F zz
where
Fttlz-2
the
in-plane
-2
2z +F
+F
coefficients
shear
eliminating
and
terms
+ Fta 1
could
be
transverse
dependent
+ F+
determined
strength
2
= 1
by
(2.5)
relevant
tests.
After
on the sign of shear stress, the
criterion reduces to:
F
-2
azzz
-2
+Fttlz
Fuu
-2
+F
2z
(2.6)
(2.6)
z zz
They achieved good agreement with their data.
The linear term in interlaminar normal
significant.
stress
is
quite
It implies that compressive average interlaminar
normal stress can inhibit delamination initiation in cases
which
interlaminar
shear
stress
dominates.
Kim
in
and Soni
performed no experiment to directly test this hypothesis.
Brewer and Lagace [34] proposed a similar
delamination initiation.
criterion
for
The Quadratic Delamination Criterion
states that delamination will initiate when:
44
-
where:
-t
a zz
2
z
sl
s2
compressive values of
zz
shear strength
for alz
= interlaminar
shear strength
for a2z
tensile interlaminar normal strength
zC
= compressive interlaminar normal strength
averaging
dimension
is
a fit parameter rather than set
equal to a value determined by composite
The
(2.7)
1
= interlaminar
z
The
t
= tensile values of azz
-c
azz=
Z
c2 [
Z2
interlaminar
measured
by
direct
shown that there
in-plane
strength
experiment.
can
be
transverse
strength.
The
parameters
a
material
can,
in
producers.
theory,
be
Lagace and Weems [35] have
significant
strength
and
difference
out-of-plane
between
normal
difference between the effects of tensile and
compressive average interlaminar normal- strength are accounted
for
by
linear
average
explicitly
term.
separate
This
quadratic
dismisses
interlaminar
normal
the
terms
ability
stress
to
of
rather than a
compressive
suppress initiation
controlled by interlaminar shear stress.
Brewer and Lagace [34] tested
[0n/+15n]s
laminates
[±15n]s,
[±15n/0n1s,
to find delamination initiation stress.
A computer-controlled testing program was used.
automatically
indicative
of
stopped
the
and
a
test
increase
The
program
when a drop in load, possibly
in
compliance
accompanying
45
delamination
initiation,
was
detected.
Delamination
initiation was verified us ing the edge replication
described
by
Klang
and
Hyer [36].
agreement with their data.
to
be
on
the
techniques
They obtained excellent
The averaging dimension was
order of a ply thickness
found
but not equal
to it.
This was verified by using prepregs of the same material
with
two different nominal ply thicknesses.
Brewer
approach
by
a
and
Lagace
[26] resulted
factor
lamination
of
up
sequence
found
the
dominated
three
to
of
strength
cannot
of
by the interlaminar
for
laminates
mode I
considerations.
different
may not
occurs.
ply
apply
varied
of the
contribution
[0n/±1 5 n]s
and
shear stress
initiation
consistently
O'Brien's
same
with different effective ply thicknesses
[±15n/0n] s'
Delamination
appears
The
predict
behavior
the
initiation
laminates
were
be
controlled
energy
in
to
delamination
by
release
rate
laminates
with
thicknesses and different fractions of G I.
directly
of
alz'
to
strain
was
before
It
initiation
The average stress mechanics of materials approaches
to work well for the laminate
Nonetheless,
applicability
more
of
work
needs
to
types
be
an
tested
to
to
verify
done
date.
the
these approaches to laminates which are not
dominated by interlaminar shear and in
such
use
Calculations showed that the delamination
[±15n]s'
appear
the
in calculated values of Gc that
even though the percentage
same.
that
thermally-induced
which
interlaminar
other
effects,
stresses,
are
46
important.
The Quadratic Delamination Criterion will be used
to correlate delamination
because
it
relies
on
initiation
an
in
this
experimentally
investigation
derived averaging
dimension rather than a manufacturing parameter.
2.3 Delamination Growth
The next phase
growth.
If
sufficiently
of
damage
delamination
large
development
initiation
interlaminar
methodologies are more likely to
necessary
that
conditions.
were
be
can
delamination
serve
fracture
sufficient
as
a
mechanics
as
well
as
The strain energy release rate curves
generated
to
initiation [5,6,22-29]
can
delamination
Rybicki
growth.
crack,
is
also
et
describe
delamination
be
to
al.
used
[5]
describe
calculated
the
critical value for strain energy release rate as a function of
delamination
size.
They found it was nearly constant during
growth.
Wang et al. [6,24] believed they
using
the
virtual
energy
the
Gc
as
available
could
be
shown in Figure 2.3.
growth
They argued that
approximated
Recall
for release is proportional
strain level.
describe
crack closure approach.
the asymptote of the R-curve
constant
could
by
that the strain
to the square
as
of
The hump in the strain energy release rate
curve and the R-curve crossed at stable delamination sizes
long
the
as
the R-curve extended above the strain energy release
rate curve at larger delamination
sizes.
For
an
asymptotic
47
LUi
CRITICAL VALUE
OF STRAIN ENERGY
RELEASE RATE, GC
L
LLJ
p-
z
LrL
ACTUAL
DELAMINATION
RESISTANCE
CURVE
LLJ
zH
>p-)
DELAMINATION SIZE
FIGURE 2.3
SCHEMATIC OF THE DELAMINATION RESISTANCE CURVE AS
APPROXIMATED BY A CRITICAL VALUE OF STRAIN ENERGY
RELEASE RATE
48
this is only possible when the strain energy release
R-curve,
rate curve has a negative
the
hump
shown
as
increased
and
slope, such as on the back
in
the
Figure 2.4.
strain
in
thLe strain energy
maximum stable delamination
release
rate
curve
could
direct
the
delaminations
t'
he
Once
above
occur.
local
strain
a
energy
unstable
the virtual crack
Since
two-dimensiona 1
than
The
R-curve
the
applicability
other
o ccur.
would
size.
closure method is based on a
model,
level
release rate curve represents
shifted
ggrowth
delamination
strain
of
energy release rate curve shifted
upward, stable delamination growth
minimum
the
As
side
of
finite
the
element
results
to
constant width delaminations along
the free edge i.s questionable.
In a subsequent
observed
growth
behavior
pattern
paper
did
for
specimens incurred
The
more detailed
analysis
of
not
Crossman
several
authors
...
is
and
Wang
[±25/90n]s
cracking
were
laminates.
before
delamination
shown
region
These
prompted to conclude that "a
to
delamination
growth
the
delamination
be
necessary
for
the
growth." Kim and Hong [25]
stated that the strain energy release rate approach
the
[23],
match the predicted delamination
transverse
initiation.
prediction
by
they
describes
observed in angle ply
laminates.
O'Brien
describe
[26] proposed
delamination
that his approach
growth.
The
could be used
assumptions made in his
derivation make his approach directly applicable only
delamination
has
a constant
to
if
the
width along the free edge and no
49
LAST STABLE
DELAMINATION
SIZE BEFORE
UNSTABLE
GROWTH
WL
/
N
I
LuJ
Co
LU
/
/
INCREASING
STABLE
DELAMINATION
SIZE
/ LOAD
-J
CD
z
LU
/
LU
--- RESISTANCE CURVE
---STRAIN ENERGY RELEASE RATE
(If
AVAILABLE AT VARIOUS LOADS
DELAMINATION SIZE
FIGURE 2.4
SCHEMATIC OF THE STRAIN ENERGY RELEASE RATE
CURVES AT VARIOUS POINTS DURING STABLE AND
UNSTABLE DELAMINATION GROWTH
50
quantity
such
as
position.
longitudinal
release rate to
that
the
more general function
and
expression
of
delamination
can be extended
that he believes
The
strain
delamination
present
form,
delamination
approach
it
should
growth in
has
shapes
to
resistance
size.
of
size.
He
curve
is a
uses
his
He
generate
an
R-curve
types.
to other laminate
general
the
limited
with
be
function
release rate approach may be able to
energy
describe
a
of delamination size and strain
data
for [+±30/±30/90/90] s specimens
level
is
delamination
delamination
of
actual
strain
equation predicts strain energy
The
independent
be
assumes
merely
longitudinal
case.
applicability
complicated
developed
to
strain
which
In
its
general
fields.
An
for
the
accounts
characteristics of more general delamination geometries.
2.4 Delamination Failure
k
The
experimental
prone
that laminates
stresses
as
found
this
Lagace
et
the
for
strength
and
was
to
documented in the literature is
delamination
will
layer thickness increases.
his
al. [37]
[0n/±15n]s,
trend
alternating
found
4 5 n/On]
[+±
this
and
for
fail
[±15n]s,
No
found for [[0/±15]s]n specimens.
laminates.
[±15n/On]s,
difference
for
delamination
initiation
and
in
Strain energy
release rate approaches would suggest that this would
trend
lower
Herakovich [20]
clustered
specimens.
at
growth,
be
the
but
not
51
final
for
explicitly
imply in their conclusion
Hong [25]
and
evaluated
strength
all
"for
has
the
caused
resulting
not
on one another,
They suggested that final failure should
necessarily to fail.
be
is
final failure is not as
that
release their constraint
to
sublaminates
noted
The delamination
simple as that.
growth
that unstable
a good estimate of ultimate strength."
practical purposes ...
Kim
Wang et al. [24] do however
failure.
after
delamination
in
of the sublaminates,
in
terms
their
of the in-plane
case,
unconstrained
angle plies.
The
in-plane
of laminates
strength
therefore relevant to this investigation.
shows
good
agreement
and sublaminates
is
One criterion which
with in-plane tensile fracture data of
graphite/epoxy is the generalized stress interaction criterion
of Tsai and Wu [38].
The criterion is applied on a ply by ply
basis to the in-plane stress
Laminated
Theory.
Plate
state
The
general polynomial of order n.
quadratic
calculated
criterion
by
Classical
can be written
as a
The most useful version is the
In tensor notation, the criterion is written
form.
as:
Fao aa
Since
the
+ F
the criterion
indices
a,
It can be reasoned
eliminated
ayaaaB
is applied
, a,
(2.8)
1
to the in-plane
stress
state,
and y can assume the values of 1 and 2.
that terms linear in shear stress should be
because the definition of positive shear stress is
52
on
dependent
these terms
remain.
are
Five
removed,
of
F
six
these
can
and
coefficients
F
determined
be
for a composite
material by performing uniaxial compressive and tensile
along
the
sixth
interaction
in biaxial
take
the
loading
major
and
axes
(e.g. a [On ] laminate
material
The
two
coefficient
is
a
test of the basic
shear
for unidirectional
F1122.
tests
This
tape)
[38].
quantifies
the
the longitudinal and transverse stresses
between
loading.
If the general criterion
form
a
of
Once
of the coordinate system.
selection
the
von Mises
axes, the value
of
the
is
assumed
to
in the principal
criterion
interaction
is
term
given
by [38]:
1122
2
F1111
This is the form of F122
2222
(2.9)
used in the version of the criterion
that has been used to achieve good agreement.
Little work has been done explicitly on
of
final
in-plane
failure
significant delamination
criterion
of
Tsai
of
damage.
specimens
Although
final in-plane
evaluated.
correlation
which
experience
the
generalized
and Wu shows good agreement with in-plane
failure when there is no delamination,
the
the
its
failure of delaminated
applicability
specimens
to
should be
53
CHAPTER
3
APPROACH TO PRESENT WORK
3.1 Overview
The
and
work is a synthesis of related experimental
present
efforts
analytical
with
designed
the
of
objective
describing and understanding the sequence of events which lead
to
failure
of
growth,
initiation,
and
final
investigating
each
phase
sections
this
chapter.
in
analysis,
has
Delamination
delamination.
three
be
for
approach
forth in subsequent
put
Details
and results will be
The
by
phases [6]:
major
failure.'-
will
induced
laminates
graphite/epoxy
of
discussed
the
in
experiments,
the
appropriate
chapters.
a
Although
initiation,
great
of
deal
work
been
has
done
two important issues remain to be resolved.
on
They
are the applicability of criteria when the interlaminar normal
stress
the
is
delamination
primary
and
the
interlaminar
importance
stress contributing to
of
thermally-induced
interlaminar stresses'/ In the delamination initiation portion
of
this
investigation,
these
issues
will
be
explored
experimentally and explained in terms of existing models.
The
failure
objective
of
the
delamination
growth
and
portion of this investigation is to gain insight into
the details of the damage sequence in general laminates.
strain
final
energy
The
release rate approach has been touted as being
54
capable
of
Although
describing
it
describing
presently
has
all
been
shown
delamination
available
growth behavior.
limitations,
can
The
could
be
some
their
is
crack.
coincident
explored.
versions
present
forms
have
model
transverse
would
need
"premature"
cracks.
cracks
in
900
be
made
to
to
initiation
The
Quadratic
that
often
Delamination
applied with minimal modification if the
vicinity
of
the
The issue of whether or not final failure
with
The
the
stable and unstable
interlaminar stress state were known in the
transverse
[6].
For example, the virtual crack closure
the
accompanies transverse
Criterion
in
Modifications
predict
delamination
give poor correlation when
describe
and O'Brien methods do not
accurately
to
of
initiation [34],
models
however.
sublaminates.
phases
unstable
validity
of
delamination
failure
growth
models
will
will
be
also
be
ascertained.
The
results of the experiments
possible modifications
models
damage
to
the
will be used to delineate
strain
energy
release
rate
so that these models more closely reflect the observed
progression.
Modifications
will
be
made
and
evaluated.
3.2 Interlaminar Normal Stress and Delamination Initiation
Excellent
stress
for
correlation
the
of
the
delamination
initiation
various laminates tested in Reference 34 has
been achieved with the Quadratic Delamination Criterion.
One
55
averaging
dimension
laminates
and
averaging
dimension
gave
ply
all
is
suggesting
thicknesses,
of
primarily
controlled
by
alz' and the contributions of
were
stresses
other
relatively
for
initiation
the interlaminar shear stress,
thermally-induced
The
small.
shear
interlaminar
the
The criterion
was tested only on laminates in which delamination
was
that
criterion
this
prediction of delamination initiation.
general
all
material parameter./-However, two
a
remain with regard to the use
issues
for
excellent - correlation
stress,
interlaminar
average value of the
a2z'
normally
will
be
negligible
in these cases since it is required by the boundary
conditions
to be zero both in the laminate
However,
edge.
free
Quadratic
stress,
normal
interlaminar
there
Delamination
azz,
choosing
by
as
laminates
can
in
and at the
the
which
The
important.
be
can be further verified by
Criterion
isolating the effects of the
well
are
interior
interlaminar
normal
stress
as
with large contributions of
laminates
thermally-induced interlaminar stresses.
and Lagace
Kassapoglou
loaded
specimens,
shear stress
laminate,
a12.
the
alz
alz
is
mainly a function
In cases where
component
Only if all the plies have
(A1 l12
[16] have shown that in uniaxially
a12 is zero
of the in-plane
throughout
will be identically
extensional-shear
the
zero [17].
terms
coupling
and A2212 in standard tensorial notation for Classical
Laminated
Plate Theory) equal to zero can a12 be avoided.
The
only plies of orthotropic fibrous materials with this behavior
are those with angular orientations
of the fibers
of
0
and
56
900
to
the
therefore
longitudinal
potentially
axis.
have significant
Conventional cross-ply
disadvantage
in
A cross-ply laminate could
the
zz and no alz [17].
laminates
context
have
[e.g. 23], 90°
are
transverse
susceptible
to
where the transverse cracks meet
are
potential
The effects
sites
of these
interlaminar
would have to be
delamination
the
plies
interlaminar
cracks
evaluated
before
models
the
could
be
to avoid 900 plies.
other option
properly applied.
-It is
therefore
elastic
parameters.
Other
First, they usually
contain
matrix systems which are not necessarily compatible
graphite/epoxy
cure
determined averaging dimension
strength
available
materials such as kevlar/epoxy and glass/epoxy
have two distinct disadvantages.
the
local
is to use 00 plies of two or more
composite systems with different
with
the
presently
desirable
different
interface
(e.g. on
for this effect are not available.
unidirectional
The points
state or the strain energy release rate)
initiation
only
in laminates
cracking.
Solutions
The
As has
of "premature" delamination initiation.
transverse
stress
unacceptable
of this investigation.
been noted in the literature
often
an
parameter
would
cycle.
and
the
The
experimentally
interlaminar
normal
have questionable applicability to
either system.
Second, there is not a
sufficient
in
properties
significant transverse
transverse
stresses, a22 .
of
to
induce
The interlaminar normal stress is
the in-plane transverse stresses.
normal
stress
would
most
likely
difference
a
function
Hence, the interlaminar
be
too
small
to
cause
57
delamination initiation before in-plane failure.
The
only composite material which will suit the needs of
the experiment is a woven graphite/epoxy fabric
material.
A
fabric made from the same fiber and matrix would be compatible
for curing and more
interlaminar
normal
likely
to
give
strength
and
consistent
values
for
averaging dimension.
The
desired interlaminar stress state can be obtained by including
plies
of
graphite/epoxy
there are 90°
tows
fabric
fiber tows in the
in
the laminate.
fabric,
splitting
Although
of
these
before delamination initiation is likely to be inhibited
by the weave of the fabric.
/The materials used in this
AS4/3501-6
and
unidirectional
Hercules
investigation
five-harness
preimpregnated graphite/epoxy fabric.
Three
Hercules
preimpregnated graphite/epoxy tape
AW370-5H/3501-6
are manufactured
were
Both
satin
material
weave
systems
with the AS4 fiber and 3501-6 epoxy. ,
laminate
types
were
chosen for this experiment.
They are [0 5U/OF]s, [0 5U/0 F/0U]s' and
[0 1OU/OF]s'
where
the
subscripts "U" and "F" denote unidirectional and fabric plies,
respectively.
normal
These gave reasonable
stress.
The
values
mechanically-induced
of
interlaminar
components of the
interlaminar normal stress were calculated using the method of
Kassapoglou
and Lagace [17].
the applied far-field
depicted
in
Figure
calculations are
systems
in
These components, as related to
stress, for the three laminate
3.1.
given
Table 3.1.
The material
for
the
parameters
unidirectional
types are
used in the
and
fabric
The interlaminar normal stresses were
58
0.03
IIDPLANE)
CMus/
u/.........
O
Id
co
co
0
-I
a
----
[OUo1/OF]S (IMIDPLANE)
--.
[OU/S/OF/OU]S
.E
(OF/OU
INTERFACE)
Ii_j
H
L.
0.02
Al
lz
d
~t
.
W
I
IL.
0.01
Z
Z
0
OC
zZ
9z
E
co
0
H
to
-5
Id
0.00
-
Z
z
1-
-
-
,
\
- I
H
0
2
1
3
4
DISTANCE FROM FREE EDGE [MM]
FIGURE 3.1
MECHANICALLY-INDUCED INTERLAMINAR NORMAL STRESS
FORS 0/0F
SPECIMENS
10
s
UiO
0
S
F
AND
[0U/0F/0]
5'
5
59
TABLE 3.1
MATERIAL PARAMETERS OF
HERCULES AS4/3501-6 UNIDIRECTIONAL GRAPHITE/EPOXY
AND HERCULES AW370-5H/3501-6 FABRIC GRAPHITE/EPOXY
AS4/3501-6
tply
E1 1
0.134 mm
AW370-5H/3501-6
0.35 mm
142 GPa
72.5 GPa
9.81 GPa
72.6 GPa
9.81 GPa
10 GPa
6.0 GPa
4.43 GPa
6.0 GPa
4.43 GPa
4.8 GPa
4.43 GPa
V1 2
0.3
0.059
v1 3
0.3
0.3
V2 3
0.34
0.3
11
'22
-0.2 pstrain/°F
1.29
strain/°F
16.0
1.29
strain/°F
ustrain/°F
60
plotted
for
the
interlaminar
critical
normal
interfaces.
stress
was
Since
only
significant
for
the
these
specimens, the critical interface was the one with the highest
value
of this component
interface
was
specimens
the
and
of interlaminar
OF/OU
The
critical
for the [ 0 5U/0F]s and [01 0 U/ 0 F s
midplane
the
stress.
interface
for
the
[0 5U/0F/0U]
of
the
interlaminar
s
specimens.
The
normal
thermally-induced
stress
were
components
calculated
using
the method of Lagace,
Kassapoglou, and Brewer [18] and found to be significant.
change
in temperature used to calculate the thermally-induced
stress state was -1560 C.
set
The
This is the difference
between
the
temperature of the epoxy matrix during curing (1770 C) and
room temperature (210 C).
stresses
can
interlaminar
Figure 3.2.
thus
be
normal
The influence
evaluated.
stress
of
The
components
thermally-induced
thermally-induced
are
depicted
in
The stress distribution for each specimen type is
plotted for the critical interface.
The
critical
are
for
the
mechanically-induced
was
constructed.
the
same
ones
observed
interfaces
stresses.
One laminate of each type
laminate,
five
standard
TELAC
were
initiation stress.
portion
350 mm
long
with
long test section as illustrated in Figure 3.3.
specimens
tested
to
determine
Table 3.2 is- the
of the investigation.
each
specimens were manufactured.
The standard specimen is 50 mm wide and
200 mm
From
test
their
a
These
delamination
matrix
for
this
61
mn
60
AT = -156
Ou
C 0t/O0 F]S CMIDPLANE)
----
COU5/OF/0 u3S (0OF/OU INTERFACE)
---it
40
I
(I oL
.\
30
W
C
0 UCO/OF]S(MIDPLANE)
.........
50
°
-
I
20
,\
10
t\
0
\,
\
.==
I
_
_
I\
-10
0
H
FIGURE 3.2
I
2
3
4
5
DISTANCE FROM FREE EDGE [MM]
THERMALLY-INDUCED INTERLAMINAR NORMAL STRESS FOR
[0U5/0 F]S' [0 U10/0F]S, AND [0 U5/ 0 F/0U]S SPECIMENS
62
TOP VIEW
SIDE VIEW
T
75 mm
- GLASS/EPOXY
l
TAB
Ip
3RAPHITE/EPOXY
STRAIN
'GAGE
200 mm
0I:]
,GRAPHITE/EPOXY
-123 FILM ADHESIVE
Ip
A
_ GLASS/EPOXY
-I
75mm
GLASS/EPOXY
50mm
50 mm
FIGURE 3.3
STANDARD TELAC TEST SPECIMEN
63
TABLE 3.2
TEST MATRIX FOR DELAMINATION
INITIATION SPECIMENS
Laminate
Number
Type
Specimens
[ 0 5u/0F]s
5
[05U/0F/0U]s
5
0
[ 0 1OU/Fs
5
aSubscript
"U"
unidirectional
Subscript
refers
to
plies
graphite/epoxy
of
of
tape.
"F" refers to plies of woven
graphite/epoxy fabric.
64
3.3 Delamination Growth and Final Failure
Several
variables
were
investigated to determine their
effect on delamination growth and final
specimen
failure.
These
are
width, effective ply thickness, lamination sequence,
character of the ply interface, and implantation of
simulated
delaminations and angle ply splits.
The
majority of research involving delamination has been
done on specimens containing
often
develope
"premature"
in
these
90°
plies.
plies
delamination
and
Transverse
serve
initiation.
as
cracks
sites
for
In order to avoid this
phenomenon, laminates containing 90° plies were
not
used
in
this investigation.
An excellent method for observing internal damage such as
delamination is a non-destructive evaluation technique such as
dye
penetrant-enhanced
determine delamination
characteristics
x-radiography.
shape
including
within the plies.
Many
and
An
size,
quantity
specimens
and
in
as
x-radiograph can
well
as
position
this
other
of splits
portion
of
the
investigation were tested to predetermined loads, their damage
state
evaluated
using
x-radiography,
and
retested.
All
The first variable investigated was specimen width.
This
specimens were eventually tested to failure.
was
selected
to
evaluate
the
hypothesis
delamination area may exist for unstable
or
in-plane
failure.
The
results
that
a critical
delamination
growth
from the specimens with
nonstandard widths can be used to determine if such a critical
65
size
For
exists and if this size is a function of specimen
example,
percentage
the
of
independent
critical
test
of
delamination
section
specimen
area
or
width.
area
an
width.
could
absolute
be
a
value
These experiments may also
detect other finite width effects.
The [+±153]s laminate was
because
it
had
been
chosen
shown
to
for
these
delaminate
investigation [34] when manufactured from a
(Hercules AS1/3501-6).
10 mm,
20 mm,
in
a
previous
similar
material
The specimens used were standard TELAC
specimens except in width.
were
experiments
The widths
30 mm,
50 mm,
used
in
and 70 mm.
these
tests
These widths
ranged from approximately seven to approximately 50 times
width
of the interlaminar stress boundary region.
the
The aspect
ratio of the test section varied from slightly less than three
to 20.
To determine
specimens,
it
the appropriate
was
necessary
initiation stress and final
laminate.
An
loads to which
additional
to
failure
two
know
the
stress
of
10 mm
to test these
delamination
the
[±153]s
wide specimens and two
30 mm wide specimens were manufactured and tested to determine
these
values.
Five specimens of each width were then tested
using constant stress increments from approximately 90% of the
observed
delamination
Damage was assessed by
after
each
this portion
The
initiation
dye
stress
to
final failure.
penetrant-enhanced
stress increment.
x-radiography
Table 3.3 is a test matrix for
of the investigation.
next
variables
investigated
were
the
lamination
66
TABLE
3.3
TEST MATRIX FOR [+±15
OF NONSTANDARD
Specimen
Width
[mm]
SPECIMENS
IDTH
Number of Specimens
Tested for Delamination
Initiation
and Final
Failure
Number of Specimens
Tested to Incremental
Load Levels and
Monitored with Dye
Penetrant-Enhanced
X-Radiography
10
2
5
20
0
5
30
2
5
50
0
5
70
0
5
67
sequence
and
laminate
types were used:
the
effective
ply
thickness.
Two
similar
[+±15n/n]s and [On/± 1 5 n]s .
In the
AS1/3501-6 graphite/epoxy version of these laminates tested in
Reference 34,
delamination
initiation
was first observed at
the +15°/-15° interface as was predicted using
the
Quadratic
Delamination Criterion.
The same interface is predicted to be
the site of delamination
initiation
from
AS4/3501-6
graphite/epoxy.
for
the
specimens
The two laminate types have
nearly identical interlaminar stress states at
interface
except
that
for
the
[0n/±15n]s
case.
between the two laminate
constrain
[0n/+15n]
delaminated
s
friction.
case.
In
Another
types
and
The
that
damaged
plies
contrast,
is
can
the
delaminated
and
significant
the
angled
then
[+15n]
be
compressive
difference
00
plies
can
plies
in
the
loaded
through
sublaminate
[±1 5 n/On]s case is prone to out-of-plane
the
+15°/-15°
the
the interlaminar normal stress at the
1 5 n/O n]
for the [+±
s case
free edge is tensile
made
peeling.
in
the
That
is,
portion of the sublaminate between the angle
ply split and the free edge peels away from the specimen.
No
load can be carried by this portion of the sublaminate.
Varying
on the
al.
interlaminar
[37].
effect
the effective ply thickness has distinct effects
stress
Increasing
of
"spreading
the
state
effective
out"
the
interlaminar stress components while
edge magnitude.
as
noted
ply
by
thickness
distributions
not
Lagace
altering
et
has the
of
the
the
free
This effect is illustrated in Figure 3.4.
The strain energy release rate curve is scaled upward and
68
__
= 0.134
--- I tPLY= 0.268
= 0.402
---tp~y
I
N
N
mmr
mm
mm
[C15/03s LAMINATE
THERMAL EFFECTS
EXCLUDED
i\
I
I
<:
CD
H
. ,
o)
I\I,
0
Ii
_
_
I
I
0
I
DISTANCE
FIGURE 3.4
_
FROM FREE
I
2
EDGE
EFFECT OF PLY THICKNESS ON THE INTERLAMINAR
STRESS STATE
mm]
69
spread
out
by the effective
the result of two effects.
ply thickness
First, the
factor n.
energy
This is
available
per
unit delaminated area is directly proportional to the laminate
thickness and,
boundary
energy
thus,
region
which
release rate
outward.
The
the
interlaminar
influences
the
shape
near
the
free
stress
of the strain
edge
is
shifted
effect on the strain energy release rate curve
energy
delamination
Second,
curve
is shown schematically
strain
n.
in Figure 3.5.
release
width
rate
The
curve
does
shifting
not
of
the
apply as
the
approaches the width of the specimen.
At
this point, interaction with the interlaminar stress
boundary
region of the far side free edge must be considered.
This was
not an issue for any specimen
in this investigation.
When the Quadratic Delamination Criterion is
interlaminar
stress
such as that of
asymptotic
solutions
Kassapoglou
lower
limit
Lagace
stress
becomes
approach
the
as
the
free
asymptote is the predicted initiation
the free edge values
effects
it
gives
an
effective
ply
large, the calculated average interlaminar
components
The
[16],
delamination initiation stress.
This limit results from the fact that
thickness
to
with a finite free edge value
and
for
applied
stress
of the interlaminar
on
the
strain
edge
values.
computed
The
using
stresses.
energy
release
rate
and
delamination initiation stress of effective ply thickness have
significant
strain
level
consequences.
feasible.
for
Since
Thin
delamination
the
strain
laminates
growth
to
energy
require
a
high
be energetically
release
rate
is
70
LUj
----
LUj
/
V)
-i -
N = 1
1%
_ __
-
_
_
_
LUj
I
I
I
mI,
zLJ
LLJ
z
H
_
,
_,
_
_
_
_
/
I
f
DELAMINATION SIZE
FIGURE 3.5
EFFECT OF PLY THICKNESS ON THE STRAIN ENERGY
RELEASE RATE
_
I
71
proportional
to
effective ply thickness, delamination growth
is energetically feasible at much lower strain levels in thick
laminates.'
Since
delamination initiation stress may have an
asymptotic lower limit, delamination growth in thick laminates
may
be energetically feasible before delamination initiation.
Thick
laminates
delamination
can
therefore
growth
can
be
used
occur
to
before
Delamination Criterion predicts delamination
allow
for a wide
effective
ply
experiments
thickness
were
One
range of possible
1,
laminate
2,
factor,
3,
of
5,
each
thickness was manufactured.
each type.
incrementally
Quadratic
initiation.
To
behavior,
the values of the
n,
in
used
this
set
of
8.
specimen
type and effective ply
This yielded
five
specimens
of
The remaining two were then
tested
from approximately 75% of the failure stress to
failure
evaluated
the
if
Of the five specimens, the first three were tested
monotonically to failure.
final
and
determine
in
after
penetrant-enhanced
5%
increments.
each
The
loading
x-radiography.
damage
increment
Table
state
was
by
dye
3.4 is a test matrix
for this set of experiments.
The third set of experiments
investigated
the
role
of
angle ply split propagation in delamination growth.
Two types
of fabric laminates were chosen.
nominally
[±20F]s
laminates.
were
both
That is, the warp fiber tows were angled
at +200 to the longitudinal
components
They
axis of
of the interlaminar
the
specimen.
All
stress state at the midplane
an angle ply laminate are identically
zero.
Therefore,
the
of
any
72
TABLE
3.4
TEST MATRIX FOR [+15 /0
AND [0 /+15
SPECIMENS
WITH DIFFERENT EFPEETIVE PLY THICRN.SSES
Lamination
Sequence
[±15/0]s
Number of Specimens
Tested Monotonically
to Failure
Number of Specimens
Tested to Incremental
Load Levels and
Monitored with Dye
Penetrant-Enhanced
X-Radiography
3
2
3
2
3
2
3
2
[+±158/08]s
3
2
[0/±15]s
3
2
( 0 2/±152]s
3
2
[(3/±153]s
3
2
3
2
3
2
[±
1 5
2/
0
2]
s
[+153/03]
[±155/05]
[05/±155]
[08/±158]
s
s
s
73
delamination
interface.
initiate
and
grow
at the the +200/-200
The 200 fiber angle was chosen because of the high
interlaminar
and
would
the
shear stress
resulting
(a1z) obtained
low
predicted
in this configuration
delamination
initiation
stress.
The difference between the experimental laminates was the
character
of
the ply surfaces at the +200/-20° interface.
five-harness satin weave has an "over four - under one"
of the fiber tows as shown in Figure
of the exposed
while
80%
fibers.
face"
3.6.
This means
fibers on one face of the ply are
of
the
exposed
the
weave
that 80%
warp
fibers
fibers on the other face are fill
These are referred to as the "warp
of
A
ply, respectively.
face"
and
"fill
One laminate was made with
only warp faces at the +200/-20° interfaces
while
the
other
was made with only fill faces at the +200/-200 interfaces.
Splits
are
observed to form within plies in association
with delamination initiation.
believed
to
be
the
primary
The delamination initiation
is
damage mode since delamination
initiations have been observed without splits in fabric plies,
but
not
vice
versa. " It is reasoned
that splits in the warp
fiber tows emanating from the +20o/-200 interface at the
edge
could
be
tows crossed
the
fill
before
crossing
therefore
inhibited from growing at the point where the
"under" the fill tows.
fiber
allow
free
tows
under a
for
could
tow.
By
contrast,
splits
in
grow farther from the free edge
The
two
types
of
specimens
the direct comparison of specimens with
essentially the same in-plane behavior and interlaminar stress
74
WARP, L
t
FILL,T -
FIGURE
3.6
SCHEMATIC OF 5-HARNESS SATIN WEAVE FABRIC
GRAPHITE/EPOXY
75
state, but a different
character
interface.
fiber tows closest to the delaminating
The laminates each yielded five standard
with
the
previous
state of the
of the splitting
specimens.
As
the first three of each
set of specimens,
group were tested to failure and the remaining two were tested
to
incrementally
increment
75%
of
the failure stress,
to
specimens,
failure
in
5%
The damage state was evaluated after each loading
increments.
Table
from
from the first three
measured
matrix
failure
for
this
portion
of
The
x-radiography.
by dye penetrant-enhanced
test
is given
this investigation
in
3.5.
The interaction
splits
of the delamination
was investigated
front and
angle
ply
in the final set of experiments.
test specimens contained "implanted" delaminations
and
The
angle
These features were achieved by implanting thin
ply. splits.
teflon film between and within the plies of a specimen
before
The nonstick property of the teflon caused the plies
curing.
to decouple
at a relatively
simulating
the
experiments.
low load
delamination
shape
approximates
This
in
a
a
prescribed
shape
in
other
observed
naturally
occurring
delamination.
The delamination
bounded
by
delamination
as
the
and
free
edge,
front approximately
illustrated
split
shape to be investigated
in Figure 3.7.
the
delamination
an
angle
ply
front
split,
to
and
a
the
split,
importance
of the
perpendicular
The relative
was triangular,
were
evaluated
by
manufacturing one set of specimens with no angle ply split and
76
TABLE 3.5
TEST MATRIX FOR [+20F]S FABRIC SPECIMENS
Character
of the
+20°/-20°
Interface
Number of Specimens
Tested Monotonically
to Failure
Number of Specimens
Tested to Incremental
Load Levels and
Monitored with Dye
Penetrant-Enhanced
X-Radiography
Warp/Warp
3
2
Fill/Fill
3
2
77
|INTRU SION
ANGLE
PLY
SPLIT
FIGURE 3.7
SCHEMATIC OF OBS
ERVED DELAMINA
TI
ON DAMAGE
78
one
set
with
delamination
an
angle
front,
ply
as
split
extending
illustrated
in
beyond
Figure
3.8.
the
No
specimens were made with the angle ply split extending exactly
to the delamination
front because that would be equivalent
to
the naturally occurring damage.
Six
sequence
because
specimens
of
used
[03/±153]s.
it
interface
was
was
each
observed
to
with an associated
sublaminate.
The
type were made.
This
sequence
delaminate
angle ply
[03/±153]s
The lamination
at
was
+15°/-15 °
the
split
in
the
because
split
(rather than both
sublaminates
thick
to one sublaminate
in the [±15n/n]s
sublaminate
thinner
ones
with
an
case).
angle
simplifies
the
Having
ply
one
maximum
of
distance
illustrated
a delamination
from
the
in Figure 3.7.
in both cases was nominally
ply split was 20 mm.
investigation
to
at
process.
each
edge
as
to
of the specimen.
can be characterized
free
An
+15°/-15°
They were aligned through the thickness so
size
[+15 n ]
relatively
interface.
with respect to the midplane
ply
split instead of two
manufacturing
positioned
angle
delamination
The
was
the
implanted
be symmetric
[-156]
laminate has an advantage over
comparable [+±15n/On]slaminate types
is confined
chosen
or
by the
"intrusion"
as
The intrusion of the
delamination
10 mm.
of the angle
The intrusion
A test matrix
is given in Table
for this
portion
of
the
3.6.
The
experiments
described in this section were designed
give
information
about
delamination growth.
the
progression
of
damage
in
They were tested to the same load levels
79
C
L
CL
C
L
C
DELAMINATION
I
I
FIGURE
3.8
SCHEMATIC OF SPECIMENS WITH IMPLANTED
DELAMINATIONS
80
TABLE 3.6
TEST MATRIX FOR [+15 /0
SPECIMENS WITH
IMPLANTED DELAMINATIOAS N8 ANGLE PLY SPLITS
Nominal Intrusion
Nominal Intrusion
of the Implanted
of the Implanted
Delamination
Angle Ply Split
[mm]
[mm]
Number of Specimens
Tested to Incremental
Load Levels and
Monitored
with Dye
Penetrant-Enhanced
X-Radiography
10
0
6
10
20
6
81
as
the
[03/±+153]s
state
damage
specimens
was
with no implanted damage.
monitored
test
with
dye
specimens
were
by the four sets of experiments
should
x-radiography.
penetrant-enhanced
each
after
The
The
eventually tested to final failure.
The data generated
of the available
aid in the evaluation
to
models in their ability
describe stable and unstable delamination growth and final
failure induced by delamination.
3.4 Analysis of Delamination Growth
The delamination shapes observed
significantly
were
in the literature.
in
this
investigation
different from those reported and modeled
Although the strain
energy
release
models work well for some cases in the literature,
work well for the damage
the
literature,
strips
along
the
the
observed
in this
rate
they do not
investigation.
In
delaminations were generally modeled as
free
edge.
All
quantities,
including
delamination width, were taken to be constant with respect
to
longitudinal position, thus effectively transforming this into
a two-dimensional problem.
literature
cracks.
usually
The laminates investigated in
contained
900
Some of the delaminations
plies
with
shapes observed
and Wang [23] were somewhat rounded but could be
as
having constant width.
in
Figure 3.7.
transverse
by Crossman
approximated
Most of the delaminations observed
in the current investigation, however, were
illustrated
the
The
similar
differences
to
that
are important.
82
The
delamination
shape is triangular.
Thus, the width
no sense constant.
Most of the delamination
angle
meaning
ply
split,
is bounded by
is not as long as the entire free edge.
region has a higher
compliance
the
is
position.
account
level
The
a
an
that a portion of the ply near the
split may be partially or totally unloaded.
strain
is in
The
delamination
Since the delaminated
than the rest of the
strong
function
of
specimen,
longitudinal
models of constant width delaminations cannot
for the effects of these differences.
The
analysis
found
inadequate to describe
investigation.
the
in
the
literature
delaminations
is
therefore
observed
this
The objective of the analysis developed herein
is to model the observed delamination more accurately
account
in
for some of these effects in an attempt
and
to extend
strain energy release rate approach to delamination growth
general
laminates.
Modifications
need
to
be
modes.
A
finite
element
method
the
in
made to the
existing methods to make them more applicable to the
damage
to
observed
equivalent to the
virtual crack closure method will provide baseline information
about
the
edge.
This information is incorporated into
model.
strain
energy available for release near the free
a
more
general
83
CHAPTER
4
GENERAL MANUFACTURING PROCEDURES
This
chapter
manufacturing
contains
procedures
descriptions
of
the
general
used throughout this investigation.
Certain specimens require the use of specialized manufacturing
procedures which are detailed in the appropriate chapters.
4.1 Preparation and Layup
The
specimens
constructed
using
TELAC [39].
arrive
manufactured
the
in
basic
this investigation were
procedures
developed
The unidirectional and fabric graphite/epoxy both
from
the
manufacturer
in
rolls
"prepreg".
The
of
semicured
preimpregnated
tape
or
graphite/epoxy
rolls
are 305 mm wide (12 inch nominal).
fabric
graphite/epoxy
nominal).
or
below
allowed
bag.
at
rolls
are
unidirectional
990 mm
wide
The
(39 inch
The epoxy matrix is B-staged and is thus stored
-180 C.
Before prepreg is prepared
to warm to room temperature
for curing,
for 30 minutes
at
it is
in a sealed
This minimizes condensation on its surface.
The prepreg
laminates
is cut into individual
in a "clean room".
plies and laid up into
The temperature
in this room
kept below 250 C and the relative humidity is kept low.
is
Rubber
gloves are worn during the cutting and laying up procedures to
avoid contamination of the ply surface with skin oil.
Razor
blades
and
precisely
milled
aluminum templates
84
covered with teflon-coated glass fabric (TCGF) are used to cut
the
prepreg
into
individual
plies.
Angle
unidirectional prepreg are first cut into precise
shapes.
halves
These
can
are
be
rectangular
cut
put
ply
in
together
with
a
to
precise
form
a
any
joint"
no
350 mm
fibers
are
The region where the two halves meet is a
which
becomes
indistinguishable
remainder of the ply during the curing process.
from
Plies
the
which
the fibers aligned with the longitudinal axis (0° plies)
have
and fabric prepreg
template.
plies
can
plies
are
precise alignment.
stacked
Plies are carefully
"good
steps
the longitudinal
at
positioned
corner"
manufacturing
enough
cut
using
a
rectangular
in a jig which
becomes
The two beams form a 90 ° angle.
into the
a
corner
reference
of
corner
the
jig.
in
later
and facilitates proper identification of
axis of the laminate.
room
allows for their
The jig consists of an aluminum plate with
aluminum beams attached.
This
be
This makes a matrix joint unnecessary.
The
two
by
angular orientation of the
cut
"matrix
trapezoidal
305 mm
The advantage of this method is that
ply.
of
half in such a way that the two
fibers.
in
plies
temperature
to
The
plies
are
tacky
stick together and maintain
proper fiber orientation.
Both sides of the laminate are covered with
"peel-ply"
material.
which protects
peel-ply
laminate
the
extends
opposite
a
sheet
of
The peel-ply is a porous nylon material
laminate
surface
approximately
the good corner.
50 mm
before
past
milling.
the
It is trimmed to
The
end of the
fit
the
85
remaining
three sides of the laminate
exactly.
4.2 The Cure
The
laminate
is
cured
on an aluminum
caul plate.
plate is coated with a mold release agent and covered
sheet
of
nonporous TCGF.
tape.
release agent.
rubber
These
held
dams
in
are
also
of
for
aluminum
coated
the
a cure plate prepared
simultaneously is shown in Figure 4.1.
the
with
pressure
with a mold
corprene
dams are placed next to the aluminum
form 305 mm by 350 mm curing areas
configuration
position
With the aid of aluminum top plates,
("cork")
dams
a
Aluminum dams with a "T" shape are
positioned on the TCGF and
sensitive
with
The
is the location
dams to
laminates.
The
to cure six laminates
The corner
formed
by
of the good corner of the
laminate.
The laminate is surrounded by several "curing
during
the
oversized
area.
preparation
sheet
of
for
curing.
nonporous
TCGF
First,
materials"
a
slightly
is placed in the curing
Then the laminate covered with peel-ply
is
positioned
with the reference corner in the corner formed by the aluminum
dams.
the
An oversized sheet of porous TCGF is placed on
laminate.
material
Precisely
are then positioned
cut
layers
of
a
in the curing area.
paper
top
of
bleeder
One layer of
bleeder material is used for every two unidirectional plies in
the laminate.
Three plies of bleeder material
every two fabric plies in the laminate.
are
used
for
An oversized sheet of
86
ALUMINUM
VACUUM
RPRENE
M
LAMINATE
LOCATION
CURE PLATE
FIGURE
4.1
NONPOROUS
TCGF
CONFIGURATION OF THE CURE PLATE FOR CURING OF
GRAPHITE/EPOXY LAMINATES
87
nonporous
TCGF
is placed on top of the bleeder.
top plate is coated with a mold release agent
An aluminum
and
placed
on
top of the TCGF.
After
all laminates
to be cured are prepared
manner,
the cure assembly
porous
TCGF and a sheet of fiberglass
serves
is covered with
as an "air breather",
volatiles
during
providing
a
large
fabric.
a
in a similar
sheet
of
The fiberglass
path
for
air
and
to be drawn to the vacuum hole and out of the system
the cure.
The
assembly
is
then
surrounded
with
a
vacuum tape sealant and covered with a high temperature vacuum
bag.
A schematic
shown
in Figure
The
of a cross-section
of the cure
assembly
4.2.
curing
of
the 3501-6 matrix
in Hercules
AS4/3501-6
and Hercules AW370-5H/3501-6 graphite/epoxies takes
an
autoclave
at an applied pressure
of 0.59 MPa
vacuum is drawn on the plate through the
nominal
value
is
of
the
vacuum
is
vacuum
place
in
(85 psig).
holes.
A
The
760 mm (30 in) of mercury
pressure differential below atmospheric pressure.
The cure is a two stage process.
one
hour
"flow
stage" at 1170 C.
The first
or
"bleeding"
of
excess
is
This
facilitates
the removal of voids by vacuum and pressure.
is a two hour "set stage" at 177°C.
complete
the
epoxy into the bleeder plies
which in turn assures proper bonding of the plies and aids
epoxy
a
The 3501-6 epoxy is at its
minimum viscosity at this temperature.
flow
stage
in
The second stage
The polymer
chains in the
most of their crosslinking during this stage.
Heat-up and cool-down
rates are in the range of 1
to
3C/min
88
11
10
7
5
/
/
/
/-1
5
8
7
6
4
11111lnl1
1
11111111111111 ll
1lI!1li
$
3
1. Cure
2
~
/'-71~
~~-T~~T~~
Key:
3\
-2
Plate
Vacuum Tape
3. Aluminum Dam
4. Corprene Rubber Dam
5. Nonporous Teflon Coated Glass Fabric
6. Laminate Covered with Peel-Ply
7. Porous Teflon Coated Glass Fabric
8.
Paper Bleeder Plies
9. Aluminum Top Plate
10. Fiberglass Fabric Air Breather
11. Vacuum Bag
2.
FIGURE
4.2
SCHEMATIC
ASSEMBLY
OF
THE
CROSS-SECTION
OF
THE
CURE
89
to
avoid
shocking of the composites.
at 1770 C in an unpressurized
postcure
the
thermal
crosslinking
process
to
oven is
completion.
An eight hour
used
to
drive
The cure cycle is
shown schematically in Figure 4.3.
4.3 Machining and Measuring
The peel-ply is
before
machining.
removed
from
the
postcured
A water-cooled diamond grit cutting wheel
mounted on a specially outfitted milling machine
mill
the
graphite/epoxy
laminates.
precise high quality cuts.
into
five
This
is
used
to
setup allows for
Each 305 mm by 350 mm plate is cut
50 mm by 350 mm specimens.
cut from the reference edge
prior
laminates
of
the
Approximately
laminate
and
25 mm is
discarded
to the cutting of the specimens.
The
width of each specimen is measured using calipers at
three points along the specimen length.
The thickness of
the
specimen
is measured using a micrometer at nine points in the
specimen
test
specimens
wide.)
section.
with
(Fewer
nonstandard
The locations
width
points
are
that
of the measurement
for
the
are less than 50 mm
points
width specimen are shown in Figure 4.4.
used
for a
standard
The average value for
measured width and thickness are reported for each specimen in
the data tables.
The
measured
control check.
It
thickness
can
be
values
seen
are
under
used
a
as a quality
microscope
"dimpling" occurs in a surface layer of pure epoxy.
that
This is a
90
AUTOCLAVE
177
PLUS 8 HOUR
\ POSTCURE
116
\ AT
770 C
66
21
._
vv
__
.Iv
_vv
.
____
TIME (MINUTES)
AUTOCLAVE
PRESSURE(MPa)
0.5
IL
I
303
1103
300
O3 duJ
TIME
VACUUM(MM
HG)
4 k
760
!
I
I
I
I
I
-
10 35
95
115
235 275 280
TIME
FIGURE 4.3
CURE CYCLE FOR AS4/3501-6 UNIDIRECTIONAL
GRAPHITE/EPOXY AND AW370-5H/3501-6 WOVEN
GRAPHITE/EPOXY FABRIC
91
l
I
01
7
lV
ENLARGED
SECTION
25
_1+
I
in
4
-8
350
II
2
25 mm
r
j
0
9
I
Jt-
III
10 mn 10 mn
50 mn
FIGURE 4.4
LOCATION OF MEASUREMENT
TELAC SPECIMEN
POINTS
ON
A STANDARD
92
result
microscopic surface features left by the peel-ply.
of
These features are helpful for the bonding of loading tabs and
strain
but
gages,
can distort the measured thickness.
they
This distortion is most evident in thin laminates.
to
nominal
the
evaluate
properly
thickness
is
effects
used
laminate
of
in
all
stress
ply
The nominal thickness of a
calculations.
unidirectional
graphite/epoxy
is
In
thickness,
and
of
0.134 mm.
order
modulus
AS4/3501-6
The
nominal
thickness of a ply of AW370-5H/3501-6 fabric graphite/epoxy is
0.35 mm.
the
The measured laminate thicknesses
nominal
values
in
are
Almost
Table 4.1.
compared
all
to
average
thicknesses were within five percent of their nominal values.
4.4 Loading
Tabs
Glass/epoxy
loading
tabs
are
specimen
from 305 mm by 710 mm laminates
SP-1002
precured
Testing and Materials
thickness
be
thickness.
loading
tabs
1.5
nominal
tabs are compared
is
[(0/90)n/0/9 0 ]s'
requirements
thickness
The
[40] recommends
between
The
The
glass/epoxy.
of the tab.
and
of 3M Scotchply
type
American
the
times
Society
for
loading
tab
the
laminate
of the laminates
in Table 4.2.
with
each
that
four
thickness
for
manufactured
The
layup
and the
for
the
n varying with the thickness
Each glass/epoxy
ply has
a
nominal
of 0.254 mm (0.01 in).
[±155/05]s
[±158/08]s,
[05/±155]s , and [08/±158]s
specimens require thicker glass/epoxy loading
tabs
than
are
93
TABLE
4.1
NOMINAL AND MEASURED LAMINATE THICKNESSES
Laminate
Nominal
Thickness
Measured
Thickness
[mm]
[mm]
2.040
1.97
[05U/OF/0U]
S
s
2.308
2.20 (1.0%)
[0 10U/0 F]s
3.380
3.28 (0.5%)
[±153] s
1.608
1.56 (3.0%)
[±15/0]5
0.804
0.86 (2.4%)
[±152/02]s
1.608
1.59 (5.1%)
[±153/03]s
2.412
2.34 (3.7%)
[±155/05]s
4.020
3.96 (4.6%)
[±158/08]s
6.432
6.55 (1.4%)
[0/±15]
0.804
0.85 (2.4%)
[02/±152]s
1.608
1.57 (4.1%)
[03/±153]s
2.412
2.36 (4.6%)
[05/±155]s
4.020
3.85 (7.8%)
[08/±158]s
6.432
6.24 (8.4%)
[±20F]s
1.400
1.41 (0.8%)
[03 /±153]sb
2.412
2.21 (1.4%)
[0 5U/
]s
0
F
aNumbers
in parentheses
(1.2%)
are coefficients
bof variation.
Specimens
containing
delaminations.
implanted
94
TABLE
4.2
NOMINAL LAMINATE AND LOADING TAB THICKNESSES
Laminate
Type
Nominal
Laminate
Thickness
Nominal
Tab
Thickness
Tab to
Laminate
Thickness
[mm]
[mm]
Ratio
[05U°/0 F]S
2.040
4.32
2.12
[O5U /OF/OU]S
2.308
4.83
2.09
[0 10U/ 0 F]s
3.380
7.11
2.10
[±153]
1.608
3.30
2.05
[±15/0]S
0.804
2.29
2.85
[±152/02]s
1.608
3.30
2.05
[±153/03]s
2.412
6.35
2.63
[±+155/05]s
4.020
8.13
2.02
[±+158/°8]s
6.432
12.19
1.90
[0/+15] S
0.804
2.29
2.85
[0 2/±1 5 2]s
1.608
3.30
2.05
[03/±153]
2.412
6.35
2.63
[05/±155]s
4.020
8.13
2.02
[ 0 8/±158]s
6.432
12.19
1.90
[±20F]s
1.400
3.30
2.05
S
S
95
readily available from the manufacturer.
[(0/90)16]s
laminates
type
laminates
of
Scotchply
SP-1002)
procedures
were
[39]
specimens.
and two
to
305 mm
type
by
710 mm
[(0/90)24] s
SP-1003 (an uncured version of
manufactured
be
Two 305 mm by 710 mm
used
as
using
standard
loading
The nominal cured ply
tabs
thickness
TELAC
for
for
these
SP-1003
is
also 0.254 mm (0.01 in).
The
glass/epoxy
laminates
are milled
into 50 mm wide by
75 mm long loading tabs on the same milling machine
cutting
graphite/epoxy.
beveled
to a 300 angle
used
for
One of the 50 mm edges of each tab is
to the plane of the tab
using
a
belt
sander.
The
tabs
are
bonded
onto
Cyanamid FM-123-2 film adhesive.
at
or
below
temperature
which
specimens
It
hold
the
to
bonding cure.
plate
-180 C.
the specimens with American
The film adhesive is
becomes
tacky
tab
place while
in
The specimens are placed on
has
are
been
covered
with
enough
an
at
other.
aluminum
nonporous
with
caul
TCGF.
The
bond
to
The specimens are covered with TCGF and 6.35 mm
mylar
corprene dam material.
plates
the
spaced far enough apart that any "bubbling" of
(0.25 in) thick steel top plates.
together
room
preparing
the excess film adhesive will not cause specimens to
each
stored
tape
This
and
The top
plates
immobilized
prevents
are
with
shifting
taped
stacks of
of
the
top
and the associated slipping of the loading tabs during
the bonding
cure.
fiberglass
air
This assembly
breather.
The
is covered with
assembly
TCGF
and
a
is surrounded with
96
vacuum tape and covered with a vacuum bag.
The
film
adhesive
vacuum (nominally
below
This
(50 psia)
of
760 mm
atmospheric)
pressure.
the
of
under
yielded
of pressure
tabs.
is cured in an autoclave
The
mercury
0.068 MPa
an
pressure
differential
(10 psig)
effective
with a full
of
applied
pressure of 0.34 MPa
of the top plates on the bonding surface
film
adhesive
is cured for two hours at
107C.
4.5 Instrumentation
A strain gage is mounted
longitudinal
each
specimen
strain level during testing.
the gage is placed
in
on
Figure 3.3.
to
monitor
In most specimens,
in the center of the test section as
The
shown
gages are aligned with the longitudinal
axis of the specimen using lines that are lightly scribed onto
the
thin surface layer of pure epoxy.
M-Bond 200 adhesive is
used to bond the gages to the specimen.
The gages used
strain
gages.
constantan
backing.
The
2.055
the
gage
Micro
gages
element
resistance
factor
0.5%.
test
These
wire
The
are
is
on
Measurements
contain
a
a
given
as
ready for testing.
is complete
thick
square
polyimide
is 120 ohms + 0.15%.
either
Once the gage is bonded to
specimen
3.175 mm
0.025 mm
of these gages
EA-06-125AD-120
the
2.04 + 0.5%
test
or
section,
as shown in Figure 3.3 and is
97
CHAPTER
5
DELAMINATION INITIATION EXPERIMENTS
Three
sets
delamination
of
specimens
initiation
stress.
methods are described in this
discussed
in
the
were tested and evaluated for
context
Testing
chapter
of
and
the
and
the
evaluation
results
objectives
of
are
this
investigation.
5.1 Edge Replication
The
damage
The
study
of
delamination initiation requires that the
state of the free edge be
method
used
nondestructively
monitored.
for detection of delamination initiation in
this investigation was edge replication. An edge
is a strip of cellulose
specimen edge.
acetate
replication
film with an impression
of the
This method has been shown to be effective
in
detecting the first signs of initiation [34].
The
specimen
give a clear
the
bob.
edges
replication.
investigation
were
The felt bobs are
solution
of
a
fine
must
be polished before testing to
The specimens
polished
this
portion
of
with a 25 mm diameter felt
continually
abrasive,
in
dipped
Kaopolite
average particle size of 0.7 microns.
in
SF,
a
colloidal
which
The solution
is
has an
mixed
by hand and contains approximately two parts water to one part
abrasive.
against
A smooth back and forth motion of the specimen edge
the
felt
bob
is
used for polishing.
The specimen
98
edges
are rinsed after polishing to prevent the solution from
solidifying
on the free edge.
Polishing
gives the specimen
a
smooth glossy finish.
Specimens
test.
the
are
replicated
before testing and after each
The original replications are made to
specimen
replications
edge
are
before
made
any
outside
load
the
maximum
deviations
is
detail
applied.
the
testing
All
machine
at
Except
for
level
is
applied stroke level of a test.
caused by large gripping
of
These
of the testing machine.
subsequent replications are made in
half
show
loads, the load
approximately half the maximum applied value.
In
preparation
of replicating
free edge.
of
the
for each replication, a 25 mm wide strip
tape is cut to the approximate
length
A small length of the edge is inaccessible
hydraulic
grips
of
the
testing
The
specimen
edge
and
the
replicating
specimen edge as shown in
acetone
The
acetone
tape
Figure 5.1.
is placed next to the tape.
is
placed
A
squirt
The acetone
closest to the specimen.
softens
the
tape
for
smoothed against the
object.
edge
the
test
replication.
with
a
finger
The
or
to
against
the
bottle
of
is sprayed on
The acetone
tape is then
other
smooth
While the replication is drying, a mark is placed on
the tape with a marker.
test
The
allowed
is
the side of the specimen
the
because
is wiped clean with a piece of
cheesecloth soaked in acetone.
evaporate
the
machine.
replicating tape is therefore slightly shorter than
section.
of
section
of
the
The mark corresponds
specimen
to a line on the
and is used as a longitudinal
99
FIGURE 5.1
POSITION OF REPLICATING TAPE DURING APPLICATION
OF ACETONE
100
This
reference.
30 to 40 mm from a loading
is usually
mark
tab.
a
Once
it
minute,
the
is
exist.
replications
The
the
with
naked
and another one is made.
each
of
replications
side
placed between two clean flat
are
replications
This keeps the
surfaces to finish drying.
for image
examined
visible
discarded
two clear
This is repeated until
one
approximately
It is immediately
is removed.
replication
for
dried
If smudges or bubbles are
clarity.
eye,
has
replication
from
curling which would make them difficult to examine.
Replications
as an individual
plies
the
and
fiber.
The
surface
matrix
interply
texture
layer
can
of
be
Softened acetate can seep into tight delamination
and
different
identified.
initiations
angle ply splits, especially when they may be "opened" as
these
features
from
illuminated
are
a
under
inspected
The difference
load.
a result of applied
of
as small
can show free edge surface features
a
highlighted
source
on
surface
texture
replications
The
microscope.
light
in
behind
replications
and
when
are
to the side.
Delamination initiations and angle ply splits appear as bright
thin
lines.
When these features are viewed directly under a
microscope, they
background
appear
as
dark
features
against
a
dark
and can be indistinguishable.
5.2 General Testing Procedures
All
specimens
in
this
investigation were tested in an
101
MTS 810
Material
Test
System equipped with hydraulic grips.
The machine was programmed to control the total stroke of
the
grips.
The f
The
resulting
constant
strain
stroke
rate
in
rate
the
was
200 mm
1.07 mm/min.
test
section of the
specimen is approximately 5400 microstrain/minute.
Specimens are aligned in the upper grip using
right
triangle.
loading
lower
tabs.
tabs.
The
upper
is
plastic
grip is closed around the upper
The lower grip is then
This
a
positioned
around
the
taken to be the "no load" position
at
which the strain gages can be calibrated.
The strain gages
conditioners
are
which
are
computer-controlled data
obtains
data
about
attached
in
load,
Vishay
turn
acquisition
the
to
strain
connected
system.
strain,
and
to
The
into
+2048
computer units.
the
computer
stroke through
analog-to-digital devices which divide the full range
channel
gage
of
the
For example, the stroke
range setting used in this investigation was +12.7 mm.
one computer unit represents 0.0062 mm of stroke.
Thus,
This is the
resolution of the stroke data.
The gage is first "balanced"
strain
in the no load position.
unit of strain is adjusted
strain
gage
conditioner.
so
it
registers
the
gain
calibration
control
value
on
the
apparent
the
of a shunt
resistance is connected in parallel with the strain gage
that
no
Then, the value of a computer
using
A
that
such
resistance of the gage corresponds with a
prescribed strain level.
The gain is then
adjusted
so
that
the data acquisition system registers the equivalent number of
+
102
computer
units.
calibrated
In
so
this investigation, the conditioner was
that
each
computer
unit
represented
six
microstrain.
After
testing.
The
recorded
the
the gages are calibrated,
lower
grips
in the notebook.
investigation
are
the specimen
is ready for
are closed and the gripping
The specimens
tested
using
in
a
this
load
portion
of
computer-controlled
testing program that allowed for simultaneous commencement
the
loading ramp and the data acquisition.
stroke data are recorded at prescribed time
the
loading
and
data
acquisition
are
control, the residual load, maximum
level are recorded
of
Load, strain, an~intervals.
When
stopped by computer
load,
and
final
stroke
in the notebook.
5.3 Load Drop Testing
Delamination initiation is associated with a drop in load
resulting from the increase in compliance.
the
detection
of
a load drop and checking
new delamination initiation has
useful
tool
stress
34].
The
for
detecting
computer
program
specimens in this portion
evaluates
the one
increment
the value
immediately
been
the
used
of
Halting tests upon
for evidence
demonstrated
delamination
to
of a
be
a
initiation
to control the tests of the
the
investigation
continually
of the load at the current data point and
previous.
The
data
acquisition
for these specimens was 0.3 seconds.
time
When the load
103
at
a
given data point is less than the value at the previous
data point, the loading and data acquisition
stopped.
This
load
drop
by
a factor of two.
of each free edge.
immediately
is taken to be an indication
possible delamination initiation.
reduced
are
The stroke
level
is
Two clear replications
The specimen
is then
of a
then
are made
completely
unloaded
and removed from the testing machine.
The
replications
magnification ranges
directly
with
examined
for
initiation.
associated
before
drop
new
If
assumed
acquisition
7X
to
50X.
They
features
indicative
If an initiation is discovered,
the
the load drop)
is
from
are
The
compared
the replications from the previous loading and
with
initiation.
are inspected under a microscope.
maximum load (i.e.
system.
delamination
the
data
point
the data point just
is taken to be the point of delamination
no new features
to
of
be
a
The
are found, the apparent
result
specimen
of
noise
in
load
the
is then retested.
data
In all
subsequent tests of that specimen, load drops observed to take
place
at lower values
of load than those seen in earlier
tests
are also assumed to be the result of system noise.
5.4 Results
Delamination initiation was detected before final failure
in
all of the specimens
in this portion of the investigation.
The stress-strain behavior was linear until
all
specimens.
delamination
for
The initiation stress, initiation strain, and
104
modulus data for each specimen are given in Data Table 1.
The
[010U/OF] s
specimens
were
all
delamination initiation after one test.
seen
to
have
Careful inspection of
the edge replications taken before the test revealed that
delaminations
had
in
fact
loading had been applied.
interlaminar
stresses
delamination.
The
tows and were
before any mechanical
This implies that thermally-induced
can
be
important
in
initiating
initiations occurred along the fill fiber
generally
unidirectional
initiated
the
plies.
closer
A
to
the
micrograph
midplane
than
the
of an edge replication
showing a delamination initiation in a [0 10U/OF]s specimen
shown
in Figure
Three
5.2.
the five [ 0 5U/OF]s specimens
of
after a load drop
program.
The
edge.
was
tests
stopped by the
stopped
is
detected
by
the
showed initiation
load
drop
testing
of the remaining two specimens were not
testing
program.
Instead,
the
tests
were
manually when visible damage was observed at the free
Edge replications confirmed damage
including
at
extensive delamination initiation.
the
free
edge
Apparently, the
magnitude of the load drops associated with the initiations in
these
specimens
was
below
the
equipment and computer program.
stress
The
of
the testing
delamination
initiation
for these two specimens can therefore only be narrowed
down to a range of stresses.
three
resolution
specimens
The initiation
stress
for
exhibiting detectable load drops was 528 MPa
with a coefficient
of variation
lower
the other two specimens was 520 MPa.
bound
for
the
of 2.6%.
The average
of
the
It is
105
FIGURE 5.2
MICROGRAPH OF EDGE REPLICATING SHOWING
DELAMINATION INITIATION IN A [010U/0F s SPECIMEN
(7X)
106
therefore
likely
delamination
that
the
initiation
load
drop
associated
with
occurred at approximately this level
and that 528 MPa is a reasonable value to use for delamination
initiation
stress
for
these
laminates.
All
delamination
initiations for these.specimens were seen along the fill fiber
tow close to the midplane.
The
same difficulty in finding a delamination initiation
point occurred with
initiation
all
upper
specimens.
The average lower bound of the
with a coefficient
of variation
bound of the range was 744 MPa
variation of 3.9%.
along
[0 5u/OF/Ou]
s
The
stress could only be narrowed to a range of values
for each specimen.
451 MPa
five
range
of 6.5%.
with
a
was
The average
coefficient
of
The delamination initiations were detected
fill fiber tows near the
F/OU interface
closer
to
the
midplane.
The delamination initiation data was correlated using the
Quadratic Delamination Criterion.
were
determined
using
Lagace [17].
the
Table 3.1.
was
the
Kassapoglou
and
stresses
were
also
fabric
graphite/epoxy
graphite/epoxy
The averaging dimension used
value
graphite/epoxy
The
unidirectional
determined
for
stresses
of
The elastic parameters used in the
AS4/3501-6
AW370-5H/3501-6
interlaminar
method
Thermally-induced
calculated [18].
for
the
The
was
AS1/3501-6
were
analysis
and
given
0.178 mm
the
in
which
unidirectional
34].
interlaminar
normal
stress
was
the
only nonzero
interlaminar stress in these three lamination sequences.
The
107
interlaminar
is
the
normal strength parameter used was 43 MPa.
value
determined
experimentally
unidirectional graphite/epoxy by direct
tests
for
This
AS4/3501-6
through-the-thickness
[35].
k The thermally-induced interlaminar stresses were dominant
in all
three
lamination
mechanically-induced
sequences.
stresses
The
were
contributions
relatively
of
small
at
delamination
initiation.
interlaminar
normal stresses accounted for 79% of the average
interlaminar
normal
[0 5U/OF]s
For
stress
specimens.
mechanically-induced
example,
at
delamination
The
components
thermally-induced
initiation
thermally-induced
of
the
and
interlaminar normal
stress at the delamination initiation stress are depicted
this
laminate
contribution
type
in
allows
Figure 5.3.
The
relatively
be
regarded
for
small
for a precise experimental determination
of the average interlaminar normal stress at initiation.
can
in
as
This
a calculated value for the interlaminar
strength parameter which can be compared with the interlaminar
normal
strength
delamination
initiation
measured from direct testing.
initiation
stress,
and
stress,
the
the
measured
calculated
The predicted
delamination
interlaminar normal
strength are given in Table 5.1.
5.5 Discussion
The
Quadratic
delamination
Delamination
initiation
stress
Criterion
for
all
correlated
three
the
lamination
108
05/of]
60
**--
40
THERMAL (AT--156
528
--- MECHANICAL(al
I
0
0
-
0
C)
MPa)
~TOTAL
S
0
0
-S00
20
bo
N
N
0
I
b
-20
I
I
3
2
DISTANCE FROM FREE EDGE, mm
1
FIGURE 5.3
THERMAL AND MECHANICAL COMPONENTS OF INTERLAMINAR
NORMAL STRESS AT DELAMINATION INITIATION AT THE
MIDPLANE OF A [05U/0 F]s SPECIMEN
109
TABLE
5.1
PREDICTED VERSUS ACTUAL INITIATION STRESS AND
CALCULATED INTERLAMINAR NORMAL STRENGTH
Lamination
Sequence
Predicted
Initiation
Stress
Actual
Initiation
Stress
Calculated
Interlaminar
Normal
[MPa]
[MPa]
Strengtha
[MPa]
[05U / 0 Fs
436
528
44.6
[05Uv/0F//0
US
681
451-744
39.4-44.0
0
0
[Olou/OF]S
acalculated at experimental initiation stress.
<43.4
110
sequences.
This was done with an interlaminar normal strength
parameter
that
was
measured
directly.
Comparison
of
calculated values from the data in this investigation with the
actual
value
shows
excellent
thermally-induced stresses and
were
also
demonstrated.
interlaminar
delamination
averaging
normal
dimension
of
used
example,
alone
the
to
averaging
dimension
was
normal
obtain
should
stresses
thermally-induced
responsible
[O10U/OF]
s
determined for a similar material.
the
The importance of
interlaminar
For
stress
initiation
agreement.
for the
specimens.
The
this agreement was one
It can
be
reasoned
that
be independent of the fiber
strength.
Since the AS1 and AS4 fibers are similar
respects,
it
in
other
is reasonable to assume the averaging dimension
determined for a composite system containing the AS1 fiber
a
good estimate
AS4 fiber.
averaging
system using the
The good correlation is further evidence that
dimension
the delaminations
an
of the value for a composite
is
a material parameter.
initiated
at the boundary
is
the
The fact that
of fabric plies is
indication that the averaging dimension may be independent
of the form of the material system (i.e. unidirectional versus
fabric).
The
initiations
occurred at the interfaces predicted by
the Quadratic Delamination Criterion.
to
form
plies.
They did, however, tend
along
fill fiber tows on the boundary
This
could
not
be
predicted
by
of the fabric
the
Delamination Criterion since the criterion and the
interlaminar
stress
analysis
assume
smeared
Quadratic
supporting
homogeneous
111
plies.
Micromechanical
position
of
the
effects
delamination
play
a
role
initiation,
in the exact
but
important
parameters such as delamination initiation stress and critical
interface
can
be
predicted
without
relaxing
homogenous ply assumptions made in Classical
the
smeared
Laminated
Plate
Theory and related analyses.
The
strain
energy
release rate approach
O'Brien [26] cannot predict
midplane
The simple rule
determining
initiation
at
for
a
symmetric laminate.
formation
of
delaminations
of
mixtures
approach
used
delamination
at
the
midplane
notation,
a
fracture
results
standard
become
fail
laminates.
to
a
This implies no energy would be available
from
Classical
nonzero
when
specimen into two unsymmetric
would
for
of
surface.
the
The
energy
for
that
the
fact
bending-stretching parameters, which are characterized by
in
the
the modulus of the delaminated region predicts no
loss of modulus
B matrix
by
] s and [0 10U/
]0 F s
for the [ 0 5U/O0 F
such as was observed
specimens.
for
delamination
as proposed
predict
Laminated
Plate
the
Theory
the delamination divides the
halves.
delamination
Thus,
this
initiation
approach
in
these
112
CHAPTER
6
DELAMINATION GROWTH AND FINAL FAILURE EXPERIMENTS
The
delamination
graphite/epoxy
are
investigation.
experiments
growth
and
explored
final failure behavior
in
this
portion
the
the
Four sets of experiments were conducted.
required
specialized
manufacturing
procedures which are described in this chapter.
of
of
experiments
of the objectives
Some
and testing
The
are reported and discussed
of
results
in the context
of the investigation.
6.1 Specialized Specimen Manufacturing Procedures
The specimens for this portion of the investigation
manufactured
Chapter 4.
using
the
Variations
basic
procedures
were
described
in
or additions to these procedures were
used to manufacture specialized specimens.
These
variations
are described here.
6.1.1 Specimens of Nonstandard Width
The
[±153]s
constructed
procedures.
with
When
specimens
only
a
one
50 mm
spacer is placed against
a
surface.
is
The
laminate
clamped in place.
of
nonstandard
variation
on
width
the
are
standard
wide specimen is milled, a metal
reference
placed
edge
on
against
The cutting surface is then
the
the
cutting
spacer and
moved
in
the
113
direction
of
the cut.
The cutting wheel extends down into a
groove in the cutting surface.
wheel,
a
specimens
used.
50 mm
wide
strip
As
is cut.
and loading tabs are cut,
The
widths
used
the
in
this
laminate
passes
the
When nonstandard width
nonstandard
spacers
are
investigation were 10 mm,
20 mm, 30 mm, 50 mm, and 70 mm.
Not all specimens
same
laminate
possible
to
for
of the same width are milled
two
reasons.
First,
it
from
would
mill all five 70 mm wide specimens
not
the
be
from the same
laminate.
Second, milling specimens of a given width from the
different
laminates
reduces
the
possibility
that
slight
manufacturing differences between laminates will affect trends
in the data.
6.1.2 Fabric Specimens
Since there are
two
primary
fiber
directions
fabric
weave, a pure matrix joint is not possible.
would
necessarily
contain
prepreg is available in 990 mm
makes
cut
fibers.
(39 in)
Any joint
Fortunately,
wide
the
prepreg.
the
This
it possible to cut angle plies in one rectangular sheet
with no joints.
rectangular
Angle ply templates are
template
to
used
to
must
be
taken
faces of each ply.
to
align
the
assure the proper angle of the warp
fibers with respect to the longitudinal axis of the
Care
in
laminate.
properly position the warp and fill
114
6.1.3 Specimens with
Ply Splits
Implanted
The unique configuration of the
and
angle
Delaminations and Angle
implanted
ply splits makes it necessary to manufacture these
specimens individually rather than to
out
of
a
[03/±153]
s
it
is
delaminations
single
cured laminate.
In the process
.
convenient
to
cut
several
The laminate
type used is
of laying up individual
lay
specimens
specimens,
up 305 mm by 350 mm major prepreg
sublaminates using standard techniques and then cut them
four
76 mm by 350 mm sublaminates.
three
major
[+153/03]T.
The
Each specimen consists of
[0 3/+1 5 3]T'
sublaminates:
into
[-156],
and
teflon film is implanted between and within
these sublaminates before curing.
A slight variation from standard
layup
[-156] sublaminates.
procedure
is
used
Normally the trapezoid of prepreg
that is cut to form the angle ply is cut exactly in half.
this
were
done for the [-156] sublaminate,
of all six plies would be aligned through
the
uncured
sublaminate
would
two
during
process.
steps
To avoid this problem,
the position
of the matrix
plies,
joint
was
and
in
separation of the
the
manufacturing
the plies were cut such that
joint varied
from the normal position.
the
joints
thickness
from ply to
two of the six plies, the joint was approximately
direction
If
have no in-plane strength at
This could result in undetected
critical
the matrix
the
this joint.
halves
to
approximately
In two of
20 mm
ply.
In
20 mm in one
the
in
remaining
the
other
115
direction.
In
the remaining
two plies, the joint was in the
normal position.
Delaminations were formed by
film
between two uncured sublaminates.
formed by implanting
the film within
along the fiber direction.
DuPont
and is designated
a nominal
In
thickness
the
surface
thin
Angle ply splits were
the
[-156]
sublaminate
The teflon film is manufactured by
film.
with
of the teflon film is placed
of
sublaminate
is 20 mm.
positioned
so
that
farthest
The
it
specimen.
This position
[03/+153] T
sublaminate
sublaminate.
the
The implant
intrusion
point
of
from the edge of the
maximum
intrusion
is at the longitudinal
is
is
illustrated
then
in
placed
is
center of the
Figure 6.1.
on
the
A
[-156]
The two sublaminates stick together and hold the
film in place.
The process
sublaminate.
is repeated on the other
Care
is
taken
implanted delaminations line up through
excess
on
such that the long edge is along the fiber angle
point
[-156]
It has
no implanted angle ply split, a
of a 76 mm by 350 mm [-156] sublaminate.
the
teflon
of 0.0254 mm (0.001 in).
specimens
is positioned
the
a
PFA 100 LP fluorocarbon
25 mm by 50 mm rectangle
and
implanting
teflon
film
protruding
from
the
the
so
side
that
the two
thickness.
free
of
The
edge is not
trimmed.
The manufacturing of specimens with implanted
splits
requires
in the uncured
razor
blade
angle
ply
that a slit be made along the fiber direction
[-156] sublaminate.
and a straight
edge.
The slit is
The straight
cut
using
a
edge is placed
116
C
L
I
I
I
I
I
11
I
25 mm BY 50 mm
,RECTANGLE OF
TEFLON FILM
I
I
I
I
I
1
l
FREE EGE
FIGURE 6.1
NOMINAL POSITION OF THE TEFLON FILM AT THE
+15o/-15° INTERFACES WHEN CONSTRUCTING A
[0 /+15 ] SPECIMEN WITH AN IMPLANTED
DE2 AMINATION
117
on clean backing paper from the prepreg to avoid contamination
of the sublaminate surface by the straight edge.
a
maximum
intrusion
sublaminate.
The
of
30 mm
position
from
of
the
the
edge
of
the
of the point where the intrusion
from the free edge is 20 mm coincides
center
The slit has
sublaminate
with
the
as illustrated
longitudinal
in Figure 6.2.
A
10 mm by 50 mm strip of teflon film is carefully placed inside
the
slit.
When the end of the strip is flush with the tip of
the slit, the excess
Unfortunately,
the
film
can
inability
be
of
trimmed
the
from
film
one
side.
to stick to the
prepreg (which is desirable in context) makes it impossible to
trim both sides without dislodging the film.
preferable
that
Therefore, it is
to have most of the excess on one side and to
side.
trim
The excess film on the other side must be folded
into the interface region.
A 50 mm by 50 mm square of teflon film is then positioned
in the slit such that its maximum
is 20 mm at the midpoint
then
be
intrusion
of the free
from the free edge
edge.
The
square
can
folded over on both sides of the sublaminate to form
two implanted
delaminations
similar to those in the
without implanted angle ply splits.
and teflon films are shown in
specimens
The positions of the slit
Figure 6.2.
The
laminate
is
completed by placing a [0 3/+1 5 3]T sublaminates on each side of
the [-156] sublaminate.
Sheets of peel-ply
size
of
extending
the
faces
of
from one end.
are cut so that they are
the
laminates
The peel-ply
with
is applied
the
nominal
an extra 50 mm
to the
faces
118
C
L
I
I
30 mm
I
·I
-I
20 mm
I
t :o
I
I
I
UP
I
I
m
l
CL
)N
rER)
i
I
i
I
t\
I
,x-1
'EVENTUALf
LOCATION
OF SPECIMEN
FREE EDGE
FIGURE 6.2
I
I
NOMINAL POSITION OF THE TEFLON FILM AT THE
+15°/-15° INTERFACES AND WITHIN THE [-15 ]
SUBLAMINATE WHEN CONSTRUCTING A [0 /1531
SPECIMEN WITH AN IMPLANTED DELAMINATION AD
PLY SPLIT
ANGLE
119
of
the
laminates.
film protruding
is
Second,
makes
no
nor the extra
from the free edge is trimmed.
essentially
exceptions.
Neither the peel-ply
the
same
as for standard
First,
only
corprene
top
plates
it critical
dam
are used.
teflon
The cure setup
specimens with two
material
is
used.
The absence of top plates
that all wrinkles
in the cure materials,
air
breather, and vacuum bag be eliminated before curing.
Approximately
10 mm
postcured specimens.
delamination
containing
and
them)
is milled
from the free edge of the
The resulting nominal intrusions of
angle
are
ply
split
10 mm
(in
those
the
specimens
and 20 mm, respectively.
Since
excess
epoxy collects
exact
position of the boundaries of the teflon film cannot be
at the
precisely ascertained.
free
edge
during
Thus, the actual
curing,
intrusion
may
the
vary
from the nominal value.
A
strain
gage
was mounted on each specimen in the same
manner described in Chapter 4.
halfway
between
the
center
However, the gage was
located
and corner of the test section.
This allowed the gage to measure far field strain with minimum
effects from the implanted delamination and loading tabs.
location
of the gage is depicted
The
in Figure 6.3.
6.2 Dye Penetrant-Enhanced X-radiography
The
requires
study
that
over a series
of
delamination
growth
and
final
failure
the damage state be nondestructively monitored
of
tests.
The
method
used
for
monitoring
120
C
L
S
CL
IMPLANTED
DELAM £NATION
FIGURE
6.3
LOCATION OF THE STRAIN GAGE ON A SPECIMEN WITH AN
IMPLANTED DELAMINATION
121
delamination
growth
The dye penetrant
liquid.
is dye penetrant-enhanced x-radiography.
used
is
DIB is applied
cotton
swab.
di-iodobutane
(DIB)
which
is
to the free edge of a specimen
with a
It is applied after a test while the specimen
at half the maximum
stroke level.
and can seep into delaminated
testing machine.
with
regions via capillary
action.
Device.
mode.
is
The
a
x-ray
Scanray
"timed
used
X-ray
in
this
Inspection
radiation"
(TIMERAD)
unexposed sheet of black and white instant film is
placed on a sensor in the x-ray
100 mm
by
instant
sheet film type 52.
x-rayed
machine
Torrex 150D
The machine is used in
An
from
The location of the DIB can be detected
x-radiography.
investigation
125 mm
is
(4 in
placed
by
chamber.
5 in
The
film
used
The portion of the specimen
on top of the film.
to be
The door to the x-ray
When
sensor detects a certain quantity of radiation, the x-ray
generator is shut off.
the
is
nominal) Polaroid PolaPan
chamber is closed and the x-ray generator is activated.
the
is
The DIB has a low viscosity
After DIB has been applied, the specimen is removed
the
a
sensor
The quantity of radiation detected
is set to 240 mR (milliRoentgens).
by
This gives an
optimal level of contrast.
The film can
camera
back.
be
The
developed
resulting
three shades of gray.
shielded
purposes
x-rays
by
the
The region of the
This is a result of the
light
a
standard
Polaroid
x-radiograph essentially shows
any portion of the specimen
white.
and
using
film
which
is
not
is for all practical
interaction
of
the
sensitive chemicals in the film.
The
122
region
medium
under
gray.
absorbs
it.
a
a
the
undelaminated
This results from the
significant
The delaminated
result
section of the laminate
of
the
fact
that
the
is a
specimen
portion of the x-rays passing through
region shows up as a dark gray.
fact
that
the
This
is
thin layers of DIB in the
delaminations absorb a large fraction of
the
x-rays
passing
through them.
Two
x-radiographs
each test.
Each details the damage on one half of the
long test section.
usually
be
200 mm
There is a small amount of overlap between
the two x-radiographs.
can
are necessary for each specimen after
The longitudinal
determined
either a loading tab or a
by
strain
position
referencing
gage.
of
damage
the position
Both
features
to
are
visible in most x-radiographs.
6.3 Incremental Load Testing
The
same
general
testing
portion of the investigation.
procedures
are used in this
The specimens are either tested
using manually controlled loading and data acquisition or with
a
computer-controlled
testing
program
simultaneous commencement of the loading
acquisition.
Load,
strain,
that
ramp
allows
and
the
for
data
and stroke data are recorded
at
prescribed time intervals.
Four specimens
specimens
load
drop
of
nonstandard
width
(two
10 mm
wide
and two 30 mm wide specimens) were tested using the
technique
described
in
Chapter 5
to
determine
123
delamination
specimens
initiation
stress.
program
before
program determines
test is stopped.
the
remaining
is
both
free
unloaded
tests
each
test
is
is entered
into the
started.
When the
that that load level has been reached,
and
X-radiographs are then
subsequent
load level
the
The stroke is reduced by a factor of two and
DIB is applied to
specimen
of
were tested using an incremental loading technique.
In these tests, a predetermined
computer
Most
edges
the
the
specimen.
The
removed from the testing machine.
taken.
of
of
The
load
same specimens
increment
between
is dependent
on the
type of specimen.
Only one of
exhibited
to
be
four
specimens
of
nonstandard
delamination
by
the
initiation
were
all
load
drop
stress
tested
testing
was
program.
513 MPa.
to failure.
variation
An
subsequent
initial
loading
to
equivalent
to
450 MPa
and
stress
The
The
four
The average failure
stress was 534 MPa with a coefficient of
increments
width
a load drop at delamination initiation large enough
detected
specimens
the
increments
of
1.0%.
loading
of 10 MPa were
chosen to be sufficient to document all delamination growth of
the specimens of nonstandard width.
The data acquisition time
increment for these specimens was 0.3 second.
The [+±20F]
[0n/±15n]s
fabric
specimens
of the same laminate
first
specimens
and
the
[+±15n/0n]s
and
were tested in groups of five specimens
type and effective
ply
thickness.
The
three specimens in each group were tested monotonically
to failure under manual control.
The remaining specimens
are
124
then
tested
incrementally
starting
observed
failure stress of the
maximum
load
level
in
first
subsequent
increments equivalent to 5% of the
stress.
The
data
at
acquisition
75%
three
specimens.
tests
was
average
time
of the average
The
increased
observed
increment
in
failure
for
these
specimens was 0.5 second.
The
tested
specimens
with
implanted
delaminations were first
at 40% of the average observed
failure load of the five
[03/±153]s
without implanted damage.
subsequent
The stress increment in
tests was 10% of the failure stress until the
level was reached.
100%
The increment after that level was reduced
to 5% of
the
increment
for these specimens was 0.5 second.
failure
stress.
The
data
acquisition
time
6.4 Results
The experimental
results are reported by specimen
type.
6.4.1 Specimens of Nonstandard Width
In
previous
work with AS1/3501-6 [±153]s specimens, the
delamination always initiated before any splits in
plies
[34].
This was also observed
the
for the AS4/3501-6
angle
[±153] s
specimen in which delamination initiation was verified by edge
replication before failure.
Each
specimen was tested to failure.
specimen, two 30 mm wide specimens and
all
For one 20 mm wide
wider
specimens,
125
"failure"
did
not
include the breaking
two separate pieces.
Failure
in these cases
have occurred
when a large fraction
load decrease
was in the range of 60%
accompanied
by massive
of the specimen
was
to
98%.
inner
plies
across
the failed region to the loading tab.
therefore
not
in
two
to
The
Failure
splitting and delamination
from
defined
of the load was lost.
plies across the entire width of the specimen.
ran
into
was
of the outer
Fibers of
the
undelaminated regions of the specimen
pieces
The specimen
was
and could carry some in-plane
load.
The stress-strain
point
of
visible
failure
graph
Table 6.1.
is
shown
in
Figure 6.4.
The average values
initiation
failure
strain.
experimental
scatter
stress
The
to
resolution
were
of
given
included
failure
moduli
are
in
the
stress,
within
of the specimen width
strain
to within
the
specimens
of
of the experiment.
nonstandard
shape
average
are
The failure stress and failure
be independent
The delaminated
loading.
The
of the Classical Laminated Plate Theory
prediction of 116 GPa.
appear
A
used to determine
appropriate calculations of average modulus,
and
the
in the [±+153]
s laminates.
Data from the four specimens
delamination
linear to
stress, and failure strain are reported for
each specimen in Data Table 2.
in
was essentially
delamination
typical stress-strain
modulus,
behavior
area and intrusion
width
were
determined
The data
were
obtained
the
delamination
of
the
after
from
during
each
incremental
x-radiographs.
growth
was
The
usually
126
500
400 _
r 1
m
300 _
L
7! !
O0
200 _
O0
100 _
0
0
I
I
I
1000
2000
3000
4000
STRAIN EMICROSTRAIN]
FIGURE 6.4
TYPICAL STRESS-STRAIN GRAPH FOR A [+±153]s
SPECIMEN
5000
127
TABLE 6.1
AVERAGE MODULUS, FAILURE STRESS, AND FAILURE STRAIN
FOR [153] s SPECIMENS OF NONSTANDARD WIDTH
Width
Modulus
[mm]
[GPa]
10
115
(4.1%)
(2.5%)
(3.3%)
116
30
116
50
70
502
515
Failure
Strain
[pstrain]
4336
(5.8%)
4318
(2.7%)
4348
(4.0%)
(3.6%)
(3.5%)
110
(1.2%)
505
(2.8%)
4600
(3.2%)
110
(5.3%)
aNumbers
508
a
(8.8%)
20
Failure
Stress
[MPa]
in
of variation.
488
(7.3%)
4687
(13.5%)
parentheses are coefficients
128
triangular.
The
triangle
was always bounded on one side by
the free edge and on another by a split in the +150 ply.
The
third
The
side
of
the triangle was the delamination
front.
delamination front usually extended from the angle
toward
the
free
edge
at approximately
delamination shape is depicted
There
were
occasionally
the [-156] sublaminate
[+153]
sublaminate
region
delamination
front
split
a right angle.
schematically
in
This
Figure 3.7.
splits along the fiber direction in
which extended
from the
to the free edge.
delaminated
ply
enlarged
coincided
in
the
In some instances,
the
slightly
with
split
one
such
of
that
these
the
splits.
Typical x-radiographs of both types of delamination fronts are
shown
in
Figure 6.5.
accompanied by visible
sublaminate
edge.
in
This
the
Larger
delaminations
out-of-plane
region
peeling
is
peeling
between
the
depicted
were
of
usually
the
[+153]
split and the free
in
the
photograph
in
Figure 6.6.
The specimens
growth
before
which
failure
exhibited
are
detectable
listed
in
delamination
Appendix A
with the
maximum stress, the strain associated with the maximum stress,
the
number
of observed delaminations, the maximum intrusion,
and the total delaminated
range
of
area associated
with each test.
stresses during which the first delamination growth
occurs is bounded for each specimen by the maximum
the
last
maximum
test
in which no delamination
An
average
first
growth
stress
was detected
stress of the first test in which a
observed.
The
and the
delamination
stress
range
of
can
was
be
129
(a)
77-.
DELAMINATION FRONT
APPROXIMATELY PERPENDICULAR
TO ANGLE PLY SPLIT
·-
(b) DELAMINATION
BORDERED BY TWO
ANGLE PLY SPLITS
FIGURE
6.5
X-RADIOGRAPHS OF TYPICAL DELAMINATIONS IN [±153]s
SPECIMENS
130
Ii
RI
I
FIGURE 6.6
PEELING
AND UNLOADING OF A
A [+153]s SPECIMEN
+153]
SUBLAMINATE IN
131
determined
for
a
group
of specimens by averaging
bounds and then the upper bounds.
stress
range,
maximum
delaminated
specimens
average
6.4.2 [+15/0O]_
The
average
first
growth
maximum intrusion before failure, and
area before
of nonstandard
The
the lower
failure are reported
for
width in Table 6.2.
and [On/±15]
[+±15n/0n]s and [0n/15n]
s
Specimens
specimens exhibited
stress-strain behavior until visible damage occurred.
stress-strain
graphs
shown in Figures 6.7
were
tested
to
for
the
and 6.8,
failure.
two
lamination
respectively.
For
specimens
the
All
with
specimen into two separate pieces.
defined
to have occurred
lost.
In
the
values of n
breaking
of the load was
usually
by between
accompanied
by
delamination and in-plane failure of the angled plies and
splitting
still
of the 0
carry
plies.
Nonetheless,
substantial
longitudinal
the
0°
load.
plies
The
Data
Tables 3
specimens).
given
scatter
in
specimens)
The average values for
Table
of
([±15n/On]
the
6.3.
value
each
126 GPa
given
and 4 ([0n/+15n]s
specimen
The moduli are all within
of
could
modulus,
failure stress, and failure strain for each specimen is
in
are
Failure was again
when a large fraction
Failure was
Typical
specimens
most of these cases, the load decreased
40% and 80% at failure.
linear
sequences
greater than one, failure did not always include the
of
the
predicted
Laminated Plate Theory for these laminate types.
type
are
experimental
by
Classical
132
TABLE 6.2
AVERAGE FIRST GROWTH STRESS RANGE, MAXIMUM INTRUSION,
AND DELAMINATION AREA BEFORE FAILURE
FOR [±153]
s
Width
[mm]
SPECIMENS OF NONSTANDARD
Average
Average Maximum
First Growth Intrusion Before
Stress Range
Failure
[MPa]
WIDTH
Average Delaminated
Area Before Failure
[cm2 ]
[mm]
10
492-497
0
0
20
487-502
0
0
30
496-505
3
2
50
474-482
8
2
70
478-483
31
22
133
600
<
4(0o
0_
I
I
0
IJ
F
2130
n
0
1000
2000
3000
4000
STRAIN [MICROSTRAIN]
FIGURE
6.7
TYPICAL STRESS-STRAIN GRAPH FOR A (+15 /0 ] s
SPECIMEN
5000
134
800
600
r
1
0-
z
LQj
V)
400
LdJ
I)
6O
200
n
0O
0
2000
4000
STRAIN [MICROSTRAIN]
FIGURE 6.8
TYPICAL STRESS-STRAIN GRAPH FOR A [0n/+15n ]
SPECIMEN
6000
135
TABLE 6.3
AVERAGE MODULUS, FAILURE STRESS, AN D FAILURE STRAIN
FOR [+15n/0 n] AND [0n/+15n] s SPECIMENS
Laminate
Type
Modulus
[GPa]
Failure
Stress
[MPa]
Failure
Strain
([strain]
125
(3.2%) a
1003
7935
(4.1%)
(6.5%)
(+152/02]s
122
(5.7%)
747
6312
(8.1%)
(10.7%)
S
123
(5.0%)
642
5997
(6.6%)
(19.5%)
[ ±153/03]
[±155/05]s
[±158/08]s
[0/±15]
[02/±152]s
[03/±+153]s
[05/±155]s
[08/±158]s
117
(8.0%)
618
(10.5%)
5626
(17.0%)
115
(6.1%)
541
5137
(2.5%)
(11.5%)
124
(3.1%)
1160
9028
(3.3%)
(5.5%)
863
7463
(6.4%)
(4.7%)
(9.4%)
123
(8.1%)
760
6570
(8.8%)
(19.1%)
123
119
669
6289
(10.5%)
(7.1%)
(15.1%)
114
618
5371
(14.1%)
(5.9%)
(6.3%)
aNumbers in parentheses
of variation.
are
coefficients
136
Two
trends
are
evident
in
the
failure data.
failure stress and strain decrease as effective ply
increases.
Second,
consistently
higher than those of
These
trends
specimens
were
thickness
values for [On/±15n]s specimens are
observed
[±15n/ 0 n]s
the
specimens.
by Lagace et al. for AS1/3501-6
[37].
The specimens
growth
the
First,
are
which
listed
exhibited
detectable
delamination
Appendix B ([±15n/On]s specimens) and
in
Appendix C ([On/±15n]s specimens) with the maximum stress, the
strain
associated
with
the
maximum
stress,
the number of
observed delaminations, the maximum intrusion, and
delaminated
area
of
each
test.
The
stress range, average maximum intrusion
maximum
delaminated
Table 6.4.
Each
area
of
before
the
total
average first growth
before
failure
failure,
are
and
reported
in
these averages is calculated using data
from only two specimens
since three of the five
specimens
of
each type were used to determine only the failure stress.
The
damage
for both laminate
into
changed as effective ply thickness increased
types.
The thinnest
two pieces upon failure.
segments
approximately
specimens
(n = 1) broke
The fracture surface had rough
perpendicular
to the free edge.
These
segments contained portions of several delaminated plies.
fracture surface
also
had
segments
which
were
The
relatively
smooth and extended along the +15° and -15° directions.
There
were relatively small delaminations along the
these
segments.
specimen
edge
of
An x-radiograph showing damage of a failed [15/0]s
is shown in Figure 6.9.
For
the
other
[+±15n/On]s
137
TABLE 6.4
AVERAGE FIRST GROWTH STRESS RANGE, MAXIMUM INTRUSION,
AND DELAMINATION AREA BEFORE FAILURE FOR
[±1 5 n/0n]s AND [0 n/+1 5 n]s SPECIMENS
Average
Average Maximum Average Delaminated
First Growth Intrusion Before Area Before Failure
Stress Range
Failure
[cm2]
Laminate
Type
[MPa]
[mm]
[±15/0]s
785-837
6
2
[±152/02]s
629-666
15
13
[+±153/03]s
512-541
34
31
15
13
32
31
2
0
20
22
25
23
13
8
9
2
[+±155/05]s
[±158/08
] s
<4 14 a
1001-1059
[0/±15]s
[02/±+152 ] s
733-772
[03/±153]s
[05/±155]s
[08/±158
< 50 2 a
s
aDelamination
occurred
in the first test of both specimens.
138
FIGURE69
X-RADIOGRAPH OF A (±15/01
S
SPECIMEN AFTER FAILURE
139
specimens,
the
thinner
delaminations
before
smaller.
of
Thicker
Few
specimens
specimens
failure,
these
but
specimens
exhibited
tended
more
to
have
more
they
were
considerably
broke
into
two
pieces.
pronounced peeling of the
delaminated [+15n] sublaminates before and after failure.
thicker
specimens
also
showed
splits in the plies upon
greater
failure.
A
The
spacing between the
photograph
of
failed
[±15n/0n]s specimens is shown in Figure 6.10.
The
[0/±15]s
specimens
exhibited
fewer
before failure than the [+15/0]s specimens.
fracture
the
surfaces
+150
-15°
and
illustrates
were
the damage
shown in Figure
delaminations
Upon failure, the
cleaner and were predominantly along
directions.
An
state of a failed
x-radiograph
which
[0/±15] s specimen
is
6.11.
Many of the thicker [On/±15n]s specimens experienced more
delaminations
failure.
than
their
[±15n/0n]s
counterparts
None of these specimens broke into two
failure.
pieces
There was no peeling of the [On] sublaminate
surface.
In
sublaminate
sublaminates
many
which
cases,
had
the
portion
delaminated
and split away
from
the
of
from
the
rest
of
before
the
upon
on the
[-1 5 2n]
neighboring
the
[-152n]
sublaminate rotated slightly such that part of the sublaminate
extended
out from the free edge.
illustrated in Figure 6.12.
This "shear out" behavior
is
The thicker specimens also showed
greater spacing between the splits in the plies upon
failure.
A
shown in
photograph
Figure 6.13.
of
failed
[0n/+15n]s
specimens
is
140
i--5~Ikr~I
I
I
I
/
r.r
A
v5/0,
a
FIGURE 6.10
3
I
"
a
J.
J1
"
I
t
PHOTOGRAPH OF FAILURE MODES OF [±15n/0 ]s
SPECIMENS
141
I
FIGURE 6.11
X-RADIOGRAPH OF A [0/+15]
FAILURE
s
S
SPECIMEN AFTER
142
!
11
SHE
I
4
POR'
OF
SUB
ANGLE
PLY
SPLIT
FIGURE
6..12
SCHEMATIC
OF THE "SHEAR OUT" OF THE [-152n ]
SUBLAMINATE IN A [0n/+15n]s SPECIMEN
143
iI
-
i
-o-3
58
2.....
h -0-
, O-u
18
I11ie'2
ic i I8 I!ti- I5sU,
t
!
__T-
;
IIi-
FIGURE 6.13
PHOTOGRAPH OF FAILURE MODES OF
SPECIMENS
0n/±15 n
]
144
It
is
not
clear how unstable delamination growth might
manifest
itself
in
defined
above,
was
complete
delamination
for all specimens
these
experiments.
and
growth
of the +15°/-15 0 and
loading
to
a
before
equivalent
amount
of
loading
In other specimens,
tab
was
coincident
that grew
to grow in
may be indicative
This is evidence that unstable
substantial
the delaminated
to a
such delaminations
is not necessarily
necessary
grew
However,
It is likely that delaminations
Thus,
unstable growth.
as
interfaces
tab and stopped would have continued
an actual part.
A
delaminations
to final failure.
of the delamination
with final failure.
growth
00/150
with values of n greater than one.
stopped prior
to the loading
failure,
always accompanied by complete or nearly
in many of these specimens,
tab
Final
of
delamination
to final failure.
delamination
may
be
failure can be induced by delamination.
If
region were to remain small
growth
and
stable,
the
strength of the specimen would not vary significantly from the
predicted in-plane strength.
however,
failure
usually
the
strength
in the specimens
occurred
of
As the delaminated region grows,
the
specimen
is degraded.
in this portion of the
Final
investigation
at or soon after delamination
growth
did not grow to the
tabs
to the
loading tab.
Delaminations
thin (n = 1) specimens.
Nonetheless,
"unstable"' growth associated
seen in Figures
loading
the
there may have been some
with final failure.
6.9 and 6.11 that considerable
associated with the fracture surface.
in
It
can
be
delamination
is
145
a
to
growth
When
loading
tab
was not accompanied by
complete delamination and final failure, it could
of
be
with the naked eye and was accompanied by an audible
detected
click.
usually
In the [+±15n/On]s specimens,
the surface plies.
usually
there was usually
In the [On/±15n]s specimens, there was
The load data also
some shear out of the inner plies.
usually
showed
peeling
a significant drop in load when growth to the
tab occurred.
The data acquisition
points
such
if
events
program had the ability to mark data
occurred.
regardless
with x-radiography.
strains
whether
or not they were monitored
The growth-to-tab stresses and associated
type are given in Table 6.5.
were
The
growth-to-tab
quite close to the final failure stresses.
with failure stress and strain, the trends are for the
and
level
strain
thickness
all
listed in Appendix D with the average values for
are
each specimen
stresses
of
for
accurately
stress could usually be determined quite
specimens
the growth-to-tab
Thus,
to
As
stress
decrease with increasing effective ply
and for the values
specimens
for [+±15n/On]s
to
be
lower than the values for [On/±15n]s specimens.
6.4.3 Fabric Specimens
The
fabric
[±20F]s
specimens
exhibited
stress-strain behavior until delaminations detectable
x-radiographs
shown in
were
formed.
Figure 6.14.
The
linear
on
the
A typical stress-strain graph is
specimens
were
all
tested
to
146
TABLE 6.5
AVERAGE GROWTH-TO-TAB STRESSES FOR
[+15n/0 n]
Laminate
Type
Average
Growthto-Tab
Stress
[MPa]
5 2/0
AND
[0n/+15 n]
Average
Growthto-Tab
Strain
SPECIMENS
Laminate
Type
Average
Growthto-Tab
Stress
[pstrain]
[MPa]
Average
Growthto-Tab
Strain
[#strain]
2]s
713
(8.8%)a
6355
(8.9%)
[ 0 2/+152]s
830
(7.2%)
6905
(7.6%)
[±l53/03]s
603
(6.5%)
5004
(10.1%)
[O3/+153]
s
710
(2.9%)
5838
(10.8%)
[±155/05]s
567
(7.5%)
4824
(6.9%)
[05/±155]
s
656
(6.1%)
5726
(16.9%)
[± 1 5 8/ 0 8]s
525
(6.3%)
4651
(8.4%)
[08/+158]s
602
(7.6%)
5584
(11.5%)
[±
aNumbers in parentheses are coefficients of variation.
147
600
I0-I
400
II
.
I
i
<n
L_
I._
Hv)
enJ
200
I
f
so
0
4000
_
8000
STRAIN EMICROSTRAIN]
FIGURE 6.14
TYPICAL STRESS-STRAIN GRAPH FOR A [+20OFS
SPECIMEN
12000
j
148
failure.
The modulus, failure stress, and failure strain for
each specimen is given in Data Table 5.
for
are
both
specimen
well
The
types are given in Table 6.6.
within
experimental
scatter
Laminated Plate Theory value of 56 GPa.
stresses
are
average
significantly
less
of
The
than
values
The moduli
the
Classical
average
failure
the value of 647 MPa
predicted for in-plane failure by the generalized criterion of
Tsai
and Wu [38].
This value was obtained using the strength
properties for Hercules AW370-5H/3501-6 listed in Table 6.7.
The specimens with
interface
had
of variation
interface
of
warp
faces
at
the
Those with
only
fill
faces
at
that
a failure stress of 530 MPa with a coefficient
variation
of
2.7%.
Given
these
relatively
coefficients of variation, a difference in failure
12.8%
+200/-20°
a failure stress of 530 MPa with a coefficient
of 4.0%.
had
only
small
stress
of
is significant.
The
delamination
specimen
types.
delaminations,
growth
Details
maximum
behavior
varied
regarding
the
for
the two
number
of
intrusion, and total delaminated area
after each test are given for the specimens monitored
by
dye
penetrant-enhanced x-radiography in Appendix E.
The
specimens
interface
with
exhibited
only
fill
delaminations
x-radiographs at lower stresses.
likely
not
which should
delaminations
faces
at the +200/-20°
detectable
from
the
These delaminations are most
formed concurrently with delamination initiation,
be
the
tended
same
to
be
for
both
specimen
types.
triangularly shaped.
The
They were
149
TABLE 6.6
AVERAGE MODULUS, FAILU RE STRESS, AND
FAILURE STRAIN FOR [±20F]S FABRIC SPECIMENS
Interface
Modulus
Failure
[GPa]
Fill/Fill
56
a
(3.8%)
470
(2.7%)
9291
(8.9%)
Warp/Warp
55
(5.3%)
530
(4.0%)
9895
(5.2%)
aNumbers
in parentheses
of variation.
Stress
[MPa]
Failure
Type
Strain
[,strain]
are coefficients
150
TABLE 6.7
STRENGTH PARAMETERS FOR HERCULES
AW370-5H/3501-6 FABRIC GRAPHITE/EPOXY
Test Type
Strength
[MPa]
Longitudinal
Tension
817
Longitudinal
Compression
779
Transverse
Tension
728
Transverse
Compression
712
Shear
105
105
Shear
151
bounded
on
one
side
by
the free edge and on the other two
sides by lines at +200 to the longitudinal
were
apparently
splits in warp fiber tows.
the delaminated region did not
splits.
axis.
coincide
lines
The boundaries
exactly
with
of
these
There were also some delaminations which were rounded
with no clear boundaries.
visible
Both
in the x-radiograph
The
specimens
interface
with
exhibited
delaminations.
These
types
of
delaminations
are
in Figure 6.15.
only
warp
smaller,
faces
more
at the +20°/-20°
clearly
defined
delaminations were bounded on one side
by a line at 200 to the longitudinal
axis
side by a line roughly perpendicular
to that.
and
on
one of these delaminations
the
other
The contrast
the x-radiographs of these features is quite low.
of
The
in an x-radiograph
An
of
example
is therefore
indicated with an arrow in Figure 6.16.
Light lines at +70° to the
visible
visible.
of
all
in
most
These
the
x-radiographs
lines indicate
plies.
They
longitudinal
in
direction
were
which delaminations were
splits in the fill
apparently
formed
fiber
after
tows
the
delaminations.
6.4.4 Specimens with
Ply Splits
Implanted
Delaminations and Angle
The specimens with implanted delaminations and angle
splits
were
all
tested
to failure.
As was observed
[03/±153]s specimens with no implanted damage,
the
ply
for the
specimens
152
FIGURE 6.15
X-RADIOGRAPH OF TYPICAL DELAMINATIONS IN [±20 ] s
SPECIMENS WITH FILL
I NTERFACE
FACES AT THE +20'/-20'
153
FIGURE 6.16
20
X-RADIOGRAPH OF TYPICAL DELANINATIONS IN
+20'/-20'
THE
AT
FACES
SPECIMENS WITH WARP
INTERFACE
154
did
not break
into two pieces at failure.
The failure stress
and failure strain are given for each specimen in Data Table 6
with
the
average
values
given
moduli
are within
experimental
value
predicted
by
in
Table 6.8.
The average
scatter of 116 GPa which
Classical
Laminated
Plate Theory.
average failure stress of specimens with implanted
splits
is the
angle
The
ply
was 11.1% lower than that for specimens with implanted
delaminations
alone.
delaminations
The
specimens
with
implanted
and no angle ply splits failed at a 2.0% higher
stress than those with no implanted damage.
This
difference
is within experimental scatter.
During
the
curing
process,
the
teflon film is weakly
bonded to the neighboring sublaminates. When
broken,
the
specimens
emitted
an
this
audible
bond
was
"click"
and
experienced a detectable increase in the strain data.
the "formation
the
point" of the implanted
sublaminates
applied
were
through
the
still
bonded
thickness
delamination
and
before
graph
this
The average values
In
specimens
implanted
split
delamination.
split,
that
event.
The
A typical
exhibiting this formation point is shown
in Figure 6.17 The modulus of each specimen
Table 6.
in
strain continuity
stress-strain behavior was linear until this event.
stress-strain
This is
with
is given
in
Data
are given in Table 6.8.
an
"formed"
implanted
at
the
angle
same
ply split, the
time
as
the
In the specimens without an implanted angle ply
a split formed spontaneously in the [-156] sublaminate
at the edge of the delaminated
region.
This usually
occurred
155
TABLE 6.8
MODULUS AND FAILURE DATA FOR [0 /+15
SPECIMENS WITH IMPLANTED DELAMINATI3N9
Nominal
Intrusion
of the
Implanted
Delamination
[mm]
Nominal
Intrusion
Modulus
[GPa]
Failure
Stress
Failure
Strain
[MPa]
[,strain]
114
(3.1%) a
775
(1.8%)
6708
(2.5%)
112
(5.2%)
697
(2.4%)
6253
(5.9%)
of the
Implanted
Angle
Ply Split
[mm]
10
0
10
20
aNumbers in parentheses are coefficients of variation.
156
400
300
-
r I
0
200
(J)
LU
a,
HCo
100
n
uJ
0
I
I
I
1000
2000
3000
STRAIN
FIGURE 6.17
4000
MICROSTRAIN]
TYPICAL STRESS-STRAIN GRAPH FOR A [0 /+15 ]
SPECIMEN WITH AN IMPLANTED DELAMINATION SO*ING
THE "FORMATION POINT" OF THE DELAMINATION
157
at
a
higher
stress
than
the
delamination formation.
formation of these angle ply splits
x-radiographs.
An
x-radiograph
delamination
and
Figure
The stresses
6.18.
delamination
in Appendix
The
and
F.
associated
both
confirmed
showing
from
an
the
implanted
angle ply split is shown
and strains at the formation
in
of the
angle ply split are given for each specimen
The average values
delamination
same for
the
was
The
formation
types
of
are
given
stresses
in
Table
6.9.
were approximately the
specimens.
The
angle
ply
split
formation stress was approximately twice as high for the cases
in which
it was not implanted,
although
variation was quite high (34.5%).
the delamination and the
before
failure.
surrounding
the
angle
the
coefficient
of
In all cases, however, both
ply
split
had
formed
well
This indicates that the global stress fields
delaminated
region
correctly
approximated
those of a naturally occurring delamination through nearly all
of the testing.
The nominal intrusions of the delaminations
The
nominal
intrusions
of
were
10 mm.
the angle ply splits were 20 mm.
After the delamination formation point, the
actual
could be determined from the x-radiographs.
The intrusions of
intrusion
the implanted delaminations and angle ply splits are given for
each specimen in Data Table 6.
15 mm
with
specimens
a
coefficient
of
The actual average values were
variation
of
8.4%
for
the
without an implanted angle ply split and 13 mm with
a coefficient
of variation
implanted angle ply split.
of 13.9% for the specimens
with
an
The nominal intrusion of the angle
158
I
k
.
9
I
t Xf
,
f
, i
1 is
h;
4iti
I 11
i.
FIGURE 6.18
X-RADIOGRAPH OF A (0 /±15
SPECIMEN WITH AN
IMPLANTED DELAMINATION ANA HE ASSOCIATED
SPONTANEOUSLY FORMED ANGLE PLY SPLIT
159
TABLE 6.9
DELAMINATION AND ANGLE PLY SPLIT FORMATION DATA FOR
[03/±153]s SPECIMENS WITH IMPLANTED DELAMINATIONS
Nominal
Intrusion
Nominal
Intrusion
DelaminatiRn
Formation
of the
Implanted
of the
Implanted
Stress
Strain
[MPa] [ustrain]
Delamination
Angle
[mm]
Ply Split
Angle Ply
b
Split Formation
Stress
[MPa]
Strain
[pstrain]
[mm]
10
0
140
1186
(8 .3%)a (8.4%)
10
20
152
1372
(14.6%) (13.0%)
aThe point at which
bneighboring plies.
The point at which
x-radiograph.
the
301
(34.5%)
implanted
152
(14.6%)
teflon
2593
(34.5%)
1372
(13.0%)
debonded
an angle ply split was first visible
Numbers in parentheses are coefficients of variation.
from
on an
160
ply
split was 20 mm.
a coefficient
The actual average value was 26 mm with
of variation
There was usually
either
specimen
type
of 8.4%.
little
delamination
before
failure.
In
some
sublaminates
delamination
instances,
extended
and
the
in the
splits
in
behavior
Figure
is
[+153]
between
the
region
of the implanted
free
edge.
In
cases,
the
these
illustrated
in
the
this
region.
x-radiograph
three
of
the
six
in
specimens with angle ply splits,
delamination grew to the end of the implanted angle ply
before
final
failure.
x-radiograph in
determined
ply
ensued.
which
This
Figure 6.20.
behavior
The
did not stop at
split.
The
delamination
end
was
exhibited
and
split
in the
strain
were
In three specimens,
of
the
implanted
total and failure
For these specimens, therefore, the stress and strain
growth
to the end of the implanted angle ply split
failure
values.
and strains are reported in Appendix G.
stress for the six specimens
variation
stress
the
occurred were set equal to the final
stresses
is
for each of the six specimens.
the delamination
at
the
6.19.
In
angle
in
delaminated
the
delamination front advanced slightly to include
This
seen
Angle ply splits did
form in the [+153] and [-156] sublaminates
region.
growth
of 3.1%.
These
The average
was 690 MPa with a coefficient
of
161
r
FIGURE 6.19
X-RADIOGRAPH OF A [O /+15 1 SPECIMEN WITH AN
IMPLANTED DELAMINATIN SHWfNG LIMITED EXTENSION
OF THE DELAMINATION FRONT
162
FIGURE 6.20
X-RADIOGRAPH OF A [0 /+15
SPECIMEN WITH AN
IMPLANTED DELAMINATIN ANA NGLE PLY SPLIT
SHOWING DELAMINATION GROWTH TO THE END OF THE
IMPLANTED ANGLE PLY SPLIT
163
6.5 Discussion
The
experimental
the objectives
results are discussed
of this
investigation.
in the context
The
discussions
of
are
divided into sections by specimen type.
6.5.1 Specimens of Nonstandard Width
The average
were
within
failure
experimental
stress
specimens.
failure stress for the five sets of specimens
This
is
scatter
independent
indicates
that
of
of
one
another.
Thus,
specimen width for these
the
mechanism
controlling
failure is also independent of specimen width.
Once
a
delamination
starts to grow, the plies decouple
and the local strength drops rapidly.
predicted
strength
by
the
parameters
laminate
and
predicted
criterion
strain.
gage
data
349 MPa
and Wu [38] using the
the
for the delaminated sublaminates.
The
strain
drops
not
quite
from
obtained
reach
this
13057
an accurate
strain
from
value
However, it should be noted that the reported
is the far-field
the
at
of the local strain
in
the
to
strain
failure.
failure
strain at the strain gage position
estimate
strength
for
The failure strain
does
Tsai
in-plane
given in Table 6.10 are 1516 MPa
failure
5842
of
The
strain
and is not
delaminated
region.
Since
the
failure
all specimen widths,
stress
is approximately
the same for
the failure of these specimens
appears
to
164
TABLE 6.10
STRENGTH PARAMETERS FOR HERCULES
AS4/3501-6 UNIDIRECTIONAL GRAPHITE/EPOXY
Test Type
Strength
[MPa]
Longitudinal
Tension
2356
Longitudinal
Compression
1466
Transverse
Tension
49.4
Transverse
Compression
186
Shear
105
165
be
contro lied
by
the
strength
in-plane
of
failure
the
sublaminates.
Apparently ,
local
sublaminate
causes stress gradients which can trigger further
of
the
delaminated
delamination and the corresponding sublaminate failure.
average
The
together.
There
growth
is a possible
stress
ranges
were
the
addition,
wider
delaminations
trend of the first delamination
specimens
before
apparently
better
specimens.
There
have
failure.
able
to
are
The
start
larger
delaminations
and
stop
a number of possible
in
release
rate
curves
other mechanisms
arresting
growth.
that
may
the
at work that are related to
a
delamination
as
a
are
wider
explanations
affect growth.
for
energy
There may be
the
function
In
reported
The re may be finite width effects on the strain
this.
close
oc curring slightly earlier in the wider specimens.
growth
of
first
probability
of
Nonetheless, when the sublaminates started
amount of
to
fail,
total delamination and final failure followed.
Nearly
failure
all
before
the
the
initiation stress
detectable
specimens
exhibited
experimentally
of
the
delamination
one
determined
specimen
initiation
This indicates that the specimen was
Fortunately,
the
stress
on
a
increments
which
behavior
was
observed.
and
delamination
exhibited
a
an edge replication.
statistical
anomaly.
for this portion
investigation were chosen conservatively to
delamination
delamination
insure
of the
that
all
Initiation is a local
effect which should be unaffected by specimen width so long as
the
specimen
is
substantially
wider
than the interlaminar
166
stress boundary layer.
Within
not appear
unstable
the
resolution
to be a definitive
delamination
of these experiments, there does
critical
growth
experiments
shows that unstable
coincide.
However,
two necessarily
these
do coincide.
delamination
or final failure.
growth and final
experiments
size
for
This set of
failure
can
do not prove that the
For example,
it is possible
that
the final failure of similar specimens would not coincide with
unstable delamination growth if the in-plane strength
of
the
delaminated sublaminates were higher.
There
front
were
for
two
stable
observed
positions of the delamination
delaminations.
In
cases,
the
delamination front was roughly perpendicular to the angle
ply
split
the
in
the
delamination.
angle
ply
sublaminate
most
isolated
In some cases, the delamination
front coincided
with an angle ply split in the angle plies in the
00
containing
the
positions
raises
plies.
The
the question
fact
that
by
sublaminate
there
of the mechanism
are
two
for arresting
delamination growth in each case.
6.5.2
X
[+15n/0n]O and [On/+15n], Specimens
The trend
stress,
average
growth-to-tab
thickness.
effective
in both sets of data is
first
stress
growth
decrease
The explanation
stress
that
'
average
range,
and
failure
average
with increasing effective ply
for this is based on the effect of
ply thickness on the interlaminar stress state.
At
167
any
stress
level,
laminates
with thicker plies have larger
regions of high interlaminar stress (although not higher
edge
magnitudes
of
interlaminar
free
stress) near the free edge.
This affects phenomena controlled by energy considerations
well
as
Since
those
controlled
delamination
as
by average stress considerations.
initiation
and
growth
appear
to
influenced by such considerations, the thicker specimens
to accumulate damage at lower stresses.
be
tend
This in turn subjects
them to failure at lower stresses.
The difference between the behavior of the [±15n/0]
[0n/±15n]s
specimens
delamination
stress
initiation
state
most
This
likely
not
considerations.
that controls
types of specimens.
constructed
is
initiation
was
the
The
s
and
related
to
interlaminar
is similar for the two
case
for
of AS1/3501-6 in Reference 34.
the
specimens
Brewer and Lagace
found that the difference in interlaminar normal stresses
was
not large enough to make the predicted delamination initiation
stresses significantly different for the two
They also observed this experimentally.
specimen
types.
The same is predicted
for the AS4/3501-6 specimens in this investigation.
Although
these specimens were not explicitly monitored for delamination
initiation, it can be assumed that the initiation stresses are
not
substantially different for the AS4/3501-6 [±15n/On]s and
[0n/±15n]s specimens.
The
attributed
sequence.
difference
to
in
behavior
the physical
The angle plies
in
after
initiation
characteristics
the
[0n/+15 n]
can
be
of the lamination
specimens
are
168
constrained
00
plies.
bending
from out-of-plane deformation after damage by the
The difference in energy directly
was
evaluated in a simple experiment.
masses were placed on a peeled sublaminate.
the
attributable
ply gave an indication
position.
This was
when
to
quantities
compared
other
Several small
The deflection of
of the energy needed
to its original
found
to
of
to
to restore it
be
negligible
energy, such as the
strain energy calculated by the O'Brien method.
Even if a region of a ply is completely
neighboring
plies,
frictional
to
peel
away
and unload.
strain energy is available
[±15n/On]s
specimens
[+±15n/0n]s specimens
which in turn subjects
stresses
and
the
at
for
any
[±15n/0n]s
delamination
stress
to
associated
specimens
The net effect
experience
them
from the
loads can still be applied.
contrast, the surface plies of the
free
debonded
In
are
is that more
growth
level.
in
the
Hence,
the
delamination growth earlier
redistribution
in-plane
of
failure
in-plane
at
lower
stresses.
The
which
thinnest
could
be
specimens
associated
(n = 1) exhibited failure modes
with
in-plane
delamination initiation stress for these
high.
When
a
and
this
increased.
is
quite
compliance.
The
local
strains apparently exceeded the level necessary
for local in-plane
When
specimens
The
significant area of the specimen delaminated,
there was a sudden increase in local
stresses
failure.
failure
occurred,
the
of
the
compliance
The local stresses
remaining
in
the
sublaminates.
local
region
and strains at the edge of the
169
failing
region
apparently
exceeded
the level necessary for
in-plane failure of the laminate and failure propagated across
the specimen width.
Failure
strength.
in-plane
of a laminate appears to be governed by in-plane
When
delamination
strength
is
the
is
local
involved,
in-plane
the
relevant
strength
of
the
delaminated sublaminates.
If
growth
is
governed by an energy consideration, then
there should be a general
thicker
specimens.
This
trend
toward
earlier
a
result
region
of
and
proportional
Details may vary,
effects of the interlaminar
finite
for
is because the available energy is
directly proportional to laminate thickness.
as
growth
dimensions.
Since
to the square of the strain
stress boundary
strain
(or
energy
stress)
is
level,
milestones of delamination growth (e.g. delamination growth to
the loading
tab) should occur at
stresses
that
are
roughly
inversely proportional to effective ply thickness.
The
feasible
fact
is
that
not
Delamination
prerequisite.
delamination
growth
is
energetically
a sufficient condition for growth to occur.
initiation
Hence,
appears
no
growth
to
be
should
a
necessary
occur
before
delamination initiation.
The
data
used to verify
growth
stress
from
some of
this portion of the investigation
these
premises.
the
average
first
range, growth-to-tab stress, and final failure
stress are plotted as a function of
for
The
can be
[+ 1 5 n/On]s
specimens
in
effective
Figure 6.21
ply
and
thickness
for the
170
1200
......... INITIATION CODC)
---- GROWTH TO TAB CG)
-I
&
_
1 000
FAILURE (TSAI-WU)
FIRST GROWTH RANGE
A
GROWTH TO TAB STRESS
a
FAILURE STRESS
800
.4
0.
LI
Vi)
I,
600
A
cn
400
200
n
ma)
S
2
!
4
I
I
6
8
NORMALIZED EFFECTIVE PLY THICKNESS, N
FIGURE 6.21
EXPERIMENTAL VALUES AND ANALYTICAL CURVES FOR
DELAMINATION INITIATION, GROWTH, AND FINAL
FAILURE OF [±15n/0n]s SPECIMENS
10
171
[On/±15 n]
specimens
Also
in Figure 6.22.
plotted are three theoretical curves.
The first is
the delamination initiation stress predicted by the
Delamination
Criterion.
Quadratic
The value of the interlaminar shear
strength Zsl used in the Quadratic Delamination Criterion
105 MPa.
This
was
the
value
determined
graphite/epoxy specimens in Reference 34.
should not be a strong function
for
was
AS1/3501-6
Since this quantity
of fiber strength,
the
value
obtained for AS1/3501-6 should be a good estimate of the value
for AS4/3501-6.
The second curve is
damaged
[0n/±15n]
the
failure
assumed
to
be
complete
The damage to the
delamination
interface and in-plane failure (in the form of
the
isolated
angle
characterization
delamination
predicted
ply
sublaminate.
of the damage state of
growth
to
the tab.
specimens
at the +15°/-15o
splitting)
The
the
specimens
strength
to the specimen.
third curve is generated by a constant strain energy
energy
delamination
the
after
The failed sublaminate was
release rate as predicted by the O'Brien method.
strain
of
This is a reasonable
assumed to carry no load and therefore contribute no
or stiffness
for
or [±15n/0n]s specimens using the Tsai-Wu
in-plane failure criterion [38].
was
stress
release
growth
specimens
with
O'Brien's equation.
rate
available
at
the
The value of
time of the
to the loading tab (or final failure,
n
equal
to
one)
was
computed
for
using
These values are given in Table 6.11.
both the [+ 1 5 n/0n]s and [0n/±15n]s
cases, the values
for
In
the
172
1200
is
INITIATION CODC)
.........
---- GROWTH TO TAB (G)
--
1000
800
0
iT
U)
I\
600
I
FAILURE (TSAI-WU)
FIRST GROWTH RANGE
A
GROWTH TO TAB STRESS
a
FAILURE STRESS
0
Q
._i
5
ol*a
%ft.
I
400
. .
.m ime.
.
200
n
0
um
I
I·
I
I
2
4
6
8
NORMALIZED EFFECTIVE PLY THICKNESS, N
FIGURE 6.22
EXPERIMENTAL VALUES AND ANALYTICAL CURVES FOR
DELAMINATION INITIATION, GROWTH, AND FINAL
FAILURE OF [0n/+15n]s SPECIMENS
10
173
TABLE 6.11
STRAIN ENERGY RELEASE RATE AT
AVERAGE GROWTH-TO-TAB STRESSES FOR
[±15n/0n ] AND [0n/+15n ] s SPECIMENS
Laminate
Type
Average
Growthto-Tab
Stress
[MPa]
Strain
Energy
Release
Rate
Laminate
Type
[J/m2]
Average
Growthto-Tab
Stress
Strain
Energy
Release
Rate
[MPa]
[J/m2]
1160
1110
1003
830
[0/±15] s
5 2/2]s
[±+1
713
839
[02/±152]s
830
1137
[+153/03]s
603
900
[03/±153]s
710
1248
[±155/05]s
567
1326
[05/±155] s
656
1775
[±158/08]s
525
1819
[08/±158]s
602
2392
[±15/0] s
aCalculated using O'Brien's method.
174
three thinnest specimen types were within experimental scatter
while
the
values
for
substantially higher.
growth
of
the
thicker
energy
to
release
rate
estimate
4.5%
the
coefficient
the
Thus, the average values of
for the three thinnest specimen
The average values of
rate were 856 J/m2
for
if
of
which
can
be
the stress at which similar damage becomes
energetically feasible.
release
were
delamination to the loading tab were delayed until
types were used to generate theoretical curves
used
types
This is what would be expected
delamination initiation occurred.
strain
specimen
strain
with a coefficient
[±15n/0n]s
specimens
variation
of
and
6.3%
of variation
1165 J/m2
for
energy
the
of
with
a
[0n/+15 n] s
specimens.
There are several possible sources for the discrepancy in
these values of strain
[±15n/On]s
and
[On/±15n]s
sublaminate is assumed
specimens,
energy
however,
to
the
release
rate.
the
modulus
both
the
specimens, the isolated angle ply
carry
peeled
load.
portion
In
the
[±15n/On]s
of the sublaminate
carries no load and therefore has no internal
If
In
strain
of this region of the sublaminate
energy.
were set to
zero for the purpose of calculating strain energy release rate
with O'Brien's method, the value of strain energy release rate
would
rise from 856 J/m2
specimens,
angle
ply
the
to
delaminated
sublaminate
may
1381 J/m 2 .
In
and split portion
carry
some
the
[0 n/15n]
s
of the isolated
load
applied
via
friction, but it has most likely yielded more internal
strain
energy than has been accounted for by O'Brien's method.
It is
175
therefore
conceivable
that
the
values
for the two types of
specimens
are
explanation
may involve the details of the
delamination
actually
quite
close.
An
alternative
situation
at
the
front (e.g. frictional loading versus peeling of
the isolated angle ply sublaminate, tensile versus compressive
values
of
the
differences
local
between
interlaminar
the
two
normal
lamination
stress).
The
sequences may mean
different conditions of applied stress may need to be
met
in
order to initiate dynamic unstable delamination growth.
The
plots have several important features.
was no delamination growth until approximately
delamination
initiation
delamination
growth
by
the
strain
stress,
even
First, there
the
when
predicted
significant
was theoretically possible as determined
energy
release
rate
curve.
This
shows
conclusively that initiation must occur before any growth
occur
and
that the strain energy release rate criterion
necessary but not
a
growth.
also
release
It
can
sufficient
rate criterion
condition
be
condition
surmised
is a necessary
but
for delamination initiation.
necessary and sufficient in both cases
governed
that
by
its
for
can
is a
delamination
the strain energy
not
a
sufficient
If the criterion were
and
each
event
were
own critical value of strain energy release
rate, delamination growth could never be delayed by
the
lack
of delamination initiation.
Once
delamination
had initiated,
it did not grow to the
loading tab until it was energetically feasible as
by the curve.
determined
This emphasizes that strain energy release rate
176
is
criterion
was
stress
by the Tsai-Wu
predicted
long
types of
as
the
above the post first ply failure stress
or
near
certain
as
thereafter
soon
Failure occurred
damage.
for
condition
necessary
a
criterion
[38].
The average maximum intrusion and delaminated area before
were
failure
Nonetheless, there was no trend
value
failure can be determined
suggesting
for
size
delamination
of
specimens per data point.
two
only
on
based
a
that
unstable
for these specimens
growth
critical
or final
type
using this
of experiment.
6.5.3 Fabric Specimens
[±20F]s fabric specimens all broke into two separate
The
their
pieces at stress levels well below
of these specimens
delaminations
in-plane
Delaminations were observed to occur in all
stress.
failure
predicted
before
final failure.
It is clear that the
contributed to the final failure and that there
is a significant
effect of the character
of the ply
interface
on the failure stress.
The
differences
manifested
in
the
in
character
specimens with warp faces at
boundaries
of
the
the
the
+200/-20o
were
interface
the delaminations.
of
character
of
In the
interfaces,
the
delamination were delineated by splits in
the warp fiber tows on one side and the fill fiber tows on the
other
side.
The
delamination front.
splits
This
had
the
affects
effect of "blunting"
the
required
for
the
energy
177
extension
of
the
delamination
front.
It appears
growth beyond the splits becomes energetically
feasible,
delaminated region grows across the specimen width.
occurs, the in-plane strength of the
the specimen
specimen
that when
the
Once this
decreases
and
fails.
In specimens
with fill faces at the +20°/-20
°
interfaces,
the delamination growth seems to have been unrestricted by any
splits
in
the fill fiber tows.
fibers caused a disturbance in
delaminations
appear
Only when splits in the warp
the
stress
to be arrested.
by
did
delaminated
on
a
local level.
specimen types seems to have
delamination
region
inducing small cracks at the +200/-20° interface
which blunted the delamination front) or decreased the
available
these
This apparently either
increased the energy needed to extend the
(perhaps
field
grows
across
The difference
affected
the
between
stress
energy
the two
at
which
the width and therefore the final
failure stress.
6.5.4 Specimens with Implanted
Ply Splits
The
results
delaminations
of
of
either
the initiation
experiments
with
and
delaminations.
The
Angle
implanted
initiation
or
apparently induce conditions favorable for
or growth of the other in these specimens.
Neither specimen type experienced substantial
the
and
and angle ply splits underscore the interaction
of angle ply splits
growth
the
Delaminations
delamination
beyond
its
implanted
growth
boundaries
of
before
178
failure
with
experienced
the
exception
growth to the
splits.
The
splits,
coupled
growth
to
with
of
the
three
end
of
the
end of the implanted
the
the
fact
implanted
that
the
implanted angle ply splits failed at a lower
indicates
extension
that
a
specimens which
angle
angle ply
specimens
average
the
of the delamination
delaminated
delaminations
formation.
the
in
specimens
with
the
implanted
must
be
conducive
to
The fact that they did not extend beyond
implanted
extend
arbitrarily
delamination
beyond
is not independent
the
indicates
that
delamination
of
their
the edge
they
cannot
and that their,>
of the growth of the delamination.
The implanted delaminations and angle ply
splits
grew beyond their boundaries until final failure.
the result of a small pocket of
teflon film.
edge
state of stress in the vicinity
delamination
of the
growth
stress,
front.
region
alone,
that edge of the
with
preexisting angle ply split can aid in the
Since angle ply splits formed spontaneously at
of
ply
resin
at
the
seldom
This may be
edge
of
the
Although the global stress state is appropriate,
the local crack tip stress field may be affected.
Russell and
Street [41] verified the existence of these resin rich regions
and determined that they can increase
at
least
the
mode II
component of delamination resistance.
The
interaction
of
the delaminations
and the angle
splits appears quite strong in these specimens.
the
details
of
what
occurs
at
their
ply
Understanding
intersection may be
instrumental to understanding how growing delaminations can be
179
arrested
and
how
arrested
delaminations can reinitiate. A
study of this interaction is warranted.
180
CHAPTER
7
ANALYSIS OF GROWTH PHENOMENON
Modifications
made
to strain energy release rate models
of delamination growth are described in this
modifications
are
compared
to
existing
chapter.
models
These
and
their
ability to accurately correlate data is evaluated.
7.1 Existing Models of Growth Phenomenon
There are two popular models of delamination growth based
on strain energy releases rate methodologies.
simple
model
They
are
the
by O'Brien and the virtual crack closure method
which is based on finite element calculations.
7.1.1 O'Brien's Method
As noted in Chapter 2, O'Brien [26]
method
for the calculation
developed
of strain energy release
a
simple
rate.
His
model was based on the calculated internal energy of laminated
and
delaminated
assumes
that
position.
size.
The
O'Brien
regions
there
of a composite specimen.
The model
is
no
variation
calculation
is
independent
of
this
could be used to
proposed
that
model
with
longitudinal
delamination
predict initiation by using a critical value of strain
release
rate
experimentally
and that growth can be described
determined
resistance
curve.
energy
in terms of an
Experimental
181
evidence
showed
that
the
critical
value
release
rate [28] was not a material
cannot
be assumed that the delamination
material parameter either.
value
of strain energy
be
determined
element
method.
parameter.
It
resistance
was
AS1/3501-6
is a
This contribution would have
by an alternative
Brewer
a
curve
release rate might be a function of the
and
method
Lagace
such as the finite
[34]
found
critical value of strain energy release rate for
initiation
therefore
O'Brien proposed that the critical
relative contribution of mode I.
to
of strain energy
function
specimens.
of
effective
Since
the
that
the
delamination
ply thickness for
modal
contribution
is
independent of ply thickness, this indicates that the critical
value
of
strain energy release rate must also be affected by
this factor.
The derivation of O'Brien's method does not
account
for
any out-of-plane effects such as interlaminar stress or energy
involved
in
sublaminates.
out-of-plane
Increased
deformation
accuracy
in
(bending)
the evaluation
of
of the
strain energy release rate can be achieved with a more general
approach.
7.1.2 Virtual Crack Closure
The
virtual
good correlation
growth
data.
crack closure method has been shown to give
in some instances
As
presently
[e.g. 6]
applied
for
delamination
in the literature,
three-dimensional problem has been modeled
by
assuming
the
that
182
there
is
no
position.
variation
The
with
problem
respect
is
to
thus
the
longitudinal
reduced
from
a
three-dimensional analysis to a two-dimensional analysis.
The
virtual crack closure method requires that the nodal
forces and displacements be accurately determined at the crack
tip.
They
can be used to determine
the relative
modal
contributions.
the change
The
in energy
software
and
available
during this investigation offered a nearly equivalent and less
computationally intensive finite
does
not
specifically
use
element
the
method.
it
product of nodal forces and
nodal displacements, it cannot technically be
virtual crack closure method.
Since
considered
the
This alternative finite element
method is described in the next section.
7.2 Finite Element Method
The alternative finite element method used as a basis for
the
present
analysis
was also a two-dimensional model.
internal energy per unit length of the specimen
directly
from
nodal
In
the
model
great
deal
of
internal
energy
for
The difference
an incremental unit of delamination
growth could be found by comparing
crack
computational
used, however, there were few enough
elements that this calculation was convenient.
in
computed
displacements and the stiffness matrix.
Normally, this would require a
effort.
was
The
was slightly extended.
two
cases
in
which
the
This is equivalent to releasing
a crack tip node in the virtual crack closure method.
183
The
finite
element
used
was
the Finite Element
Analysis Basic Library (FEABL) which
was
developed
Department
of
code
Aeronautics
Massachusetts
and
Institute
Astronautics
of
in
the
at
the
Technology [42].
The
two-dimensional rectangular element used had eight nodes
(one
at
Each
each
node
corner
had
and one at the midpoint
three
displacement
degrees
of each side).
of
freedom
(linear
As a result of symmetry considerations, only one
quarter
displacement in each direction).
of
the
specimen
needed
to be modeled as long as the specimen
width was substantially wider
boundary
contained
layer
and
four
the
layers
than
the
interlaminar
delamination
itself.
layer was divided into three regions.
the layer
delamination.
Each
of elements of equal thickness.
layer was modeled along its length by twelve
to represent
stress
elements.
ply
Each
Each
Four elements were used
from the free edge to the
tip
of
the
Three elements were used to represent a 0.1 mm
long region in front of the delamination
tip.
The
remainder
of
the
layer between the crack tip region and the centerline
of
the
specimen
was
represented
by
five
elements.
elements in each region were skewed toward the crack tip.
sizing of elements
and the size of the mesh used
ranges of delamination
Each
elements.
six
ply
ply
was
size are discussed
represented
by
for
in Appendix
The
The
various
H.
a mesh of four by twelve
Since only one quarter of a specimen was modeled, a
specimen
could
be
modeled
by
a twelve by twelve
element mesh with 144 elements and 489 nodes.
This
mesh
is
184
shown
in Figure 7.1.
The
elastic parameters used for AS4/3501-6 were the same
ones use in the
interlaminar
listed in Table 3.1.
calculated
be
stress
software
and
The only exception was that the software
the value of an out-of-plane
shear modulus,
3.62 GPa from elasticity considerations.
in Table
analysis
3.1 is 4.8 GPa.
This difference
G 2Z,
to
The value listed
is not
believed
to
have a significant effect on the results.
The strain energy release
as the negative
rate in this context is defined
of the derivative
of
internal
energy
of
a
partially delaminated specimen with respect to the area of the
delamination:
udel
G
aA
(7.1)
del
If
the
quantity
two-dimensional
Udel
element
model
is
used,
a
can be defined as the internal energy per unit
length of the specimen.
length, a.
finite
Udel is a
function
of
delamination
Since Udel is internal energy per unit length, the
strain energy
release rate can be written
as:
aUdel
aa
(7.2)
Strain energy release rate curves were calculated for the
[±153]s' [±15/01s, and [0/±15]s specimens.
The derivative was
185
z
l
IF
DELAMINATION
SIZE
L
h
DELAMINATION
--
om
P-
LOCATION
W..
mm
i
i
FIGURE 7.1
It
m
.
I
E
m
PLY
JTHICKNESS
t-- T.
!d,
FINITE ELEMENT MESH USED FOR A SIX PLY LAMINATE
186
approximated
as
the
length divided by
are
curves
The applied
is 10000
rate
the
shown
delamination
width.
release rate as a function
of delamination
The value of strain
energy
to the square
release
rate
of
the
energy
release
factor n as discussed
size
release
strain
level.
curves can be computed
[±15n/On]s and [On/±15n]s specimens by scaling the
strain
of
plots
for other strain levels by considering
can be calculated
energy
The
Figures 7.2 through 7.4, respectively.
in
strain (1.0%).
strain
in
change
that it is proportional
The
in the internal energy per unit
strain level in these and all subsequent
energy
strain
change
values
in Chapter 3.
specimens
asymptote.
In
asymptote.
of
rate and the delamination size by the
The strain energy release rate curves calculated for
[±153]s
for
seem
fact,
to
there
monotonically
is
a
slight
the
approach
hump
before
an
the
The hump is much more visible for the [±15/0]s and
[0/±15]s specimens.
This hump was observed for other laminate
types by Wang and Crossman [6] in their virtual crack
closure
analyses.
The
analysis
of
the
[0n/±15 n]
specimens
complication which could not be rectified with
surfaces of
the
longitudinally
delamination
and
through-the-thickness
Although
this
a
available
computed displacements of the upper and lower
The
software.
the
contained
were
toward
direction
is possible
in
opposite
each
as
other
shown
for an infinitely
in
directions
in
the
Figure 7.5.
thin element,
it
would require portions of two different sublaminates to occupy
187
"N 2500
LLi
L
2000
1500
L
L
I
1000
500
Z
H
0
0
I
I
5
10
15
20
(I)
DELAMINATION INTRUSION MM]
FIGURE 7.2
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
DELAMINATION INTRUSION FOR A [+15 J SPECIMEN
USING A TWO-DIMENSIONAL FINITE ELEMENT MODEL
188
(J
CMz
2000
Lij
LU
1 500
LLJ
(I)
LUj
Ij
1000
LU
cm
C.D
z
LU
500
LUi
zH
0
0
V)
FIGURE 7.3
I
I
5
10
.I
15
DELAMINATION INTRUSION
20
CMMJ
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
SPECIMEN
DELAMINATION INTRUSION FOR A [+15/0
USING A TWO-DIMENSIONAL FINITE ELEMEnT MODEL
189
CM
L: 2000
500
-)
LLJ
1000
LLJ
z
500
LLI
WL
zH
Y)
FIGURE 7.4
0
0
I
I
I
I
5
10
15
20
DELAMINATION INTRUSION CMM]
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
DELAMINATION INTRUSION FOR A [0/±15] SPECIMEN
USING A TWO-DIMENSIONAL FINITE ELEMENT MODEL
190
DEFORMED
POSITION
OF [0 /+15
SUBLARINATf
EFORMED
ITION
'ORMED
;ITION
[-15
1
3LAM I ATE
X. -
- "1
FIGURE 7.5
CL
_-_
DISPLACEMENTS OF THE DELAMINATION SURFACE FOR
[0 /+15 ] SPECIMENS AS DETERMINED BY THE FINITE
ELEMENT MTHOD
191
the
same
space
at
the
same
physically impossible.
higher
than
that
time,
Thus,
the
calculated
by
which
actual
is,
of course,
energy
state
the finite element method.
That is, not as much energy has been released as was
to
have been.
occur
during
there would
released.
computed
The frictional forces that would result cannot
be easily determined.
which
is
be
in
In the limit, they could approach those
perfect bonding.
effect
Therefore,
no
If this were the case,
delamination
and
no
energy
the analysis can only provide an upper
bound for strain energy release rate values for the [On/±1 5 n]s
specimens.
7.3 Geometrically Integrated Finite Element Method
A
problem with the O'Brien method and the various finite
element models is
analyses
which
that
ignore
delaminations.
In
they
are
based
variations
many
in
on
two-dimensional
width
in
actual
specimen types, the effects of such
variations could be significant.
In the specimens
the
observed
stress
in this investigation,
delaminations
fields
associated
were
with
roughly
the
triangular.
must
be
modified
to
of
The
these specimens are thus not
constant with respect to longitudinal position.
models
majority
include
details
The
existing
of
varying
delamination width.
The
finite
which to start.
element model can serve as a good point from
It contains
the
basic
elements
of
strain
192
energy
release
interlaminar
method
rate
stress
analyses,
boundary
can be modified
the delamination
including
region.
the effect of the
The
finite
to a more general delamination
width, a, is allowed
to
be
a
element
shape if
function
of
longitudinal position.
The
premise
delaminated
of
the
proposed
specimen
can
be
differentially thin dx1
strip
can
element
analysis
broken
strips.
The
is
that
the
down conceptually into
contribution
of
each
be calculated in terms of a two-dimensional finite
model.
The
strips
three-dimensional model.
are
then
The differential
assembled
change
in
into
a
energy
with respect to a differential change in delamination area can
then be determined.
Since
the contribution
of each
strip
is
calculated
in
terms of a model of constant width delaminations, the accuracy
of the analysis
width
does
position.
between
should be
not
change
satisfactory
if
delamination
rapidly with respect to longitudinal
This is the case in the portion
the
the
of the delamination
free edge and the angle ply split.
The accuracy
should also be acceptable along the delamination front because
any
effects
of
any
of the different delamination widths on one side
dx 1
slice
in
question
should
be
approximately
counteracted by the effects of the delamination widths on
other
side.
The
the contribution
delamination
most likely source of inaccuracy should be
of the region near the
front
the
and
intersection
the angle ply split.
of
the
At this point,
the stress fields surrounding the delamination front and angle
193
ply
split
interact.
perturbations
Fortunately,
In
addition,
there
are
stress
associated with the tip of the angle ply split.
this area
is
relatively
small,
so
account
for the stress
any
error
introduced should also be small.
This
method
does
not explicitly
fields at the delamination
location
of
front.
Since this
is
the
actual
growth, no claim can be made as to any knowledge
of the conditions
contributions
at the crack tip
of
should, however,
strain
energy
give a good
(e.g. the
relative
release rate).
estimate
of
the
modal
This method
total
strain
energy release rate.
The proposed analysis thus evaluates the change in energy
in
each
differential
differential
integrated
changes
over
differential
the
change
dx 1
in
energy
the
entire
of
the
delaminated
specimen
and
can
area.
divided
is
by
the
convenient
of
release rate as applied to the two-dimensional
unit
specimen
then be found for any change in delamination size
by integrating the strain energy release rate with respect
delamination
for
This
By integrating the definition
model (equation 7.2), the change in energy per
length
specimen
in area to obtain a global value for the
strain energy release rate.
strain
strip
width.
choice
A
reference
is the energy
in a laminated
delamination
size
integration.
The value of Udel for
of
zero
energy can be defined.
can
be
chosen
a
specimen.
as
a
delamination
zero is the energy per unit length of a laminated
to
A
The
limit of
size
specimen:
of
194
_
_
Ulam - Udel =
aa
(7.3)
G(x)dx
0
where: Ulam = internal
specimen
G
energy
per unit length of a laminated
= the strain energy release rate
the
two-dimensional
opposed
x
determined
element
from
model (as
to the overall value for the specimen)
= distance
If equation
finite
from the free edge.
7.3 is integrated
along the entire
length
of
the
specimen, it gives the change in internal energy as a function
of delamination
width:
Ulam - Udel =
1
-1
aG(x)dx
(7.4)
dx1
0
where: Ulam = internal energy of the laminated specimen
Udel
21
In
internal energy
specimen
of
the
partially
= length of the specimen.
practice,
the
integration
rate with respect to distance
necessary
for
this
from
approach.
of strain energy release
the
free
edge
integral
Since
not
width,
this
was equal to the difference between this quantity at
limits
determined
was
Since an output of the finite
element analysis was a value for energy per unit
the
delaminated
of
integration.
That
quantity
for a wide range of delamination
the
internal
energy
of
a
was
easily
sizes.
specimen
with
no
delamination is a constant, the strain energy release rate can
195
be
recovered
equation
identically
7.4 with
by differentiating the integral in
respect to the delaminated
a(Ulam-
Udel)
-=
adel
aAdel
area:
G(7.5)
SAde1
The integral which describes the difference in energy
between
the laminated and delaminated states can be written:
Ulam - Udel =
I
-1
An
analyze
observed
all the
analysis
can
G(x) dx dx1
0
triangular
delamination
delaminations
be
directly
in
this
applied
bordered
front
angle ply split.
schematically
In
the
was always
[-152n]
which
delaminated
triangles with other
The triangle
modeled
and
on
the
third
side
by
a
is modeled as perpendicular to the
model
of
the
delamination
is
shown
in Figure 7.6.
specimens
in
in this investigation,
to be totally delaminated
one sublaminate
(i.e. the [+15n ]
the [+±153]s and [±15n/O n]s specimens
sublaminate
sublaminates
ply,
The
observed
sublaminates
The
on one side by the free edge, on the second side
by a split in an angle
delamination
shape was used to
investigation.
to
dimensions or even more general shapes.
was
(7.6)
also
region.
in
the
[On/±15n]
and the
specimens).
These
contained an angle ply split bordering the
No load
can
be
transferred
into
this
196
N
REGION
REGION
FIGURE 7.6
SCHEMATIC MODEL OF THE DELAMINATION IN THE
ANALYSIS
197
portion
of
the
frictional
[0n/+15n]
ply
loading
of
specimens.
s
with
the possible exception of
[-15 2n]
the
sublaminate
in
the
This implies that this portion
of
the
is unloaded and contains no internal energy.
is indicated
the
sublaminate
as region A in Figure 7.6.
free edge and the delamination
loaded
by
in-plane
approximation,
Figure
7.6
the
is
shear
strain
set
The
region
between
front could conceivably
mechanisms.
level
This region
in
As
region B
equal to the strain level
the specimen at that longitudinal position.
a
as
be
rough
shown
in
for the rest of
Thus,
this
area
can be modeled with the two-dimensional finite element model.
The
unloaded
portion of a sublaminate
was modeled
finite element analysis by totally removing
that region.
This accounts
that portion of the
changes
An
The
finite
for
the
fact
for
the
original
The
that this portion
carried no load and contained
noted
energy
element
no
internal
modified
show
the
angle
actually containing
the
[-1 5 2n]
that
the
of the sublaminate
energy.
plies
As
release
was
The
intrude into the space
sublaminate.
Again,
this
change in internal energy for this condition
may be overestimated and therefore that the calculated
energy
mesh
finite element analysis, there is a
that
shows
in
mesh
complication with the model for the [On/±15n]s specimens.
results
in
example of the modified mesh for a
six ply specimen is shown in Figure 7.7.
accounts
elements
for the lack of internal
sublaminate.
accordingly.
the
in the
rate
is
an
upper bound.
release rate curves calculated for
the
strain
The strain energy
[±153]s,
[±1 5 n/ 0 n]s,
198
DELAMINATION
A
ANGLE
PLY
SPLIT
LOCATION
X2
I
!
DELAMINATION
SIZE
LY
NESS
FIGURE 7.7
MODIFIED FINITE ELEMENT MESH USED FOR A SIX PLY
LAMINATE WHICH ACCOUNTS FOR A PORTION OF A PLY TO
BE UNLOADED
199
and
[0n/±15n]s
an unloaded
specimens from the two-dimensional model with
portion
are shown in Figures 7.8,
7.9,
and 7.10,
respectively.
The
strain energy release rate curves calculated for the
[±1 5 3]s,
[±15n/On]s,
and
[On/±15n]s
specimens
using
geometrically integrated finite element model and the
delamination
configuration
Figures 7.11,
7.12, and 7.13, respectively.
the
curves
element
averages
of
generated
method
are
shown
asymptotes
assumed
in Figure 7.6 are shown in
The asymptotes
of
by the geometrically integrated finite
approximately
equal
to
the
(i.e. by the areas of regions A and B in
the
the
of
the
curves
weighted
Figure 7.6)
generated
by
the
two-dimensional finite element method.
7.4 Effects of Finite Specimen Size
The
modifications
to
the analysis
up to this point are
accurate for an infinitely wide and infinitely long
Delaminations
in
actual
specimens, however, have dimensions
which are not negligible when compared to
the
test section.
specimen.
the
dimensions
of
The primary assumption that breaks down is
that the strain level
is
positions.
implicitly assumed in the derivation of
This
is
a
constant
for
O'Brien's equation and in the selection of
all
a
longitudinal
two-dimensional
finite element in the virtual crack closure and finite element
methods.
In
actuality,
delaminated region is
the
local
substantially
compliance
higher
than
in
the
elsewhere.
200
4000
__
_
LJ
L-J
LU
3000
0
LL
2000
LLJ
z
zH
1000
LU
0
1:
0
I
I
I
5
10
15
20
DELAMINATION INTRUSION [MM]
FIGURE
7.8
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
DELAMINATION INTRUSION FOR A [+15 ] SPECIMEN
WITH A PARTIALLY UNLOADED [+153] U.LAMINATE
USING A TWO-DIMENSIONAL FINITE ELEMENT MODEL
201
I1
ACAA
;bUU
LU
O-
2000
Li
(-)
1500
I-LLJ
LJ
LJ
-
1000
-
CD
LU
500
-
LU
H
U3
I
0
0
$
I
I 0
II
15
20
DELAMINATION INTRUSION [MM]
FIGURE 7.9
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
DELAMINATION INTRUSION FOR A (±15/0] SPECIMEN
WITH A PARTIALLY UNLOADED [+15] SUBLRMINATE USING
A TWO-DIMENSIONAL FINITE ELEMENT MODEL
202
rl
2500
LLU
2000
LI
1500
L
LJ
1000
-
CD
500
-
LJ
I
0
0
,)
FIGURE 7.10
5
II
10
15
DELAMINATION INTRUSION
20
MM]
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
DELAMINATION INTRUSION FOR A [0/±15] SPECIMEN
WITH A PARTIALLY UNLOADED [-15] SUBLRMINATE
USING A TWO-DIMENSIONAL FINITE ELEMENT MODEL
203
r-1
oJ
8000
Li
LLJ
6000
LU
LU
-
4000
LL
CD
2000
LL
Wd
zH
0
0
CI)
FIGURE 7.11
I
I
I
I
10
20
30
40
50
DELAMINATION INTRUSION [MM]
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
DELAMINATION INTRUSION FOR A [+15 ]
SPECIMEN
USING A GEOMETRICALLY INTEGRATED IAITE ELEMENT
MODEL
204
m
"-1
2500
L-i
LU
2000
1 500
Ld
Qa
CD
LU
-J
1000
500
L1
CD)
ZL
zH
i7
0
I-o)
FIGURE 7.12
0
1
2
3
4
5
DELAMINATION INTRUSION [MM]
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
DELAMINATION INTRUSION FOR A [+15/0] SPECIMEN
USING A GEOMETRICALLY INTEGRATED FINITE ELEMENT
MODEL
205
m
2500
r-1
LLJ
p-
2000
Lr
1 500
J
LIJ
1000
CD
zLd
LL
H
0:
500
0
0
I)
F-
FIGURE
I
I
I
I
I
2
3
4
DELAMINATION INTRUSION
7.:13
5
MM]
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
DELAMINATION INTRUSION FOR A [0/+151 SPECIMEN
USING A GEOMETRICALLY INTEGRATED FINfTE ELEMENT
MODEL
206
Since
the
loading
is
quasistatic
displacement
controlled
loading, any delamination growth is accompanied by an increase
in
the local strain
decrease
This
level in the delaminated
in the local strain level in
behavior
delamination
The
laminated
region.
was observed experimentally in cases where the
occurred
far from the gage.
differential
evaluated
the
region and and a
change
explicitly.
The
in
internal
energy
must
be
internal energy can be expressed
as:
Udel=
}
2
U
C2
l 1E
Eloc dV
dV
(7.7)
where: Eloc = local longitudinal modulus
e11
= local longitudinal
strain.
After a differential change, the internal energy becomes:
Ude + dUdel
II
(
11
+ de1 1
)
( Eloc + dEloc ) dV(7.8)
After simplification and removal of higher order
terms,
this
becomes:
dUde1
An
-
|
( 2e11 Eloc de11 + C2
approximate
model
for
describing
dV
(7.9)
the longitudinal
207
level
strain
was
used.
The
strain level and modulus were
The
assumed to be functions solely of longitudinal position.
local
the
at each longitudinal
modulus
average
weighted
of the delaminated
the modulus
weighted
modulus
width)
was set equal to
of
values
the
for
the
delaminated regions. As with O'Brien's model,
and
laminated
(by
position
average
(by
of an unloaded
region was
thickness)
sublaminate
of
set
equal
to
the
the sublaminates.
was set to
zero
in
The
these
calculations.
It
becomes
convenient
terms of an average
level
level,
e
.
The
average
in
strain
is defined as the total applied displacement divided by
the specimen
c
where:
strain
to carry out all calculations
*
length:
6
21
(7.10)
S = total applied
displacement.
An effective specimen modulus can be defined in terms
of
the
resultant stress level at the given applied displacement:
Eeff =
*
(7.11)
where: Eeff = effective longitudinal modulus for the specimen
ao
= resultant
stress level.
It can be shown that the effective
modulus
is given by:
208
21
Eeff=
ocx)
d
(7.12)
1
-1
both sides of equation 7.9 are divided through by a
When
differential
change
in delamination
using
model
that
this
integrates
to
is
exactly
the
1
express
the
integrand
means
that
when
a
in
a
occurs
growth
in
strain
the energy obtained
in the
in
strain
the
decrease
increase
2
21
dc
to:
loc
dV
del
(7.13)
differentiating
the
In order to perform the integration
7.6.
strain
level,
the difference
between
, the ratio
)
=
tll 1
X
x
)
quantity
in
in terms of
is introduced
the square of the local
level and the square of the overall
6(x
in
corresponding
to
equivalent
overall
to
area is equivalent
ddel
equation
term
displacement loading, the energy
equivalent
dU del
dAd
=
is
be
the derivative of internal energy with respect
Thus,
to delaminated
This
can
this
region by
delaminated region by the
level.
it
delamination
in the laminated
released
level
of
quasistatic
under
specimen
Physically,
zero.
amount
differential
first
the
shown
area,
to
strain
strain level:
(7.14)
209
After
the
proper
substitutions,
the
expression for strain
energy release rate becomes:
G = dAd
I
(x
1
G(x,
)
) dx dx 1
(7.15)
The strain energy release rate curves generated
five
[±153] s
specimen
types
(i.e. widths
the five [+±15n/On]s specimens
and 8) are shown in Figures 7.15.
[On/±lSn]s
shown
specimens
in Figures
types
types
The
(i.e.
the
of 10 mm, 20 mm,
30 mm, 50 mm, and 70 mm) are shown in Figure 7.14.
for
for
The curves
(i.e. n = 1, 2, 3, 5,
curves
n = 1, 2,
for
the
3, 5, and
five
8)
are
7.16.
The shape of the curves for the [±15n/On]
and [0n/+15n]
s
specimens does not vary a great deal with increasing effective
ply thickness.
scaled
with
The curves
respect
major difference
to
are
for
effective
all
practical
purposes
ply thickness.
The only
in shape is related to the relative width
of
the interlaminar stress boundary region.
The
shapes
of the five curves for the [±153]
of nonstandard width are quite different.
thickness
is
the curves
is a function
For
The
the same for all the curves.
s
specimens
effective
The difference
of the aspect ratio of the
ply
in
specimen.
thin specimens, a delamination which stretches completely
across
the
specimen
specimen
length.
delaminated
region.
is
The
still
not
compliance
very
long
compared
to
is relatively high in the
Thus, the ratio of local
strain
in
the
210
40000
O MM
.........
LI
---- 20 MM
LLI
----
(M
F-
70 MM
---
I
LU
<C
/
/
/
I
MM
MM
30000 _
LUi
30
20000
/
I
/
t
/
/
/
CD
a
z
zH
10000
0.
'4
/
/0
- -
:.
-
-
-
-
--
-
-
---
-
-
-
llJ
0
I
I
10
20
I
I
CY
0
40
50
O)
DELAMINATION INTRUSION
MM]
FIGURE 7.14
30
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
DELAMINATION INTRUSION FOR [+15
SPECIMENS OF
NONSTANDARD WIDTH USING A GEOME4RiCALLY
INTEGRATED FINITE ELEMENT MODEL INCLUDING THE
EFFECTS OF FINITE SPECIMEN DIMENSIONS
211
U-
25000
Ill
LLJ
p-
20000
__
.
.
.........[:0 5/03 s
....
52/023s
C4.
53/03,3
-- Ci1l
E
55/053s
_ _Ci
(n) 15000
1
58/08)s
Lo
-
_
LL
.-,,,
10000
CD
LJ
_~~ _
_
,,,,,-......
-
- .
_
-
_-
_
000
--
_
Ii!
m ~m
mm
Lmm
~mm
~
~..
m
l
~
l
m
.m
m
m
~-
mm
m
m
m
I
m
~
l
m
~
m
l
LLJ
zH
ry
H
C--
FIGURE 7.15
0
0
I
I·
1I
I·
10
20
30
40
50
DELAMINATION INTRUSION [MM]
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
SPECIMENS
DELAMINATION INTRUSION FOR [+15 /0
USING A GEOMETRICALLY INTEGRATEB FN TE ELEMENT
MODEL INCLUDING THE EFFECTS OF FINITE SPECIMEN
DIMENSIONS
212
(J
\ esUUU
m'mAN
~
ILJ
F- 20000
....-
/
[0 2 / 15 2 3S
-'-.0
-
LLi
3 /&i153
C[Os/
(/) 15000
LLJ
_-
I
....-
IS_
E--
-
3S
5s]s
I
10000
CD
LL
Z
,ram
5000
LU
H
__r
_
_
_
_
_
_
_
,...............................
nl
U
0
10
20
30
40
50
DELAMINATION INTRUSION [MM]
FIGURE 7.16
STRAIN ENERGY RELEASE RATE AS A FUNCTION OF
DELAMINATION INTRUSION FOR (0 /+15
SPECIMENS
USING A GEOMETRICALLY LNTEGRA ED FNITE ELEMENT
MODEL INCLUDING THE EFFECTS OF FINITE SPECIMEN
DIMENSIONS
213
delaminated
the ratio
strains
region
to the average strain level and therefore
in Equation
7.15 is quite high.
The
high
local
imply high local energy density which in turn implies
a large amount
delaminated
of energy available
area.
Hence,
for
release
per
the strain energy release
unit
of
rate curve
rises rapidly with increasing delamination size.
In wider specimens, a
specimen
local
length
does
delamination
not necessarily
strain to average strain level.
specimen
ratio
has
the
most
the
imply a large ratio of
In fact,
most
curve
large
will
at
not
most
rise
longitudinal
rapidly.
of
the
and has a strain energy
positions.
In the limit,
infinitely wide specimen has no significant changes
modulus
of
a relatively high compliance, implying that the
will not be
Thus,
along
in
an
local
release rate curve such as the
one shown in Figure 7.11.
Care must be taken when determining
level
from data.
local
strain level
respect
the
The strain level obtained
and
is
affected
to the delamination.
by
overall
strain
from the gage is a
its
location
with
The overall strain level cannot
be inferred from the stroke data because of uncertainty
about
strain
shear
applied
deformation
during
gripping
of the relatively
and
significant
thick loading
level is an excellent parameter with which to
loading
situation,
tabs.
The stress
characterize
but care must be taken to divide
a
it by the
effective modulus rather than the nominal modulus to determine
the overall
The
strain level.
maximum
stress recorded
in each test in which growth
214
occurred
cannot
intrusion
of that test.
significant
be
In
fact,
there
is
undoubtedly
delamination
Although
at
the
the
of maximum
point
intrusion
intrusion
in the previous
observed
of
stress cannot be
definitively determined, it can be approximated in most
as the maximum
a
drop associated with delamination growth in
load
displacement controlled loading.
the
associated with the maximum
arbitrarily
cases
test of that
specimen.
7.5 Results
The strain energy release rate was
test
in
which
test.
detectable
calculation
no
methods
are
could
were
finite
finite
integrated
effects.
the
because
not
used:
element
be
the
size
of
determined.
O'Brien's
method
grew to a
the
Four
equation,
with
no
the
assumed
the geometrically integrated finite element method
unloading,
with
The case in which the delamination
initiation
two-dimensional
each
The intrusion used was the value from
size was not considered
delamination
for
the maximum intrusion increased in value from
the previous test.
previous
calculated
dimension
finite
element
effects,
method
and
with
the
geometrically
finite
dimension
The calculated values of strain energy release rate
given
for
various
the
Appendices I ([±+153]
s
methods
specimens),
of
calculation
J ([±15n/0n]s
in
specimens),
and K ([0n/±lSn]s specimens).
This
strain energy
release rate data can be used to plot
215
points
on a delamination resistance curve.
(O'Brien's
specimens using each calculation method
two-dimensional
finite
element
Plots for [153]
method
with
s
equation,
no
assumed
unloading, geometrically integrated finite element method with
no effects of finite specimen
finite
integrated
element
specimen
finite
method
each
using
calculation
method
through 7.24, respectively.
each
using
Plots
calculation
for
in
specimens
Figures 7.21
[0n/±15n]s
shown
are
Figures 7.17
[±15n/0n]s
shown
are
method
the effects of
in
shown
for
Plots
geometrically
including
are
dimensions)
through 7.20, respectively.
and
dimensions,
in
specimens
Figures 7.25
through 7.28, respectively.
7.6 Discussion
The critical value
cause the
delamination
independent
of
of
specimen
effective ply thickness.
curve
release
should
be
all
specimen
types
a
unit
width,
Thus,
relatively
four
However,
a
is
a
This
factor
should
be
delamination intrusion, and
the
flat
of
methods
area.
delamination
for
calculation
resistance
specimen type.
each
and
all
three
show a marked deviation from a constant value
in the experimental delamination resistance curve.
often
rate
the change in global internal energy necessary to
of
measure
of strain energy
of
two
or
There
is
more between values for similar
delamination sizes.
There
are
several
possible
sources
for
these
216
r-1
Lfi
2:
1000
-LI
LL
A
0
800
0
LL
_mO
600
LLJ
_J
LU
400
200
Ld
-i
I
0
0
10
I
20
0
30 MM WIDE
A
50
0
70 MM WIDE
MM WIDE
I
I
I
I
30
40
50
60
DELAMINATION INTRUSION
FIGURE 7.17
70
MM]
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE
RATE AS A FUNCTION OF DELAMINATION INTRUSION FOR
[±153]s SPECIMENS USING O'BRIEN'S METHOD
217
N
rl
1:
N'.
.AA
1 UUU
A
a
LLI
800
V
A*
LJ
30MM
800
WIDE
H
09
400
C9
Lu
200
LU
z
0
0
,)
FIGURE 7.18
o
a
30 MM WIDE
50 MM WIDE
0
70 MM WIDE
I
I
I
I
I
10
20
30
40
50
I
80
70
DELAMINATION INTRUSION [MM]
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE
RATE AS A FUNCTION OF DELAMINATION INTRUSION FOR
[+15
SPECIMENS USING A TWO-DIMENSIONAL FINITE
ELEMENT MODEL
218
r-
N-
2000
Li
LU
1 500
C,
LUj
LLJ
A
1000
3
LJ
H
bJ
x
cr.
500
0
Il
MM WIDEO
_
I
0
10
I
20
o
30 MM WIDE
A
O
50 MM WIDE
70 MM WIDE
I
I
I
30
40
50
_I _ _
60
70
an
DELAMINATION INTRUSION
FIGURE 7.19
MM
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE
RATE AS A FUNCTION OF DELAMINATION INTRUSION FOR
[+15
SPECIMENS USING A GEOMETRICALLY
INTEGRATED FINITE ELEMENT MODEL
219
r 1
57
-
L
1-
-m-__A_
Zuu
e
UU
o
0
2000
LY
O)
<;
o O
1500
A
O
J
LL
QY
Z
1000
500
LL
H
-0
f
u
03
FIGURE 7.20
0
10
0
30 MM WIDE
A
50
MM WIDE
O
70
MM WIDE
I
II
I
I
20
30
40
50
DELAMINATION INTRUSION
60
70
MM]
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE
RATE AS A FUNCTION OF DELAMINATION INTRUSION FOR
SPECIMENS USING A GEOMETRICALLY
[+15
INTEgRaTED FINITE ELEMENT MODEL INCLUDING THE
EFFECTS OF FINITE SPECIMEN DIMENSIONS
220
2000
V
LIJ
V
V
7
V
1500
0
0
LUJ
ob
LL
1000
II
yop
11*4
*
$e"
CD
zLJ
zH
LLJ
500
o
c1 1 5 /O3s
A
C
o
C153/033S
o
C 15S/0s3s
V
t
lw
I)nc
l
0
10
II
20
-
52/023s
4 158/08]s
I-
I
30
40
50
Y3
FIGURE 7.21
DELAMINATION INTRUSION EMM]
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE
RATE AS A FUNCTION OF DELAMINATION INTRUSION FOR
+±15n/0n]
s SPECIMENS USING O'BRIEN'S METHOD
221
rl
N
2000
U
V
V
V
L
V
v
1500
L
C')
L
0:
A
of
t~4o
1000
(1)
o
o
'aoo
LUj
II
z
o
EC15/03s
AO
Ei15
0
CI1:lS/Os3
o
El 56/O6 3s
v
ECilS/O3s
500
LUi
Z
H
0
FIGURE 7.22
2 /O 2
s
s
I
I
I
I
10
20
30
40
50
DELAMINATION INTRUSION
MM]
0
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE
RATE AS A FUNCTION OF DELAMINATION INTRUSION FOR
SPECIMENS USING A TWO-DIMENSIONAL
[+15 /0
FINI E ELgMENT MODEL
222
'N
J
5000
L-I
4000
-J 3000
(LL)
LLJ
Ln
z
z
2000
1000
Ld
-1
0
(I)
FIGURE 7.23
0
10
20
30
40
50
DELAMINATION INTRUSION MM]
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE
RATE AS A FUNCTION OF DELAMINATION INTRUSION FOR
[+15 /0
SPECIMENS USING A GEOMETRICALLY
INTE8RA Efo FINITE ELEMENT MODEL
223
I"-
5000
I:
N
LL
V
4000
V
_
LL
w
V
O
El
V
3000
V
-J
LJI
A
2000 _07
z
zH
c3
-
LI
0
Ci 15/03 S
&
C: S2/023
o
'v
CE:15 5 /0s
40
1000 _1
O Ci153 /0 3 3s
LLJ
0
(/)
FIGURE 7.24
S
5
s
C4 I 58//0 83
I
I
I
I
10
20
30
40
50
DELAMINATION INTRUSION
MM]
0
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE
RATE AS A FUNCTION OF DELAMINATION INTRUSION FOR
SPECIMENS USING A GEOMETRICALLY
[+15 /0
INTEBRAEb FINITE ELEMENT MODEL INCLUDING THE
EFFECTS OF FINITE SPECIMEN DIMENSIONS
224
N
2500
I-
V
LI
V
2000
0
v
0 03
LL)
1500
o0 o
Lui
-j
Li
A
A
1000
CD
LL
zLd
500
o
EO/ 153s
A
CO2 /+1523s
O
C03 /k 153 ] s
Wt
ZL
o
WL
v
zH
::
I
FIGURE 7.25
I_
10
20
EOs/1583s
I
40
50
DELAMINATION INTRUSION
MM]
0I
cn
II
COs0/5
1Sss
30
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE
RATE AS A FUNCTION OF DELAMINATION INTRUSION FOR
[0n/+15n]s SPECIMENS USING O'BRIEN'S METHOD
225
-
"%N
2500
LL
V
V
L:
2000
0
v
LL
Cr)
1 500
o
LL
A
A
1 000
C.D
-
z
LU
500 _
LL
zH
H
o
CO/k15] s
a
C02/m152 ]s
Z
C0O3 /
V
CEO/lS]
v
0
pnf
FIGURE 7.26
I
IC
153]s
s
co8/mlse]s
I
40
50
DELAMINATION INTRUSION
MM]
0
10
20
30
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE
RATE AS A FUNCTION OF DELAMINATION INTRUSION FOR
[0 /+15 ] SPECIMENS USING A TWO-DIMENSIONAL
FIRITE ELEMENT MODEL
226
N
rL
5000
4000
(i
o
E0/kI 5s
v
C02/523S
o
COs/ 1Ss] s
V
C08/1
5s
V
V
3000
0
O0
LI
-J
LJ
2000
aOo
O
A
I
W7
zH
1000
a
0
I
I
I
10
20
30
40
50
DELAMINATION INTRUSION [MM]
FIGURE 7.27
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE
RATE AS A FUNCTION OF DELAMINATION INTRUSION FOR
[0 /+15
SPECIMENS USING A GEOMETRICALLY
INTEGRATED FINITE ELEMENT MODEL
227
r
N
5000
u-i
4000
C:
L
3000
LLJH
Ld
2000
C,)
LU
zH
1000
0
O
V)
10
20
30
40
50
DELAMINATION INTRUSION EMM3
FIGURE 7.28
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE
RATE AS A FUNCTION OF DELAMINATION INTRUSION FOR
10 /+15 I SPECIMENS USING A GEOMETRICALLY
IN EGRA EB FINITE ELEMENT MODEL INCLUDING THE
EFFECTS OF FINITE SPECIMEN DIMENSIONS
228
discrepancies.
It
can
be
argued
that
many of the larger
delamination sizes correspond to growth after
loading
tab
and
it
therefore
may
be
growth
degree
delamination
of
scatter
sizes,
is
also
especially
to
Nonetheless, the
observed
for
the
inappropriate
characterize them with the models presented.
large
to
the
for
small
[+±15n/On]s
and
[0n/15 n]s specimens.
Some of the observed scatter may result
in
the
from
variations
material and from experimental procedures.
of magnitude of this variation should be
The order
approximately
equal
to the scatter observed for nominally identical specimens with
the same or similar delamination
variation
occasionally
data in Appendices
material
and
sizes.
The
amount
of
such
can be seen to be as much as 20% in the
I, J, and K.
experimental
the observed deviations.
It
is
thus
unlikely
that
variation is a primary source for
Two
70 mm
wide
[+153]s
specimens
with similar sized delaminations showed a large discrepancy in
the calculated critical value of strain
(34%),
but
energy
release
rate
in both cases the "delamination growth" was final
failure after
growth to the loading tab.
In such
cases,
the
applicability of the present models is questionable.
It
is
expected
that the critical
value of strain energy
release rate would be independent of effective ply
There
should
be
no
change
relative modal contributions to
when
the
lamination
effective
sequence.
ply
in
thickness.
the local constraint
strain
thickness
Nonetheless,
is
energy
release
changed
it
can
or the
rate
for a given
be
seen
in
229
Figures 7.21
through 7.28
that the experimental delamination
resistance curves calculated using
functions
of
effective
ply
these
models
thickness.
The
are
strong
dependence on
effective ply thickness would limit the utility of the general
approach
unless
it
can
be
shown that the resistance
determined for a thin laminate of a given specimen
in
general
specimens.
give
a
lower
bound
for
curve
type
will
the values of thicker
This appears to be the case for the laminate
types
in this investigation.
The experimental delamination resistance curve calculated
using these methods is also a strong
sequence.
Since
the
constraint
function
of
energy
release
rate
model, the calculated critical
release
rate
sequences.
could
be
were
However, it would not be
delamination
size
contributions
of
for
the
strain
different lamination
expected
for a given specimen
energy
to
type.
vary
substantially
for
a single specimen.
model
Figure 7.29.
Given
for
a
[O3/+153] s
specimen
is
state
shown
the
in
A clear upward trend is observed.
the
significant deviations from a constant strain
energy relase rate calculated from the data, it is
to
can
For example, the
experimental delamination resistance curve obtained using
present
with
It can be seen
from the data in Appendices I, J, and K, however, that it
vary
to
not incorporated into the
value
different
lamination
intact sublaminates on
damaged sublaminates and the relative modal
strain
of
impossible
definitively which strain energy release rate model
is most accurate.
The geometrically integrated finite element
230
m
5000
_
_
LI1
Cl)
4000
_
3000
_
LJ
w
p-
2000
_
CD
ry
LJ
1000 _
zH
(l1
Z>
0
0
I
I
I
I
10
20
30
40
50
DELAMINATION INTRUSION [MM]
FIGURE 7.29
EXPERIMENTAL VALUES OF STRAIN ENERGY RELEASE RATE
AS A FUNCTION OF DELAMINATION INTRUSION USING A
GEOMETRICALLY INTEGRATED FINITE ELEMENT MODEL
INCLUDING
THE
EFFECTS
OF
FINITE SPECIMEN
DIMENSIONS
231
method
with
corrections
for
the effects of finite specimen
dimensions should give more reliable results than the
which
do not account for delamination
finite specimen dimensions.
methods
shape or the effects of
However, with the
data
obtained
herein, this cannot be directly ascertained.
A
possible
extension
of the strain energy release rate
approach might involve the close
field
examination
of
the
stress
and strain energy release conditions near the angle ply
splits.
These splits
present
analysis.
were
I The
not
key
explicitly
modeled
to understanding
in
the
the process of
initiating and arresting dynamic delamination growth
may
lie
in determining the interaction of the angle ply splits and the
delamination.
angle
ply
The stress fields surrounding
the
tip
of
the
split bordering the delamination, the delamination
front, and any angle ply
delaminated
interface
split
which
in
a
ply
adjacent
to
the
is lying across the path of the
delamination front should be ascertained.
Other mechanisms may also be at work.
could
account
calculated
critical
specimens of
intrusion
for
the
value
different
size,
observed
they
effective
and different
The
between
the
be
thickness,
sequence.
totally
local
different
If some of
rather
than
might explain the different values obtained for
of the delamination
energy
ply
stacking
nominally identical specimens with
growth
difference
mechanisms
of strain energy release rate for
the mechanisms were shown to
global,
These
criterion
is
similar
is observed
a
necessary
intrusions.
to be a dynamic
but
not
The
event.
sufficient
232
condition
arrest
for
a
growth.
dynamic
ascertainable
from
is
hypothesis
The conditions necessary to start and
delamination
the
data
in
growth
this
that the delamination
Thei r
to reinitiate
growth.
DIB to
seep
hypothesized
the
splits
in
were not visible
were
the
adjoining
and
angle
in.
The
splits
delamination,
preceding
if
in the x-radiographs.
the
crack
opening
too small to allow a detectable
timing
the
of
the
formation
amount
of
of
of
these
is also unknown.
If they form away from
they
difficult
could
Alternatively, they could result
wave
One
investigation.
dynamic growth above the value needed for simple
However, this could be the result
splits
not
presence would then increase the energy needed
Suc h
these
are
front can be blunted
arrested when it runs across splits
plies.
event
be
dynamically
delamination front.
done to evaluate these possibilities.
from
to
a
detect.
stress
More work should be
233
CHAPTER
8
SUMMARY OF PRESENT WORK
Jamison's
composites
statement
[43]
is
an
regarding
eloquent
the
failure of advanced
summary
"Failure can be preceded by a complex and
ensemble
of
discrete
graphite/epoxy
damage
composites
of
the
interacting
modes."
that
it
has
work
has
of
is a complicated process which has
Research
several stages, each of which appears
reveal additional intricacies with every
present
global
Delamination
defied numerous attempts at simple explanation.
shown
problem:
attempted,
with
investigation.
has
to
The
some success, to resolve
issues of delamination initiation, growth, and final failure.
8.1 Delamination Initiation
Delamination
failure
of
Delamination
initiation
is
graphite/epoxy
initiation,
are in general necessary rather
release
fields.
mechanics
rate,
The
are
critical
induced
by
than
methodologies,
derived
delamination
in
be
insufficient
initiation
even
over
though
in
the
delamination.
to some
Nonetheless, energy criteria
sufficient
conditions.
such as the strain energy
terms
of
crack
tip
stress
initiation occurs, by definition,
without a preexisting interlaminar crack.
may
stage
like any event, is controlled
extent by energy considerations.
Fracture
a
large
Local stress levels
enough
initiation
areas
and
to form the
growth
may
be
234
energetically feasible.
The
existence of high stress gradients and possible weak
singularities near free
inappropriate.
edges
Inhomogeneity
makes
and
point
stress
initial flaw distribution
become potentially important micromechanical issues.
of
an
average
considering
a
effectively
stress
approach
large
enough
become
criteria
mitigates
region
unimportant.
Thus,
The
use
these effects by
that
an
these
issues
average
stress
approach can be used to characterize this complex behavior.
The Quadratic Delamination Criterion has been shown to be
an
acceptable
criterion
several reasons.
data
in
this
for
delamination
initiation
First, it gives excellent agreement
and previous [34] investigations.
for
of
the
Second, the
experimentally determined averaging dimension appears to be
material
parameter
parameter.
Fourth,
Third, the interlaminar normal strength
determined
the
a
by
potential
direct
experiment
importance
of
worked
well.
thermally-induced
interlaminar stresses and interlaminar
normal
demonstrated.
Quadratic Delamination
Criterion
is
It
appears
sufficient
that
to
the
describe
the
stresses
were
initiation
of
The Quadratic Delamination Criterion can thus be used
to
delamination in graphite/epoxy composites.
accurately
predict
delamination
taken, however, to include the
stresses
and
initiation.
must be
of
thermally-induced
interlaminar normal stress (
) as well as the
interlaminar shear stress (z).
effects
Care
235
8.2 Delamination Growth and Final Failure
Energy criteria are necessary but insufficient conditions
for delamination growth as well
The
data
in
this
delamination
as
investigation
initiation
before
delamination
show
that
there
can
initiation.
there
be
must be
delamination
growth.( Thus, the difference between initiation and growth is
that an interlaminar
crack is
fracture
methodologies
mechanics
release rate
initiation
more
likely
already
to
present.
such
apply
This
makes
as the strain energy
once
the
delamination
has formed.
Laminates
with
greater
effective
shown to be susceptible to delamination
stresses.
These
interlaminar
susceptible to
laminates
stress
near
have
the
delamination
ply thicknesses were
initiation
larger
free
regions
edge.
initiation,
at
of
Thus,
growth,
lower
high
they are
and
final
failure at lower stresses, as was shown experimentally.
The analysis described in Chapter 7 contains more details
of
the
observed
damage
state
than
previous
models
evaluating the strain energy available for release at
delamination
sizes.
Unfortunately,
any
in
various
increased accuracy
cannot be adequately evaluated with the available
data.
The
theoretical curves of strain energy release rate as a function
of delamination intrusion
delamination
shape
possibility.
in
Chapter 7
show
that
and finite specimen dimensions may affect
delamination growth.
this
depicted
The previous models did not account
for
The experimentally determined delamination
236
resistance
curves indicated that the critical value of strain
rate
energy release
stacking
thickness,
be
can
reasoned
was
not
constant
sequence, or delamination intrusion.
that
(with
factors
these
the
in
modifications
methods
analytical
It
possible
the
value.
exception of stacking sequence) should not affect this
Thus,
ply
effective
with
not
were
sufficient to explain the observed behavior.
There
release
energy
strain
investigation.
between
in the
at work which are not modeled
are phenomena
rate
approaches
resin
The delamination grows in a thin
two inhomogenous layers.
in
used
It
is
important
layer
These layers can affect the
crack
global and local stress fields and present obstacles to
extension.
this
that
phenomenon
these
be
investigated.
These
modes.
The most
splitting.
at
neighboring
their
plies are subject to their own damage
prevalent
one
in
this
investigation
In most cases, the delaminations induced splitting
boundaries
and
within
the
delaminated
Depending on the orientation with respect to the
front,
splits
that
region.
delamination
form ahead of the delamination front can
blunt it and hinder its advance.
parts
was
Designers must
be
wary
as
which are not susceptible to these phenomena may suffer
growth at significantly lower stresses.
The evidence shows that the delamination
ply
split
interact
and
the
angle
strongly.,iFor example, the ability of a
split to arrest delamination growth across it is
by the fact that one side of the delaminations
demonstrated
of the [±153] s,
237
[+±15n/0n]s
ply
[0n/±15n]s specimens was bounded by an angle
and
split.
The
details
of
investigated
both
analytical
investigation
this
analytically
critical
delamination
growth of any specimen type.
The
experimentally.
a
full
models
the
include
which
analysis
be
size was found for the unstable
rate
release
The strain energy
calculated using the modified analysis did not exhibit
curves
the local minimum needed for a
as
illustrated
stable
critical
specimens
The
feature.
of specimen width
conceivable,
strain
however,
that any
this
exhibit
of nonstandard width experienced no
on
final
stress.
failure
It
is
that, since specimen width affects the
energy
release
rate,
final
failure
in
therefore
delamination
It is unlikely
in Figure 2.4.
model based solely on global stress fields will
effect
should
and the angle ply splits.
delamination
size
and
might
three-dimensional finite element
No
interaction
it
some
could
delay
specimen
growth
and
If
the
types.
controlling parameters for initiating and arresting growth are
determined
on a local level, there may be no definitive
global
value for critical delamination size.
delamination failure is relatively straightforward
Final
Final
to describe but rather complicated to actually predict.
failure
can
delaminated
only
occur
sublaminates
of
the
is exceeded in a local region.
The
if
the
in-plane
complications lie in determining how and
and
what
determining
the
resulting
the
local
in-plane
stress
stresses
strength
growth
when
fields are.
as
a
occurs
Only by
function
of
238
delamination
size
and
shape
can
an
engineer
accurately
forecast what delamination damage will trigger final failure.
The
constraint
sublaminates
therefore
can
by
affect
important.
specimens,
the
intact
the
For
[On/+15n]
sublaminates
local
stress
example,
in
sublaminates
on
damaged
state
and
the
had
[0n/±15n]s
a
significant
effect on the damaged [-1 5 2n] sublaminates.
constraining
constraint enabled the damaged sublaminate
the laminate strength and stiffness.
to
is
contribute
The
to
In contrast, the damaged
sublaminates in the [+15n/On]s specimens peeled away,
leading
to lower laminate stiffness and strength.
The
only
differences
for the fabric specimens were the
different characteristics of the ply interfaces, yet there was
a
significant
change
in
release rate
model
predict
difference
any
specimen types.
delayed
in
the
used
failure stress.
in
in
this
The strain energy
investigation
growth
would
behavior between the two
Nonetheless, unstable delamination growth was
specimens
with
warp
faces at the critical
interface.
This in turn lead to delayed final failure.
emphasizes
the
necessity
state of stress
not
and
This
of modelling the three-dimensional
interaction
of
the
delaminations
and
splits.
Since
delamination
delamination
growth
initiation,
it
may
applications to keep design stresses
initiation
stress.
An
appropriate
cannot
be
below
post
occur
advisable
the
without
in
most
delamination
first ply failure
239
criterion
and
may
stiffness
be to assume that a part has only the strength
characteristics
sublaminate.
However,
nonconservative
if
this
of
the
could
strongest
intact
potentially
be
partially failed neighboring sublaminates
can induce stress concentrations in the critical sublaminate.
240
CHAPTER
9
CONCLUSIONS AND RECOMMENDATIONS
The
progression
of
damage
in graphite/epoxy specimens
leading to failure induced by delamination
and
analyzed.
has
been
studied
The data presented herein have resulted in the
following conclusions:
1.
Delamination
stages:
is the result
delamination
of
a
progression
initiation,
of
delamination
damage
growth, and
final in-plane failure of the delaminated sublaminates.
2.
Delamination initiation can be accurately
predicted
with
the Quadratic Delamination Criterion.
3.
The
averaging
Criterion
dimension
appears
to
in
be
the
a
Quadratic Delamination
material
interlaminar strength parameters appear to
the
values
measured
directly
in
parameter.
be
The
equivalent
interlaminar
to
strength
experiments.
4.
Thermally-induced
in delamination
interlaminar
interlaminar
initiation
stresses
stresses must be included
calculations.
alone
can
Thermally-induced
cause
delamination
initiation.
5.
The Quadratic Delamination Criterion is
valid
even
when
241
the
strain
energy available for release is greater than that
needed to make initiation energetically feasible.
criterion
is
thus a necessary
but insufficient
The
energy
condition
for
prerequisite
to
delamination initiation.
6.
Delamination
initiation
is
a
necessary
delamination growth.
7.
No
critical
delamination
size for unstable delamination
growth or final failure was observed.
8.
There was no observed effect of specimen width on
failure
stress.
9.
Thicker laminates have larger regions of high interlaminar
stresses and therefore tend to suffer delamination initiation,
accumulate damage, and fail at lower stresses.
10.
The
final failure of graphite/epoxy specimens in tension
is
an
in-plane
strength
phenomenon.
The
delamination growth and the constraint by intact
on
damaged
sublaminates
stress
failure.
sublaminates
sublaminates.
The
state must be known to accurately predict final
Delaying delamination
final failure.
of
must be known in order to determine
the local stress state in the delaminated
local
amount
growth
can
therefore
delay
242
11.
The
current
strain
energy
release
rate
model
is
insufficient to properly model delamination growth.
12. There is a strong interaction between the delamination and
the angle ply
splits.
split.
Depending
delamination
on
front,
delamination
Delaminations
the
relative
angle
growth
can
ply
or
induce
orientation
failure.
This
ply
of
the
splits can either facilitate
hinder
its
advance.
characteristics can therefore affect delamination
final
angle
interaction
must
Interface
growth
and
be fully modeled to
achieve more acceptable results.
Although several important aspects of failure induced
delamination
before
have
final
been
failure
identified, more knowledge is needed
can
be
accurately
extension of this knowledge to realms of
quasistatic
uniaxial
considered.
The
by
tensile
following
predicted.
loading
loading
other
should
recommendations
are
also
The
than
be
therefore
made:
1.
The mechanisms for arresting delamination growth should be
investigated and analyzed.
Useful
experimental
information
might be gained from specimens with implanted angle ply splits
placed strategically in specimens in an attempt
the arrest
2.
The
of a delamination
three-dimensional
to
duplicate
front.
state
of
stress
and the related
243
strain
energy
release
rate
conditions,
including relative
modal contributions, should be analyzed for
the
delamination
region
front and the angle ply split.
case of a "blunted" delamination
with
the
front might be
near
The special
investigated,
special attention paid to the tip of the angle ply split
as the extension
of this split may be the key to
reinitiating
delamination growth.
3.
The
applicability
of these conclusions
situations should be evaluated.
of
"fatigue
limits"
for
determined to ascertain
each
the
to cyclic
Specifically,
the
loading
existence
delamination stage should be
damage
tolerance
of
composite
parts to early stages of delamination damage.
Some
questions
have
been answered regarding failure of
graphite/epoxy induced by delamination.
done
to
give
engineers
the
tools
More
they
work
need
must
to
be
avoid
delamination in efficiently designed aerospace structures.
244
REFERENCES
B. T.,
1. Rodini,
and
Eisenmann,
and
J. R., "An Analytical
of
Edge Delamination in
Investigation
Experimental
Composite Laminates," Proceedings of the Fourth Conference
Structural
Design,
1978,
on Fibrous Composites in
San Diego, California, pp. 441-456.
T.,
2. Johannesson,
P.,
Sjbblom,
and
R.,
Seld6n,
"The
Detailed Structure of Delamination Fracture Surfaces in
Graphite/Epoxy Laminates," Journal of Materials Science,
Vol. 19, 1984, pp. 1171-1177.
R.
3. Pipes,
"Influence
B.,
Kaminski,
B.
E.,
Pagano,
and
N.
J.,
of Angle-Ply
of the Free Edge upon the Strength
Laminates," Analysis of Test Methods for High Modulus
Fibers and Composites, ASTM STP 521, American Society for
Testing and Materials, 1973, pp. 218-228.
4. Kim, R. Y., and Soni, K. Y., "Experimental and Analytical
Studies On the Onset of Delamination
in
Laminated
Composites," Journal of Composite Materials, Vol. 18,
1984, pp. 70-80.
5. Rybicki,
E. F., Schmeuser,
Release Rate Approach
Free-Edge Delamination
Materials,
6. Wang,
D. W., and Fox, J., "An
for Stable Crack
Problem," Journal
Energy
Growth in the
of Composite
Vol. 11, 1977, pp. 470-487.
A. S. D.,
and
Crossman,
F. W.,
"Initiation
and
Growth of Transverse Cracks and Edge Delamination in
Composite Laminates. Part 1. An Energy Method," Journal
of Composite
pp. 71-87.
Materials,
Vol. 14
Supplement,
1980,
7. Tsai,
S. W.,
and Hahn, H. T., Introduction to Composite
Materials, Technomic Publishing Co., Inc., 1980.
8. Rybicki, E. F., "Approximate Three-Dimensional Solutions
for Symmetric Laminates Under In-Plane Loading," Journal
of Composite
Materials,
Vol. 5, 1971, pp. 354-360.
9. Wang, A. S. D., and Crossman,
F. W.,
"Some New Results
in
Edge Effects in Symmetric Composite Laminates," Journal of
Composite
Materials,
Vol. 11, 1977, pp. 92-106.
10. Pipes, R. B., and Pagano, N. J., "Interlaminar
Composite
Laminates
of
Journal
pp. 538-548.
Under
Composite
Uniform
Axial
Materials,
Vol.
Stresses
in
Extension,"
4,
1970,
245
N. J.,
11. Pagano,
Sequence
Composite
Materials,
12. Puppo,
A. H.,
Pipes,
R.
B.,
of
of
Journal
"Interlaminar
Shear in
Generalized
Plane
Stress,"
Materials,
Vol. 4,
H. A.,
Under
Composite
and
Influence
Strength,"
Vol. 5, 1971, pp. 50-57.
and Evensen,
of
Journal
pp. 204-220.
"The
R. B.,
Laminate
on
Composites
Laminated
13.
Pipes,
and
Stacking
N. J.,
Pagano,
"Interlaminar
1970,
Stresses
in
Approximate Elasticity Solution," Journal
September 1974,
Mechanics,
Vol. 41,
Composites - An
of
Applied
pp. 668-672.
14. Hsu,
P. W.,
and
C. T.,
Herakovich,
"A
Perturbation
Solution for Interlaminar Stresses
in
Bidirectional
Design
Testing and
Laminates," Composite Materials:
(Fourth Conference), ASTM STP 617, American Society for
15.
Testing
and Materials,
Pagano,
N.
Model,"
J.,
and
1977, pp. 296-316.
Soni,
International
S. R.,
Journal
Variational
"Global-Local
of Solids and Structures,
Vol. 19, No. 3, 1983, pp. 207-228.
Method
16. Kassapoglou, C., and Lagace, P. A., "An Efficient
for the Calculation of Interlaminar Stresses in Composite
Materials,"
December
Journal
of
Applied
Mechanics,
Vol. 53,
1986, pp. 744-750.
17. Kassapoglou, C., and Lagace, P. A., "Closed Form Solutions
and
Field
in
Angle-Ply
Stress
for the Interlaminar
Cross-Ply
Laminates,"
Vol. 21, 1987,pp.
18. Lagace,
Journal
of
Composite
and
Brewer,
Materials,
292-308.
P. A., Kassapoglou,
C.,
J. C.,
"An
Efficient Method for the Calculation of Interlaminar
in Composite Materials Due to Thermal and
Stresses
Mechanical Effects," International Symposium on Composite
Materials and Structures, Beijing, China, June 1986.
S. S., and Choi,
19. Wang,
Laminates:
Composite
Singularities,"
September
20. Herakovich,
Journal
of
Applied
Mechanics, Vol. 49,
1982, pp. 541-548.
C. T.,
Strength of Angle-Ply
Materials,
I., "Boundary-Layer Effects in
Edge
Stress
Part 1 - Free
"Influence
Layer
of
Laminates,"
Journal
Thickness
of
on
Composite
Vol. 16, 1982, pp. 216-226.
under
Tensile
21. Lagace, P. A., "Delamination Fracture
Loading," Proceedings of the Sixth Conference on Fibrous
Composites
in Structural Design, AMMRC MC 83-2, Army
Materials and Mechanics Research Center, November 1983.
246
F. W.,
22. Crossman,
Warren,
W. J., Wang, A. S. D., and Law,
G. E., "Initiation and Growth of Transverse Cracks and
Part 2.
Laminates.
Composite
Edge Delamination in
Experimental Correlation," Journal of Composite Materials,
1980, pp. 88-108.
Vol. 14 Supplement,
F. W., and Wang, A. S. D.,
23. Crossman,
"The
Dependence
of
Transverse Cracking and Delamination on Ply Thickness in
Graphite/Epoxy Laminates," Damage in Composite Materials,
ASTM STP 775, American Society for Testing and Materials,
1982, pp. 118-139.
Crossman,
A. S. D.,
24. Wang,
and
F. W.,
G. E.,
Law,
"Interlaminar Failure in Epoxy Based Composite Laminates,"
Design and Applications, National
Advanced Composites:
Special Publication 563, 1979,
Standards
of
Bureau
pp. 255-264.
25.
Kim,
K.
S.,
and
C. S.,
Hong,
Journal
Laminated
Materials,
Vol. 20, 1986, pp. 423-438.
26. O'Brien,
Growth
"Delamination
Composites,"
Angle-Ply
of
T. K., "Characterization
in
Composite
of
Onset
Delamination
and Growth in a Composite Laminate," Damage in Composite
Materials, ASTM STP 775, American Society for Testing and
1982, pp. 140-167.
Materials,
27.
O'Brien,
T.
Simonds,
R. A.,
K.,
Johnston,
N.
J.,
Morris,
D.
"A Simple Test for Interlaminar
H.,
and
Fracture
Toughness of Composites," SAMPE Journal, July/August 1982,
pp. 8-15.
28. O'Brien, T. K., "Mixed-Mode Strain-Energy-Release
Edge
Delamination of Composites,"
on
Effects
Technical Memorandum 84592, January 1983.
Rate
NASA
D. H.,
and
29.
T. K.,
O'Brien,
Johnston,
N. J.,
Morris,
Simonds, R. A., "Determination of Interlaminar Fracture
Toughness and Fracture Mode Dependence of Composites using
the
Edge
Delamination
Test,"
Proceedings
of
the
Conference of Testing, Evaluation, and
International
Quality Control of Composites, University of Surrey,
Guilford, England, September 1983, pp. 223-232.
30. Broek, D., Elementary
Third Edition, Martinus
1982,
p.
31. Whitney,
Engineering Fracture Mechanics,
Nijhoff Publishers, The Hague,
17.
J. M.,
and
Nuismer,
R. J.,
"Stress
Fracture
for
Laminated Composites Containing Stress
Criteria
Concentrations," Journal of Composite Materials, Vol. 8,
1974, pp. 253-265.
247
32. Kim,
R. Y.,
and
Soni, K. Y., "Delamination
Laminates Stimulated
Materials:
Testing
of Composite
by Interlaminar Shear," Composite
and Design (Seventh
Conference),
ASTM STP 893, 1984, pp. 286-307.
33. Soni,
K. Y.,
and
Kim,
R. Y.,
"Failure
of
Composite
Laminates due to Combined Interlaminar Normal and Shear
Stresses," Composites '86: Recent Advances in Japan and
the United States, 1986, pp. 341-350.
34. Brewer,
J. C.,
and
Lagace,
P. A.,
"Quadratic
Stress
Criterion for Initiation of Delamination," submitted to
Journal of Composite Materials
35. Lagace,
P. A., and Weems,
D. B., "A
Through-the-Thickness
Strength Specimen for Composites," Proceedings of the ASTM
Second Symposium on Test Methods and Design Allowables,
Phoenix, Arizona, November 1986.
36. Klang,
E. C.,
and
Hyer,
M. W.,
"Damage
Initiation
at
Curved Free Edges:
Applications to Uniaxially Loaded
Plates Containing Holes and Notches," Proceedings of the
ASTM Second United States-Japan Symposium on Composite
Materials, Hampton, Virginia, June 1983.
37. Lagace,
P.,
Brewer, J., and Kassapoglou,
of Thickness on Interlaminar Stresses an
Straight-Edged
Laminates,"
Journal
Technology
pp. 81-87.
38. Tsai,
and
Research,
S. W., and Wu,
Strength
of
Materials,
39. Lagace,
E. M.,
Vol. 9,
"A
C., "The Effect
Delamination in
of
Composites
No. 3,
Generalized
Fall 1987,
Theory
for
Anisotropic Materials," Journal of Composite
Vol. 5, 1971, pp. 58-80.
P. A., Brewer, J. C., and Varnerin,
C. F.,
"TELAC
Manufacturing Course Notes,"
Edition 0-3,
Technology
Laboratory
for
Advanced
Composites,
Report 88-4,
Massachusetts Institute of Technology, September 1987.
40. "Standard
Test
Method
for
Tensile
Properties of
Fiber-Resin
Composites,"
ASTM Designation D 3039-76,
American Society for Testing and Materials, 1976.
41. Russell, A. J., and Street, K. N., "Factors Affecting the
Interlaminar Fracture Energy of Graphite/Epoxy Laminates,"
Progress
in
Science and Engineering of Composites,
Proceedings of the Fourth International Conference on
Composite Materials, Tokyo, 1982, pp. 279-286.
42. Orringer, O., and French, S. E., Finite Element Analysis
Basic Library User's Guide, Aeroelastic and Structures
Research Laboratory,
Department
of
Aeronautics and
248
Astronautics, Massachusetts
Cambridge, MA, 1972.
43. Jamison,
R. D.,
"The
Role
Institute
of
Microdamage
Failure of Graphite/Epoxy Laminates,"
and Technology,
of
Technology,
in
Composites
Vol. 24, 1985, pp. 83-99.
Tensile
Science
249
DATA TABLE 1
FABRIC/UNIDIRECTIONAL SPECIMENS
Specimen
Thickness
Width
Modulus
[mm]
[mm]
[GPa]
Delamination
Initiation
Stress
[MPa]
OU5F1-0-1
0U5F1-O-2
OU5F1-O-3
OU5F1-0-4
OU5F1-0-5
(1.2%)c
49.90
49.86
49.84
49.90
49.88
49.88
(0.05%)
2.23
2.20
2.20
2.17
2.18
2.20
(1.0%)
49.88
49.79
49.91
49.87
49.73
49.83
(0.15%)
3.28
3.27
3.29
3.26
3.30
3.28
(0.5%)
49.87
49.83
49.98
49.87
50.03
49.92
(0.17%)
1.99
1.98
2.00
1.94
1.96
1.97
OU5F1U1-O-1
OU5F1U1-0-2
OU5F1U1-0-3
OU5F1U1-0-4
OU5F1U1-0-5
OU1OFl-O-1
OU10OF1-0-2
OU10OF1-0-3
OU10OF1-0-4
OU10OF1-0-5
115
114
121
112
121
117
(3.6%)
119
117
118
117
121
118
518
523
493-841 a
547-1048 a
544
Delamination
Initiation
Strain
[pstrain]
4320
4518
4020-67 14 a
4764-9240 a
4398
4412
(2.3%)
528
(2.6%)
503-755a
431-747 a
448-717 a
441-717 a
435-786 a
a
451-744
4152-6204 a
3570-6036a
3840-6156 a
3756-5982a
5604-10131a'
4182-6902a
(1.4%)
126
117
123
123
120
122
e
e
e
e
e
e
e
e
e
e
(2.8%)
aBounded values - an exact delamination initiation point was not found.
bData from bounded values not included.
cNumbers in parentheses are coefficients of variation.
Final strain value was estimated - strain gage was broken.
eDelamination existed before mechanical loading.
250
DATA TABLE 2
NONSTANDARD WIDTH (±153]s SPECIMENS
Specimen
Thickness
[mm]
315A0-W10-1
315A0-W10-2
315A0-W10-3
315A0-W10-4
315A0-W10-5
315A0-W10-6
315A0-W10-7
1.58
1.55
1.54
1.58
1.62
1.64
1.51
1.57
(2.9%)a
315A0-W20-1
315A0-W20-2
315A0-W20-3
315A0-W20-4
315A0-W20-5
315A0-W30-1
315A0-W30-2
315A0-W30-3
315A0-W30-4
315A0-W30-5
315A0-W30-6
315A0-W30-7
315A0-W50-1
315A0-W50-2
315A0-W50-3
315A0-W50-4
315AO-W50-5
315A0-W70-1
315A0-W70-2
315A0-W70-3
315A0-W70-4
315A0-W70-5
1.53
1.52
1.48
1.51
1.59
1.53
(2.6%)
Width
Modulus
[mm]
[GPa]
10.20
10.14
10.16
10.14
10.15
10.15
10.12
10.15
(0.24%)
20.11
20.15
20.21
20.24
20.18
20.18
(0.25%)
105
113
101
113
127
128
115
115
(8.8%)
115
118
113
114
120
116
(2.5%)
490
486
501
505
501
537
538
4458
(4.1%)
509
527
494
484
4290
4632
4146
4026
4140
4662
(5.8%)
4374
4404
4416
4236
496
502
(3.3%)
(2.7%)
4158
4318
4308
4410
124
510
112
113
526
534
(0.30%)
(4.0%)
1.52
1.53
1.54
1.58
1.53
50.14
110
109
50.18
50.18
50.23
50.12
50.17
[(strain]
508
487
501
(2.7%)
29.94
30.04
[MPa]
537
30.08
30.17
30.13
29.94
30.00
Failure
Strain
120
116
112
113
1.66
1.59
1.56
1.56
1.64
1.55
1.58
30.04
Failure
Stress
4356
4404
4092
4590
4278
4348
111
112
109
(3.6%)
(3.5%)
497
4536
508
488
526
507
4626
4392
4656
4788
rIr
(1.5%)
(0.08%)
1.56
1.54
1.50
1.49
1.62
69.60
70.03
69.96
113
109
452
509
4020
4572
105
501
5004
70.05
69.97
104
118
69.98
rT0
(0.08%)
(5.3%)
(3.4%)
(1.2%)
(2.8%)
450
529
(7.3%)
aNumbers in parentheses are coefficients of variation.
4600(3.2%)
4236
5604
4687
(13.5%)
251
DATA
TABLE
3
[ +15n/0 n ] s SPECIMENS
Thickness
Specimen
[mm]
15A1-0-1
15A1-0-2
15A1-0-3
15A1-0-4
15A1-0-5
0.87
0.84
0.88
0.88
0.84
0.86
(2.4%)a
215A1-0-1
215A1-0-2
215A1-0-3
215A1-0-4
215A1-0-5
1.54
1.48
1.61
1.69
1.62
.59
(5.1%)
315A1-0-1
315A1-0-2
315A1-0-3
315A1-0-4
315A1-0-5
2.27
2.29
2.46
2.40
2.27
2.34
(3.7%)
515A1-0-1
515A1-0-2
515A1-0-3
515A1-0-4
515A1-0-5
815A1-0-1
815A1-0-2
815A1-0-3
815A1-0-4
815A1-0-5
aNumbers
in
Broken gage
Width
[mm]
50.11
49.90
49.25
50.10
49.17
49.71
(0.93%)
50.14
50.18
50.10
50.25
50.24
50.18
(0.13%)
50.06
50.03
50.21
49.75
49.54
49.92
(0.54%)
4.11
4.03
4.11
3.87
3.69
3.96
(4.6%)
(0.37%)
6.59
6.60
50.20
50.19
6.64
6.53
6.40
6.5(1.4%)
49.98
parentheses
50.08
50.13
50.09
50.21
49.73
50.05
50.29
50.02
50.12
(0.25%)
Modulus
[GPa]
127
122
130
124
120
Failure
Stress
Failure
Strain
[MPa]
[pstrain]
(3.2%)
1072
1016
941
1033
954
1003
(4.1%)
115
117
125
132
119
122
(5.7%)
680
706
825
793
732
747
(8.1%)
121
118
132
127
118
123
(5.0%)
123
118
128
115
103
17
(8.0%)
120
116
123
112
105
T15
(6.1%)
are coefficients
8386
8298
7086
8058
7848
7935
(6.5%)
5862
5880
7410
6516
5892
(10.7%)
592
672
698
622
624
(6.6%)
b
7608
6114
5112
5154
(19.5%)
599
528
4962
7134
5520
5832
4680
(10.5%)
(17.0%)
544
545
558
535
522
4710
5256
4620
6090
5010
616
707
642
5137
541
(2.5%)
(11.5%)
of variation.
252
DATA TABLE 4
[0n/±15n]s SPECIMENS
Specimen
Thickness
[mm]
15B1-0-1
15B1-0-2
15B1-0-3
15B1-0-4
15B1-0-5
215B1-0-1
215B1-0-2
215B1-0-3
215B1-0-4
215B1-0-5
315B1-0-1
315B1-0-2
315B1-0-3
315B1-0-4
315B1-0-5
515B1-0-1
515B1-0-2
515B1-0-3
515B1-0-4
515B1-0-5
815B1-0-1
815B1-0-2
815B1-0-3
815B1-0-4
815B1-0-5
0.84
0.84
0.88
0.86
0.83
0.85
Width
Modulus
[mm]
[GPa]
Failure
Stress
Failure
Strain
[MPa]
[pstrain]
(2.4%)a
49.78
50.03
49.69
50.20
50.13
49.97
(0.44%)
123
122
131
123
122
124
(3.1%)
1177
1203
1140
1106
1176
1160
(3.3%)
9396
9594
8490
8550
9108
9028
(5.5%)
1.53
1.50
1.64
1.64
1.56
1.57
(4.1%)
50.16
50.00
50.26
50.31
49.89
50.12
(0.35%)
118
115
132
130
118
123
(6.4%)
908
802
856
891
859
863
(4.7%)
7560
6768
7674
8484
6828
7463
(9.4%)
2.29
2.38
2.53
2.35
2.25
2.36
(4.6%)
50.16
50.24
50.22
50.08
50.25
50.19
(0.14%)
725
727
694
792
860
6228
6144
4932
7302
8244
(8.8%)
(19.1%)
4.09
4.02
4.06
3.67
3.41
3.85
(7.8%)
50.23
50.13
50.14
49.88
50.10
50.10
(0.26%)
718
681
600
702
643
669
(7.1%)
6810
6564
4668
7098
(15.1%)
6.80
6.57
6.40
5.91
5.50
50.12
50.14
50.14
50.20
50.13
50.15
(0.06%)
659
631
640
581
577
618
(5.9%)
4998
5202
5220
5592
5844
5371
(6.3%)
(8.4%)
120
119
140
122
114
(8.1%)
126
126
131
108
103
IT
(10.5%)
130
120
126
103
92
114
(14.1%)
6306
6289
aNumbers in parentheses are coefficients of variation.
253
DATA TABLE 5
[±20f]s FABRIC SPECIMENS
Specimen
Thickness
[mm]
F20F-0-1
F20F-0-2
F20F-0-3
F20F-0-4
F20F-0-5
[mm]
1.39
1.41
1.41
1.41
1.39
Modulus
[GPa]
Failure
Stress
Failure
Strain
[MPa]
[pstrain]
50.24
50.24
50.23
50.20
50.24
50.23
58
53
58
56
55
56
(0.8%)
(0.03%)
(3.8%)
1.39
1.41
1.42
1.42
1.40
1.41
(0.9%)
50.16
50.20
50.24
50.24
50.27
50.22
60
55
54
52
55
530
9984
9954
9348
9895
(0.08%)
(5.3%)
(4.0%)
(5.2%)
1 4
F20W-0-1
F20W-0-2
F20W-0-3
F20W-0-4
F20W-0-5
Width
a
55
467
488
471
452
473
470
(2.7%)
545
551
540
513
502
9258
10638
8832
8436
9294
9291
(8.9%)
9516
10674
aNumbers in parentheses are coefficients of variation.
254
DATA TABLE 6
[03/+153]s SPECIMENS WITH IMPLANTED DELAMINATIONS
Specimen
Thickness Width Intrusion Intrusion Modulus Failure Failure
[mm]
[mm]
of the
of the
[GPa] Stress Strain
[MPa]
[pstrn]
Implanted Implanted
Delamination Angle
[mm]
Ply Split
[mm]
315B1-DlO-AO-1
315B1-D10O-AO-2
315B1-DlO-AO-3
315B1-D10-AO-4
315B1-DlO-AO-5
315B1-DlO-AO-6
315B1-D10O-A20-1
315B1-D10O-A20-2
315B1-D10O-A20-3
315B1-D10O-A20-4
315B1-D10O-A20-5
315B1-D10O-A20-6
49.84
2.22
14
50.02
2.22
16
49.91
2.16
16
15
2.20
49.92
49.87
2.18
13
49.98
2.26
16
49.92
2.21
15
(1 .6 %)a (0.13%) (8.4%)
2.21
2.24
2.20
2.16
2.24
2.23
2.21
(1.4%)
50.03
14
12
50.13
46.05
10
50.03
14
50.19
14
50.19
15
49.44
13
(3.36%) (13.9%)
116
111
111
115
110
119
114
(3.1%)
26
25
26
26
27
25
26
(2.9%)
114
117
106
115
104
118
112
(5.2%)
aNumbers in parentheses are coefficients of variation.
Milling error resulted in the loss of 4 mm from one edge.
6756
6906
6708
775
6636
6822
781
6420
754
775
6708
(1.8%) (2.5%)
787
789
762
5970
5766
6372
719
6132
687
6984
712
6498
694
6253
697
(5.9%)
(2.4%)
698
674
255
APPENDIX TO DATA TABLES
SPECIMEN NOMENCLATURE
identified using variations of a standard
are
Specimens
TELAC
three bit code.
type
of
the
The first bit
second
The
specimen.
indicates
or
bit
the
laminate
set
of
bits
identifies any unusual characteristic of the specimen, such as
or the size of an implanted
width
a nonstandard
The final bit is the specimen
The laminate
number.
is usually of the form nQm.
notation
represents the angular orientation of the
to
respect
axis
longitudinal
the
delamination.
plies
angled
with
Since
degrees.
in
The
the
laminates in this investigation were balanced, the angle plies
can
be
by
represented
therefore
no ambiguity
100
angles
under
denotes
the number
to
together
are
when the prefix
by
preceded
of plies of the
an
form
0 and 90.
between
numbers
n is added as
orientation
of
ply
effective
is
long
as
The value of n
a zero.
same
There
greater
stacked
nominal
a
letter code indicating
the
relative position of any 00 plies.
An "A" indicates that
the
The
thickness.
00
plies
are
Q
represents
located
at the midplane
that they are on the laminate
number
of
laminate.
0
ply
groups
Hence, 15B1
The
surface.
in
each
represents
while a "B" indicates
half
a
"m"
of
[0/±15]s
the
denotes
the symmetric
laminate
and
315A1 represents a [±153/03]s laminate.
A
different version of this basic code is used to denote
laminates
containing
fabric
plies.
The
laminates
which
256
contained
only
longitudinal
fabric
axis.
plies
The
fabric
plies
angles
lamination
normally be designated 20AO.
that
had
of
+200
sequence
to
[±20]s
the
would
A prefix "F" is used to indicate
are used.
A suffix "W" or "F" is used to
denote whether the ply faces at the
+20o/-20°
interface
are
warp or fill faces.
The
fabric
laminates
plies
which
contained
contained
only
0°
sequences were therefore designated
letter/number
sequences.
A
number
of
fabric
plies.
by
a
The
zero
lamination
followed
by
"U" and a number indicated that
number of unidirectional plies.
that
both unidirectional and
An "F" and a number inducated
plies.
Thus,
OU5F1
indicates
a
[05U/OF]s laminate, OU5FlU1 indicates a [0 5u/OF/Ou]s laminate,
and OUlOF1 indicates a [0 10U/OF]s laminate.
The second bit or set of bits often
and size of machined notches.
given a middle bit of "O".
in
this
features
investigation.
which
are
the
type
Unnotched specimens are usually
No notched specimens
Nonetheless,
some
the
were
tested
specimens
denoted with middle bits.
with nonstandard widths (including
have
indicates
group
have
The specimens
that
actually
the standard width) are given a second bit with a prefix
"W" followed by a
number
indicating
the
nominal
width
in
millimeters.
The
specimens with the implanted delaminations are given
two middle bits.
number
The first has a prefix
indicating
delamination
the
nominal
from the free edge.
"D"
intrusion
followed
of
by
a
the implanted
The second has a prefix
"A"
257
followed
by
a number indicating the nominal intrusion of the
implanted angle ply split from the free edge.
the
delamination
was at the +15°/-15
°
The facts
interface
that
and that the
implanted angle ply splits were in the [-156] sublaminate were
not encoded in the specimen designations.
The
final
bit
is
differentiates the data from
This
bit
the
nominally
is a simple integer.
one to five.
specimen
It was convenient
number.
identical
This
specimens.
In most cases, it ranged from
to manufacture
six each of the
specimens
with
implanted
specimens
each
of the 10 mm and 30 mm wide [±153]s specimens
delaminations.
An
extra
were made to determine delamination initiation stress.
the final bit had values as high as seven.
two
Thus,
258
APPENDIX A
DELAMINATION GROWTH DATA FOR [±153]s
SPECIMENS OF NONSTANDARD WIDTH
Specimen
Stress
[MPa]
Associated
Strain
Number
[pstrain]
315AO-W30-3
315AO-W50-1
[mm]
[mm2]
451
459
467
477
4116
4176
4254
4368
4452
4536
0
0
0
1
1
F
0
0
0
3
3
F
4086
4170
4266
4350
4452
4524
4626
4284
0
0
0
0
0
0
1
F
0
0
0
0
0
17
F
5700
4080
4164
4206
4332
4392
4386
1
2
2
2
2
F
4
4
4
4
5
F
30
45
45
45
48
5765
3972
4044
4152
4236
4308
4404
4506
4590
4656
0
0
0
0
0
0
1
1
F
0
0
0
0
0
0
1
2
F
448
459
468
477
489
498
508
460
450
460
467
480
488
486
315AO-W50-4
Delaminated
Area
3978
497
315AO-W50-3
Maximum
Intrusion
449
468
487
426
441
490
315AO-W50-2
of
Delaminations
447
459
467
478
487
497
509
517
526
4164
4356
3936
4081
0
1
1
3
Fa
0
6
16
16
F
0
0
90
575
785
3000
0
0
0
15
20
4300
0
0
0
0
0
0
300
0
0
0
0
0
0
3
10
7390O
7390
a"F" denotes failure.
259
APPENDIX A (Continued)
DELAMINATION GROWTH DATA FOR [±153]
SPECIMENS OF NONSTANDARD WIDTH
Specimen
Stress
[MPa]
Associated
Strain
Number
[pstrain]
315AO-W50-5
449
4116
459
4182
4362
468
480
315AO-W70-1
315AO-W70-2
[mm]
[mm 2 ]
0
0
0
0
14
14
352
412
412
452
445
444
4020
4698
4690
0
1
0
0
28
F
F
2225
5210
449
460
4080
4188
4284
4386
4470
4566
4572
3888
0
0
0
0
0
0
1
F
0
0
0
0
501
491
4272
4404
4470
4572
4806
5004
5796
0
0
1
1
1
2
FO
F
450
4236
422
3971
450
460
3852
3870
471
3936
479
490
500
4002
4056
4134
4242
4308
4368
4488
4430
450
460
469
480
489
315AO-W70-5
Delaminated
Area
487
498
508
479
489
500
509
433
315AO-W70-4
0
0
2
2
2
3
Maximum
Intrusion
4458
4536
4680
4788
471
315AO-W70-3
of
Delaminations
509
519
529
536
529
a"F" denotes failure.
Fa
14
14
F
0
0
45
F
0
0
540
6366
0
0
0
0
0
0
4272
9273
0
0
10
28
53
60
225
1283
F
11792
1
F
29
2480
12350
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
F
O
F
5
5
F
27
F
0
0
0
0
0
0
0
0
0
1998
12895
260
APPENDIX B
DELAMINATION GROWTH DATA FOR
[±15n/On]s SPECIMENS
Specimen
Stress
[MPa]
Associated
Strain
Number
[s train]
15A1-0-4
760
809
861
928
965
1033
15A1-0-5
761
812
857
911
954
215A1-0-4
556
593
631
0
0
1
8
11
8058
Fa
6246
6624
0
2
4
0
0
1
3
8
F
0
0
2
84
320
F
0
7350
7848
10
0
2
2
3
F
F
F
4140
4422
4662
4950
5190
5466
5784
6516
0
0
0
0
1
0
0
0
6966
16
40
112
158
6
26
2564
F
F
F
4476
4794
5118
5400
5598
5892
0
0
3
0
0
4
4
4
F
0
0
51
77
88
0
610
7206
0
1
2
3
3
F
0
1
558
591
622
3834
4056
4302
4866
5112
492
529
556
593
624
595
4086
4380
4614
4908
5154
5874
0
0
1
2
3
F
777
793
553
591
630
674
700
732
315A1-0-5
[mm]
Delaminated
Area
[mm2]
4
740
315A1-0-4
7344
Maximum
Intrusion
0
0
0
2
6
667
701
215A1-0-5
5718
7032
6558
7032
of
Delaminations
494
526
a"F" denotes failure.
4
5
F
0
0
9
F
6
1
8
26
26
1395
2867
F
F
0
0
3
5
0
0
41
88
42
3310
F
F
261
APPENDIX B (Continued)
DELAMINATION GROWTH DATA FOR
[±15n/0 n]s SPECIMENS
Specimen
Stress
Associated
[MPa]
Strain
Number of
Delaminations
[ustrain]
515A1-0-4
1
1
1
2
2
1
2
22
28
1045
2620
Fa
F
F
1
1
2
2
F
2
516
4134
4680
5238
412
3522
4032
4026
4392
5286
6090
1
1
1
2
2
F
2
442
470
495
523
535
415
440
469
495
522
512
3744
3918
4758
4476
5010
4734
558
592
599
815A1-0-4
815A1-0-5
[mm]
Delaminated
Area
[mm2]
4458
4404
4650
5568
5832
497
525
515A1-0-5
Maximum
Intrusion
493
528
a"F" denotes failure.
F
4
3
F
2
5
5
5
32
32
3408
3408
F
F
2
16
2
3
3
3
12
12
4
3
13
32
382
387
1696
2878
F
F
F
262
APPENDIX
C
DELAMINATION GROWTH DATA FOR
[On/+15n]s SPECIMENS
Specimen
Stress
Associated
[MPa]
Strain
Number of
Delaminations
[pstrain]
15B1-0-4
15B1-0-5
Maximum
Intrusion
[mm]
Delaminated
Area
[mm2]
881
940
1000
1059
1033
7134
7314
7728
8190
8550
0
0
0
1
0
0
0
2
Fa
F
882
6960
7368
7776
8196
8604
9108
0
0
0
1
0
0
0
0
0
1
2
F
3
11
FO
4926
5214
5544
5862
6930
7914
8484
0
0
0
1
0
0
0
0
2
7
4
2
30
30
2241
4000
F
F
F
5118
5472
5766
6078
6408
6828
6990
0
0
0
1
0
0
0
0
0
0
1
2
9
F
31
311
F
4350
4614
4866
5178
5436
6588
6858
7182
7302
5
5
5
6
7
6
5
5
2
2
3
3
22
27
34
55
23
24
24
24
1049
2231
2248
F
F
942
1001
1059
1119
1176
4
F
0
0
0
10
F
0
F
215B1-0-4
646
693
735
773
813
857
891
215B1-0-5
646
690
730
771
813
859
857
315B1-0-4
541
575
609
646
681
717
752
789
792
a"F" denotes failure.
4
5
F
0
0
2
2261
F
263
APPENDIX C (Continued)
DELAMINATION GROWTH DATA FOR
[O/+15 n]s SPECIMENS
[n-
Specimen
315B1-0-5
Stress
Associated
[MPaj
Strain
[pstrain]
539
575
611
647
684
719
753
788
515B1-0-5
[mm]
[mm 2 ]
23
23
42
53
100
249
2407
2407
2411
F
Fa
F
502
534
567
603
642
668
702
4554
1
1
2
2
4
5
F
1
1
4
4
36
36
19
19
1437
F
F
502
4932
5226
5550
5874
6216
6306
1
2
2
2
5
F
1
1
1
1
6
F
1
534
4596
4890
5274
5592
6786
3
4
6
8
F
1
2
13
13
F
435
4914
5232
5532
5844
6
7
7
F
1
3
4
F
7
19
485
516
549
565
483
517
547
577
a"F" denotes failure.
5436
5742
6144
7158
7470
4836
5136
5550
5832
6726
7098
3
3
3
3
4
9
Delaminated
Area
7866
581
815B1-0-5
Maximum
Intrusion
8244
568
602
635
643
815B1-0-4
Number of
Delaminations
1
1
3
3
4
5
6
6
6
824
860
515B1-0-4
4542
4854
5184
ns
25
25
25
1
1
655
4
4
4
116
F
5
14
372
F
50
F
264
APPENDIX
D
GROWTH-TO-TAB STRESSES FOR
[±15n0n]s AND [0 n/+1 5 n]s SPECIMENS
Specimen
Growthto-Tab
Stress
[MPa]
215A1-0-1
215A1-0-2
215A1-0-3
215A1-0-4
215A1-0-5
618
706
717
793
732
713
(8.8%)
315A1-0-1
315A1-0-2
315A1-0-3
315A1-0-4
315A1-0-5
556
647
619
568
624
603
(6.5%)
515A1-0-1
515A1-0-2
515A1-0-3
515A1-0-4
515A1-0-5
616
591
565
558
503
567
(7.5%)
815A1-0-1
815A1-0-2
815A1-0-3
815A1-0-4
815A1-0-5
aNumbers
544
545
558
485
495
525
(6.3%)
in p
Growthto-Tab
Strain
Specimen
[MPa]
[#ustrain]
7248
5880
6240
6516
5892
Growthto-Tab
Stress
215B1-0-1
215B1-0-2
215B1-0-3
215B1-0-4
215B1-0-5
908
747
823
813
[pstrain]
7560
6954
6090
6930
6990
6355
857
830
(8.9%)
(7.2%)
(7.6%)
725
727
694
681
723
710
6228
b
5646
4722
4494
5154
5004
(10.1%)
315B1-0-1
315B1-0-2
315B1-0-3
315B1-0-4
315B1-0-5
(2.9%)
4962
5250
4362
4650
4896
4824
(6.9%)
515B1-0-1
515B1-0-2
515B1-0-3
515B1-0-4
515B1-0-5
4710
5256
4620
4194
4476
4651
815B1-0-1
815B1-0-2
815B1-0-3
815B1-0-4
815B1-0-5
(8.4%)
687
650
600
702
643
(6.1%)
659
584
640
549
577
602
(7.6%)
arentheses are coefficients of variation.
Broken gage.
Growthto-Tab
Strain
6 -95
6144
4932
5436
6450
(10.8%)
5292
5268
4668
7098
6306
(16.9%)
4998
6582
5220
5274
5844
5584
(11.5%)
265
APPENDIX E
DELAMINATION GROWTH DATA FOR
2
OFs FABRIC SPECIMENS
[+±
Specimen
Stress
[MPa]
Associated
Strain
Number of
Delaminations
[s train]
F20F-0-4
6348
6768
7236
7680
8436
0
11
6474
6966
7440
8148
8760
9294
3
11
0
1
8
513
7638
8100
8766
9438
9954
410
438
465
492
502
7344
7758
8604
9174
9348
357
381
406
429
452
F20F-0-5
357
381
404
429
453
473
F20W-0-4
411
437
465
492
F20W-0-5
a"F" denotes failure,
entire width.
including
16
19
Fa
0
0
2
4
4
F
46
149
235
23
23
one
F
9
45
86
6
F
F
0
1
3
3
F
0
4
F
F
0
299
515
0
2
3
8
least
[mm2]
4
15
F
Delaminated
Area
[mm]
2
3
3
13
20
20
F
at
Maximum
Intrusion
2
54
116
F
0
22
142
251
F
delamination across the
266
APPENDIX
F
DELAMINATION AND ANGLE PLY SPLIT FORMATION DATA FOR
[03/±153]s SPECIMENS WITH IMPLANTED DELAMINATIONS
Delamination
Formation
Strain
Stress
Specimen
[MPa]
[pstrain]
Angle Ply
b
Split Formation
Stress
Strain
[MPa]
[pstrain]
315B1-D10-AO-1
315B1-D10-A0-2
315B1-D10-A0-3
315B1-D10-A0-4
315B1-D10-A0-5
315B1-D10-A0-6
315B1-D10-A20-1
315B1-D10-A20-2
315B1-D10-A20-3
315B1-D10-A20-4
315B1-D10-A20-5
315B1-D10-A20-6
148
150
128
123
144
148
140
(8.3%)
148
188
146
146
121
162
152
(14.6%)
aThe point at which
bneighboring plies.
The point
the
1218
1266
1110
1020
1266
1236
1186
(8.4%)
1266
1716
1338
1344
1206
1362
1372
(13.0%)
implanted
362
314
315
123
263
431
301
3024
2874
2778
1020
2226
3636
2593
(34.5%)
(34.5%)
148
188
146
146
121
162
1266
1716
1338
1344
1206
1362
1372
(13.0%)
(14.6%)
teflon
debonded
at which an angle ply split was first visible
X-radiograph.
CNumbers in parentheses are coefficients of variation.
from
on an
267
APPENDIX G
GROWTH OF THE DELAMINATION TO THE END OF THE
IMPLANTED ANGLE PLY SPLIT IN [0 /+15
SPECIMENS
WITH IMPLANTED DELAMINATIONS AND ANGE SPLY SPLITS
Specimen
Stress
[MPa]
315B1-D10-A20-1
315B1-D10-A20-2
315B1-D10-A20-3
315B1-D10-A20-4
315B1-D10-A20-5
315B1-D10-A20-6
698
674
719
663
707
680
690
(3.1%)
Strain
Same as
[pstrain]
Failure?
5970
5766
6372
5652
6648
5808
6036
(6.5%)
Yes
Yes
Yes
No
No
No
aNumbers in parentheses are coefficients of variation.
268
APPENDIX
H
SIZING OF THE ELEMENTS IN THE FINITE ELEMENT MESH
The
element mesh used in this investigation is a
finite
two-dimensional
of the
model
perpendicular
cross-section
the loading direction.
to
calculation, all models used an
0.134 mm,
the
values were
of
value
nominal
scaled
For the purposes
of
thickness
of
effective
for
ply
The
a ply of AS4/3501-6.
for
appropriately
specimen
the
other
ply
effective
thicknesses.
From
symmetry
cross-section
needed
the
cross-section
modeled
one
specimen and the thickness of the
one half the thickness
the
modeled
of
the
width of the
cross-section
was
of the specimen.
full-sized model would have
change
internal
in
internal energy in
involved
in
the
verified
using
of
numerical
full-sized
the x 2 face which
the
was sufficient
release
two versions)
would
entire
The
represent
be
model.
solution
accuracy
of
because
A
the
small compared to the
The
roundoff
error
would
then
become
this
approach
was
models without the constraints on
the
test section.
(i.e. that
inappropriate
been
energy
the
large.
unacceptably
energy
half
width
actual specimen width was not used in most cases.
The
center
Thus, the
to be modeled.
was
one quarter of the
only
considerations,
the
symmetry
conditions
at
the
It was found that the accuracy
asymptotic
value
of
strain
rate did not differ by more than 1% between
as long as the delamination
did
not
extend
the
to
269
within
two boundary
region widths of the far free edge.
Since the calculated internal energy per unit length is a
function of model width, the widths of the
consistent
for
similarly
small widths were used.
sized
model
had
delaminations.
The model
widths
to
be
Relatively
used
for
various
delamination sizes are shown for the various specimen types in
Table H.1.
The thickness of
quarter
of
the
Figure 7.1.
regions.
delamination
centerline
with
was
four
a
region extending
"skewing
that the boundaries
boundary
was
one
divided
wide
element
the
rest
three
region over the
wide
of
into
region
which
tip, and a five
the
way
to
the
The elements in each region were
tip, as
shown
in
Figure 7.1,
factor" for each region of 1.9.
of the elements
in a
region
This means
of
width
w
n elements are at the following distances from the
of the region:
d
W -i 1.9
i == 1,2,3,...,n n
The boundaries of the twelve elements in
this
model
in front of the delamination
of the specimen.
containing
the
was
element
three
toward the delamination
a
in
ply thickness as was illustrated in
a
surface,
0.1 mm
element wide
skewed
nominal
element
The width of the model
There
extended
each
investigation
are
size, a, and the halfwidth
given
in
(H.1)
the
model
used
in
terms of the delamination
of the specimen,
b,
in
Table H.2.
270
TABLE H.1
FINITE ELEMENT MODEL WIDTHS USED
FOR VARIOUS DELAMINATION SIZES
Specimen
Type
Model
Width
Range of
Delamination
[mm]
Sizes
[mm]
[+15]
s
[+15/0]
[0/+15]
1.0
2.5
5.0
16.7
0.001-0.100
0.100-0.500
0.500-2.500
2.50-15.0
2.3
5.7
11.4
50.0
0.001-0.200
0.200-1.000
1.000-3.000
3.00-40.0
2.78
0.001-0.200
6.94
0.200-1.000
13.88
50.0
1.000-3.000
3.00-40.0
271
TABLE H.2
POSITION OF BOUNDARIES OF FINITE ELEMENTS ACROSS MODEL WIDTH
Element
Number
Position of Boundaries
Inside
Outside
Boundary
Boundary
**
1
*
**
0
mm)
0.621(b-a-0.1
0.825(b-a-0.1
0.953(b-a-0.1
mm)
mm)
mm)
2
3
4
0.346(b-a-0.1
0.621(b-a-0.1
0.825(b-a-0.1
5
6
7
8
0.953(b-a-0.1 mm)
b-a-0.1 mm
b-a-0.463 mm
b-a-0.124 mm
b-a-0.1 mm
b-a-0.463 mm
b-a-0.124 mm
b-a
b-0.928a
9
b-a
10
11
b-0.928a
b-0.732a
12
b-0.421a
mm)
mm)
mm)
0.346(b-a-0.1
b-0.732a
b-0.421a
b
Position given in distance from the centerline of the
specimen
a = width
b = width
modeled
of delamination
of the model = halfwidth
of specimen
being
272
The
elements
centerline
are numbered one through twelve starting at the
of the specimen.
273
APPENDIX
I
STRAIN ENERGY RELEASE RATE CALCULATIONS FOR
[±153]s SPECIMENS OF NONSTANDARD WIDTH
Specimen
Stress
[MPa]
Associated
Intrusion
[mm]
Strain Energy Release Rate Calculationsa
A
B
C
D
[J/m2 ]
[J/m 2 ]
[J/m2 ]
[J/m2 ]
315AO-W30-3
487
441
6
16
797
654
796
653
1177
967
1585
2265
315AO-W50-1
497
3
830
829
1220
1332
315AO-W50-2
460
17
711
710
1051
1704
315AO-W50-3
488
4
5
801
794
800
486
793
1180
1174
1323
1353
517
526
1
2
899
898
929
1303
1362
1341
930
315AO-W50-5
508
14
868
867
1283
1908
315AO-W70-1
444
28
663
662
980
1639
315AO-W70-2
433
45
630
629
931
2061
315AO-W70-3
489
501
491
5
804
844
803
843
811
810
1187
1248
1199
1312
10
28
315AO-W70-4
422
29
599
598
885
1506
315AO-W70-5
529
27
941
940
1391
2288
315AO-W50-4
aKey: A
B
C
D
-
O'Brien's Method
Finite Element Method
Geometrically Integrated Finite Element Method
Geometrically Integrated Finite Element Method with Finite
Dimension Effects
1445
1575
2268
274
APPENDIX
J
STRAIN ENERGY RELEASE RATE CALCULATIONS FOR
[±15n/On]s SPECIMENS
Specimen
Stress
[MPa]
15A1-0-4
Associated
Intrusion
[mm]
Strain Energy Release Rate Calculationsa
A
[J/m 2 ]
B
[J/m 2 ]
C
[J/m2 ]
D
[J/m2 ]
711
768
1110
1197
1128
1257
1366
1552
928
965
1033
1
3
8
880
709
767
878
911
2
3
685
751
682
749
1066
1101
954
1168
1228
740
2
6
26
904
996
1038
900
777
793
993
1035
1412
1547
1611
1459
1709
2318'
215A1-0-5
732
4
884
881
1377
1467
315A1-0-4
558
1
6
771
780
1112
1236
591
865
863
610
26
921
918
1346
1429
2057
593
624
595
3
5
870
964
876
868
960
873
1359
1500
1355
1426
1624
2307
1137
1284
1446
1480
1173
1292
1441
1475
1569
1880
2243
2297
1825
2088
3150
3379
15A1-0-5
215A1-0-4
315A1-0-5
515A1-0-4
42
1481
525
558
592
599
22
28
515A1-0-5
516
2
1098
1105
1608
1786
815A1-0-4
495
535
2
32
1617
1889
1657
1883
2275
2932
2637
4504
1278
1617
1799
1286
1612
1862
2521
2802
2685
2114
3028
3412
4127
815A1-0-5
440
495
522
512
1
2
3
12
13
32
1730
1793
1724
aKey: A - O'Brien's Method
B - Finite Element Method
C - Geometrically Integrated Finite Element Method
D - Geometrically Integrated Finite Element Method with Finite
Dimension Effects
275
APPENDIX K
STRAIN ENERGY RELEASE RATE CALCULATIONS FOR
[On/+15 n]s SPECIMENS
Specimen
Stress
[MPa]
Associated
Intrusion
[mm]
Strain Energy Release Rate Calculationsa
A
B
C
D
[J/m 2 ]
[J/m 2 ]
[J/m 2 ]
[J/m2 ]
15B1-0-4
1106
2
1009
1007
1574
1625
15B1-0-5
1119
1
2
1033
1141
1031
1139
1618
1643
1838
2
1091
1089
1308
1709
1969
1764
1310
1176
215B1-0-4
813
891
215B1-0-5
315B1-0-4
515B1-0-4
1
2
9
1091
1218
1212
1094
1213
1210
1720
1908
1881
1748
609
2
3
918
1148
1273
1553
917
1145
1271
1550
1442
1798
1975
2410
1490
1158
1280
1403
1156
1277
1401
1828
1813
2000
2187
2842
1903
1374
1700
2030
2109
2667
3155
2143
2844
4176
1723
1702
2645
2666
2688
684
815B1-0-4
815B1-0-5
23
24
1970
2172
1887
2747
3393
719
753
3
4
9
860
25
1831
567
642
1
4
19
1326
1
6
1663
643
516
549
565
1
2
13
1757
1863
2775
2821
1989
2034
3158
2107
2103
3289
3264
4004
517
547
577
1
3
4
1764
1870
1989
2204
2785
3124
3465
702
515B1-0-5
3070
813
859
857
681
717
792
315B1-0-5
30
1779
635
1700
2033
1706
1975
2198
2130
2526
4046
2931
2831
aKey: A - O'Brien's Method
B - Finite Element Method
C - Geometrically Integrated Finite Element Method
D - Geometrically Integrated Finite Element Method with Finite
Dimension Effects
3280
3696
MITLibraries
Document Services
Room 14-0551
77 Massachusetts Avenue
Cambridge, MA 02139
Ph: 617.253.5668 Fax: 617.253.1690
Email: docs@mit.edu
http://libraries. mit. edu/docs
DISCLAIMER OF QUALITY
Due to the condition of the original material, there are unavoidable
flaws in this reproduction. We have made every effort possible to
provide you with the best copy available. If you are dissatisfied with
this product and find it unusable, please contact Document Services as
soon as possible.
Thank you.
Some pages in the original document contain
pictures or graphics that will not scan or reproduce well.