THE EFFECT OF PLY THICKNESS ON THE INITIATION
AND GROWTH OF DELAMINATION IN GRAPHITE/EPOXY
LAMINATES WITH HOLES UNDER COMPRESSIVE CYCLIC LOADING
by
STEPHEN C. NOLET
S.B. Massachusetts Institute of Technology
(1982)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS OF THE
DEGREES OF
MASTER OF SCIENCE IN
AERONAUTICS AND ASTRONAUTICS
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
January 1984
@
Massachusetts Institute of Technology 1984
Signature of Author
Department 6f Aeron-'atic
and Astronautics
January 13, 1984
Certified by
/
James W. Mar
Thesis Supervisor
Accepted by
Harold Y. Wachman
Chairman, Depar mental Graduate Committee
Archives
MASSACHUZETTS INSTiTUTE
OF TECHINOLOGY
L;_
1
LIBRARIES
THE EFFECT OF PLY THICKNESS ON THE
INITIATION
AND GROWTH OF DELAMINATION IN GRAPHITE/EPOXY
LAMINATES WITH HOLES UNDER COMPRESSIVE CYCLIC LOADING
by
STEPHEN CHARLES NOLET
Submitted to the Department of Aeronautics and Astronautics
on January 13, 1984 in partial fulfillment of the
requirement for the Degree of Master of Science
ABSTRACT
The effect of "effective ply thickness" on initiation
and growth of damage in [+-45xn/Oxn] s (qhwew n=1,2, and 3)
graphite/epoxy laminates with 6.35 mm holes under compressive
Static and cyclic
cyclic loading has been investigated.
compressive testing was done on axially loaded sandwich
Out-of-plane Moir6 interferometry and pulse-echo
specimens.
ultrasonic inspection was used to monitor cyclic test
The compressive static
specimens for delamination damage.
tests on the [+-45xn/Oxn] s sandwich specimens showed no
"effective ply thickness" dependence on the compressive
Cyclic tests on the [+-45/0] s
fracture stress of 423 MPa.
specimens showed three different types of damage development
one, a damage mode that
for the same applied peak stress:
led to immediate transverse failure; two, delamination that
initiated at the hole edge and grew radially from the hole;
and three, a delamination that initiated at the top and
bottom of the hole and grew longitudinally within the width
However, all the [+-45x2/0x2] s and [+-45x3/0x3] s
of the hole.
laminates developed only the longitudinal delamination type
The growth of longitudinal delamination was
of damage.
found to be a linear function of the logarithm of the
This damage initiates earlier
number of applied load cycles.
as the "effective ply thickness" and/or peak cyclic stress
Furthermore, the growth rate increases with
increases.
Longitudinal delamination
"effective ply thickness."
develops due to splitting in the 00 plies of the laminate
interface
and subsequent shear failure of the -450/0
This mode of damage was also
splits.
between the 0
results of
observed in two tensile cyclic tests.
residual strength testing showed that laminates with
longitudinal delamination had an average residual tensile
This is approximate a 50% increase over
stress of 640 MPa.
3
the ultimate tensile stress of 455 MPa determined from
static tensile tests on six coupons and eight sandwich
specimens (uncycled) of the [+-45/0] s laminate.
Thesis Supervisor:
Title:
James W. Mar
Jerome C. Hunsaker Professor of
Aerospace Education
ACKNOWLEDGEMENTS
It is very difficult to express in a page or two the
gratitude that I have for so many people that have helped
in one form or another during the course of this research.
To all of you who put in your two cents worth, lent an
encouraging word or just hung around to make me smile, I
offer you my thanks.
There are several very special people that I want to
First, and most important I'd like to
thank personally.
thank my thesis supervisor, Professor James W. Mar for his
advise, guidance and optimistic nature that contributed so
In a similar vein
deeply in the completion of this thesis.
I owe a deep thanks to Professor Paul a. Lagace. The effort
Professor Lagace has contributed not only to this work but
every facet of the Technology Laboratory for Advanced
Composites is often overlooked, however, this author
extends his deepest gratitude toward Paul and all he has
given to me.
After five and one half years in the lab, I have seen
a good many friends and fellow students come and go, but one
constant I have always been able to count on is Albert
Thanks Al, for sharing your technical advice, and
Supple.
My
Keep on our tails, it keeps us in shape!
experience.
thanks goes out to Alan Shaw who always had just the right
piece of equipment for me; Don Wiener who has taught me
I'd like to
almost everything I know about machining.
put up with
who
Lee
Ping
to
thanks
of
note
a
special
offer
in shape.
funding
R.A.
my
keeping
and
time
this
all
for
me
Delores who helped in pulling this manuscript
To Debra and
together I extend my appreciation.
The best part of TELAC are the people; the students,
who have personally spent their own time
and my friends
Tony Vizzini,
are what this lab is all about.
to assist me
who has developed nearly every last line of software used
for testing and data reduction spent literally scores of
Thanks Tony,
hours working his magic especially for me.
I wish to thank John Brewer
you're really something else.
all the materials
talents in procuring
for his logistic
for my research, his efforts, too, can often be overlooked.
I owe a special debt of gratitude to the undergraduates,
Chris Dunmire, Chris Winters and Seifu Alemayehu for
To the
their efforts in helping me complete this work.
rest of our gang, Mark, Mark, Doug, David, Bob, Hatem,
Steve, David, Christos, Sim, Jeff, Karen, Lisa, Sigong and
all the rest who I had the fortune to work with, I say thanks
for being around.
No work can successfully come to a conclusion without
the support, understanding and good times that a group of
My life here was made so much more
friends can offer.
enjoyable because of MIE and those, who one way or another
So here goes,
have been adopted by this fine organization.
Tommy, Osc, Jeff, Robin, Frank, Brew, Wayne, Bobby, Bruce,
Roy, Jolle, Swanee, Paul, Bully, Katie, Dana, Eric, Ducky,
Veds, Barb, Anthony and Patty and all the others that you
guys will tell me I forgot, thanks for all the good times;
that seems to be the one thing you get to keep from here.
To my good friend Peter Vedder I
You made it worthwhile.
A warm thankowe alot, its really good to have a friend.
you goes to Paul and Robin for all their hospitality,
(2152 pitches, downstairs, Paul, and not one hit batsman,
not bad).
We made it Babs, its off to California!
6
DEDICATION
This ones for Barbara Ann and my
parents, love is still the greatest
thing in the world.
7
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. The work was sponsored by the Air Force
Office of Scientific Research under contract number
AFOSR-F49620-83-K-0015. Dr. Anthony K. Amos is the contract
monitor.
TABLE OF CONTENTS
PAGE
CHAPTER
1
INTRODUCTION
20
2
THEORETICAL BACKGROUND
29
2.1
UNIDIRECTIONAL
29
2.2
MULTIDIRECTIONAL LAMINATES
2.3
CHARACTERISTICS
CYCLIC DAMAGE
2.4
TECHNIQUES IN EVALUATING
COMPOSITE DAMAGE ACCUMULATION
3
4
5
6
EXPERIMENTAL
COMPOSITES
33
OF COMPRESSION
PROCEDURE
3.1
AXIAL SANDWICH SPECIMEN
FABRICATION
3.2
SPECIMEN IDENTIFICATION
3.3
STATIC TESTING PROCEDURE
3.4
CYCLIC TESTING PROCEDURE
3.5
RESIDUAL TENSILE STRENGTH TESTS
3.6
NON-DESTRUCTIVE INVESTIGATION
TECHNIQUES
67
TEST RESULTS
73
4.1
STATIC TESTS
73
4.2
CYCLIC TESTS
84
4.3
RESIDUAL STRENGTH TESTS
DISCUSSION
126
132
5.1
STATIC TESTS
132
5.2
CYCLIC TESTS
133
5.3
RESIDUAL STRENGTH TESTS
147
5.4
SUMMARY
150
CONCLUSIONS AND RECOMMENDATIONS
152
9
TABLE OF CONTENTS
(Continued)
PAGE
156
REFERENCES
APPENDIX 1
Specimen Selection and Verification
160
APPENDIX 2
Shear Lag Analysis on -450/00
Interface With a Delamination
173
LIST OF FIGURES
FIGURE
1
2
3
'PAGE
RADIAL DAMAGE GROWTH SEQUENCE IN
[+-45/0]
LAMINATE WITH 6.35 MM HOLE (TYPE 1) UNDER
COMPRESSIVE CYCLIC LOADING AS OBSERVED BY
GRAVES [REF. 1]
24
LONGITUDINAL DAMAGE GROWTH SEQUENCE IN
[+-45/0]sLAMINATE WITH 6.35 MM HOLE (TYPE 2)
UNDER COMPRESSIVE CYCLIC LOADING AS OBSERVED
BY GRAVES [REF. 1]
25
DAMAGE GROWTH SEQUENCE IN [+-45/0]sLAMINATE
WITH 12.7 MM HOLE UNDER COMPRESSIVE CYCLIC
LOADING AS OBSERVED BY FANUCCI [REF. 2]
26
GROWTH OF DELAMINATED AREA OF [+-45/0]s
LAMINATES WITH 12.7 MM HOLE UNDER COMPRESSIVE
CYCLIC LOADING AS DETERMINED BY FANUCCI
[REF. 2]
28
POSSIBLE MECHANISMS OF MATRIX CRACK GROWTH
AT A FIBER INTERFACE IN A COMPOSITE PLY AS
SUGGESTED BY KIM AND EMBERT [REF. 3]
30
OFF AXIS COMPOSITE PLY IN UNI-AXIAL LOADING
WITH A MATRIX CRACK PARALLEL TO THE FIBERS
SUBJECT TO NORMAL (MODE 1) AND SHEAR (MODE II)
STRESS COMPONENTS
32
SCHEMATIC OF MATRIX INTERFACE BETWEEN TWO
PLIES SHOWING A DELAMINATION CRACK
35
CONFIGURATION OF COMPRESSIVE SANDWICH TEST
SPECIMEN
49
TELAC CYCLE FOR HERCULES AS1/3501-6
GRAPHITE/EPOXY
51
10
LOCATION OF THICKNESS ANDWIDTH MEASUREMENTS
53
11
LOCATION OF LONGITUDINAL AND TRANSVERSE
STRAIN GAGES PLACED ON STATIC TEST SPECIMENS
59
12
DEFINITION OF DELAMINATION LENGTH, a
64
13
CONFIGURATION OF TENSILE RESIDUAL STRENGTH
TEST COUPON
66
PHOTOGRAPH OF MOIRE INTERFEROMETRY TEST
SET-UP
71
4
5
6
7
8
9
14
FIGURE
PAGE
72
15
PHOTOGRAPH OF ULTRASONIC TEST SET-UP
16
STRESS-STRAIN PLOT OF TYPICAL
STATIC COMPRESSIVE TEST
[+-45/0]
STRESS-STRAIN PLOT OF TYPICAL
STATIC COMPRESSIVE TEST
[+-45x2/0x2]
STRESS-STRAIN PLOT OF TYPICAL
STATIC COMPRESSIVE TEST
[+-45x3/0x3s
17
18
19
20
21
22
23
24
25
26
27
28
s
81
s
82
83
RADIAL DELAMINATION GROWTH SEQUENCE IN
SPECIMEN FCB 145Al-1A UNDER COMPRESSIVE
CYCLIC LOADING
86
RADIAL DELAMINATION GROWTH SEQUENCE IN
SPECIMEN FCB 145Al-5A UNDER COMPRESSIVE
CYCLIC LOADING
87
RADIAL DELAMINATION GROWTH SEQUENCE IN
SPECIMEN FCB 145Al-7A UNDER COMPRESSIVE
CYCLIC LOADING
88
RADIAL DELAMINATION GROWTH SEQUENCE IN
SPECIMEN FCB 145Al-8A UNDER COMPRESSIVE
CYCLIC LOADING
89
RADIAL DELAMINATION GROWTH SEQUENCE IN
SPECIMEN FCB 145A1-11B UNDER COMPRESSIVE
CYCLIC LOADING
90
PHOTOGRAPHS OF LONGITUDINAL DELAMINATION
GROWTH SEQUENCE IN SPECIMEN FCB 145Al-2A
UNDER COMPRESSIVE CYCLIC LOADING
91
PHOTOGRAPHS OF LONGITUDINAL DELAMINATION
GROWTH SEQUENCE IN SPECIMEN FCB 145Al-4A
UNDER COMPRESSIVE CYCLIC LOADING
92
PHOTOGRAPHS OF LONGITUDINAL DELAMINATION
GROWTH SEQUENCE IN SPECIMEN FCB 145Al-9A
UNDER COMPRESSIVE CYCLIC LOADING
93
PHOTOGRAPHS OF LONGITUDINAL DELAMINATION
GROWTH SEQUENCE IN SPECIMEN FCB 145A1-10A
UNDER COMPRESSIVE CYCLIC LOADING
94
PHOTOGRAPHS OF LONGITUDINAL DELMINATION
GROWTH SEQUENCE IN SPECIMEN FCB 145A1-10B
UNDER COMPRESSIVE CYCLIC LOADING
95
FIGURE
PAGE
29
SKETCH ILLUSTRATING RADIAL DELAMINATION
96
30
SKETCH ILLUSTRATING LONGITUDINAL DELAMINATION
97
31
MAGNIFIED PHOTOGRAPH OF CROSS-SECTION OF
[+-45/0]s SPECIMEN CONTAINING A LONGITUDINAL
DELAMINATION
100
32
PLOT OF THE LONGITUDINAL DELAMINATION LENGTH,
2a, VERSUS THE LOGARITHM OF THE NUMBER OF
APPLIED LOAD CYCLES FOR THE [+-45/0]s SPECIMENS 102
33
SKETCH ILLUSTRATING INITIATION OF LONGITUDINAL
DELAMINATION AT TOP AND BOTTOM OF HOLE IN
104
[+-45xn/0xnls LAMINATE
34
PLOT OF LONGITUDINAL DELAMINATION LENGTH,
2a, VERSUS THE LOGARITHM OF THE NUMBER OF
APPLIED LOAD CYCLES FOR SPECIMEN FCB 245Al-6
105
PLOT OF LONGITUDINAL DELAMINATION LENGTH,
2a, VERSUS THE LOGARITHM OF THE NUMBER OF
APPLIED LOAD CYCLES FOR SPECIMEN FCB 245Al-7
106
PLOT OF LONGITUDINAL DELAMINATION LENGTH,
2a, VERSUS THE LOGARITHM OF THE NUMBER OF
APPLIED LOAD CYCLES FOR SPECIMEN FCB 245Al-8
107
PLOT OF LONGITUDINAL DELAMINATION LENGTH,
2a, VERSUS THE LOGARITHM OF THE NUMBER OF
APPLIED LOAD CYCLES FOR SPECIMEN FCB 245Al-9
108
PLOT OF LONGITUDINAL DELAMINATION LENGTH,
2a, VERSUS THE LOGARITHMOF THE NUMBER OF
APPLIED LOAD CYCLES FOR SPECIMEN FCB 245Al--10
109
PLOT OF LONGITUDINAL DELAMINATION LENGTH,
2a, VERSUS THE LOGARITHM OF THE NUMBER OF
APPLIED LOAD CYCLES FOR SPECIMEN FCB 245Al-11
110
PLOT OF LONGITUDINAL DELAMINATION LENGTH,
2a, VERSUS THE LOGARITHM OF THE NUMBER OF
APPLIED LOAD CYCLES FOR SPECIMEN FCB 245Al-12
111
PLOT OF LONGITUDINAL DELAMINATION LENGTH,
2a, VERSUS THE LOGARITHM OF THE NUMBER OF
APPLIED LOAD CYCLES FOR SPECIMEN FCB 245A1-13
112
PLOT OF LONGITUDINAL DELAMINATION LENGTH,
2a, VERSUS THE LOGARITHM OF THE NUMBER OF
APPLIED LOAD CYCLES FOR SPECIMEN FCB 245A1-14
113
35
36
37
38
39
40
41
42
FIGURE
43
44
45
46
47
48
49
50
51
52
53
A1.1
A1.2
A1.3
PAGE
PLOT OF LONGITUDINAL DELAMINATION LENGTH,
2a, VERSUS THE LOGARITHM OF THE NUMBER OF
APPLIED LOAD CYCLES FOR SPECIMEN FCB 345Al-2
115
PLOT OF LONGITUDINAL DELAMINATION LENGTH,
2a, VERSUS THE LOGARITHM OF THE NUMBER OF
APPLIED LOAD CYCLES FOR SPECIMEN FCB 345Al-3
116
PLOT OF LONGITUDINAL DELAMINATION LENGTH,
2a, VERSUS THE LOGARITHM OF THE NUMBER OF
APPLIED LOAD CYCLES FOR SPECIMEN FCB 345Al-4
117
PLOT OF LONGITUDINAL DELAMINATION LENGTH,
2a, VERSUS THE LOGARITHM OF THE NUMBER OF
APPLIED LOAD CYCLES FOR SPECIMEN FCB 345Al-5
118
GRAPHIC ILLUSTRATION OF LINEAR RFGRESSION
PARAMETERS, A AND B
122
SPLITTING OF 0 DEGREE PLIES
LAMINATE AT HOLE EDGE
IN [+-45xn/oxn]
s
136
SKETCH ILLUSTRATING LONGITUDINAL DELAMINATION
IN [+-45xn/Oxnls LAMINATE
138
SCHEMATIC MODEL OF REGION BETWEEN 00
SPLITTING WITH DELAMINATION AT -450/00
INTERFACE
139
PHOTOGRAPH OF LONGITUDINAL DELAMINATION IN
[0x2/+-45x2]s TENSILE CYCLIC SPECIMEN
145
PLOT OF LONGITUDINAL DELAMINATION LENGTH,
2a, VERSUS THE LOGARITHM OF THE NUMBER OF
APPLIED LOAD CYCLES
146
PHOTOGRAPH OF [+-45x2/0x2]s
RESIDUAL STRENGTH TEST
COUPON AFTER
149
STATIC COMPRESSIVE TEST STRESS-STRAIN PLOT
OF BACK TO BACK STRAIN GAGE READINGS OF
COUPON SPECIMEN UNDER SUPPORT OF
ANTI-BUCKLING GUIDE PLATES
162
CONFIGURATION OF STATIC TENSILE COUPON
TEST SPECIMEN
164
STRESS-STRAIN PLOT FOR TYPICAL STATIC TEST
OF [+-45/0] s TENSILE COUPON SPECIMEN
166
14
FIGURE
A1.4
A1.5
A2.1
A2.2
PAGE
STRESS-STRAIN PLOT FOR TYPICAL STATIC TEST
OF [+-45/0]s TENSILE SANDWICH SPECIMEN
167
SCHEMATIC OF THE CONSTRUCTION OF ALUMINUM
HONEYCOMB CORE USED IN SANDWICH SPECIMENS
170
SCHEMATIC MODEL OF REGION BETWEEN 00
SPLITTING WITH DELAMINATION AT -450/00
INTERFACE
174
PLOT OF SHEAR STRESS, FROM SHEAR LAG ANALYSIS,
IN -450/00 INTERFACE VERSUS THE DISTANCE FROM
THE EDGE OF THE DELAMINATION
181
LIST OF TABLES
PAGE
TABLE
1
2
3
4
5
6
7
8
9
10
11
MEASURED THICKNESS, WIDTH AND HOLE DIAMETER
FOR [+-45/0]s SPECIMENS
54
MEASURED THICKNESS, WIDTH AND HOLE DIAMETER
FOR [+-45x2/0x2]s SPECIMENS
55
AVERAGE THICKNESS, WIDTH AND HOLE DIAMETER
SPECIMENS
FOR [+-45x3/0x31]
56
TELAC VALUES FOR UNIDIRECTIONAL HERCULES
ASI/3501-6 GRAPHITE/EPOXY
76
STATIC COMPRESSIVE TEST RESULTS FOR THE
[+-45/0]s SPECIMENS
77
STATIC COMPRESSIVE TEST RESULTS
[+-45x2/0x2]s SPECIMENS
13
14
15
16
78
STATIC COMPRESSIVE TEST RESULTS FOR THE
[+-45x3/0x3]s SPECIMENS
79
CYCLIC TEST RESULTS FOR THE [+-45/0]s
SPECIMENS
99
CYCLIC TESTS RESULTS FOR THE [+-45x2/0x2],
SPECIMENS
CYCLIC TEST RESULTS FOR THE
SPECIMENS
[+-45x3/0x3]
119
s
120
RESULTS OF LINEAR REGRESSION OF LONGITUDINAL
DELAMINATION LENGTH VERSUS LOGARITHM OF
NUMBER OF CYCLES FOR [+-45/0].
12
FOR THE
DATA
123
RESULTS OF LINEAR REGRESSION OF LONGITUDINAL
DELAMINATION LENGTH VERSUS NATURAL LOGARITHM
OF NUMBER OF CYCLES FOR [+-45x2/0x2], DATA
124
RESULTS OF LINEAR REGRESSION OF LONGITUDINAL
DELAMINATION LENGTH VERSUS NATURAL LOGARITHM
OF NUMBER OF CYLES FOR [+-45x3/0x3] s DATA
125
RESIDUAL TENSILE STRENGTH TEST RESULTS FOR
[+-45/0]s SPECIMEN DELINEATED BY DAMAGE TYPE
128
RESIDUAL TENSILE STRENGTH TEST RESULTS FOR
[+-45x2/0x2]s SPECIMENS
129
RESIDUAL TENSILE STRENGTH TEST RESULTS FOR
[+-45x3/0x3,s SPECIMENS
130
16
PAGE
TABLE
A1.1
STATIC TENSILE TEST RESULTS FOR BOTH
[+-45/0]s COUPON AND SANDWICH SPECIMENS
168
NOMENCLATURE
2a
A
total length of longitudinal delamination
i, area of flaw
2.
B
CLPT
cm
C.V.
(da/dn)o
linear regression parameter for the growth of
longitudinal delamination (y-intercept)
linear regression parameter for the growth of
longitudinal delamination (slope)
Classical Laminated Plate Theory
centimeters
coefficient of variation
initial rate of damage growth at damage initiation
E
modulus of elasticity
F
Fahrenheit
G
1.
shear modulus
2.
strain energy release rate
GPa
h
gigapascals
ply layer thickness
Hg
mercury
Hz
hertz
kg
kilograms
LAS P
Laminate Analysis Software Package
LEFM
Linear Elastic Fracture Mechanics
In
m
natural logarithm
meters
min
minutes
mm
millimeters
MPa
megapascals
n
number of plies making up effective ply thickness
N
1.inewtons
2. number of load cycles
3.
N
load per unit length
load cycle at which damage initiation occurs
NDI
Non-Destructive Inspection
psig
pounds per square inch gage
R
stress amplitude ratio
S
compliance
t
thickness
u
displacement in the x-direction
U
strain energy density
V
Volume
o
degrees
a
constant in shear lag analysis
constant in shear lag analysis
E
strain
y
shear strain
Scoefficient
of mutual influence
6
lamination angle
a
stress
T
shear stress
v
Poisson's ratio
-s
microstrain
Subscripts
I
Mode I
II
Mode II
III
Mode III
c
critical value
m
matrix
tot
total
l,x,L
longitudinal direction
2,y,T
transverse direction
3,z
through-the-thickness direction
CHAPTER 1
INTRODUCTION
strength and stiffness are desirable material char-
High
properties
these
The
anisotropic
tailoring
a composite permits structural
of
to attain highly efficient designs.
the
to
subject
not
property
Advanced composites have
but include additional benefits.
advantages
these
only
Combine
with extremely low material weight and very
efficient structures can be created.
not
applications.
structural
aerospace
in
acteristics
corrosion
Composites are
problems suffered by metals.
Also, composites such as graphite/epoxy exhibit very low therexpansion
mal
structures
in
resulting
that maintain their
precise dimensions for delicate instrumentation.
Composites
in aircraft for many years.
used
been
have
airplanes have used fiberglass composites for many pri-
Light
mary structures but heavily loaded structures in high performand large transport aircraft have not yet been made from
ance
composite materials.
of
time
reason
heavily
why
The limited ability to predict the life-
loaded
composites
composite
have
been
structures
used
is a primary
sparingly for these
applications.
The
concept
of
material
damage
tolerance has been an
important part of engineering design for several years.
ar
Line-
Elastic Fracture Mechanics (LEFM) is applied to metals for
predicting the growth rate of cracks under fatigue
accurately
Through the use of non-destructive inspection (NDI)
loading.
calculate the "safe-life" of the damaged part.
and
cracks
inspection schedule can be designed to locate
an
techniques,
understanding
developed
well
The concept of longevity and a closely related
for longevity.
important part of aircraft
an
and damage tolerance refer to
a structure to withstand some inherent flaws
of
ability
are
Longevity
design.
structural
the
tolerance,
damage
term,
a metal's fatigue behavior
of
relatively easy to design and certify
structure
metal
makes
A
and service damage for a specified duration before this damage
is
found
design
inspection.
through
other words, engineering
such that material flaws grow as slowly as
be
should
In
possible and the strength of the structure (residual strength)
during
service
must
always be greater than the design limit
loads.
Conversely,
lytical
materials
schedule
critical.
an incomplete understanding and lack of ana-
techniques with respect to damage growth in composite
makes
to
it
difficult
to design a proper inspection
ensure the discovery of damage before it becomes
Therefore,
certification
requires extensive and costly testing.
of
composite structure
As a result, engineers
are hesitant to design with composites for heavily loaded primary structure.
important mechanism of damage in composites occurs in
An
the
the
fibers.
Material
delaminations,
Under
the
can
mechanisms
mostly
flaws,
exist
of
they
reach
in
throughout
repeated
influence
until
extend
transfer
shear
altering
of
capability
carrying
load
the
affects
due to static or cyclic loading
damage
Matrix
matrix.
the
the composite by
between matrix and
form of voids and
a composite structure.
loads, these matrix flaws
critical size and the composite
a
fractures.
It is therefore necessary to further investigate the damage growth in composite materials, specifically graphite/epoxy
which is currently used in a number of aerospace applications.
The
current
need
investigation
is
specifically motivated by the
understand how different types of damage initiate in
to
laminates.
identical
Two previous investigations are of par-
ticular importance to the current work.
Graves
[1] conducted an investigation on the progressive
accumulation
damage
[+-45/0]s,
in
four different laminates, [0/+-45]s,
and
[0/+-30]s
[+-30/0]s.
Experimental
work
included compression-compression fatigue of four-point bending
specimens
with 6.35 mm holes.
Visual and tactile inspections
were made of the specimen at various intervals of cyclic testing and qualitative sketches were drawn allowing a progressive
damage
type
sequence
of
to
be
deduced for each laminate type.
The
damage depended on both layup and stacking sequence.
result of particular interest here is illustrated in
the
But
Figures 1 and 2 where the [+-45/0]s laminate appears to exhibit
and
as
parallel
perpendicular
direction.
the loading
to
to
the
After 40,000 cycles
Figure 2a shows an identical specimen
failed.
specimen
at the same stress amplitude but damage initiated at a
loaded
different
much
edge
ic) the damage extends radially from the hole as well
lb
the
hole
In Figure (la), the
a relatively small number of cycles (see Figures
in
loading;
the
at
initiates
damage
damage patterns.
distinct
very
two
location.
In
this case longitudinal damage
starts at the edge of the hole parallel to the load direction.
Damage
(Figures
growth
2b and 2c) is slow, and the specimen
lasts 157,000 cycles.
of
80%
Over
[+-45/0]s
specimens tested by Graves
Results by Fanucci [2]
like that in Figure 2.
damage
showed
the
in a study on axially loaded sandwich specimens with [+-45/0]s
all showed damage modes similar to Figure 1.
laminates
specimens
test
These
were made with 12.7 mm holes (versus 6.35 mm)
and were tested at approximately the same ratio of peak stress
to
ultimate stress.
that
nation
he
Fanucci's work was more comprehensive in
used a quantitative NDI technique to measure delamiduring
size
testing,
as
pictures of the delamination damage.
progressive
damage
imental study.
sequence
well
as
obtaining direct
Figure 3 illustrates the
prominent
in
Fanucci's exper-
The technique of Moire interferometry was used
Fatigue: #6 .[45/0]s
Failure @ 40,000 cycles
10,000
cycles
Prior to
loading:
surface
flaw
30,000
cycles
/
38,000
cycles
40,000
cycles
FIGURE 1
RADIAL DAMAGE GROWTH IN [+-45/0]s LAMINATE
WITH 6.35 MM HOLE (TYPE 1) UNDER COMPRESSIVE
CYCLIC LOADING AS OBSERVED BY GRAVES [REF. 1]
Fatigue: #37
±4_5/0]
s
Failure @ 156,000 cycles
20,000
cycles
40,000
cycles
100,000
cycles
000 cycles
crack
140,00
cycles
c ra ck 0
FIGURE 2
1 0
00 0 cy 1es
LONGITUDINAL DAMAGE GROWTH SEQUENCE IN [+-45/0]s
LAMINATE WITH 6.35 MM HOLE (TYPE 2) UNDER
COMPRESSIVE CYCLIC LOADING AS OBSERVED BY
GRAVES [REF. 1]
0 CYCLES
500
6500
13000
25000
50000
87500
97500
VA...
75000
FIGURE 3
DAMGE GROWTH SEQUENCE IN [+-45/0]s LAMINATE WITH
12.7 MM HOLE UNDER COMPRESSIVE CYLIC LOADING AS
OBSERVED BY FANUCCI [REF. 2]
to
delamination
obtain
data; areas within the largest Moire
are assumed to be delaminated.
fringe
Figure 4, which is a plot
very quickly as failure approaches.
for
several
The damaged area grows
of delamination area versus the loga-
specimens
of the number of cycles shows exponential growth of the
rithm
delaminated area.
The results of these two investigations show that different
damage modes can occur in the same laminate under various
In this study, the [+-45/0]s laminate is consid-
conditions.
damage
determine
is,
were
sites
under
monitored
to
and rate of delamination
laminates of the form [+-45xn/Oxn]s, where n=1, 2, and 3,
made.
eration
and
initiation
were
holes
on laminates of various ply thicknesses, that
Tests
growth.
loading
cyclic
compression-compression
mm
6.35
with
Laminates
ered.
The variation of ply thickness allows the consid-
of
the
effect of out-of-plane stresses on the onset
of delamination damage.
growth
Through the use of Moire
interferometry and ultrasonic inspection, the growth of delamination
damage
was monitored for specimens under compressive
cyclic loading.
In
chapter 2, previous work will be reviewed.
a
description
Test
results
contains
setup.
discussion
of
these
of
the
experimental
Chapter 3
procedure and
are described in chapter 4 with a full
results
in chapter 5.
recommendations appear in chapter 6.
Conclusions and
o RUN NUMBER
a .UN
+ RUN
X RUN
R UN
+ RUN
X RUN
Z RUN
Sy RUN
X RUN
Z RUN
I RUN
SRUN
10A
NUMBER
NUMBER
NUMBER
NUMBER
NUMBER
NUMBER
NUMBER
NUMBER
NUMBER
NUMBER
NUMBER
NUMBER
NUMBER
. RUN NUMBER
,RUN NUMBER
12A
128
5A
.53
2A
2B
13q
132
88
15
16
9A
93
Cc
LL
Cr
CL
a:
a
aL
O
3
4
5
6
LOG CYCLES
FIGURE 4
GROWTH OF DELAMINATED AREA OF [+-45/0]s
LAMINATES WITH 12.7 MM HOLE UNDER COMPRESSIVE
CYCLIC LOADING AS DETERMINED BY FANUCCI [REF. 2]
CHAPTER 2
THEORETICAL BACKGROUND
fatigue
crack
initiation and
been well researched for homogeneous metals.
has
growth
of
characterization
The
The
study of the nucleation, subsequent growth, and coalescence of
cracks
form
to
voids
presents difficulty in modeling its fatigue behav-
anisotropy
simple
the
even
in
ior
Such is
A composite's inhomogeneity and
the case for composites.
not
led to an analytical
predicting a metal's fatigue behavior.
for
approach
has
metals
in
multidirectional
are
characterization
of
case.
When
all the possible associated
with
laminates
sequences
stacking
unidirectional
considered,
the
general
a composite's response to cyclic loading
becomes extremely complicated.
2.1 Unidirectional Composites
unidirectional
unnotched
For
composites under uniaxial
tension-tension fatigue, Kim and Embert [3] described the posmechanisms
sible
in
the
the
both
Figure
As
transverse
5
They proposed that flaws
propagate and coalesce to produce cracking in
matrix
matrix.
of damage growth.
cycling
to
and
continues, matrix cracks propagate
parallel
to the loading direction.
illustrates the possible ways in which a transverse
crack
matrix
fiber/matrix
interface
(a)
fiber break
(b)
matrix crack
(c)
FIGURE 5
POSSIBLE MECHANISMS OF MATRIX CRACK GROWTH AT A
FIBER INTERFACE IN A COMPOSITE PLY AS SUGGESTED
BY KIM AND EMBERT [REF. 3]
crack can grow:
matrix
the loading direction may be arrested at the
to
transversely
1) At low strains a crack propagating
fiber matrix interface; 2) If the strain level is high enough,
at the crack tip may exceed the fracture stress
stresses
the
macrocrack
a
as
acts
result in fiber failure; 3) Now the crack
and
fiber
the
of
an
opening mode until it reaches
where the local shear stresses may result
interface,
another
in
in a shear failure of the matrix leading to progressive extension of the matrix crack parallel to the fibers.
[4] measured the propagation of matrix cracks par-
Daken
direction
load
to
allel
in
notched
and
(holes
slits)
unidirectional graphite/epoxy laminates under tensile loading.
This
growth of matrix cracks parallel to the fibers is called
the hole edge where stress levels are highest.
at
originated
natural
of
tip
the
Again,
highest.
varied
logarithm
of
split length varies linearly with
the
accumulated
number
of load
The 00 splitting in specimens with slits initiated at
cycles.
the
total
the
Experimentally,
the
that splitting in specimens with holes
found
He
splitting.
linearly
slit
where the stress concentration is the
it was observed that the total split length
with
the
natural
logarithm
of
number of
applied cycles, which implies that the rate of split growth is
a
decreasing
slope
cycles
of
was
function
split
found
of the number of cycles applied.
The
length versus the logarithm of the number of
to
depend on the applied stress level and
FIGURE 6
OFF AXIS COMPOSITE PLY IN UNI-AXIAL LOADING
SUBJECT TO NORMAL (MODE I) AND SHEAR (MODE II)
STRESS COMPONENTS
flaw
size.
cycles
to
The
y-intercept,
split
a
function
of the number of
initiation also depended upon the flaw type
(hole or slit).
off-axis
For
cyclic
loads,
subjected
opening
to
unidirectional
the
crack
level,
normal
to the fiber direction and a shear mode
increasing
angle,
The result of cyclic loading is mixed
growth parallel to the fibers.
the
tensile
displacement components (see Figure 6): an
parallel to the fibers.
mode
under
tip of a crack initiated in the matrix is
two
mode
laminates
At a given strain
crack-tip opening displacement will increase with
fiber
matrix
angle; in other words, for increasing fiber
cracks become more like Mode I cracks.
Hashin
[5], showed that the opening crack mode was more critical than
the
shear
observing
mode
that
by
experimentally
the
critical
fiber angle and
for
crack propagation
decreased with increasing lamination angle.
Cyclic failure in
off-axis
laminates
propagates
the
(9
>
strain
varying
00) will occur when a matrix crack
entire width of the laminate.
At this point,
the laminate separates into two or more pieces.
2.2 Multidirectional Laminates
The
tional
the
features
laminates
same
as
of
under
damage growth in unnotched multidirecrepeated tensile loads are basically
in unidirectional laminates with the additional
damage
mode
presence
of
of
interface
delamination.
interlaminar
between
Delamination is caused by the
stresses
which
act on the matrix
two plies of differing fiber angle.
Thus,
delamination damage is dependent on the matrix properties.
It
has
mechanism
been
in
cracking
by
multidirectional
in
off-axis
growth)
(out-of-plane
interfacial
plies
grow
cracks
resulting
these
suggested
Talreja [6] that the damage
laminates
(in the plane of loading).
toward
quickly
which
regions.
begins with matrix
cause
ply
The
interfaces
stress concentrations in
The delamination crack will grow
under the influence of interlaminar normal and shear stresses.
Interlaminar
nate
can
stresses
also
delamination.
enough
plies
to
the
an
important role in the initiation of
If a component of interlaminar stress is large
cause a local failure of the interface between two
to
(see
grow
play
that occur at the free edge of a lami-
Figure 7), a delamination will occur and continue
during
individual
cyclic loading.
Delamination then separates
plies to unconnected (in the third direction)
unidirectional plies and damage proceeds as described above.
2.3 Characteristics of Compression Cyclic Damage
Whereas
results
compression-compression cyclic loading in metals
in the closing of microcracks and thus limited damage
development
(compression
loading tends to sharpen cracks and
FIBER
INTERFACE
FIGURE 7
SCHEMATIC OF MATRIX INTERFACE BETWEEN TWO PLIES
SHOWING DELAMINATION CRACK
growth
crack
increase
experimental
loading);
tension-compression cyclic
in
rates
studies
[7-9) in composite materials
shown that compressive cyclic loading is much more crit-
have
ical to damage development than tension-tension loading.
of
case
the
In
compression-compression
edge effects can lead to delami-
notched
loading,
fiber
composites
under
and
delami-
splits
initiate near the notch edge at a lower applied
will
nations
to that in the
high interlaminar normal and shear stresses.
to
due
nations
free
Also,
splits.
fiber
similar
is
progressive growth of matrix cracking and
the
case,
tensile
development
damage
Initial
than
unnotched laminates, but the damage mech-
anisms are similar.
The suggested sequence [8] of failure is:
level
stress
stress
interlaminar
and/or
exist,
at
leads
cracking
matrix
exhibit
rapid
laminates
may
at
interface where cracks
growth
away
from
compressive
under
loading
may
due to instabilities that do not exist
under tensile loading conditions.
delaminate
the
Delaminated regions grow until local insta-
in
Delaminations
at
delamination through
ply buckling and eventually laminate failure.
yield
bilities
effects
progressive
delamination due to high interlaminar stresses
free edge.
a
to
A ply or group of plies may
the total laminate; this "sublaminate"
buckle under loading which results in large peel stresses
the edges of the delamination.
propagation
of
damage
This effect leads to rapid
and failure.
The instability of thin
sublaminates
is
an
important
reason why compression cyclic
loading is most critical.
The
of
initiation
damage is also highly dependent upon
the stress field created by the following combination of laminate
conditions:
angled
4)
plies
the
type
of
flaw
in the laminate; 2) the
used in the laminate; 3) stacking sequence; and
thickness of each composite ply.
possible
exists
1)
combinations
many
possible
Thus, given all the
of the above laminate conditions there
sequences
of
damage
development and
growth.
2.4 Techniques in Evaluating Composite Damage Accumulation
A broad range of techniques have been proposed to predict
the
life
cyclic
and/or
loading.
the damage growth rate of a composite under
Most have been rather unsuccessful in model-
ing
a general laminate's response.
the
fact that the models fail to take into account the varied
This is most often due to
nature of the damage present in a "generalized" composite laminate.
curve
Most techniques that have been developed are based on
fitting
of
experimental
data rather than attempts to
model the actual mechanisms of damage initiation and growth.
The most simple cyclic models attempt to predict residual
strength;
after
i.e., the ultimate strength of a composite laminate
a given number of applied loading cycles.
Hahn and Kim
[10)
introduced
assumption,
concept of the strength-life equal rank
the
which
assumes
that
a specimen's rank in static
strength is equal to its rank in cyclic life.
This assumption
simply means that in a given set of test specimens, the specimen
with the highest static strength will also have the long-
est
cyclic
life; the weakest specimen will have the shortest
life.
cyclic
on
Based
strength-life
equal
rank
Chou and Croman [11] proposed a model of residual
assumption,
Their degredation equation contains a
degredation.
strength
the
single parameter which can be adjusted to fit test results and
to produce a family of curves illustrating the
then
be
rate
at which residual strength decreases with cyclic loading
at
a
The model has two drawbacks:
amplitude.
stress
given
a lack of generality in that any given laminate requires
one,
a
used
set
of
tests to determine strength and life
experimental
and
distributions,
two,
the
model- fails to account for the
possibility of increased residual strength, which is suggested
by
Whitcomb
[12]
who
found
an
increase
in
the residual
strength of notched laminates.
Ratwani
assume
decrease
laminate.
Kan
[13]
proposed
a model to predict the
residual strength that has a more physical basis.
compressive
They
and
that
with
the
compressive
increasing
residual
delamination
area
strength
in
a
will
given
Once again this model has similar shortcomings for
cyclic testing must be done to determine
the number of cycles
failure for a given laminate under study as well as deter-
to
stress
a critical delamination area for a given minimum
of
mination
Experiments
level.
confirmed
the validity of their
equations and a good feature of the model is its applicability
cyclic
to
adjusted
be
can
loading spectrums.
account
to
They also claim that the model
for
an
increase
in residual
strength.
The process of damage accumulation by delamination, fiber
splits,
etc., leads to progressive reduction in the stiffness
of a composite laminate.
a
measure
of
This stiffness loss has been used as
damage in composites under cyclic loading.
An
attempt was made by O'Brien and Reifsnider [14] to predict the
stiffness-loss in boron/epoxy laminates at failure from a criterion
the
using
laminate's
secant
modulus.
They found,
however, that the growth of damage and stiffness loss was load
history
dependent
and
therefore
the criterion could not be
generally applied.
More recent work by Reifsnider [15], and by Highsmith and
Reifsnider [16] have shown a close correlation between composite
stiffness
cross-plied
lag
analysis
stress
loss
and the extent of transverse cracking in
laminates.
around
Their work centered on a simple shear
a "theoretical" matrix crack.
From the
distribution calculated around the crack and stiffness
measurements made at various stages of load cycling, they were
able to predict the transverse crack density (number of cracks
in
a
given
Ell,
volume) for a set of given laminate stiffnesses,
E 2 2, G
1 2.
Using
a
technique of edge replication, an
actual
value for the transverse crack density was established
in
experimental
an
laminates.
ical
This
test program on unnotched graphite/epoxy
value correlated very well with the analyt-
predictions.
Highsmith
and
Reifsnider found that the
measured
equilibrium
reduction
in stiffness occurred coincided with an equilibrium
stiffness
levels
where
no
further
transverse crack density which was stress level dependent.
Another method for predicting the location of damage initiation
in an unnotched laminate considers the effect that an
individual
ply
has on its surrounding neighbors.
The effect
is a constraint that one ply puts on another due to a mismatch
in
elastic
Reifsnider
properties
[17]
in
plies
introduced
the
through
a simple observation.
age
the
in
00
plies
differing fiber angle.
concept
of
ply-constraint
In an unnotched laminate, dam-
consists
splitting along the fibers.
of
primarily
of
longitudinal
If the 0* ply is constrained by a
90* ply in a [0/90]s laminate, Classical Laminated Plate Theory
(CLPT)
transverse
450
in
shows
stress,
that
uniaxial
a2 2 '
loading
in the 00 ply.
induces a positive
The introduction of
plies in the [+-45/0]s laminate induces a compressive a
22
the 0* ply for the same loading condition.
tory,
(0/90]s
Reifsnider
laminate
In the labora-
observes more longitudinal splitting in the
for
a
given number of loading cycles at a
given
stress
suggests
result
ply
amplitude than in the [+-45/0]s laminate.
constraints
This
the possibility of looking at the effects of
and
elastic mismatch to delay initiation of
damage due to repeated loading.
The
analysis
Herakovich [18] used the analysis
to static loading.
applied
to
developed from this concept was originally
look
at
along
delaminations
the free edge of unnotched
It is well known that
specimens under static tensile loading.
cause
of delamination) exist in
due to the presence of a mismatch in the engineer-
composites
ing
(the
stresses
interlaminar
properties
between
are
interlaminar
stresses
nation
originate),
will
plies.
highest
To
analyze
where
the
(and hence where delami-
Herakovich
studied the mismatch of
Poisson's ratio, '12' and the coefficient of mutual influence,
(shear strain divided by longitudinal strain, E1 2 /Ell)
'12, 1 ,
A mismatch of Poisson's ratio between
between adjacent plies.
adjacent plies would result in different transverse strains if
the
plies
were
not
bonded together.
In a perfectly bonded
laminate, identical strains result, but the Poisson's mismatch
causes the introduction of non-zero interlaminar stresses, a zz
and
ayz'
results
at
in
the
free
edge.
Similarly a mismatch in r12, 1
a non-zero interlaminar shear stress,
free
edge of perfectly bonded laminates.
that
interlaminar
Xz
,
at the
Herakovich predicts
stresses will be the largest between plies
with the greatest mismatch of v12 and '12,1'
Klang and Hyer [19] expanded this analysis to look at the
effect
of
ply
constraint around a curved free edge with the
of
goal
specific
interlaminar
the
determining
stresses
magnitude
relative
of
between different plies around a hole.
The analysis remains relatively simple because the rotation of
v12
constants
engineering
and
r12,1
around
a
hole
is
straightforward
by calculating the mismatch between different
adjacent
at
plies
prediction
of
can be made.
varying
the
locations around a hole.
location of maximum interlaminar stresses
It is reasoned that damage will initiate at this
location
under cyclic loading.
imental
results
While Klang and Hyer's exper-
not
were
entirely
in
agreement
with
the method does predict the possibilty of damage
predictions,
initiation
Then a
sites
around a hole which are not at the sites of
maximum in-plane stress; this is commonly observed in the labNo
oratory.
a
stress,
zz
inititation.
A
more
suggestion
or
a
xz
,
detailed
is
is
given
more
as to which interlaminar
important
for
delamination
approach to the problem of determining
damage location sites is through the use of finite elements to
calculate
the interlaminar stresses at any point in a general
laminate.
Use of the finite element method is well suited to
calculating
stesses around a hole or other irregularly shaped
boundaries.
Whitcomb [12] conducted a finite element study on
a
notched
laminate
composed
of
0*, 450 and 900 plies.
He
the
in
variation
stacking
various
investigated
Through
initiation
the
predicted
and showed a large
interlaminar stresses for each
calculated
sequence.
stacking
sequences
analytical work, Whitcomb
this
sites
of damage (delamination and
matrix
cracking) in a compression cyclic test program.
x-ray
radiography
and
replication
edge
Using
techniques
on
graphite/epoxy test specimens, the damage sites as well as the
type
damage
of
were
Experimental results con-
determined.
the finite element calculations in that the damage was
firmed
vary from one stacking sequence to another, and the
to
found
sites were correctly predicted as areas having the
initiation
An important result of this
stresses.
interlaminar
largest
study showed that comparison of observed damage locations with
as
stresses
est
well
to
attempting
with
requires
stresses
calculated
normal
as
that
both
interlaminar shear
stresses must be considered in
predict damage sites.
That is, both locations
highest interlaminar shear stress and locations of highnormal
stress
will
be sites of damage initiation under
by
Carlsson [20] found similar results
cyclic loading.
A
using
recent
a three-dimensional finite element analysis in a 28-ply
graphite/epoxy
loading.
ment
study
with
a
6 mm hole under compressive
NDI techniques were used to confirm the finite ele-
findings
analysis
laminate
in
a
cyclic
test study.
The finite element
accurately predicted initiation of delamination with
respect
to
the
damage
Matrix
hole.
damage location between plies and around the
due
to
cracking
also predicted
was
in-plane finite element stress calculations elsewhere
through
around the hole.
Finite element analysis appears to be a powerful tool for
predicting damage areas in composites.
sive
the elements to recalculate stresses after
of
modeling
In fact, with progres-
first damage, a sequence of damage growth could be constructed
for any given laminate.
of
characterization
The
delamination
as a damage mode
occurs solely in the matrix suggests the use of a frac-
which
mechanics approach to describe its behavior.
ture
The strain
release rate, G, of a planar body containing a flaw of
energy
area,
is
A,
a
measure
of the rate at which elastic strain
energy is stored as the flaw area increases:
dU
dA
G =
(2.1)
et. al. [21] conducted a study to determine val-
Wilkens
ues of the strain energy release rate in graphite/epoxy interfaces.
He
measure
G
specimen
good
designed
for
for
Mode
Mode
approximation
results
from
a
double cantilevered test specimen to
I
(tensile opening) cracks and a shear
II (forward shear) cracks.
of
the
In general, a
total strain energy release rate
adding the contribution of each mode.
Assuming
negligible
Mode
III
contribution,
the
total strain energy
release rate can be written as:
Gto t = G I + GII
Wilkens
(2.2)
experimentally determined G I and GII for both a crack
in a 00/00 interface and in a 00/900 interface.
the
growth-rate
at
exponent for a Mode I delamination operating
percentage of GIc (>70% of the critical load) was
high
a
Delaminations growing in this condition will
extremely large.
grow
rapidly
percentage
therefore
to
of
failure.
GIc
thought
rather
than
a
growth,
on
the
damage
He found that
growth
will
to
be
potential
Delaminations operating at a low
grow very slowly.
somewhat
cyclic
Mode I damage is
of a static design issue
problem.
Mode
II damage
other hand, was found to be much like Mode I
in aluminum and must be considered as a cyclic
design issue.
An
a
The
encouraging result of Wilkens' work was that he found
similar
value
for
GIIc for these two orthotropic layups.
possibility exists that GIIc may be dependent only on the
matrix material and not the layup or stacking sequence.
An
application of the strain-energy release rate to pre-
dicting
the onset and growth of delamination was conducted by
O'Brien
[22].
unnotched
He studied the growth of edge delamination in
coupons
and
modeled
the
subsequent
stiffness
From
lation.
the
equation
for total strain energy release
(2.2), we can express the strain energy, U, as a product
rate
of
and a simple rule of mixtures calcu-
CLPT
through
reduction
strain energy density and the volume of the body.
the
If
expression is differentiated in equation (2.1), the fol-
this
lowing expression for the strain energy release rate results:
(2.3)
G = -V (2 /2) (dE/dA)
where dE/dA is the rate of stiffness change as the flaw grows,
and V is the volume of the body.
O'Brien
and
loaded
recorded
c .
From
the
this
reduction,
Gc
predicted
the
[+-45/0/90]s
analysis,
be
a
[+-30/+-30/90x2]s
strain level at the onset of delamination,
value
was
a
calculated rate of stiffness
determined.
Using this value for Gc, he
onset
and
and
laminates.
indicating
unique
laminates in tension
growth
of
Experimental
edge
delamination
in
results confirmed the
that the strain energy release rate may
characteristic material property of a composite
material.
The
expense.
results
The
delamination
age
location
analysis
that
O'Brien obtained came at considerable
ability
to predict stiffness reduction due to
damage requires, a priori, knowledge of the damand direction of growth.
Finite element stress
was used to determine at which ply interface delami-
47
nation would occur.
modulus
these
a
Furthermore, while he modeled the loss of
as a linear relationship of the delamination area for
test conditions, much work is still required to develop
meaningful
relationship
loading conditions.
for
notched
laminates and other
CHAPTER 3
EXPERIMENTAL PROCEDURE
3.1 Axial Sandwich Specimen Fabrication
a
of
selection
compression
successful test program.
ate
specimen
compression
is
gation
in
instabilities
Structural
outlined
in
thin
plates
make
the
specimen a critical part of any
The process of choosing an approprifor the work done in this investiAppendix 1.
Axially loaded sandwich
specimens were chosen and used for all the compression testing
in
this
It
consists
of
side
reason
was
its
The specimen chosen is pictured in Figure 8.
study.
of two flat composite laminates bonded to either
a reinforcing aluminum honeycomb core.
for
An important
the choice of an axially loaded sandwich specimen
ability
to
allow non-destructive inspection during
testing to monitor delamination development.
laminates
Composite
preimpregnated
unidirectional
made from Hercules AS1/3501-6
were
tape.
Teflon-coated aluminum
templates and a Stanley razor knife were used to cut the individual
plies
for each laminate.
Laminates were laid up in a
special
jig
designed to aid in the precise alignment of each
in
the
laminate.
ply
The
effective
ply
thickness
of a
[+-45xn/Oxn]s laminate was altered by varying n, where n=1, 2,
or
3.
For
a
nominal single ply thickness of 0.134 mm, the
GLASS/EPOXY LOADING TAB
354 KG/M 3 ALUMINUM
HONEY COMB
T
72 KG/M 3
ALUMINUM
HONEYCOMB
350 mm
SFILM
S50
mm
TOP VIEW
-A
25.4
-- ADHESIVE
mm
SIDE VIEW
(NOT DRAWN
TO SCALE)
FIGURE 8
CONFIGURATION OF COMPRESSIVE SANDWICH TEST
SPECIMEN
laminates
constructed
would
have
a
nominal "effective ply
thickness" of (n x 0.134 mm).
laid up composite laminates were prepared for curing
The
by placing a sheet of nylon peel-ply on each side of the laminate.
Six
x 305 mm laminates were cured at a time on a
350
large flat aluminum plate coated with mold release.
The plate
covered with a sheet of guaranteed non-porous teflon fab-
was
ric, and the composite laminates were positioned on this sheet
of
Standard curing materials: porous teflon fabric,
teflon.
paper and non-porous teflon were placed on each lami-
bleeder
nate.
aluminum
Individual
top
were placed on each
plates
laminate to provide even pressure distribution.
of
woven
fiberglass
assembly,
and
resistent
nylon
the
airbreather
assembly
was
was
laid
vacuum
A large piece
over the entire
bagged
with
heat
vacuum bagging and pressure sensitive vacuum
tape.
A
vacuum hose was fitted to the plate and a vacuum of 25
to 30 inches of Hg was drawn over the cure assembly.
tem
was
carefully
checked
for
leaks
The sys-
before the plate was
placed inside a five-foot long, three-foot diameter autoclave.
The
composite
one
hour
A
pressure
laminates
were cured in a two step process: a
hold at 240*F followed by a two hour hold at 350 0 F.
of
85 psig was applied throughout the cure.
complete cure cycle is shown schematically in Figure 9.
The
After
AUTOCLAVE
TIME
AUTOCLAVE
PRESSURE(PSI)
85
10 35
95 115
235 275280
TIME
VACUUM (IN. HG)
28
S1I
10 35
FIGURE 9
I
I
95 115
I
235
I
275280
TIME
TELAC CYCLE FOR HERCULES AS1/3501-6
GRAPHITE/EPOXY
curing,
the
laminates
were
removed
from
the
plate
and
postcured in an oven for eight hours at 350 0 F.
The
laminates
diamond-encrusted,
were cut with a high-speed, water-cooled,
circular
saw.
The
saw was mounted on a
precision milling machine that has been specially modified for
cured
cutting
Five 350 x 50 mm coupons were cut
composites.
from each laminate.
Nine
with
a
Three
thickness
micrometer
width
proper
gram
measurements
to
ensure
measurements
dimensions
were
taken of each coupon
the quality of the composite.
were
taken
to guarantee that the
of the specimen had been attained.
A dia-
of the locations where each thickness and width measure-
ment were taken appears in Figure 10 and the averages for each
coupon
0.138
appear
mm,
in
was
Tables
1-3.
An average ply thickness of
obtained for all the laminates with a coeffi-
cient of variation of 2.2%.
This value is consistent with the
value supplied from the manufacturer of 0.134 mm.
The
each
6.35 mm diameter holes were drilled in the center of
coupon
with
a
two
step
process.
A
high
speed
diamond-encrusted drill was used to bore a hole slightly under
the
desired
diameter.
used to polish the hole.
the
A second bit, a fine grit reamer, was
This second step brought the hole to
desired diameter and provided a smooth finish to the com-
posite
diameter
edge
were
around
the
hole.
Measurements
of
the
hole
taken using hole gages and calipers and appear
1
2
3
S12.5
mm
50 mm
7
FIGURE 10
8
9
LOCATION OF THICKNESS AND WIDTH MEASUREMENTS
TABLE 1
MEASURED THICKNESS, WIDTH AND HOLE DIAMETER FOR [+-45/0] s SPECIMENS
Thickness
[mm]
Specimen
I.D.
Width
[mm]
Hole
diameter
Thickness
[mm]
Specimen
I.D.
Width
[mm]
[mm]
[mm ]
STC145AI-1
-2
-3
-4
-5
-6
STB145Al-1A
-1B
-2A
-2B
-3A
-3B
-4A
-4B
-5A
-5B
-6A
-6B
-7A
-7B
-8A
-8B
SCB145Al-1A
-1B
-2A
-2B
-3A
-3B
-4A
-4B
-5A
-5B
-6A
-6B
.854
.851
.850
.858
.837
.847
.862
.856
.826
.830
.866
.843
.861
.840
.860
.867
.857
.864
.843
.848
.817
.850
50.17
50.10
50.22
50.17
50.04
50.18
50.20
50.02
49.99
49.86
49.74
49.94
49.96
49.98
49.95
49.90
50.00
50.01
49.87
49.96
49.96
50.00
6.38
6.38
6.37
6.40
6.35
6.38
6.38
6.39
6.41
6.41
6.36
6.37
6.41
6.35
6.41
6.44
6.35
6.37
6.39
6.39
6.40
6.38
.862
.848
.815
.870
.853
.859
.866
.816
.854
.851
.859
.844
49.92
49.94
49.88
49.90
49.91
49.93
49.81
49.89
49.96
49.87
49.91
49.40
6.40
6.40
6.35
6.36
6.39
6.42
6.38
6.41
6.40
6.40
6.41
6.38
Average thickness = .846 mm
Coefficient of variation = 1.5%
Hole
diameter
SCB145Al-7A
-7B
-8A
-8B
-9A
-9B
FCB145Al-1A
-1B
-2A
-2B
-3A
-3B
-4A
-4B
-5A
-5B
-6A
-6B
-7A
-7B
-8A
-8B
-9A
-9B
-10A
-10B
-11A
-11B
-12A
-12B
-13A
-13B
-14A
-14B
-15A
-15B
-16A
-16B
.836
.831
.854
.832
.828
.840
.828
.842
.856
.847
.837
.849
.836
.829
.838
.856
.851
.847
.835
.841
.837
.828
.846
.847
.832
.857
.861
.852
.845
.837
.833
.844
.849
.829
.854
.851
.840
.846
49.98
49.98
49.82
49.96
49.93
49.80
49.74
49.77
49.82
49.82
49.88
49.72
49.83
49.80
49.76
49.84
49.85
49.80
49.83
49.80
49.82
49.78
49.78
49.80
49.76
49.76
49.80
49.82
49.84
49.76
49.82
49.83
49.79
49.78
49.72
49.81
49.90
49.93
6.39
6.41
6.42
6.36
6.38
6.41
6.41
6.37
6.38
6.39
6.41
6.40
6.37
6.42
6.41
6.40
6.38
6.37
6.39
6.41
6.41
6.42
6.38
6.39
6.41
6.40
6.40
6.39
6.41
6.42
6.41
6.41
6.43
6.38
6.37
6.39
6.41
6.39
TABLE 2
MEASURED THICKNESS, WIDTH AND HOLE DIAMETER FOR [+-45x2/0x2]s SPECIMENS
Specimen
i.D.
Thickness
[mm]
Width
[mm]
Hole
Diameter
Specimen
I.D.
Thickness
[mm]
Width
[mm]
[mm]
[mm]
SCB245AI-1A
-lB
-2A
-2B
-3A
-3B
-4A
-4B
-5A
-5B
-6A
-6B
-7A
-78
-8A
-8B
1.563
1.614
1.621
1.629
1.547
1.592
1.626
1.645
1.639
1.541
1.570
1.632
1.630
1.619
1.639
1.615
49.56
49.49
50.01
50.03
49.79
49.75
50.36
49.90
50.31
49.86
49.80
50.46
49.74
50.44
49.74
49.80
6.39
6.44
6.41
6.40
6.41
6.49
6.41
6.42
6.38
6.41
6.42
6.41
6.44
6.47
6.41
6.42
FCB245AI-1A
-lB
-2A
-2B
-3A
-3B
1.486
1.589
1.617
1.593
1.472
1.470
49.95
49.99
49.94
49.99
49.98
49.92
6.43
6.41
6.38
6.42
6.41
6.40
Average thickness = 1.569 mm
Coefficient of Variation = 3.6%
Hole
Diameter
FCB245AI-4A
-4B
-5A
-5B
-6A
-6B
-7A
-7B
-8A
-8B
-9A
-9B
-10A
-1OB
-11A
-11B
-12A
-12B
-13A
-13B
-14A
-14B
1.571
1.619
1.588
1.477
1.492
1.571
1.589
1.473
1.494
1.516
1.511
1.541
1.613
1.554
1.577
1.490
1.531
1.529
1.480
1.620
1.618
1.647
49.91
49.96
49.89
49.95
49.94
49.95
49.95
49.98
49.97
49.95
49.97
49.98
49.95
49.95
49.92
49.94
49.95
49.94
49.97
49.98
49.96
49.97
6.41
6.42
6.40
6.40
6.41
6.41
6.39
6.39
6.43
6.40
6.41
6.40
6.40
6.44
6.41
6.39
6.42
6.41
6.41
6.46
6.41
6.39
TABLE 3
AVERAGE THICKNESS, WIDTH AND HOLE DIAMETER FOR [+-45x3/0x3] s SPECIMENS
Thickness
[mm]
Specimen
i.D.
Width
[mm]
Hole
Diameter
[mm]
SCB345Al-1A
-lB
-2A
-2B
-3A
-3B
-4A
-4B
-5A
2.349
2.316
2.351
2.411
2.298
2.391
2.356
2.347
2.429
49.78
49.86
49.88
49.85
49.70
49.79
49.82
49.81
49.84
6.46
6.47
6.43
6.46
6.47
6.49
6.49
6.47
6.45
-5B
2.311
49.83
6.50
Average thickness = 2.357 mm
Coefficient of variation = 1.8%
Thickness
[mm]
Specimen
I.D.
FCB345A1-1A
-IB
-2A
-2B
-3A
-3B
-4A
-4B
-5A
-5B
Width
[mm]
Hole
Diameter
[mm]
2.423
2.299
2.286
2.354
2.389
2.380
2.372
2.326
2.333
49.75
49.83
49.81
49.82
49.79
49.78
49.81
49.81
49.78
6.48
6.49
6.51
6.42
6.48
6.46
6.50
6.43
6.45
2.416
49.81
6.46
57
with
the
thickness
more
thorough
and width measurements in Tables 1-3.
A
description of the coupon manufacturing proce-
dure is outlined in Reference 23.
complete,
Once
bonded
aluminum
to
to
make
up
the
sandwich
honeycomb core with FM-123-2 film adhesive manufactured
Cyanimid.
The core was made from a 180 mm by 60
by
American
mm
central piece of low density (72 kg/m3) honeycomb.
tion
was
of
bonded with a room temperature cure epoxy to both ends of
The low density honeycomb was used
reduce the stiffness of the core to a negligible amount in
the
test
end
allowed
sure
A sec-
density (354 kg/m 3 ) honeycomb, 90 mm by 60 mm,
high
the low density honeycomb.
to
then
Two coupons were bonded to either side of an alu-
structure.
minum
honeycomb
were
coupons
graphite/epoxy
the
to
crushing.
section, while the high density honeycomb on either
the specimen to be gripped with sufficient pres-
avoid
The
slippage
bonding
225 0 F
while
procedure
preventing
was
the
carried
core
out
from
in
an
autoclave
at
bond
performed to place [0/90]ms fiberglass loading tabs
on
was
each
Scotchply
[+-45/0]s
and
35 psig for two hours.
end of the specimen.
1003
type
I
A secondary
Eight ply tabs (m=2) made from
glass/epoxy
were
bonded
on
each
sandwich specimen, 12 ply tabs (m=3) were placed on
[+-45x2/0x2]s and [+-45x3/0x3]s sandwich specimens.
In order to obtain data to determine longitudinal modulus
and Poisson's ratio, a longitudinal and transverse strain gage
were
of every specimen used in static
face
each
on
placed
Micro-Measurements EA-06-125AD-120 strain gages were.
testing.
The location of these 10 mm x 6 mm
used for all static tests.
gages (foil size) are shown in Figure 11.
The measured longi-
tudinal
modulus served as a means of quality assurance in the
program
by comparing the measured modulus with predicted val-
ues.
that
specimens
All
no
inspected by ultrasound to assure
were
major voids or delaminations existed in the specimen
prior to testing.
3.2 Specimen Identification
Specimen
identification
was
made
via
a
simple
ten
letter/digit code:
XXXn45A1-00
XXX
n
=
=
SCB
(Static Compression Beam)
STB
(Static Tension Beam)
STC
(Static Tension Coupon)
FCB
(Cyclic Compression Beam)
1, 2, or 3
("effective thickness" of each ply,
i.e. n x 0.134 mm)
45A1
=
Shorthand identification of laminate type
[+-45xn/Oxn]s
00
=
Digits indicating specimen number in the series
of tests.
~
;
50 mm
-A
12.5
mm a-
ii
.3 -
FIGURE 11
mm
LOCATION OF LONGITUDINAL AND TRANSVERSE STRAIN
GAGES PLACED ON STATIC TEST SPECIMENS
For
cyclic compression beam
in the [+-45x2/0x2]s laminate family.
nine
number
specifies
FCB245A1-09
example,
Note also
that
the
letter A or B following the specimen number identi-
fies
the
individual
specimen.
letter
B
The
coupons used on either face of the test
A corresponds to the front face while
letter
corresponds
to the back face.
All specimens had a
6.35 mm hole.
3.3 Static Testing Procedure
Both
tensile
and compressive static testing was carried
out in a 100,000 pound MTS 810 servo-hydraulic testing machine
with the use of hydraulic grips.
Specimens were first aligned
and gripped in the self-aligning grips of the testing machine.
The zero load condition was prescribed with the top end of the
the
upper
grip head while the lower end of the
specimen
in
specimen
was left ungripped.
All calibration of strain gages
was performed at this point and the channels zeroed.
began by gripping the bottom of the specimen.
The test
For compressive
specimens, load was applied at a constant displacement rate of
0.33 mm/min (approximately 1800 ps/min) until failure occured.
Failure
was
percent
drop
defined
in
load
as the point at which a greater than 50
was observed.
Strain gage leads were
wired to a multichannel set of amplifiers/conditioners.
Load,
stroke, and
strain data were taken automatically by a DEC PDP
11/34 computer and stored on magnetic disk.
Nine
145A1
specimens,
eight
245A1
specimens and five
specimens were tested under static compressive loading.
345A1
these static tests, a value for the compressive ultimate
From
stress for specimens with a 6.35 mm diameter hole was obtained
of
the three laminates.
Longitudinal modulus data
for
each
and
Poisson's ratio were also determined and compared to val-
ues
predicted from Classical Laminated Plate Theory to assess
the quality of the specimens.
3.4 Cyclic Testing Procedure
All
same
cyclic runs were performed under load control on the
MTS 810 testing machine as the static tests.
generator
provided
frequency
of
stress/minimum
change
the
to
applied
the
stiffness
to
Hz.
waveform for sinusoidal loading at a
A constant stress ratio of 0.1 (maximum
stress)
was
used for for all tests.
A small
in the stiffness of the composite resulted in drift of
adjusts
the
7
the
A function
This drift in load was due
feedback loop of the testing machine which constantly
the
of
testing
yield
loading of up to 5%.
loading
the
to
match the control position.
As the
composite changes, the control position of
machine will not be at exactly the right setting
the desired loading.
The higher the test frequency
the more the system tends to drift from this control position.
Because of this effect, higher frequencies of testing were not
two
faces,
specimen consists of two graphite/epoxy
each
Since
chosen.
of cyclic data were gathered from each test
sets
run.
Delamination growth was monitored during each cyclic test
by
of
one
two NDI methods as described in section 3.6.
145A1
fourteen
specimens
were
out-of-plane Moire interferometry.
were
imens
monitored for damage through
The first five 245A1 spec-
also monitored with the Moire set-up.
and
specimens
all
345A1
five
All
Nine 245A1
specimens were monitored for
delamination damage through ultrasonic inspection.
Moire
were
of 5000 cycles.
frequency
into
fed
were
photographs
taken automatically at a preset
Pulses from the function generator
an electric counter which fired cameras posi-
tioned in front of both sides of the specimen as well as triggering short bursts from the strobe lights at the peak load of
each cycle.
This generated a set of damage propagation photothe
duration
of the cyclic test.
Delaminations
graphs
for
tended
to grow quickly once initiated in many tests.
If this
growth rate exceeded approximately 10 mm per 5000 cycles, then
the
frequency
cycles.
of
picture taking was increased to every 2000
This size is defined as the maximum width of the dam-
age area in any direction.
Ultrasonic
2000
Digital
testing
was
accomplished
with a Nova-Scope
Pulse-Echo Ultrasonic Thickness Gage with a NDT
Instruments
D1R
damage
was
monitored with ultrasound, the tests were stopped
at
to
50
transducer.
For
5000 cycle intervals to allow for inspection using
the
6.35 mm diameter transducer.
was
chosen
mm
the cyclic tests in which
The frequency of inspection
to ensure that damage would not grow more than 10
in any direction between inspection intervals.
onset
of
delamination,
every
1000
inspected
the
by
onset
length
cycles.
of
the
the
laminate was inspected at least
The area around the hole was thoroughly
ultrasound
of
Before the
for delamination initiation.
delamination,
After
a ruler was used to measure the
delamination,
as indicated by the ultrasonic
technique, in terms of the maximum straight-line distance from
the hole edge to the edge of the delamination (see Figure 12).
These
measurements,
which
are
accurate
to
0.5
mm,
were
recorded along with the number of applied load cycles.
All
or
two,
could
ble
cyclic tests were stopped when one, failure occurred
damage
grew
to a size at which it was felt failure
occur before the next inspection cycle.
to
prevent
failure
It was desira-
of damaged cyclic specimens so that
tensile residual strength tests could be run.
HOLE
EDGE
FIGURE 12
DEFINITION OF DELAMINATION LENGTH, a
3.5 Residual Tensile Strength Tests
strength tests were run to determine the effect
Residual
of
accumulated
damage
the
the
during
cyclic tests on the
strength of the graphite/epoxy specimen.
tensile
A number of
tests could not be conducted due to the fact that the specimen
during cyclic loading or the specimen was sectioned to
failed
oven at 300 0 F for ten minutes.
heated
composite
the
between
from
the honeycomb.
each
coupon
of
Loading tabs were bonded to both ends of
by the procedure previously described in section
A total
specimens were cycled and out of these 8 failed.
35
process.
specimen,
this
mented
with
Figure
11
test.
section
Since there are two coupons per sandwich
All
testing.
longitudinal
to
resulted in 46 coupons for tensile
procedure
strength
residual
Four
sectioned, and four coupons were damaged in the
were
debonding
in
and the honeycomb breaks down at this
resulting in the specimen depicted in Figure 13.
coupons
each
The film adhesive bond
and the graphite/epoxy sheets were easily removed
temperature
3.1
intact specimens were placed in a pre-
The
damage.
observe
provide
and
the specimens were instru-
transverse strain gages as in
modulus and Poisson's ratio data from
The testing procedure is the same as is described
3.3
except
that the tensile coupons were loaded
monotonically to failure in tension under a constant displace-
TOP VIEW
SIDE VIEW
T
75 mm
GLASS/EPOXY
TAB
GRAPHITE/EPOXY
200 mm
-GRAPHITE/EPOXY
FM-123 FILM ADHESIVE
I-
GLASS/EPOXY
75 mm
GLASS/EPOXY
50 mm
FIGURE 13
CONFIGURATION OF TENSILE RESIDUAL STRENGTH
TEST COUPON
ment rate of 0.33 mm/min giving a strain rate of approximately
1800 ps/min.
3.6 Non-Destructive Investigation Techniques
When a set of closely spaced parallel lines are laid over
a
second set of parallel lines, a type of interference occurs
placing
and
specimen
a grid of fine lines to the surface of a
etching
or
bonding
displacements can be obtained by
In-plane
common.
is
body
The application of Moire
the derivation of strains in a deformable
for
interferometry
Moire effect.
the
called
is
that
identical "master grid" over these
an
lines.
As
the specimen deforms, the bonded grid deforms and
creates
an
interference
determined
be
can
in
the
with the master grid.
at
any
The
form of fringes where each
a line of constant displacement.
is
fringe
is
pattern
interference
pattern
The displacement
fringe by counting the number of
fringes from the point of interest to a point of known (usually
zero) displacement.
the "pitch" (lines per mm) to determine the displacement
with
at
This so called "fringe order" is used
chosen
the
interferometry
glass
with
flat
surface
directed
useful
form of Moire
is out-of-plane interferometry.
If a plate of
point.
Another
very
etched parallel lines is placed parallel with the
of a specimen and a collimated beam of light is
at an oblique incidence to the glass, the glass will
68
cast a set of parallel shadows on the surface of the specimen.
If the surface of .the specimen undergoes out-of-plane deformadeform which produces an
An accurate meas-
of the displacement can be determined
magnitude
the
of
to
pattern with the glass plate.
interference
ure
begin
will
shadows
the
tion,
with knowledge of the pitch of the glass plate, angle of incidence of the light, and fringe order at the chosen point.
as
investigation, the magnitude of displacement is not
this
for
of
tend
to
a
to
method
areas
can be determined.
areas
cause
as
of
out-of-plane
Delaminated areas
deformation
under
These deformations can be seen with Moire
loads.
interferometry
undergoing cyclic loading, the
composite
delamination
compressive
By applying
as the locations of displacements.
important
this
But
a set of fringes.
The outermost fringe is
considered as the border of the delaminated area.
Moire
The
of
sisted
lines
test
set-up used for this investigation con-
x
10 cm glass plates with etched parallel
cm
10
(254 lines/cm) positioned parallel to both faces of the
specimen.
The
plates
three-degree-of-freedom
clamps
within 0.5 mm of the composite.
positioned
composite
function
vided
a
were
that
held
could
by
a
align
set
of
the glass
Collimated strobe lights were
at an angle of 450 and a distance of 50 cm to each
face.
generator
The
strobes were fired by a pulse from the
at the peak load of the cycle.
This pro-
stop action view of the specimen during testing with
the
pattern
Moire
The
composite.
clearly
surface
of
displayed over both faces of the
the composite was spray painted
silver enamel to increase the contrast of the Moire pat-
with
A photograph of the Moire test set-up
for photographs.
terns
is shown in Figure 14.
Another very common form of non-destructive inspection is
use of pulse-echo ultrasound.
the
This form of inspection is
very well suited for locating delaminations in a composite.
small
A
linked to an ultrasonic device held in con-
transducer
tact with a solid object sends out pulses of ultrasonic waves.
These
waves
speed
of
to
sound
and
transducer.
calculate
amount
the
medium.
When the ultrasonic pulse
crack in the body, etc.), the wave is reflected back
or
the
in
some type of interface (the back face of the solid, a
reaches
void
penetrate the solid and travel through it at the
of
time
the
the
A sensor can receive the reflected pulse
distance
the pulse traveled based on the
pulse took to travel through the solid.
Based
on this principle, the device can indicate the location
of
void or discontinuity in a solid.
a
If a delamination is
present in a composite plate, the ultrasonic wave will reflect
off
the surface created by the delamination and this is indi-
cated by the ultrasonic inspection device.
For this study, areas of delamination could be determined
by
moving the transducer over the surface of the specimen and
identifying
the regions where delamination exists.
Figure 15
70
shows
test.
the ultrasonic inspection of a specimen during a cyclic
throughout
sonic
that
Note
the
the
specimen
remains
in the test set-up
duration of cyclic testing so that the ultra-
inspection is conducted with the specimen still mounted
in the grips.
~=~=;r=~sn~LI
~=~-~-I-7=
111
1
FIGURE
L
-- ~- .- r
14
I
II
~
_~ c
I-~---~I1I 11 L-.
'
.1~1
~_.__._._~_
PHOTOGRAPH OF MOIRE INTERFEROMETRY TEST SET-UP
~L-~slul-uPruPsl-
FIGURE
C~I_
15
qls~41V1- ~ I-4-_L11--_
~C_
~_ -- C--~I^-- LI~
13---111-1
I I
~--.L-*-~IOC___ ~UI Ykl
PHOTOGRAPH OF ULTRASONIC TEST SET-UP
--
il*- _~ iijliliili_~5^i~ir-~~-jlLii~
CHAPTER 4
TEST RESULTS
4.1 Static Tests
Computer
software
handling
the
for
were
plots
x-y
data
experimental
from each static test.
divided
by cross-sectional area) versus strain
generated
with a graphics routine written for an
(load
Stress
has been developed (see Reference 24)
A
plotter.
computer program, LIN6 [24], that reads the
applied stress and strain gage data from the magnetic disk and
then determines the linear regions was used on the data generated
every
from
static test specimen.
The program computed
the
slope of each linear region and provided hardcopy output.
The
modulus
the
of the
region
linear
first
Poisson's
was taken as the slope of the
specimen
the
of
was
ratio
stress-strain plot.
taken
Similarly,
as the initial slope of the
transverse strain versus longitudinal strain plot.
tests
Static
specimens
the
laminate
tests.
dix
1.
tensile
coupons
and tensile sandwich
were used to ascertain the validity of the sandwich
specimen
test
of
and
for
determine the basic tensile properties of
comparison
with tensile residual strength
These test results are described completely in AppenThe average static ultimate stress is 455 MPa with a
coefficient of variation of 6.3%
It is assumed that the applied stress in each face of the
sandwich
specimen
divided
by
of
thickness
composite
and
mm
0.134
measured
the
one
of
face.
second
for
each
eight 245A1 and five 345A1 specimens
145A1,
face
The ultimate strength
Frac-
not necessarily cause failure in the
did
When one composite face fractured, the specimen
bend
then
could
(due
to
the
eccentricity of loading) and
the
stress in the opposite face, preventing failure.
results
of the 145A1 static compression tests yielded an
relieve
The
width
specimen before fracture of either composite face.
ture
area.
specimen was defined as the maximum stress carried by
the
the
cross-sectional
was determined by using the nominal ply
tested in compression to failure.
were
of
area
Nine
specimen.
total
the
Cross-sectional
the same and equal to the applied load
is
average
compressive fracture strength of 423 MPa with a coef-
ficient
of variation of 9.1%.
the
seven
first
value
theoretical
core
was
The average Poisson's ratio of
specimens was 0.59, which is well below the
This indicated that the aluminum
of 0.69.
restricting
the
transverse
strain.
The problem,
is also discussed in Appendix 1, was easily overcome by
which
the
changing
orientation
of
the
aluminum honeycomb in the
specimen.
A
computer
program, Laminated Analysis Software Package
(LASP), uses the equations of Classical Laminated Plate Theory
to calculate the modulus and Poisson's ratio of any given lam-
The
inate.
unidirectional ply properties of Hercules
basic
AS1/3501-6 graphite/epoxy used for calculating the theoretical
properties of the [+-45xn/Oxn]s laminate are shown in Table 4.
modulus
theoretical
The
predicted from LASP is 57.7 GPa and
the Poisson's ratio is 0.69.
145A1
static
Two
were
specimens
These
in
oriented
honeycomb
yielded
an
average
modulus
of
57.9
not
the
manner
tested
to
Poisson's
GPa.
significantly
specimens
were
constructed with the
described in Appendix 1.
failure
ratio
and the test data
of 0.72 and an average
The modulus and ultimate strength are
affected by the rotation of the honeycomb;
however, the Poisson's ratio is affected and is now very close
to
the theoretical value of 0.69.
All the following sandwich
test specimens were constructed with the honeycomb oriented so
the restriction of transverse strain was minimized.
that
all
nine 145A1 compressive static tests, the average fracture
stress
The
For
is
423
modulus
coefficients
MPa and the coefficient of variation is 9.1%.
is 56.3 GPa and the Poisson's ratio is 0.62 with
of
variation
of
4.4%
and
10.0% repectively.
Individual 145A1 static compression results are shown in Table
5.
Identical
static
tests
test specimens.
were carried out on the 245A1 and 345A1
The mean fracture stress of the 245AI
specimens is 421 MPa and the coefficient of variation is 7.7%.
The
average longitudinal modulus and Poisson's ratio are 57.4
TABLE
4
TELAC VALUES FOR
UNIDIRECTIONAL HERCULES AS1/3501-6
GRAPHITE/EPOXY
Elastic Constants
Ultimate Stresses
t
EL
130 GPa
ET
10.5 GPa
11c
.28
T
22
GLT
6.0 GPa
a11
t
1661 MPa
1698 MPa
53.9 MPa
a2 2 c
221
MPa
a12
105
MPa
TABLE 5
STATIC COMPRESSIVE TEST RESULTS FOR THE [+-45/01s SPECIMENS
Specimen
I.D.
Compressive
Ultimate
Strength
Longitudinal
Modulus
[GPa]
Poisson's
Ratio
[MPa]
SCB145A1-I
377
406
422
483
57.1
58.8
51.2
57.7
.61
.64
.54
.59
-6
-7
395
401
479
57.8
54.7
54.0
.55
.60
.58
-8*
-9*
385
462
59.6
56.0
.73
-2
-3
-4
-5
Average
C.V.
423
42
9.1%
9. 1 %
6.,6
.71
56.3
.62
4.4%
10.0%
10.0%
4.4%
*These two specimens were constructed with the honeycomb core rotated
90 degrees.
TABLE 6
STATIC COMPRESSIVE TEST RESULTS FOR THE [+-45x2/0x2]ss SPECIMENS
Compressive
Ultimate
Strength
Specimen
I.D.
Longitudinal
Modulus
[GPa]
Poisson's
Ratio
[MPa]
*
58.6
.68
-2
-3
420
387
59.9
52.4
.70
.68
-4
-5
469
428
58.4
55.6
.70
.69
-6
-7
-8
389
462
395
421
7.7%
58.7
59.4
56.5
.66
.72
.72
57.4
.69
SCB245Al-I
Average
C.V.
4.1%
4.1%
2.8%
2.8%
*Specimen slipped grips of testing machine before failure; increased
grip pressure prevented slippage in all later tests.
TABLE 7
STATIC COMPRESSIVE TEST RESULTS FOR THE [+-45x3/0x3]ss SPECIMENS
Specimen
Compressive
Longitudinal
Poisson's
I.D.
Ultimate
Modulus
Ratio
Strength
[GPa]
[MPa]
SCB345AI-1
-2
-3
-4
-5
Average
C.V.
446
438
374
482
55.5
60.3
51.5
410
429
8.4%
57.5
60.2
57.0
5.8%
.67
.69
.63
.71
.68
.68
3.9%
(C.V.=4.1%) and 0.69 (C.V.=2.8%) respectively.
coefficient of variation of 8.4%.
a
with
of the 345A1 specimens is 429 MPa
strength
ultimate
average
ratio
is
0.68
shown
in
Tables
57.0
is
modulus
tudinal
The average longi-
(C.V.=5.8%) and the Poisson's
GPa
(C.V.=3.9%).
6
Similarly, the
The individual test results are
7 for the 245A1 and 345A1 specimens
and
respectively.
An
ply
result
important
of these tests is that there is no
thickness dependence on the static strength of this lami-
nate.
stress
Typical
versus
longitudinal strain plots are
shown in Figures 16-18 for all the different static test specimens.
Note that effective ply thickness does not effect the
stress-strain
diagrams.
All
the plots are nearly linear to
with only a small decrease in slope near the fracture
failure
strength of the specimen.
LIN6 calculates approximately a 10%
loss in modulus at the failure load of all the composite specimens.
The
similarity
of both the longitudinal modulus and
Poisson's ratio with laminated plate theory increases our conof the test specimen.
The average
fidence
in
the
validity
modulus
of
all
compressive static tests is 56.9 MPa and the
average
Poisson's
ented
to
minimize
ratio of specimens with the honeycomb oritransverse
strain
restriction
is 0.69.
These values compare with the predicted values of 57.7 MPa and
0.69.
SCB
50
CL
4008
LLJ
380
145A1-8
E .= 59.6 GPa
L
HLi
280
H
100
L)
6000
=o-
8000
LONGITUDINAL STRAIN ECs3
FIGURE 16 STRESS-STRAIN PLOT OF TYPICAL
COMPRESSIVE TEST
[+-45/0]s STATIC
W'% W'% r-
bUL0
6008-
E
588
L
1
A
t'\AIA
Lz z
A 1 -. 5
= 52.4 GPa
400
L
S300
Lj
280
CL
() I)
o
0
0
2000
4000
6000
8000
LONGITUDINAL STRAIN Es]
FIGURE 17 STRESS-STRAIN PLOT OF TYPICAL
COMPRESSIVE TEST
[+-45x2/0x 2] STATIC
SCB 345A -2
6800
EL = 60. 3 GPa
0
300
c1
0
0)
L
)
Li
0/,
0,
C-)
2000
4000
68800
8000
1080008
LONGITUDINAL STRAIN Ets3
FIGURE 18
STRESS-STRAIN PLOT OF TYPICAL [+-45x3/0x3]s STATIC
COMPRESSIVE TEST
4.2 Cyclic Tests
first
The
series
of compressive cyclic load tests were
on the 145A1 laminates.
completed
The first twelve specimens
at a peak stress amplitude of 287 MPa (69% of ulti-
were
run
mate
stress).
Two tests were run at 253 MPa (60% of ultimate
and two were run at 320 MPa (76% of ultimate stress).
stress)
photographs were taken automatically by the test set-up
Moire
described in section 3.3 and audible signs of damage were listhe
by
operator of the test.
The results of the
tened
for
145A1
cyclic tests show very little consistency in the devel-
the test ended.
before
damage grow on both composite faces
However, the data from each test does
of three categories.
clicking
loud
One, rapid delamination
of
and
popping
sounds.
This type of damage
perpendicular to the load direction and caused fail-
extended
ure
In only two of the sixteen
over a large area around the hole that was accompanied
growth
by
one
into
fall
symmetric
did
specimens
damage.
delamination
of
opment
specimen
the
within
only a few cycles.
This rapid
failure
mode was difficult to record through the Moire set-up
because
the
This
type
damage grew to failure within only a few cycles.
of damage, which will be referred to as transverse
delamination,
occurred
in
five specimens.
Two, other tests
showed delaminations that formed along the hole edge at one or
more locations.
These delaminations grew under cyclic loading
perpendicular
of
to
and parallel to the load direction.
delamination
increased
in
was
usually
slow
Growth
at first but as the area
size the growth became very rapid.
This damage
was observed in seven specimens and growth sequences are shown
in
Figures
19-23.
This damage will be referred to as radial
delamination because of the tendency for this damage to extend
in
all directions.
Three, the other four specimens exhibited
damage growth that initiated along the hole edge and grew parallel
to
the
loading
direction.
This
damage, which only
extended
along the longitudinal axis of the laminate, will be
referred
to
as
longitudinal
delamination.
Photographs of
specimens with this type of damage growth are shown in Figures
24-28.
It
is
important to note that the damage is no wider
than the diameter of the hole.
longitudinal
delaminations
Sketches of typical radial and
are illustrated in Figures 29 and
30 for clarity.
Two specimens (FCB 145A1-13 and FCB 145A1-14) were tested
at
the
of
not
a
peak
ultimate stress).
transverse
show
stopped.
FCB
stress amplitude of 253 MPa (approximately 60% of
any
On
Both specimens developed small regions
delamination
growth
damage, but the damaged area did
after 400,000 cycles so the tests were
the other hand, two specimens (FCB 145AI-15 and
145AI-16) were cycled at a peak stress of 320 MPa (76% of
ultimate
cycles
stress).
One
specimen
broke after only 3900 load
while the other lasted only 800 cycles before failing.
FIGURE 19
0 CYCLES
15,000
50,000
55,000
RADIAL DELAMINATION GROWTH SEQUENCE IN SPECIMEN
FCB 145Al-1A UNDER COMPRESSIVE CYCLIC LOADING
ii
FIGURE 20
0 CYCLES
165,000
225,000
239,000
RADIAL DELAMINATION GROWTH SEQUENCE IN SPECIMEN
FCB 145Al-5A UNDER COMPRESSIVE CYCLIC LOADING
:"~~
~sll
--l~-~----F
FIGURE 21
J-Y
- -~._-~L_~_I~Y-Be~DLa*i-~ils--~bD-.
^---
_-
-I~___ _I
0 CYCLES
70,000
110,000
144,000
RADIAL DELAMINATION GROWTH SEQUENCE IN SPECIMEN
FCB 145Al-7A UNDER COMPRESSIVE CYCLIC LOADING
. :;I~Iy-C.:
--i-LSP~-~-e~-i~i~i6
1 -- :
~I
~-~ILIOLL~rP--
FIGURE 22
~e~--I
I
~~-C
9 ".~-~e~
~'-
~-7~a~s;lS~rrrs~c~l~;
0 CYCLES
10,000
35,000
55,000
~;1~
rs~C-~:~_EL.~-~;-d;;;;r~e~C~
i
RADIAL DELAMINATION GROWTH SEQUENCE IN SPECIMEN
FCB 145Al-8A UNDER COMPRESSIVE CYCLIC LOADING
FIGURE 23
0 CYCLES
10,000
15,000
20,000
RADIAL DELAMINATION GROWTH SEQUENCE IN SPECIMEN
FCB 145A1-11B UNDER COMPRESSIVE CYCLIC LOADING
ip-r~B ,
~
II
~----------
L~
_I ~_Ln~---l-F--------
91
FIGURE 24
0 CYCLES
240,000
260,000
275,000
PHOTOGRAPHS OF LONGITUDINAL DELAMINATION GROWTH
SEQUENCE IN SPECIMEN FCB 145Al-2A UNDER COMPRESSIVE
CYCLIC LOADING
----------- ;~T
-~-~=~=-1
~'---- --- r:~P~--2------
~_~ ~_~__~II-----------~C--
FIGURE 25
---- r-c__l~~l ~~J
~--------C
_L-I~8 1110i19-_I_--JI
-__ r*-a----_.---____
0 CYCLES
165,000
200,000
215,000
I~1C~ -
PHOTOGRAPHS OF LONGITUDINAL DELAMINATION GROWTH
SEQUENCE IN SPECIMEN FCB 145Al-4A UNDER COMPRESSIVE
CYCLIC LOADING
---
e-.T._~l__l~1
FIGURE 26
0 CYCLES
42,000
50,000
80,000
PHOTOGRAPHS OF LONGITUDINAL DELAMINATION GROWTH
SEQUENCE IN SPECIMEN FCB 145Al-9A UNDER COMPRESSIVE
CYCLIC LOADING
---
~-
~Pc~e-~EZL~RI
FIGURE 27
LP I-I
0 CYCLES
120,000
140,000
160,000
PHOTOGRAPHS OF LONGITUDINAL DELAMINATION GROWTH
SEQUENCE IN SPECIMEN FCB 145A1-10A UNDER COMPRESSIVE
CYCLIC LOADING
-- -~-- -=---- -~---a
~
I
FIGURE 28
0 CYCLES
100,000
115,000
160,000
PHOTOGRAPHS OF LONGITUDINAL DELAMINATION GROWTH
SEQUENCE IN SPECIMEN FCB 145A1-10B UNDER COMPRESSIVE
CYCLIC LOADING
FIGURE
29
SKETCH ILLUSTRATING RADIAL DELAMINATION
~-n-y
..
f
,i
i
i:
Ii
FIGURE 30
SKETCH ILLUSTRATING LONGITUDINAL DELAMINATION
specimens exhibited the type 1 damage described earlier.
Both
A brief summary of the 145A1 test results is shown in Table 8.
developed 35mm negatives taken during the tests were
The
from the rear onto a large ground glass table
each
projected
top.
A measurement was made from the hole edge to the edge of
delamination, as shown by Moire interferometry, to deter-
the
total damage length in each photograph.
the
mine
of each damage measurement was determined by measuring
length
diameter
hole
the
The actual
in
the enlarged negative and scaling all
lengths proportionally to the actual hole diameter.
inspection
An
of the longitudinal delamination was made
to verify the NDI results.
nation
made
A cut was made through the delami-
in one of the damaged coupons.
The transverse cut was
by a water-cooled diamond-encrusted blade resulting in a
The edge of the cut was placed
smooth surface for inspection.
under a stereomicroscope at 50x and the delaminated cross section
cross
seen
was
observed.
section.
delamination
hole)
and
inspection
00
31 is a photograph of a typical
symmetric
delaminations can be clearly
as both -45* plies have delaminated from the 00 plies in
center
the
Two
Figure
of the laminate.
is
approximately
Note also that the width of the
6.35
mm (the diameter of the
is centered in the laminate as is the hole.
reveals
Close
that two matrix splits are located in the
plies at either end of the delamination.
99
TABLE 8
CYCLIC TEST RESULTS FOR THE [+-45/0]sS SPECIMENS
Peak
Compressive
Stress
Specimen
I.D.
Damage
Type
Number of
Cycles to
Initiation
Number of
Cycles at
Completion of
Test
[MPa]
FCB145Al-lA
-1B
287
2
NDD
15,000
64,400
-2A
287
3
240,000
305,000
3
230,000
-2B
-3A
-3B
-4A
-4B
-5A
-5B
287
287
287
-6A
-6A
-6B
287
-7A
287
NDD
------
1
10,000
10,100*
3
NDD
160,000
------
290,000
2
145,000
239,000*
NDD
------
NDD
------
1
48,600
2
60,000
48,600*
144,000
-7B
NDD
------
-8A
-8B
2
NDD
15,000
------
55,400*
-9A
-9B
3
NDD
42,000
------
92,600
120,000
100,000
161,000
------
23,000
10,000
23,000
-10A
-10B
287
-11A
287NDD
-1lB
-12A
3
3
2
3,300
287
1
NDD
------
-13A
-13B
-14A
-14A
-14B
253
NDD
2
-----155,000
253
NDD
-15A
-15B
320
1
NDD
3,900
------
3,900*
-16A
-16B
320
1
NDD
800
------
800*
-12B
2
------
165,000
3,300*
400,000
Note: All tests run at 7 HZ with R = 0.1
* Test Stopped due to failure
Damage Key: NDD = no detected damage; 1 = transverse delamination;
2 = radial delamination; 3 = longitudinal delamination
l10
lilliIII-
FIGURE 31
ll
MAGNIFIED PHOTOGRAPH OF CROSS-SECTION OF
[+-45/0]s SPECIMEN CONTAINING A LONGITUDINAL
DELAMINATION
101
length,
damage
total
The
2a,
versus the logarithm of
applied load cycles is plotted in Figure 32 for five specimens
longitudinal delamination.
exhibited
which
damage grew symmetrically on both
The plot shows that while the number of
hole.
the
of
sides
if
as
plotted
is
length
The delamination
cycles to damage initiation varies from 49,000 to 250,000, the
appears to vary linearly with the logarithm of
length
damage
the number of applied load cycles.
the thin ply 145A1 laminates, the results of both
Unlike
the
345A1
and
245A1
All specimens tested developed the longitudi-
growth.
damage
cyclic tests revealed a single mode of
nal type of delamination described earlier.
tested at 287 MPa, four at 265 MPa and two at 287
were
imens
MPa
peak
the
Moire
The first five specimens were tested using
stress.
set-up and a stress level of 287 MPa.
test
serious
a
revealed
tests
Eight 245A1 spec-
deficiency
in
These
the Moire method.
After a hundred thousand cycles had been applied to each specdamage
no
imen,
set-up.
type
specimens
Two
inspected
of
been
had
under
a
detected
the interferometry
were cut and the cross sections were
microscope.
Both specimens had the same
damage found in the cross section of the 145A1 lami-
nate with longitudinal delamination.
technique
by
used
here
was
Unfortunately, the Moire
not sensitive enough to detect the
out-of-plane deformation of the delaminated plies in the 245A1
laminates.
In this case, the delaminated plies were twice as
102
188
max
88
r'
A
145A1-2 A
o
145A1-4 A
145A 1-9 A
145A1-18 A
145A1-18 B
a
E
E
v
+
Li
= 287 MPo
3:
FLD
z
480-
-J
Ld
L<
+1
280
+
aj
I
1E4
I
- - ~-~-oil--
SIll
I
i E5
,t
I
I
II
-
Il
- -~---
1E
NUMBER OF CYCLES
FIGURE 32
PLOT OF THE LONGITUDINAL DELAMINATION LENGTH, 2a,
VERSUS THE LOGARITHM OF THE NUMBER OF APPLIED
LOAD CYCLES FOR THE [+-45/0]s SPECIMENS
103
as in the 145A1 laminates and the out-of-plane deforma-
thick
All later cyclic testing was
tion was thus considerably less.
the ultrasonic inspection method outlined in
using
completed
section 3.4.
inspection clearly revealed that longitudinal
Ultrasonic
delamination
to
parallel
the
a
as
load
in
Damage
applied.
cycles
at the hole edge and traveled
initiated
damage
function of the number of load
the 245A1 laminate developed in
virtually all of the specimens tested.
bottom
and
top
the
at
tiated
Generally, damage ini-
of the hole and grew nearly
symmetrically as shown in Figure 33.
length,
The
a,
was
measured from the hole edge to the
as
indicated by ultrasonic inspection
delamination
edge
of
(see
Figure 33).
The total delamination length, 2a, has been
function
a
of
the
logarithm
of the number of
plotted
as
applied
load cycles for nine specimens at various stress levThese
els.
that developed only on one side of the
Delaminations
pages.
hole
plots (Figures 34-42) appear on the next several
were
the
about
as
plotted
hole.
if the damage had grown symmetrically
The same linear relationship is observed as
in the 145A1 damage growth plots.
The
type
of
cycles.
plots show that the delamination growth rate of this
damage
is
Furthermore,
a
declining
the
function
of the number of
number of cycles to initiation of
delamination increases as the stress level decreases.
Another
104
FIGURE 33
SKETCH ILLUSTRATING INITIATION OF LONGITUDINAL
DELAMINATION AT TOP AND BOTTOM OF HOLE IN
[+-45xn/Oxn]s LAMINATE
105
245A1- 6
FCB
O'max
= 287 MPa
100
A
A
A
A
A
A
A
A
88
S-1
E
E
Li
A
FACE A
o FACE B
A
60
CD
z
LLJ
I
-_J
LU
WD
40
28
a I
1E3
I
1LM~
~ lI u
i
I I
1
I
1
I1I I111
III
IE4
NUMBER OF CYCLES
FIGURE
34
PLOT OF LONGITUDINAL DELAMINATION LENGTH,2a,
VERSUS THE LOGARITHM OF THE NUMBER OF APPLIED
LOAD CYCLES FOR SPECIMEN FCB 245Al-6
IE5
106
FCB 245A1-7
cr max = 287 MPo
188
4l
80
ot
**A
E
E
A
6-
*
_tJ
CD
zI
FACE A
FACE B
48
A
(.D
AAA
28
1E3
1E4
NUMBER OF CYCLES
FIGURE 35
PLOT OF LONGITUDINAL DELAMINATION LENGTH, 2a,
VERSUS THE LOGARITHM OF THE NUMBER OF APPLIED
LOAD CYCLES FOR SPECIMEN FCB 245A1-7
1E5
107
FCB 245A1-8
max = 265 MPa
o88
A
o
n
FACE A
FACE B
E
Li
z
W
-J
60
40
(lu
CD
AO
r\
I
I I
I
1L
IA
I
I
1E3
I
mI
I
I
I
311
I
1E4
NUMBER OF CYCLES
FIGURE 36
PLOT OF LONGITUDINAL DELAMINATION LENGTH, 2a,
VERSUS THE LOGARITHM OF THE NUMBER OF APPLIED
LOAD CYCLES FOR SPECIMEN FCB 245A1-8
I
l I
1E5
108
FCB 245A1-9
max = 265 MPa
188
Be
AA
A
FACE A
> FACE B
A
80
S1=
II
A
A
Ah
A
A
E
E
Li
80
A o0
A
I
D
z
ILd
-j
O
0
0
A
480
W
CD
z.
20
0
1E3
I~~~
llr
•~
I
I
II
S
a
3
I
11,11
I 1
-•
1
I
1E4
NUMBER OF CYCLES
FIGURE 37
PLOT OF LONGITUDINAL DELAMINATION LENGTH, 2a,
VERSUS THE LOGARITHM OF THE NUMBER OF APPLIED
LOAD CYCLES FOR SPECIMEN FCB 245A1-9
1E5
109
FCB 245A1-10
Cr
max
= 243 MPa
188
88
r-'l
I
E
A
FACE A
+
FACE B
E
680
AAA
LiJ
I
2:
Z
LD
z
Ld
-J
A
40
C
CD
28
Q=
8
1E3
-
L1fi1
II I
II I I If
aI
a
I
aI Ia aaaal
1 11
1E4
NUMBER OF CYCLES
FIGURE 38
PLOT OF LONGITUDINAL DELAMINATION LENGTH, 2a,
VERSUS THE LOGARITHM OF THE NUMBER OF APPLIED
LOAD CYCLES FOR SPECIMEN FCB 245A1-10
1E5
110
FCB 245A1-11
cr
max
= 243 MPa
80
E
E
A
FACE A
SLi
*
FACE B
-
LJ
U
40
I
IE3
I
I I
I I I II
IA
1 4
I9
1
1I I 1 tItI
IE4
NUMBER OF CYCLES
FIGURE 39
PLOT OF LONGITUDINAL DELAMINATION LENGTH, 2a,
VERSUS THE LOGARITHM OF THE NUMBER OF APPLIED
LOAD CYCLES FOR SPECIMEN FCB 245A1-11
IE5
111
FCB 245A1-12
cr
max
= 265 MPa
188
88
'A FACE A
+ FACE B
En
E
E
60
I
CD
z
LLJ
-
LUi
CD
(_9
/I
I
1E3
e,,,,,,l
I
I
I
I
I I I I I
IE4
NUMBER OF CYCLES
FIGURE 40
PLOT OF LONGITUDINAL DELAMINATION LENGTH, 2a,
VERSUS THE LOGARITHM OF THE NUMBER OF APPLIED
LOAD CYCLES FOR SPECIMEN FCB 245A1-12
IE5
112
FCB 245A1-13
m
max
= 265 MPa
188
A
FACE A
o
FACE B
88
A
m
E
E
LJ
A
68
"-
A
O
CD
z
LUJ
-i
LLJ
CD
A
O
aA
A
A
O
00
zl
(_9
<[,
aI
1E3
I
I
f~e~ltL~
__I
I II
Il
IE4
NUMBER OF CYCLES
FIGURE 41
PLOT OF LONGITUDINAL DELAMINATION LENGTH, 2a,
VERSUS THE LOGARITHM OF THE NUMBER OF APPLIED
LOAD CYCLES FOR SPECIMEN FCB 245A1-13
IE5
113
FCB 245A1-14
= 287 MPa
max
A
o
FACE A
FACE B
A
A
r-1
E
E
I
Fz
Ld
,I
-J
AA
AA
AA
40
A
Ld
C(D
z:
0
A A
A A_
A
I
1E3
rI
I
*
I
I
I
I
I
I Ii
1
11
SI
I
I
I
I
t It
1E4
NUMBER OF CYCLES
FIGURE 42
PLOT OF LONGITUDINAL DELAMINATION LENGTH, 2a,
VERSUS THE LOGARITHM OF THE NUMBER OF APPLIED
LOAD CYCLES FOR SPECIMEN FCB 245A1-14
IE5
114
levels
stress
peak
at
cycling
this
that
is
observation
important
damage occurred during
as low as 57% of the static
ultimate strength.
were
tests
section
test
the
The
at a stress level of 265 MPa (63% of
delamination extended nearly the entire length
A
ultimate).
of
cycled
was
test
first
done on five 345A1 specimens.
was
testing
Similar
cycled
after only 500 cycles.
The four other
at a peak compressive stress level of 243
and 221 MPa (57% and 52% of ultimate).
Delamination length is
plotted as a function of the logarithm of the number of cycles
in Figures 43-46.
growth characteristics for this set of specimens are
The
245A1 specimens except that damage initiates
similar
to
the
earlier
in
these
52%
thicker
ply specimens.
At applied stress
of the laminate's ultimate strength a delami-
levels
of
nation
extends
from
50,000
cycles.
A summary of the 245A1 and 345A1 cyclic tests
end
to
end in the specimen after only
is given in Tables 9 and 10.
The
longitudinal
delamination growth data can be corre-
lated by the equation proposed by Daken [4] for split growth:
2a = -A + B In(n)
is
the
where
N
total
delamination
the
(4.1)
number of applied load cycles and 2a is the
length.
Experimentally, 2a is the sum of
delamination length from the top of the hole, at, and the
115
FCB 345A1-2
= 243 MPa
max
100
AO
88
A
FACE A
o FACE B
rl
E
E
Lii
LAA
I-
aM
O
OO
O
CD
z
Lui
I
40
LJ
CD
w
(_9
Q:
Q:
AA
IE3
1E4
NUMBER OF CYCLES
FIGURE 43
PLOT OF LONGITUDINAL DELAMINATION LENGTH, 2a,
VERSUS THE LOGARITHM OF THE NUMBER OF APPLIED
LOAD CYCLES FOR SPECIMEN FCB 345A1-2
1E5
116
FCB 345A1-3
= 221 MPa
max
18800
A
88
,
i i
A
FACEA
FACE B
A
4
E
E
Li
0
680
0
FCD
z
02:
-J
U
&&
48
A
O
AA
C
u\
280
A
A
0
IES
A
A
AL I
I II
Imiii!
I
~I
I IffII ILjJ
1
1E4
NUMBER OF CYCLES
FIGURE 44
PLOT OF LONGITUDINAL DELAMINATION LENGTH, 2a,
VERUS THE LOGARITHM OF THE NUMBER OF APPLIED
LOAD CYCLES FOR SPECIMEN FCB 345 Al-3
IE5
117
FCB
cr
345A1-4
max
= 221 MPa
188
A
FACE A
0
FACE B
88
r-1
E
A
E
-r
A
A&
AA
MAA
FA*
z
48
-4
0
LJ
CD
A
0
4
A
I
a1
1E3
I
I
4 1,+
A *
I
I
I I I filI
1E4
NUMBER OF CYCLES
FIGURE 45
PLOT OF LONGITUDINAL DELAMINATION LENGTH, 2a,
VERSUS THE LOGARITHM OF THE NUMBER OF APPLIED
LOAD CYCLES FOR SPECIMEN FCB 345A1-4
1E5
118
FCB 345A1-5
max
= 221 MPa
100
r
A
FACE A
*
FACE B
¢I¢
E
E
Li
60 -
A
*
CD
-r
L9
o
40
A
A
A
-
L
(D
20
00
O
Q=
000
¢
4
O
01E3
aa
AA
i
L L 4 444AA
I
I I I I,
1E4
NUMBER OF CYCLES
FIGURE 46
PLOT OF LONGITUDINAL DELAMINATION LENGTH, 2a,
VERSUS THE LOGARITHM OF THE NUMBER OF APPLIED
LOAD CYCLES FOR SPECIMEN FCB 345A1-5
1E5
119
TABLE 9
CYCLIC TESTS RESULTS FOR THE [+-45x2/0x2]ss SPECIMENS
Specimen
I.D.
Peak
Compressive
Stress
Damage
Type
Number of
Cycles to
Initiation
of Test
[MPa]
FCB245A1-lA
287
-lB
-2A
-2B
NDD
------
NDD
------
NDD
NDD
I
Number of
Cycles at
Completion
NDD
I
110,000
-I
- - -
-3A
-3B
287
-4A
-4B
287
NDD
3*
-----Unknown*
12,000
-5A
-5B
287
287
NDD
3*
U-----Unknown
841,00
3
-6B
-7A
-8A
-8B
-9A
-9B
-10A
-10OB
-11 B
-12A
-12B
12,000
1,000
3
7,000
3
7,000
60,000
-----3,000
70,000
33
6,000
11000
1320,000
3
3
1,500
3,500
NDD
3
-11A
6,000
1,500
287
-7B
-13A
-13B
-14A
-14B
83,000
NDD
1
14,000
All tests ran at 7 HZ with R = 0.1
First five specimens monitored with Moire interferometry, all
others monitored with ultrasound
*Longitudinal delamination found by sectioning coupon
Note:
Damage Key:
NDD = no detected damage; 1 = transverse delamination;
2 = radial delamination; 3 - longitudinal delamination
120
TABLE
10
CYCLIC TEST RESULTS FOR THE [+-45x3/0x3]ss SPECIMENS
Peak
Compressive
Stress
[MPa]
Damage
Type
Number of
Cycles to
Iniation
Number of
Cycles at
Completation
of Test
FCB 345Al-1A
-lB
265
3
3
<500
<500
3,000
-2A
-2B
243
3
3
1,000
1,000
9,000
-3A
-3B
221
3
3
3,000
9,000
59,000
-4A
221
3
6,000
85,000
3
10,000
3
3
14,000
6,000
Specimen
I.D.
-4B
-5A
-5B
221
Note: All tests ron at 7Hz with R = 0.1
Damage Key:
NDD = No damage detected
1 = Transverse delamination
2 = Radial delamination
3 = Longitudinal delamination
50,000
121
length from the bottom of the hole, ab
absolute
growth
value
curve
of
.
The variable A is the
the y-intercept and B is the slope of the
as shown in Figure 47.
A computer program [24]
was
used to determine the best fit of a straight line through
the
growth
results
longitudinal
delamination.
From
the
of this least squares linear regression, A and B were
determined
nation
of
data
for
each
growth.
delamination
The
coupon
exhibiting longitudinal delami-
number
of
cycles
to
initiation
of
and the rate of delamination growth at the onset
of delamination are easily derived from A and B:
(4.2)
= eA/B
N
0
The results of these calculations are tabulated for the 145A1,
245AI
and
N =131,000
o
the
345A1
in
Table
11-13
respectively.
A value of
(da/dN) =.00057 mm/cycle were determined from
and
o
average 145A1 linear regression results at a stress level
of
287
MPa.
of
cycles
At a stress level of 287 MPa the average number
to
delamination
was determined to be 2900 with a
of 0.010 mm/cycle for the 245A1 specimens.
This
growth
rate
result
shows clearly that the number of cycles to damage ini-
tiation
is
much
less
as
the
ply
thickness is increased.
Similarly the damage growth rate increases in the 245A1 specimen.
At 265 MPa, the average N is 5300 cycles and the initial
average growth rate is 0.0071 mm/cycle.
The average number of
122
2a
[mm ]
tan-lB
In
N
[cycles]
A
FIGURE 47
GRAPHIC ILLUSTRATION OF LINEAR REGRESSION
PARAMETERS, A AND B
TABLE 11
RESULTS OF LINEAR REGRESSION OF LONGITUDINAL DELAMINATION LENGTH
VERSUS LOGARITHM OF NUMBER OF CYCLES FOR [+-45/0]sS DATA
da
correlation
coefficient =
R
(dN o
Peak
Compressive
Stress [MPa]
A
[mm]
FCB 145A-2A
287
1702
137
.996
248,000
.00028
-4A
287
2167
180
.876
169,000
.00053
-9A
287
1013
95
.993
43,000
-10A
287
1303
112
.989
112,000
.00050
-10B
287
862
76
.982
85,000
.00045
Specimen
I.D.
B
[mm/cycle]
N
[cycles]
Avrg
11,0,.05
Average
131,000
[mm/cycle]
.0011
.00057
TABLE 12
RESULTS OF LINEAR REGRESSION OF LONGITUDINAL DELAMINATION LENGTH VERSUS NATURAL
LOGARITHM OF NUMBER OF CYCLES FOR [+-45x2/0x2]s DATA
Peak
Compressive
Stress [MPa]
A
[mm]
287
287
482
846
63
98
.991
.995
2100
5600
.015
.0088
-7A
-7B
-14A
-14B
287
287
287
287
345
340
294
381
45
45
39
47
.920
.987
.968
.991
2600
1900
1900
3300
.0087
.012
.010
.0071
Average
FCB 245A1-8A
-8B
-9A
-9B
-12A
412B
-13A
-13B
2900
.010
265
265
265
265
265
265
265
265
604
612
460
352
452
294
337
340
66
69
52
40
57
43
41
40
9400
7100
.0035
.0049
FCB 245A1-10OA
243
355
243
39
*
.989
.965
.982
.933
.991
.978
.936
.964
Average
.990
6900
6600
3100
930
3700
4900
5300
9000
.0038
.0030
.0091
.023
.0055
.0041
.0071
.0022
*
,
-11A
243
-11B
243
795
Specimen
I.D.
FCB 245Al-6A
-6B
-10B
*
B
[mm/cycle]
*
79
*
correlation
coefficient=
R
*
.920
*
30,000
*
Average
* Indicates that no damage was detected on this coupon
during the test.
N
[cyces]
19,500
(da)
dNo
[mm/cycle]
.0013
*
.0018
TABLE 13
RESULTS OF LINEAR REGRESSION OF LONGITUDINAL DELAMINATION LENGTH VERSUS NATURAL
LOGARITHM OF NUMBER OF CYCLES FOR [+-45x3/0x3] s DATA
Peak
Compressive
Stress [MPa]
A
[mm]
FCB 345Al-1A
-1B
265
265
*
*
*
*
*
*
*
*
FCB 345Al-2A
-2B
243
243
291
230
43
35
.962
.940
870
710
.025
.024
FCB 345AI-3A
-3B
-4A
-4B
-5A
-5B
221
221
221
221
221
221
228
502
337
349
610
239
28
55
38
38
63
29
.928
.907
Specimen
I.D.
B
[mm/cycle]
correlation
coefficient=
R
Average
* Damage had grown from end to end of specimen after
first inspection interval of 500 cycles.
.901
.957
.970
.976
Average
No
[cycles]
(da
A 0
[mm/cycle]
*
*
790
.024
3400
9200
.0041
.0030
7100
9700
16,000
3800
8200
.0027
.0020
.0020
.0038
.0029
126
cycles
before
stress
level
initiation
damage
specimens tested at a
241 MPa is 19,500 cycles and the growth rate at
initiation is 0.0018 mm/cycle.
This result indicates that the
cycles to initiation increases as the stress level
of
number
for
decreases and the initial growth rate is a decreasing function
The results of the linear regression
of applied stress level.
for the 345A1 specimens are consistent with the other results.
At
applied
an
and the average (da/dN)o is 0.024 mm/cycle.
cycles
age
stress level of 241 MPa the average N
is 790
The aver-
number of cycles before damaged initiation is 8200 cycles
at a peak stress level of 221 MPa for the 345A1 specimens; the
initial growth rate is 0.0029 mm/cycle at this stress level.
4.3 Residual Strength Tests
Static
for
except
were
tests
tensile
sectioned
observe
to
conducted
on
every coupon
failed during compressive cycling or
that
those
were
damage.
The coupons were loaded
until failure to determine the effect that delamination damage
has on the strength of the laminate.
The
reported
results
in
of
Table
the
14
145A1
residual strength tests are
along with a brief description of the
damage in the coupon at the time of the test.
teen
145A1
coupons
coupons
A total of fif-
were tested for residual strength, three
were sectioned and the remaining fourteen failed dur-
127
ing
cyclic
inspection
ultrasonic
firmed
Before each 145A1 coupon was loaded, an
testing.
the
damage
was
conducted.
state
of
This inspection con-
the laminate as found by Moire
interferometry.
residual strength tests indicate an average residual
The
strength
of
MPa with a coefficient of variation of 14%.
564
Note that the average measured modulus of 56.7 (C.V.=5.6%) and
Poisson's
ratio
of
significantly.
over
a
small
interpreting
0.66
Since
area
(C.V.=3.7%) have not been affected
the
measurements
(about
0.1
of strain are taken
cm2), care must be taken in
the stiffness data since this data may not truly
represent the response of the entire coupon since damage under
a gage would cause readings to be different locally.
the
data
uniaxial
shows
clearly
tension
strength
the
of
the
However,
laminate in
has increased due to the damage accumulated
during compressive cyclic loading.
The
residual
strength
test
results
for the 245A1 and
345A1 laminates are reported in Tables 15 and 16 respectively.
The
strength data again shows nearly a 50% increase in static
strength
due
to longitudinal delamination damage in the com-
posite.
The
average
of the 245A1 data is 674 MPa
strength
with a coefficient of variation of 9.0%.
mens,
the
coefficient
average
fracture
stress
of variation of 9.8%.
For the 345A1 speciis
605
MPa
with
a
The average modulus of the
245A1 data is 54.9 GPa with the coefficient of variation equal
128
TABLE 14
RESIDUAL TENSILE STRENGTH TEST RESULTS FOR [+-45/0]
SPECIMEN DELINEATED BY DAMAGE TYPE
Specimen
I.D.
Tensile
Fracture
Stress
Longitudinal
Modulus
[GPa]
Poisson's
Ratio
Damage
Type
[MPa]
FCB145AI-1B
-4B
-7B
-9B
-11A
-13A
Average
C.V.
512
534
552
551
565
546
55.9
60.1
57.7
56.5
58.9
66.9
.656
.633
.662
.659
.661
.678
543
3.1%
59.3
6.2%
.658
2.0%
FCB145Al-1A
-7A
-13B
-14B
Average
C.V.
400
620
444
520
58.6
58.8
66.6
58.4
.621
.677
.676
.673
496
17%
60.6
5.2%
.662
3.6%
FCB145Al-2A
-2B
-4A
-9A
-10B
Average
C.V.
611
565
720
680
639
643
8.3%
60.9
53.7
53.2
58.4
58.9
57.0
5.3%
.732
.650
.669
.624
.661
,-
Damage Key:
NDD
1
2
3
no detected damage
transverse delamination
radial delamination
longitudinal delamination
.667
5.4%
NDD
NDD
NDD
NDD
NDD
NDD
2
2
2
2
3
3
3
3
3
129
TABLE 15
RESIDUAL TENSILE STRENGTH TEST RESULTS FOR [+-45x2/0x2]s SPECIMENS
Fracture
Stress
Specimen
I.D.
Modulus
[GPa]
Poisson's
Ratio
[MPa]
FCB245Al-1A
-1B
719
691
53.8
55.7
.846
.647
-2A
-2B
566
662
-4A
-5A
669
624
42.2
53.9
56.3
48.9
.540
.647
.547
.596
-6A
-6B
-7A
-7B
704
690
683
584
57.5
58.6
51.0
49.3
1.023
.662
.613
.564
-8A
-8B
670
729
61.9
63.9
.653
.821
-9A
-9B
755
634
56.1
49.6
.698
.570
-10A
-10B
602
662
48.1
59.1
.551
.689
-11A
-11B
761
734
59.6
61.7
.561
.694
-13A
-14A
-14B
550
46.5
.555
780
686
674
9.0%
59.1
60.8
54.9
10.3%
.649
.593
.653
17.8%
Average
C.V.
130
TABLE 16
RESIDUAL TENSILE STRENGTH TEST RESULTS FOR [+-45x3/0x3] s SPECIMENS
Sepcimen
I.D.
Tensile
Fracture Stress
Modulus
[GPa]
Poisson's
Ratio
[MPa]
FCB345Al-lA
-1B
-2A
-2B
-3A
-3B
-4A
-4B
-5A
-5B
Average
C.V.
527
649
533
568
583
700
650
691
561
587
49.4
51.2
.578
.637
51.3
50.2
51.4
63.8
63.2
57.7
51.6
58.2
.633
.582
.567
.700
.730
.514
.603
.530
605
9.8%
54.8
9.5%
.608
10.9%
131
to
10.3%.
The average modulus of the 345A1 data is 54.8 GPa
and the coefficient of variation is 9.5%.
a
slight
stiffness
decrease
of
of
approximately
There appears to be
5% in the longitudinal
cycled specimens but the data shows a wide
the
scatter compared to the tests on undamaged coupons.
The aver-
age Poisson's ratio from the 245A1 tests is 0.65 and the coefficient
Poisson's
of
of
variation
ratio
variation
is
17.3%.
Similarly,
the
average
of the 345A1 data is 0.61 with a coefficient
equal
to 10.9%.
These large variations can be
explained by the presence of local damage.
132
CHAPTER 5
DISCUSSION
5.1 Static Tests
The
there
results
is
no
ply
of
the
compressive
thickness
static tests indicate
dependence
strength of the [+-45xn/Oxn]s laminate.
that
static
failure
on
the compressive
Lagace has shown [25]
in composites can occur due to in-plane
stresses, or out-of-plane stresses that exist at the edge of a
notch
in
shown
that interlaminar stresses cause delamination and fail-
ure
in
a
composite
some
influence
laminate.
laminates.
of
His experimental work has
Laminates
interlaminar
that
fail
that
not
from
a
laminate.
This
for
however,
stresses.
stresses
primary
interlaminar
equal
It can be con-
the compressive static tests done in this study,
out-of-plane
play
to the
stresses can show a ply thickness
dependence on their static ultimate strengths.
cluded
due
does
stresses
different
that
role
static
at the edge of a 6.35 mm hole do
in
not
around
ply
the
static
necessarily
the
is
imply
of this
that
the
free edge of the hole are
thicknesses.
failure
failure
It
does
suggest,
primarily due to in-plane
133
5.2 Cyclic Tests
results
The
of
the
cyclic tests clearly show a
145AI
variety of damage modes in the [+-45/0]s laminate.
exhibited a rapid delamination mode where areas of dam-
imens
age
Five spec-
grew
large
enough
to
failure within a few load
cause
after delamination initiated.
cycles
Another seven specimens
developed radial delaminations that grew to some extent.
four
ever,
specimens
delamination
that
extended
Furthermore,
this
longitudinal
total)
coupons
(six
only
in
How-
developed
a
the loading direction.
damage
growth is quite slow
to the transverse delamination observed in the other
compared
The
specimens.
laminates
exhibiting
longitudinal
damage
continued to withstand thousands of load cycles before
growth
testing was stopped.
explanation for these different damage types may come
An
the consideration of strain energy release rates as dis-
from
Chapter 2.
cussed
in
gests
that
observed
the
our
in
The results of Wilken's [19] work sug-
transverse
and
radial
delamination damage
study can be modeled as a crack between two
plies that is growing under a tensile opening mode, i.e., Mode
I.
This is consistent with Wilken's experimental results for
an interfacial crack under tensile cycling where he found that
crack
growth
under
the
was very rapid.
action
of
The delamination growth occurs
normal stresses that
arise from local
134
instabilities,
the
delaminated
ply (or plies) buckles under
compression .which generates large peel stresses (out-of-plane
normal
stresses)
which
act
to
enlarge the delamination as
cycling continues.
The longitudinal delamination growth may actually be modas
eled
operating under Mode II (shear) extension.
crack
Wilken's test results support this possibility because
Again,
he
a
found
that
exhibited
growth
a
that
interfacial
an
crack
under Mode II loading
slow growth rate.
The longitudinal delamination
was
the cyclic tests had the same
observed
in
characteristic.
it
Furthermore,
can
versus
similar
of
both in-plane and
logarithm
the number of applied load
of
The observed linear relaionship of equation (4.1) is
to
splitting growth in unidirectional laminates
the
Therefore, the mechanism
longitudinal delamination occurs after longitudinal splitin
ting
showed
between
and
the
holes determined by Daken [2].
with
that
First, consider the plots of damage
delamination damage mode.
cycles.
shown
shear play an important role in the longitudinal
interlaminar
length
be
the
0O
plies of the [+-45xn/Oxn]s laminate.
Daken
that the growth of splitting was due to in-plane shear
the
matrix
and fibers as was discussed in Chapter 2
that the 00 splitting during cyclic loading will occur at
stress
applied
levels
stress
near 15% of the static ultimate strength.
levels
in
this
test
The
program (221-320 MPa)
135
in
result
at
occur
ply.
It is therefore likely splitting will
either
side
of
levels.
stress
side
either
the hole in the 00 plies at these
The photograph of the cross section of a damin Figure 31 shows that cracks in the 0* plies
laminate
aged
at
00
the
of
MPa)
of the compressive ultimate strength (1691
30%-40%
of
order
of 492-712 MPa, which is on the
stresses
ply
0O
of
the delamination do exist.
These cracks
imply that splitting initiated at the hole edge.
The situation of 0* splitting in a loaded [+45n/-45n/0n]s
illustrated in Figure 48.
is
laminate
Clearly, the 00 plies
between the splits carry only load transferred from the angled
through
plies
shear in the ply interface.
If the load level
is gradually increased, the ply interface, which transfers the
to the 00 plies, will fail.
loading
The result of this fail-
ure is the longitudinal delamination mode.
above
The
reasoning
implies
that for a laminate under
cyclic
loading, the longitudinal delamination will follow the
growth
of
failure
shear
00
plies.
area
00
splitting.
The delamination is a result of a
of the -450/00 interface between splits in the
This is why the observed delamination occurs in an
only as wide as the hole.
depends
length
results.
on
on
Since the delamination growth
split growth, a linear dependence of delamination
the logarithm of the number of applied load cycles
136
TOP VIEW
co
SIDE VIEW
SPLITS
SPLI
6.35 mm
-_
I
FIGURE 48
I
SPLITTING OF 0 DEGREE PLIES IN
[+-45xn/Oxn]s LAMINATE AT HOLE EDGE
137
The results from performing
tudinal
delamination
linear regressions on longi-
growth data show a strong dependence on
ply thickness and applied stress level on the growth of longitudinal
delamination.
This result implies that the level of
shear stress which causes 0* splitting is dependent on the ply
thickness and of course dependent on the applied stress level.
It
is
damage
not expected that the growth rate of longitudinal
will
be equal to the growth rate of 0* splitting in a
unidirectional laminate.
the
angled
plies
compressive
the
rate
clear
to
lags
a
[+-45xn/Oxn]s
laminate
induces
a
transverse stress in the 0*0 ply which will affect
of
0*
whether
the
in
This is simply because the effect of
in the laminate.
Also it is not
or not the length of the delamination is equal
length
behind
splitting
of the 00 splits or if the delaminated region
the
splits by some characteristic distance (see
Figure 49).
An
important
specimens
is,
in
result
developed
part,
is that all of the 245A1 and 345A1
longitudinal
delamination.
This result
due to the magnitude of the interlaminar shear
stress
cxz
Figure
50 is a simple schematic "model" of the region between
the
0*
splits.
delaminated
is
at
the
The
-45*/0* interface between the 0O
splits.
diagram shows that part of the area is
at the -450/00 interface and the rest of the area
still perfectly bonded.
The 0* ply carries no load in the
section that has delaminated, therefore, it has been "removed"
138
DELAMI NATED
REGION
SPLIT IN
00 PLY
r
6.35
mm
"LAG"
DISTANCE
FIGURE 49
SKETCH ILLUSTRATING LONGITUDINAL
DELAMINATION IN [+-4 5xn/0xn]s
LAMINATE
139
[+-45]
N00[+-45]
N11
-450
matrix
ti00ltl
layer
t0]
f
l
0
oo
N [0]
*x
FIGURE 50
SCHEMATIC MODEL OF REGION BETWEEN 00
SPLITTING WITH DELAMINATION AT -45o/0o
INTERFACE
140
from the sketch for clarity.
is
load
A shear lag analysis outlined in Appen-
shows that the magnitude of the interlaminar shear is
2,
dix
into the 0* ply through the interlaminar
introduced
component axz.
shear
At the edge of the delamination,
strongly dependent on the ply thickness of the laminate.
The
determine
may
it
because
of this shear component is very important
magnitude
not the longitudinal
or
whether
The 145A1 test
delamination will occur between the 00 splits.
interlaminar
287
MPa.
age
was
shear
failure
splits is near
occurs between 0O
This conclusion is drawn from the fact that no damin
found
145A1
specimens cycled at slightly lower
Transverse delamination growth can also devel-
stress levels.
op
the uniaxial stress level at which an
that
indicate
results
near the same peak stress level of 287 MPa and becomes the
dominant
mode
damage
as loading is increased.
In the 145A1
specimens cycled at approximately 287 MPa there is a "competidamage
tion"
of
shear
failure
delamination
tudinal
increased
occurs between the 0O
for
splits before transverse
initiates, then the specimen will exhibit longi-
delamination
interlaminar
It appears that if the interfacial
modes.
shear
the
growth.
between
the
In
other
-45*/0*
words,
plies
were
if
the
to be
same in-plane applied stress, then longi-
tudinal delamination might be the only damage observed.
This is the case in the 245A1 and 345A1 specimens; at the
same
in-plane
stress level, the interlaminar shear stress in
141
the
split
result
region is higher than in the 145A1 specimens.
is
that only longitudinal delamination is observed in
The other damage modes do not occur in these
these specimens.
the thicker plies are more stable and will
because
specimens
not
The
buckle
delamination growth at the stress levels
causing
where longitudinal delamination is observed.
Another
possible
explanation
as
to
why
longitudinal
delamination was not always observed in the 145A1 specimens is
the possibility that longitudinal splitting did not develop in
Flaggs
specimens.
these
and Kural [26] conducted an exper-
imental study on [+-0/90xn]s laminates, where n took on values
of
1,
these
the
this
and 8.
4,
2,
unflawed laminates to determine the thickness effect of
900
on
the initiation of transverse splitting in
They
determined the transverse strength of the
layer
layer.
and
graphite/epoxy
multidirectional
over
at
They performed static tension tests on
found
that
90*
plies
constrained in a
laminate showed a large increase in strength
"unconstrained" laminates.
That is, splitting initiated
stress levels in the 900 plies of 2.5 times the transverse
strength of a unidirectional ply tested in transverse tension.
Furthermore,
increased,
ated
as
number of 90* plies in the laminate was
the 90* ply stress level at which splitting initi-
decreased,
900 ply.
the
approaching
the stength of an unconstrained
They use the term "in-situ strength" to describe the
142
change in the strength of a composite ply as it is constrained
in a laminate.
ation
of in-situ strength may apply to the initi-
concept
The
of 0* splitting in a laminate as well.
growth
and
the 145A1 laminate, the number of consecutive 0O
In
plies is two;
are constrained on two sides by -45* plies.
The
these
plies
245A1
laminates have four consecutive 0* plies which are cononly
strained
is
laminate
by
sides
-45* plies.
The result of
that the in-situ strength of the
suggests
Kural
and
Flaggs
two
on
with increasing ply thickness.
decreasing
Even
though stresses in the 00 plies of the 145A1 laminate are well
the
above
stress,
splitting
unidirectional
the
in-situ
strength may still be higher, thus splitting does not develop.
But,
we
as
increase
which
decreases
ply
results
the
in-situ strength
splitting
and longitudinal
thickness,
0O
in
delamination due-to shear failure.
If
the
is
delamination
longitudinal
a
result
of an
interlaminar shear failure, then it should occur in tension as
well
as
sequence
in
should
interlaminar
Therefore,
compression
have
shear
the
same
loading.
little
between
type
In addition, the stacking
effect
the
0*
on
the
value
of the
ply and the angled ply.
of delamination should occur in a
[0/+-45]s laminate under tensile cyclic loading.
A simple experiment was run to support the proposed mechanism of longitudinal delamination growth.
A [+-45]s laminate
143
and
[+-45x23s
a
laminate were laid up and cured in the same
Five 350 mm x 50 mm coupons
[0x2]t laminates were also cured.
cut from each laminate and 6.35 mm holes were drilled in
were
A razor blade was used to cut two,
the center of each coupon.
50
and
Two [0]t laminates and two
as all previous specimens.
manner
mm
long,
00 splits at the hole edge in four [0]t coupons
[0x2]t
four
00 coupons with splits were
The
coupons.
bonded to the [+-45]s and [+-45x2]s laminates with a room temcure
perature
epoxy.
This bonding procedure resulted in two
[0//+-45]s
coupons and two [0x2//+-45x2]s coupons, where "//"
represents
a
room-temperature
cure epoxy bondline.
coupons had 6.35 mm holes and the 0O
All the
plies contained splits on
either side of the hole.
Loading
tabs were bonded on each end of all four coupons
and a tensile static test was performed on each coupon following
the procedure described in section 3.1.
by
loading
the
specimen
in
200
The test was run
increments
pound
and
monitoring, with the ultrasonic technique, the regions between
the
0* splits after each increment of loading.
cation
of
subsequent
splits
in
nificantly
load,
each
delamination
the 0* plies.
lower
specimen
exhibited
During appli-
split growth and
at the 00/+45* interface between the
The delamination occurred at a sig-
stress level of 88 MPa in the [0x2/+-45x2]s
coupons than the stress level of 132 MPa in the [0/+-45]s coupons.
These tests demonstrate that longitudinal delamination
144
is a result of an interlaminar shear failure of the ply interthe
between
face
00
an angled ply in the regions
and
ply
between splits in the 0* plies.
coupons, a [0//+-45]s and a [0x2//+-45x2]s laminate,
Two
were constructed in the same manner as the four previous specthat
except
imens
mum
stress
500
cycle
and R=0.1.
level
The testing was interrupted at
intervals and the growth of delamination was moni-
0*
the
between
longitudinally
Delaminations
inspection.
ultrasonic
via
ply
grew
and the 450 ply on both
The delamination occurred along with
of each specimen.
sides
Both
were cycled under tensile loading at the same maxi-
specimens
tored
no splits were cut in the 0* plies.
Observation of the specimen during
splitting in the 00 plies.
testing revealed that splitting initiated at the hole edge and
grew
Again,
vertically.
the
delamination
between the splits in the 0* plies.
the
delaminated
shows
51
Figure
00
peeled
regions
only
As the cycling continued,
away from the laminate.
delamination
this
occurred
clearly
in
the
[0x2//+-45x2]s specimen.
The
rithm
of
specimen
which
delamination length, 2a, is plotted versus the loganumber of applied load cycles for a [0//+-45]s
the
in
Figure
indicates
coefficient,
52.
nearly
R=.954).
A
a
linear regression was performed
linear
relationship (correlation
The results of the least square linear
r~-s~--- a
I
145
FIGURE 51
PHOTOGRAPH OF LONGITUDINAL DELAMINATION IN
[0x2/+-45x2]s TENSILE CYCLIC SPECIMEN
146
TENSILE COUPON
tee
E+-45/03s
SPECIMEN
A
88
r r
E
E
FCD
zLJ
-j
I
68
48
CD
(_9
r<
28
@
1E3
I
I
I
I I I II
I
I
I
I I i __
IIl _
1E4
NUMBER OF CYCLES
FIGURE 52
PLOT OF LONGITUDINAL DELAMINATION LENGTH, 2a,
VERSUS THE LOGARITHM OF THE NUMBER OF APPLIED
LOAD CYCLES
IE5
147
regression indicate that delamination initiation is after 3640
cycles.
The initial growth rate (da/dN)o is 0.00573 mm/cycle.
5.3 Residual Strength Tests
The
residual
cyclic
loading
tensile
strength
The
test
can
between
thicknesses.
results
of
show
that
increase
the
damage due to
unidirectional
the [+-45xn/Oxn]s laminate with a hole.
however,
the
This
tests
actually
of
results,
strength
the
strength
145A1
indicate
coupons
a large difference in
and
the other two ply
variation can be explained by considering
the
145A1
specimens separately as shown in
Table 14.
The 145A1 residual strength data has a very large scatter
(coefficient
345A1
data.
also varied.
broken
can
an
of
But
variation = 14.0%) compared to the 245A1 and
the type of damage in the 145A1 coupons is
If the residual strength of the 145A1 coupons is
down according to the type of damage in the coupon, it
be
seen that coupons with longitudinal delamination have
average
tensile strength of 643 MPa.
This result is very
close to the residual strength of the 245A1 and 345A1 coupons.
Notice that the average residual strength of specimens with no
detectable
after
have
delaminations
have an average strength of 543 MPa
cyclic loading and coupons with transverse delamination
an
average
strength of 496 MPa, which is very near the
148
uncycled
strength
of
470
MPa
determined
from
the static
tensile coupon testing.
Generally, an increase in strength of nearly 50% is found
in
the coupons with longitudinal delamination.
in
tensile
the
hole.
strength
Through
This increase
is due to the presence of damage around
mechanisms of stress redistribution, the
hole no longer causes a stress concentration in the laminate's
00
plies.
The data from Lagace's experimental work [27] indi-
cates
the
MPa.
This compares closely to the average strengths of these
notched
other
as
unnotched
laminates
strength of a [+-45/0]s laminate is 667
with longitudinal delamination damage.
In
words, the laminate has become nearly notch-insensitive
the fracture is controlled by the 0* plies which no longer
see the effect of the notch.
Post-mortem
gitudinal
failure observation of the coupons with lon-
delamination
confirms
the
hypothesis that the 0O
plies in the region between splits carry no load after delamination.
Figure
53
is
residual strength testing.
entire
the
a photograph of a 245AI coupon after
The 0* fibers fractured across the
width of the laminate except for the 6.35 mm region in
center
of
the
laminate where 0' splitting had occured.
These fibers remained unloaded during the static test and thus
do not break when the laminate fails.
However, it is important to point out that the longitudinal damage mode is not beneficial to the integrity of the com-
IIIIIl
I
I
149
FIGURE 53
PHOTOGRAPH OF
STRENGTH TEST
[+-45x2/0x2]s
COUPON AFTER RESIDUAL
150
posite.
The
increase
uniaxial
tension.
in
strength
observed
only
in
The effects of compressive and transverse
have not been investigated.
loading
was
Under these loading con-
longitudinal delamination could lead to buckling and
ditions,
subsequent
growth
of delamination at stress levels below the
undamaged strength of the laminate.
5.4 Summary
thickness does not affect the static strength of the
Ply
laminate with 6.35 mm holes.
[+-45xn/Oxn]s
However, a thick-
ness effect has been found on the damage mode and growth rates
Longitudinal delamination
in
specimens under cyclic loading.
is
an important damage mode in all the laminates tested.
number
of
tudinal
cycles to initiation and the growth rate of longi-
delamination
is
strongly
thickness and applied stress level.
ness
and
The
the
higher
the
dependent
upon
the
ply
The larger the ply thick-
applied stress level, the earlier
damage initiates and the higher the initial damage growth rate
becomes.
plies
of
splitting
direction.
interface
It
has
been shown that splitting occurs in the 0*
the laminates with longitudinal delamination.
This
initiates at the hole edge and grows in the loading
An
interlaminar
results
in
shear
failure
in
the -450/00
the longitudinal delamination.
It has
been shown that the magnitude of the interlaminar shear stress
151
00
between
splits
that
postulated
not
in
is dependent on the ply thickness.
It is
the 145A1 specimens this shear stress is
always great enough to cause a shear failure so that lon-
gitudinal
delaminaton is not always observed.
However, it is
also possible that the in-plane shear stress that initiates 0*
splitting
before
since
may not always be high enough to bring on splitting
other
damage
in-situ
the
Longitudinal
initiate
modes
strength
delamination
to
increase
the 145A1 laminate
change with ply thickness.
is also observed in tensile cyclic
loading in [0/+-45]s laminates.
found
may
in
Longitudinal delamination was
the uniaxial tensile strength of a cycled
coupon but the strength of the laminate with this type of damage has not been determined for other loading conditions.
152
CHAPTER 6
CONCLUSIONS AND RECOMMENDATIONS
From
the
tests
completed
in this investigation we are
able to draw the following conclusions:
1.
compressive
static
The
strength of [+-45xn/Oxn]s lami-
nates with 6.35 mm holes is not dependent upon the effective
ply
thickness of the laminate.
This suggests that
failure is due only to in-plane stresses.
2.
initiates and grows at the hole edge in the 00
Splitting
plies
due to compressive cyclic loading in [+-45xn/Oxn]s
laminates.
3.
In
the
region
above the hole.and between the splits, a
large axz exists in the -450/00 interface.
sufficiently
large,
then
this
If the axz is
region of the interface
will delaminate.
4.
As the ply thickness is increased, the interlaminar shear
stress
axz
at the -450/0* ply interface, between the 00
splits, increases for the same applied uniaxial stress.
153
5.
A
second delamination mode which characterizes itself by
growth,
occurs often in the 145A1
transverse
direction
specimens.
This damage can be associated with ply insta-
bilities
therefore
and
observed most often in the thin
ply laminates.
6.
is a linear dependence of the longitudinal delami-
There
on the logarithm of the number of applied
length
nation
cycles.
7.
The number of cycles to initiation of longitudinal delamination
decreases
with
increasing ply thickness and/or
increasing peak stress level.
8.
The
growth
initial
increasing
ply
rate of delamination increases with
thickness
and/or increasing peak stress
level.
9.
The
growth
[+-45xn/0xn]s
rate
of
longitudinal
delamination
in
laminates is similar to the growth rate of
splitting in unidirectional laminates.
10.
Longitudinal
delamination will occur under tensile load-
ing as well as compressive loading.
154
11.
Residual strength tests show nearly a 50% increase in the
uniaxial
of a coupon which has longi-
strength
tensile
tudinal delamination damage due to cyclic loading.
on the results of this test program, the following
Based
work is recommended to further our understanding of the development of damage in composite materials:
1.
investigate the effect of
to
initiation and growth of splitting in
the
on
thickness
required
are
Experiments
unidirectional laminates with holes under static loading.
This
of
should include a study of the effect
investigation
thickness
ply
the
in-situ
strength
of
a
under the constraint of angled plies
ply
unidirectional
on
in a laminate.
2.
A
study is needed to determine what effect hole size has
initiation of longitudinal splitting in 00 plies
on
the
in
a multidirectional laminate.
effective
prediction
This work could lead to
of the development of longitudinal
delamination.
3.
The
relationship
the
length
determined.
of
between the length of 0* splitting and
longitudinal
Cyclic
testing
delamination
needs
to be
of [0Oxn/+-45xn]s laminates
155
with
to
results
cyclic
the
in
splitting
dust
would
holes
the
in
test.
a
be
an effective method of monitoring
outer 0* plies.
the
surface
of
clear
view
Application of chalk
composite before testing
of the 0*
splitting during a
Ultrasonic monitoring can give an accurate
picture of delamination length during the test.
4.
A
detailed study of the effect that longitudinal delami-
nation has on the strength of a composite in a variety of
loading
conditions
compression,
should
transverse
be
made; i.e., longitudinal
loading,
and
biaxial
loading
could be applied to investigate a composite's response in
the presence of such damage.
156
REFERENCES
1.
"The Effects of Compression-Compression
Graves, M.J.,
Fatigue on Balanced Graphite/Epoxy Laminates With Holes,"
MIT, Department of Aeronautics and Astronautics, S.M.
Thesis, 1979.
2.
Fanucci, J.P., "Damage Initiation and Propagation During
Compressive Fatigue of Flawed Graphite/Epoxy Composites,"
MIT, Department of Aeronautics and Astronautics, Ph.D.
Thesis, 1981.
3.
"Axial Fatigue Failure
and Embert, L.J.,
Kim, H.C.,
Sequence and Mechanisms in Unidirectional Fiberglass Composites," J. Composite Materials, Vol. 12, April 1978,
p.139.
4.
"Splitting Initiation and Propagation in
Daken, M.H.,
Flawed Unidirectional Graphite/Epoxy Composites Under
Tension-Tension Cyclic Loading," MIT, Department of Aeronautics and Astronautics, S.M. Thesis, 1983.
5.
Hashin, Z. and Rotem, A., "A Fatigue Failure Criterion
for Fiber Reiforced Materials," J. Composite Materials,
Vol. 7, October 1973, p. 448.
6.
"Fatigue of Composite Materials: Damage
Talreja, R.,
Mechanisms and Fatigue-Life Diagrams," Proceedings of the
Royal Society of London, A 378, 1981, pp. 461-475.
7.
"Ascertainment of the
Ryder, J.T., and Walker, E.K.,
Effect of Compression Loading on the Fatigue Lifetime of
Graphite/Epoxy Laminates for Structural Applications,"
AFML-TR-76-241, Air Force Materials Laboratory, Dayton,
Ohio, December 1976.
8.
Rosenfeld, M.S. and Huang, S.L., "Fatigue Chacteristics
of Graphite/Epoxy Laminates Under Compression Loading,"
J. Aircraft, Vol. 15, No. 5, May 1978, p. 264.
157
9.
Ramani,
S.V. and Williams, D.P., "Notched and Unnotched
Fatigue Behavior of Angle-ply Graphite/Epoxy Composites,"
ASTM STP 636, 1977, pp. 27-46.
10.
Hahn, H.T. and Kim, R.Y., "Proof Testing of Composite
Materials," J. Composite Materials, Vol. 9, 1975, p. 297.
11.
Chou, P.C. and Croman, R., "Residual Strength in Fatigue
Based on the Strength-Life Equal Rank Assumption," J.
Composite Materials, Vol. 12, April 1978, p. 177.
12.
"Experimental and Analytical Study of
Whitcomb, J.D.,
Fatigue Damage in Notched Graphite/Epoxy Laminates," ASTM
STP 723, 1981, pp. 48-63.
13.
Ratwani, M.M. and Kan, H.P., "Delamination-Based Compression Residual-Strength Prediction Model for Composand
of
Aeronautics
Institute
American
ites,"
Astronautics, AIAA paper 83-0872, 1983.
14.
O'Brien, T.K, and Reifsnider, K.L., "Fatigue Damage Evaluation Through Stiffness Measurements in Boron-Epoxy LamJ. Composite Materials, Vol. 15, January 1981,
inates,"
p. 55.
15.
K.L.,
"Some Fundamental Aspects of the
Reifsnider,
Fatigue and Fracture Response of Composite Materials,"
Proceedings, 14th Annual Society of Engineering Science
Meeting, Lehigh University, Bethlehem, Pa., 14-16 November, 1977.
16.
Highsmith, A.L. and Reifsnider, K.L., Stiffness-Reduction
Mechanisms in Composite Laminates," ASTM STP 775, 1982,
pp. 103-117.
17.
Reifsnider,
K.L.,
"The Effect of Lamination-Induced
on Fatigue Damage Development at Internal
Stresses
Flaws," Composites Technology Review, Vol. 3, No. 1,
Spring 1981, p. 17.
158
18.
Herakovich, C.T., "On the Relationship Between Engineering Properties and Delamination of Composite Materials,"
J. Composite Materials, Vol. 15, July 1981, p. 336.
19.
Klang, E.C. and Hyer, M.W., "Damage Initiation At Curved
Free Edges: Application to Uniaxially Loaded Plates Containing Holes and Notches," Presented at ASTM Second
United States-Japan Symposium on Composite Materials,
Hampton, Va., June 1983.
20.
Carlsson, L., "Interlaminar Stresses at a Hole in a Composite Member Subjected to In-plane Loading," J. Composite Materials, Vol. 17, May 1983, p. 238.
21.
Eisenmann, J.R., Camin, R.A. Margolis,
Wilkens, D.J.,
"Characterizing Delamination
and Benson, R.A.,
W.S.
Growth in Graphite-Epoxy," ASTM STP 775, 1982, pp.
168-183.
22.
"Characterization of Delamination Onset
O'Brien, T.K.,
and Growth in a Composite Laminate," ASTM STP 775, 1982,
pp. 140-167.
23.
Lagace, P. and Brewer, J., TELAC Manufacturing Course,
Class Notes, Edition 0-2, Technology Laboratory for
Advanced Composites, Report 81-14, Sept., 1981.
24.
Vizzini, A.J and Lagace, P.A.,"TELAC Computing Facility:
Software Description", Technology Laboratory for Advanced
Composites, Report in preparation.
25.
Lagace, P.A., "Delamination Fracture Under Tensile Loading", presented at Sixth Conference on Fibrous Composites
in Structural Design, New Orleans, Louisiana, January,
1983.
26.
Flaggs, D.L., "Experimental Deterimination of the In-Situ
Transverse Lamina Strength in Graphite/Epoxy Laminates",
J. Composite Materials, Vol. 16, 1982, p.103.
159
27.
Lagace, P.A., "Notch Sensitivity and Stacking Sequence",
to be presented at ASTM Seventh Symposium on Composite
Materials:
Testing
and
Design,
Philadelphia,
Pennsylvania, April, 1984.
28.
Phillps, E.A, "Effects of Truncation of a Predominantly
Compression Load Spectrum on the Life of a Notched
Graphite/Epoxy
Laminate",
ASTM STP 723,
1981, pp.
197-212.
160
APPENDIX 1
SPECIMEN SELECTION AND VERIFICATION
A1.1 Specimen Selection
An ideal compression test specimen must minimize stresses
to specimen bending or support configuration.
due
The method
of data acquisition can place further restrictions on the conA thorough search of litera-
figuration of any test specimen.
ture and testing of certain compression methods led to a final
of the test specimen to be used in this investigation.
choice
It
be pointed out that while many methods reported in
should
literature have been used with success, these experiments
the
generally were conducted with relatively thick (greater than 5
mm) test specimens.
as
inates
thin
The current investigation deals with lam-
as
0.8
thus
mm,
risk of compressive
the
instability is greater.
Anti-buckling
plates
guide
specimen
been used in previous
buckling
under
compression
studies
to
loading.
Static tests done as part of this investigation used
a
prevent
have
configuration
Walker [7].
to
identical
teflon
specimen
and
performed by Ryder and
This method consists of supporting a gripped test
coupon with two metal plates.
with
tests
to
reduce
the plates.
The aluminum plates were coated
surface
friction between the loaded
Cutouts in the support plates were
161
made
around
tractions
the
from
cutouts
also
in
affecting
were
the
the
on
made
composite to prevent surface
stress field around the flaw;
both
plates at the location of
A quantitative measure of coupon
gages.
strain
back-to-back
and insight to the extent of pure compressive loading
bending
was
hole
these tests showed that at loads
of
Results
obtained.
below the fracture stress, buckling of the cutout region
well
the back-to-back strain gages at the cutout as
from
measured
indicated by the divergence of strains
as
place
taking
was
shown in Figure A1.1.
Phillips showed that the cyclic life of a composite laminate was dependent upon the cutout size in the support plates.
He
that
found
cyclic
the
around
field
is
cutout
produced shorter compressive
results indicate that the stress
These
[28].
lives
cutouts
larger
not purely compressive.
Other
stress components induced through bending appear to affect the
damage
development during cyclic loading.
cation
of
the
NDI
usual
techniques
The in-test appli-
on a specimen between
support plates is impossible without visual access to the surface
of
the
compression
composite.
The use of anti-buckling plates for
was
testing
rejected
because
of
these
deficiencies.
Another
method
of
collecting
compression data is with
sandwich specimens consisting of two identical composite laminates
bonded
to
a
low stiffness reinforcing core.
Axially
162
E 03
2.B0
a REAR
1.03
-2. e3
FIGURE A1.1
0.0
CUPOi
MICR£fSTPAIN
1.06
2.00
E84
STATIC COMPRESSIVE TEST STRESS-STRAIN PLOT
OF BACK TO BACK STRAIN GAGE READINGS OF COUPON
SPECIMEN UNDER SUPPORT OF ANTI-BUCKLING GUIDE
PLATES
163
were
specimens
test
sandwich
loaded
chosen
several
for
A sandwich specimen provides support over the entire
reasons.
ensures
no
buckling.
The
delaminate
without the influence of external supports.
are
methods
NDI
Also,
easy to apply on both sides of the sandwich
allows
which
specimen
local
of the composite is free to
surface
outside
which
coupon
composite
the
of
surface
specimens
to be monitored for damage
without removing them from the testing machine.
Compressive loads can be applied to the sandwich specimen
axial
either
through
loading
or four-point bending.
Axial
application of load was chosen over four-point bending because
it
affect
might
is
felt
was
difficult
the geometric curvature applied to the specimen
damage development.
use
to
Also, Moire interferometry
during testing with the specimen under
four-point bending.
A1.2 Verification of the Test Specimen
[+-45/0]s
tensile
monotonically
to
Six
tested
tensile
conducted
ture
stress,
were
failure.
with 6.35 mm holes were
The configuration of the
coupon specimen is shown in Figure A1.2.
were
the
coupons
45A1
also
These tests
to derive the basic tensile properties (fraclongitudinal
laminate
modulus, and Poisson's ratio) for
with a 6.35 mm hole.
These tensile tests
used as basic data for comparison with the tensile
164
TOP VIEW
SIDE VIEW
TI
75 mm
GLASS/EPOXY
TAB
GRAPHITE/EPOXY
200 mm
GRAPHITE/EPOXY
FM-123 FILM ADHESIVE
,GLASS/EPOXY
75 mm
SGLASS/E
50 mm
FIGURE A1.2
CONFIGURATION OF STATIC TENSILE COUPON
TEST SPECIMEN
165
Fracture
tests.
strength
residual
data
were obtained for
these six specimens and the average fracture stress was deterbe 470 MPa with a coefficient of variation of 6.2%.
to
mined
the six tensile coupons is 58.9 GPa
of
modulus
average
The
Poisson's
average
the
ratio
0.70
is
(C.V.=3.1%)
and
(C.V.=1.8%).
Calculations from Classical Laminated Plate The-
ory predicts EL =57.7 GPa, and vLT=0.69 for this laminate.
A
of eight [+-45/0]s sandwich specimens were tested
set
tensile
loading.
It
is
that the average failure stress of a set of sandwich
expected
specimens
be lower than a set of tensile coupon speci-
would
is because the strength of the sandwich specimen
This
mens.
under
failure
to
monotonically
is limited to the strength of the weakest of the two composite
faces
on
ultimate
a
strength is reduced to 443 MPa in this specimen with
The average modulus and
of variation of 6.4%.
coefficient
major
In fact, the data shows the average
specimen.
the
Poisson's
are
ratio
58.3
GPa
(C.V.=2.4%)
and 0.69
(C.V.=2.1%) respectively.
These
that
show
results
the
aluminum core has little
influence on the engineering properties in the sandwich specimen with the discrepency in ultimate strength due to the probabilistic
nature
stress-strain
the
of
plots
strength
of
composites.
of both a coupon specimen and a sandwich
specimen are shown in Figures A1.3 and A1.4.
are
nearly
Typical
identical,
The plots, which
are nearly linear to failure and show
166
STC
145A1 -3
EL = 59.6 GPa
58800
300
z
28800
w
uJ
w
H-r
F0
1800
2000
4000
8000
LONGITUDINAL STRAIN ECs]
FIGURE A1.3
STRESS-STRAIN PLOT FOR TYPICAL STATIC TEST
OF [+-45/0]s TENSILE COUPON SPECIMEN
167
STB
588
n
E
L
145A1-2
= 60.0 GPa
400
uJ
Co
_J
2800
H
Col
z,
wL
H
LONGITUDINAL STRAIN [As]
FIGURE A1.4
STRESS-STRAIN PLOT FOR TYPICAL STATIC TEST
OF [+-45/0]s TENSILE SANDWICH SPECIMEN
168
TABLE A1.1
STATIC TENSILE TEST RESULTS FOR BOTH [+-45/0] s
COUPON AND SANDWICH SPECIMENS
Specimen
I.D.
STC145AI-1
-2
-3
-4
-5
-6
Average
C.V.
STB145Al-1
-2
-3
-4
-5
-6
-7
-8
Average
C.V.
Tensile
Longitudinal
Ultimate Strength Modulus
[MPa]
[GPa]
56.1
429
483
56.8
59.6
443
460
60.3
511
61.1
496
59.5
470
58.9
6.2%
3.1%
409
404
440
426
464
457
446
496
443
6.4%
59.4
60.0
58.0
59.1
57.8
57.8
58.7
55.2
58.3
2.4%
Poisson's
Ratio
.70
.68
.69
.72
.71
.70
.70
1.8%
.69
.69
.65
.69
.69
.70
.70
.69
.69
2.1%
169
a 10% loss of modulus at fracture.
than
less
The individual
tensile test results are shown in Table A1.1.
A1.3 145A1 Static Compression Tests
initial
The
static
compression tests were completed on
[+-45/0]s sandwich specimens.
Seven specimens were tested and
the average compressive fracture strength was determined to be
with an associated coefficient of variation of 9.1%.
423
MPa
The
average
longitudinal
modulus
55.9
was
GPa
mean
and
Poisson's ratio was 0.59.
experimental Poisson's ratio of 0.59 compared to a
This
value
predicted
that
shows
of 0.69 raised concern.
in compression, the honeycomb core is restricting
transverse strain which affects the Poisson's ratio.
the
for
reason
thin
Figure
The
this effect is explained through consideration of
the construction of the honeycomb.
of
This result clearly
strips
of
aluminum, preshaped and bonded together.
this
shows
A1.5
Aluminum honeycomb is made
construction.
All
tensile
and
compressive sandwich specimens had been made with the "ribbon"
(strips
Under
deforms
verse
of
aluminum)
longitudinal
and
strain.
perpendicular
tensile
loading,
to
the
the load direction.
honeycomb
easily
the Poisson's effect causes a compressive transUnder
this
compressive
strain,
the ribbon
simply bends at each cell (like a hinge) and does not restrict
170
BONDED
RIBBON DIRECTION
FIGURE A1.5
SCHEMATIC OF THE CONSTRUCTION OF ALUMINUM
HONEYCOMB CORE USED IN SANDWICH SPECIMENS
171
composite from straining in the transverse direc-
bonded
the
tion.
compression,
longitudinal
Under
effect
results
ribbon
is
however, the Poisson's
in a tensile transverse strain.
significantly
stiffer
under
this
The aluminum
tensile state
resulting in a large reduction of the transverse strain in the
The problem is overcome by rotating the honeycomb
composite.
90';
that
that
the
the aluminum core should be cut and bonded so
is,
direction of the aluminum ribbon coincides with the
direction of negative strain in the specimen.
static
Two
145A1
panels
were
constructed
honeycomb oriented in the above described manner.
the
These spec-
tested monotonically to failure and the test data
were
imens
with
yielded an average ultimate strength of 424 MPa and an average
modulus
57.8 GPa.
of
The modulus and ultimate strength were
affected by the rotation of the honeycomb.
not
significantly
The
average
the
theoretical value of 0.69.
mens
the
were
Poisson's
constructed
negative
ratio was 0.72 which is very close to
All the following test speci-
with the honeycomb ribbon parallel to
strain direction.
Static test results of 245A1
and 345AI show good correlation with plate theory (see section
4.1).
172
A1.4 Summary of Specimen, Selection and Verification
The choice of a compression test specimen was constrained
by
the
testing.
need
to
apply
non-destructive
techniques
during
Several different types of specimens were considered
and the sandwich specimen was chosen as having the most desirable
configuration
available.
The
specimen
was carefully
scrutinized to ensure that the data obtained from cyclic testing would be reliable and reproducible.
Comparison of tensile
sandwich tests with tensile coupons show no differences in the
response
are
of the composite under loading.
properly
attained
Material properties
with the sandwich specimen and static
compression tests show no instability problems as the ultimate
strength
inspected
is
approached.
during
testing
The sandwich specimen can be easily
and
its outer surface has no con-
straints that might inhibit delamination damage.
173
APPENDIX 2
SHEAR LAG ANALYSIS OF A -450/00
INTERFACE
CONTAINING A DELAMINATION
When splitting occurs in the 00 plies of a [+-45xn/Oxn]s
laminate, load is transferred into the plies between the splits
by shear in the matrix layer at the -450/00
interface.
If a
delamination initiates at this interface in part of the region
between the splits in the 00 plies, then the 00 plies in that
region cannot carry load.
This case is illustrated in Figure
A2.1 for load applied in the longitudinal direction.
In the
figure, the part of the 00 ply which is delaminated is not
shown for clarity.
The reference point of x=0 in this case is
measured from the edge of the delamination.
A uniaxial
load per unit length of N11 is applied far-field in the
x-direction.
It is assumed that all derivatives with respect
to y are equal to zero and that the longitudinal stiffness of
the matrix layer is negligible such that it only carries shear
load.
Given these facts and the coordinate system defined, the
boundary conditions can be stated as follows:
N [+N [0
4 5
](x)
(x)
= N11
(x
<
0)
(A2.1a)
= 0
(x
< 0)
(A2.1b)
174
t[+-45]
N
00
N[+-45]
11
matrix
layer
FIGURE A2.1
SCHEMATIC MODEL OF REGION BETWEEN 00
SPLITTING WITH DELAMINATION AT -450/00
INTERFACE
175
N[+-45] (+o)
= N[+-
N[
= N[01
(+c)
]
[0
4 5]
]
= N11
matrix
T
(rix
) = 0
xz
4 5]
group and N[0
(A2.ld)
[o]
N[+-45] + N[0
where N[+-
(A2.1c)
(A2.1e)
(A2.1f)
is the load per unit length in the [+-45] ply
]
is the load per unit length in the [0] ply.
The
load per unit length is defined as the integral over the thickL
ness of the layer:
N = a * tlayer
(A2.2)
The displacement in the x-direction in each ply group can
be realted to the applied load by considering the inverted
stress-strain equation:
Exx = SXX a XX
(A2.3)
and the strain-displacement relation:
du
dx
duxx
(A2.4)
Using equation (A2.4) in equation (A2.3) and integrating over
the thickness of the ply layer gives:
h
du
du
dx
S
N
xx xx
(A2.5)
where h is the thickness of the ply layer, and the compliance,
176
xx,
is:
1 -
Sxx
v
E
v
xy yx
(A2.6)
xx
The shear strain in the adhesive is the difference in displacement of the two composite layers divided by the thickness of
the matrix layer:
m
Y -,
u[+-45]
- U[ 0 ]
(A2.7)
t
m
Differentiating with respect to x and using equation (A2.5)
yields:
dy
=m
dx
S[+-45]N [+-45]
t
t[+-45]
m
[_
ot[0]
t[O]
(A2.8)
j
It is now necessary to relate this to the shear stress in the
matrix.
First, the shear stress-strain relation for the matrix
gives:
T
m
m
xy = Gm y xy
where Gm is the shear modulus of the matrix.
(A2.9)
The shear stress
in the matrix can be related to the loading in the ply layers
by considering the first of the three stress equilibrium
equations:
177
do
xx
da
+
dx
xy
+
dy
do
xz
0
(A2.10)
dz
Remembering that all derivatives with respect to y are zero and
integrating the equation over a layer thickness results in:
dN
+
xx
= 0
(A2.11)
dx
Since this holds throughout the ply layer, at the ply layer/
matrix layer
interface, the following holds true:
d[0]
dx
_=
d[+-45]
dx
dx
=
Tm
xz
(A2.12)
Thus, using equations (A2.12) and (A2.9) in equation (A2.8) and
differentiating once with respect to x yields a second order
homogeneous differential equation for the shear stress in the
matrix which, upon rearranging terms, takes on the form:
2m
d T
- aT m
xz
xz = 0
dx 2
(A2.13)
where:
S-
Gm
t
m
S [ 03
0]
t[0 ]
[+- 4 5 1
S+-45
t[+-45
(A2.14)
178
The solution to equation (A2.13) is of the form:
m
T
xz
(x)
= Be
-/Ex
(A2.15)
where 8 is a constant to be determined.
This equation satis-
fies the boundary condition expressed in equation (A2.1f).
Equation (A2.15) is placed into equation (A2.12) and then integrated with respect to x to yield the following two equations:
1
N[0
N[
+- 45
Bee -/Ax + C1
1[-45
Be
]
+ C2
(A2.16a)
(A2.16b)
where C 1 and C 2 are constants resulting from the integration.
Applying the boundary conditions at x = 0, equations
(A2.1a) and
(A2.1b), yields the equations for these constants in terms of 6:
(A2.17a)
C 1N
B
2 = N11
(A2.17b)
The value of B can be found by using the boundary condition
expressed in equation (A2.1d) in equation (A2.16a) to yield:
S=-A N[0
]
(A2.18)
179
or, using equation (A2.2):
S=-/[ot[
(A2.19)
Summarizing, the expression
for the shear stress in the
matrix layer is:
m (x) =-/7
xz
t[ [ 0 ](
[00 ]
with a as defined in equation (A2.14).
(A2.20)
This equation clearly
shows a dependence of the shear stress in the matrix on the
thickness of the 00 ply layer.
For the [+-45xn/Oxn]s graphite/epoxy laminates considered
here, the following properties are of importance:
tply
= 0.134 mm
t[ 0 ]
= n * tply
t[+-45]= 2n * tply
The ply properties and far-field stress distribution can be
determined from Classical Laminated Plate Theory and the
basic unidirectional ply elastic constants for ASl/3501-6
graphite/epoxy in Table 4.
A plot of the shear stress in the
matrix versus the distance from the edge of the delamination
can then be made.
The distance from the free edge, x, is nor-
malized by the square root of the thickness of the matrix layer.
Plots of the shear stress for the three "effective ply thicknesses"
(n=1,2,3) are shown in Figure A2.2.
The effect of
180
"effective ply thickness" on the value of the shear stress in
the matrix layer can clearly be seen.
181
I
LL
SI
,
I.
F-
I
II
I
1
1
I
IX
1
W
IN -450/00 INTERFACE
r
//VERSUS THE DISTANCE FROM
FIGURE
A2.2 PLOT OF SHEAR
STRESS,
FROM SHEAR LAG ANALYSIS,
"T
/
/
-
C° H>