CCMS-85-12
 

VIRGINIA TECH 

CENTER FOR jig;' 

COMPOSITE MATERIALS'" 

AND STRUCTURES 

Fatigue Damage in Notched 

Composite Laminates under 

ITension-Tension Cyclic Loads 

7: 7 w.W. Stinchcomb K.L. Reifsnider 

E.G. Henneke G.R. Kress 

to September 1985 

Virginia Polytechnic 

4.) 4 Institute 

4 o and 

State University 

Blacksburg, Virginia 

. -.- 24061 

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Par. , , 

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COLLEGE OF ENGINEERING
 

VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY 

Blacksburg, Virginia 24061 

ENGINEERING SCIENCE AND MECHANICS 

703/961-5259
 

October 31, 1985
 

Dr. T. K. O'Brien
 

MS 188E
 

NASA Langley Research Center
 

Hampton, Virginia 23665
 

Dear Kevin:
 

Enclosed, please find 3 copies of the report "Fatigue Damage in 

Notched Composite Laminates Under Tension-Tension Cyclic Loads." This 

is the final report for NASA Grant NAG-1-232. 

- Results from the program have been presented at the US/Japan 

Conference on Composite Materials sponsored by ASTM and NASA Langley
 

(June, 1983) and have been published in ASTM Special Technical
 

Publicat-ion P6 4y Recent -Advances in Composite MaterialsJn tha.United
 

States and Japan. Also, data developed on this program was used to
 

evaluate a new, and very promising, transducer to measure acoustic
 

emission. Copies of the technical paper reporting the results of that
 

study are also included.
 

* We thank you for the opportunity to conduct this investigation
 

under the sponsorship of NASA Langley.
 

Sincerely,
 

W. W. Stinchcomb
 

Professor
 

enclosures
 

WWS/bw
 
College of Engineering
 

Virginia Polytechnic Institute and State University
 

Blacksburg, Virginia 24061-4899
 

Fatigue Damage in Notched Composite Laminates
 

Under Tension-Tension Cyclic Loads
 

W. W. Stinchcomb* 	 K. L. Reifsnider*
 

E. G. Henneke* 	 G. R. Kress**
 

Department of Engineering Science and Mechanics
 

September 1985
 

Final Report
 

Grant number NAG-1-232
 

Prepared for: 	 NASA Langley Research Center
 

Hampton, Virginia 23665
 

* Professor, 	Engineering Science and Mechanics 

** 	 Researcher, Institute for Structural Mechanics, DFVLR, 

Braunschweig, West Germany. Formerly, Graduate Research 

Assistant, Engineering Science and Mechanics Department, 

Virginia Tech. 
Abstract
 

Composite materials are established as reliable and
 

efficient materials for a large number of structural applications. Although composites have gained a widespread use, we
 

do not, as yet, have a precise and complete understanding of
 

the mechanisms of damage development in composite materials.
 

Recent research results have pointed out the need to treat
 

damage as a collective condition; i.e., a damage state, rather
 

than as an assembly of discrete and independent damage
 

modes. The process of the development of the damage state and
 

the subsequent response of the composite laminate throughout
 

the loading history can then be related.
 

This report presents the results of an investigation to
 

determine the damage states which develop in graphite epoxy
 

laminates with center holes due to tension-tension cyclic
 

loads, to determine the influence of stacking sequence on the
 

initiation and interaction of damage modes and the process of
 

damage development, and to establish the relationships between
 

the damage states and the strength, stiffness, and life of the
 

laminates. Two quasi-isotropic laminates were selected to
 

give different distributions of interlaminar stresses around
 

the hole. The laminates were tested under cyclic loads
 

(R=0.1, 10 Hz) at maximum stresses ranging between 60 and 95
 

percent of the notched tensile strength. Damage was monitored
 

i
 
nondestructively throughout the loading history using stereo
 

X-ray radiography, acoustic emission monitoring, and stiffness
 

change. Some specimens were deplied after- specific numbers of
 

cycles to determine the nature and distribution of damage,in
 

each ply around the hole and to confirm the components and
 

size of the damage state observed nondestructively. Fatigue
 

life and residual strength tests were also performed.
 

Fatigue damage in the two laminates included matrix
 

cracks in all plies followed by delaminations. The density of
 

matrix cracks and the distribution of the damage zone (matrix
 

cracks plus delaminations) in laminates cycled at the same
 

percent of notched tensile strength were strongly dependent on
 

the local constraint and distribution of interlaminar stresses
 

as governed by the stacking sequence. The distinctly
 

different damage states which developed in the two initially
 

quasi-isotropic laminates due to similar load histories
 

produced stiffness changes of 15-20 percent, different rates
 

of residual strength degradation, and a factor of four
 

difference in fatigue life.
 

The results of this study are interpreted to establish
 

relationships between the loading history, the progressive
 

development of the damage state, and the response of the
 

notched laminates.
 

li
 
v 

TABLE OF CONTENTS
 

Page
 

Abstract . . . ....................
 

List of Figures................... 


I. 1.0 	 Introduction........... ........ .
 

II.. 2.0 	 Experimental Procedures............9
 

2.1 Material and Specimens...... . .. 	 9
 

2.2 Mechanical Tests. ........ ..	 I.10
 

2.3 Monotonic Loading Tests ............ 	 12
 

2.4 Sequential Loading Tests ............ 13
 

2.5 Fatigue Tests...... 	 ......... . 14
 

2.6 X-Ray 	Radiography......... ..... . 15
 

2.7 Deply 	Technique ................ 19
 

2.8 Moire 	Technique ................ 20
 

2.8.1 Purposes......... ..... ... 20
 

2.8.2 Theoretical Background ......... 21
 

2.8.3 Loading Fixture. . .......... 	 26
 

2.8.4 	 Preparation of Specimens for
 

Moire Tests ............. 29
 

2.8.5 Test Matrix ...... ......... 33
 

III. 3.0 	 Discussion of Test Data ........ ...... 35
 

3.1 X-Ray Photography. ..... . ........... 	 35
 

3.1.1 A-Specimens . ....... .35
 

3.1.1.1 	 Quasi-Static Damage Patterns" 35
 

3.1.1.2 	 Fatigue Damage Patterns . . . 38
 

3.1.2 B-Specimens ... .. . . . ....... 42
 

3.1.2.1 	 Quasi-Static Damage Patterns 42
 

3.1.2.2 	 Fatigue Damage Patterns . 45
 

3.1.3 Fatigue Damage at High Load Level 51
 

3.2 Deply Technique ................ 	 53
 

3.2.1 A-Specimen. . ............ 54
 

3.2.2 B-Specimen . .............. 	 56
 

3.3 Moire Interferometry .......... 	 .... 57
 

3.3.1 A-Specimen 	 . . 60
 

3.3.1.1 	 Fringe Pattern of the
 

Undamaged Specimen 6o
 

3.3.1.2 	 Onset of Fatigue Damage . 60
 

3.3.1.3 	 Fringe Pattern of the
 

Highly Damage&--Specimen 63
 

iii
 
3.3.2 B-Specimen . . .	 65
 

3.3.2.1 	 Fringe Pattern of the
 

Undamaged Specimen ..... 65
 

3.3.2.2 Onset of Damage-......... 67
 

3.3_.2.3 	 Fringe Pattern of the
 

Highly Damaged Specimen . . . 67
 

IV. 4.0 	 Results .................... 71
 

4.1 Initial Tensile Strength ........... 	 71
 

4.2 Initial Stiffness.. 	 ............ 74
 

4.3 S-N Data ................... 	 76
 

4.4 Stiffness Degradation........ .....
 .	 76
 

4.4.1 Interrupted Stiffness Recording . . 76
 

4.4.2 Continuous Stiffness Recording ..... 80
 

4.5 Residual Strength ............... 	 85
 

4.6 Damage Patterns....... ..
........ 	 88
 

4.7 Damage and Mechanical Response ........ 	 92
 

V. 5.0 	 Conclusions................. 104
 

VI. 6.0 	 References ..... .............. 108
 

iv
 
LIST OF FIGURES
 

Figure 	 Page
 

1. Penetrant Distribution in a Delaminated Area . .. 18
 

2. Transmissive Moire Test Set Up. ........... 23
 

3. Interference of Two Wavefronts of Coherent Light . 25
 

4. Reflective Moire Test Set Up with Virtual Grating . 27
 

5. Loading Fixture .............. 	 ...... 30
 

6. Quasi-Static Damage in an A-Laminate . ....... 36
 

7. Fatigue Damage in an A-Laminate ............. 40
 

8. A-39 after 600K Cycles at 80 Percent Load Level . 41
 

9. Quasi-Static Damage in a B-Laminate . ... .... 43
 

10. Quasi-Static Damage in a B-Laminate ......... 	 46
 

11. Fatigue Damage at Low Load Level in a B-Laminate . 48
 

12. Fatigue Damage after 1 Million Cycles in B-Il . . 50
 

13. Fatigue Damage at High Load Level in a B-Laminate 52
 

14. Delaminations on A-Laminate Interfaces ........ 55
 

15. Delaminations on B-Laminate Interfaces ....... 58
 

16. Fringe Patterns of an Undamaged A-Laminate ..... 61
 

17. 	 Fringe Patterns for an Undamaged and Slightly
 

Damaged A-Laminate ......... .. ...... 62
 

18. Fringe Pattern of the Highly Damaged A-Laminate . . . 64
 

19. Fringe Pattern of an Undamaged B-Laminate ...... 66
 

20. 	 Fringe Patterns for an Undamaged and Slightly
 

Damaged B-Laminate ................ 68
 

21. Fringe Pattern of the Highly Damaged B-Laminate . 69
 

v 
22. Static Tensile Strength ............... 	 72
 

23. Static Stiffness .................. 	 75
 

24. S-N Curves ..................... 	 77
 

25. Stiffness and Residual Strength Versus Life ..... 78
 

26. Stiffness Degradation Versus Logarithmic Cycles 82
 

27. Stiffness Degradation Versus Linear Cycles ..... 83
 

28. Residual Strength of an A-Laminate ...... .... 86
 

29. Residual Strength Versus Linear Cycles ....... 89
 

30. 	 Strain Concentration Versus Crack Length for an
 

A-Laminate .................... 93
 

31. 	 Strain Concentration Versus Cycles for an
 

A-Laminate .................... 94
 

32. Residual Strength Versus Crack Length ........ 96
 

33. Strain Concentration Versus Residual Strength . . 97
 

34. 	 Zero-Deg-Crack Length Versus Number of Cycles for
 

an A-Laminate ................... 98
 

35. 	 Zero-Deg-Crack Length Versus Number of Cycles for
 

B-Laminates .................... 99
 

36. 	 Fracture Surfaces of Type A Laminates: (a) monotonic 

tension, no prior damage; (b) monotonic tension 

after 500,000 cycles at amax = 0.8 0 ult; and 

(c) fatigue failure after 1.3 million cycles-at
 

=max o.8 ault .. ............... 101
 

37. 	 Fracture Surfaces of Type B Laminates: (a) monotonic
 

tension, no prior damage; (b) monotonic tension
 =
 after 200,000 cycles at amax 0.8 ault;
 

and (c) fatigue failure after 220,000 cycles
 = 
 at amax 0.8 ault" .. *.*....................... 102
 

vi
 
I
 

1.0 INTRODUCTION
 

Composite materials hve gained widespread use and
 

increased consideration for primary and secondary structures
 

in aircraft and other vehicles. These stiff, strong, lightweight materials can be used to effect decreases in weight
 

and increases in the durability of such structures. If
 

these advantages are to be fully realized, however, it must
 

be possible to meet specific design requirements for
 

aircraft and space structures. We do not, as yet, have a
 

precise or complete understanding of the mechanisms of
 

damage development in composite materials. Mechanisms have
 

been identified and studied in a fragmented and casual
 

way. Lists of the contributors to damage (such as fiber
 

breakage, matrix cracking, debonding, delamination, etc.)
 

are commonly made and fracture modes are frequently
 

described in a general way.
 

To develop a more complete understanding of the response
 

of composite laminates, a unified, coherent, and 

concentrated investigation of damage processes (not just 

damage components) must be made. The general objective of 

the experimental phase of these investigations should be to
 

identify a well defined damage state (or states) which are
 

1
 
12
 

characteristic of the material response, i.e., a state which
 

is defined by the material properties and parameters,
 

primarily. It is also necessary to determine how this state
 

(or states) develops into a fracture event or produces the
 

other aspects of behavior of engineering concern during 

service. 

Modeling depends greatly on both investigative endeavors. 

A model of response cannot be well set if the damage state is
 

not well defined. Models of fatigue damage, residual
 

strength, and stiffness degradation for- unnotched laminates
 

[1,2] are based on uniform distributions of damage that are
 

reflected by terms such as 'characteristic damage state
 

(CDS)', for example. These uniformities of damage do not
 

exist in a global sense, however, in notched laminates where
 

the stress state and the damage state associated with the
 

notch are local, nonhomogeneous, and complex. All the modes
 

of damage normally found under tensile loading conditions are
 

present and combine in ways related to the local geometry and
 

states of stress. For example, the local stress state is very
 

complex, nearly always three-dimensional for ahgle ply
 

laminates, even when the applied stress is unidirectional.
 

And, of course, there are always sharp gradients- of stress in
 

the neighborhood of a stress raiser. Given the inherent
 

complexity of composite materials, and the complex­
3
 

ity of the stress state at a notch, it is not too surprising
 

to find that an understanding of fatigue damage in notched
 

laminates is incomplete.
 

The objectives of the present work are 
to determine the
 

nature of damage induced' in graphite epoxy laminates with
 

center holes by cyclic tensile loading and to establish the
 

influence of such damage on the strength, stiffness and life
 

of the laminates.
 

The complexity of damage mechanisms in composite materials requires complementary inspection techniques for complete description of the damage state.
 

Sendeckyj [3] 
 found that the X-ray technique makes damage, namely matrix cracks and delaminations, visible but is
 

restricted in observing spatial distribution of damage. The
 

deply- technique 
 [4] complements the X-ray radiography
 

because of its ability to identify specific planes of delamination. In the 
same sense electron microscopy can detect
 

fiber cracks as well as the results of debonding; that is,
 

the pullout of fibers at fracture surfaces. X-ray radiography and deply technique are different in the sense that the
 

former is a nondestructive test (NDT) method while the latter inevitably destroys the test specimen.
 

Damage events during the loading process can be detected
 

by acoustic emission 
recording. It yields, in combination
 
4
 

with the simultaneously recorded load-strain curve, information on the load and strain levels at which damage occurs;
 

however, attempts to determine the contributing damage modes
 

through analysis of acoustic emission- signals have not been
 

successful..
 

Since, the strain field in notched specimens is, nonuniform, it is difficult to decide what strain measurement
 

technique gives the most valuable information. However, the
 

moire technique [5] provides insight into the complete nonhomogeneous in-plane strain field. Furthermore, the moire
 

technique can be applied to damaged laminates to 
determine
 

changes in the local strain field. When moire data are used
 

in conjunction with other NDT data, the effects 
of various
 

damage modes on laminate response can be measured [6]. A
 

widely used investigative method measures' stiffness change
 

as an indicator of damage in materials [7]. Camponeschi and
 

Stinchcomb [8] pointed out that a quasi-isotropic laminate
 

exhibits a different response than its constituent sublaminates. For instance, the response of a [0,90,+45,-45] lami5
 

nate cannot be predicted by knowing the behavior of the 

[0,90] s and the [45,-45]s sublaminates. In contrast, if 

predictions for the response of yet untested laminates are 

desired, they should be based on considerations like stress 

analyses including edge effects and constraint effects. 
5
 

For designing as well as -for research purposes many
 

stress analyses for laminates with -notches have been developed. Satisfactory stress analyses which 
account for hole
 

related edge effects require either- finite element models,
 

with many degrees of 
freedom, thus demanding sophisticated
 

economical storage and computation techniques, or the skill--:
 

ful use of simplifying assumptions that 
lead to approximations of undetermined accuracy.
 

Stress analysis of notched laminates may help to under­

-stand and predict the onset of damage in the form of matrix
 

-cracks and delamination. However, the damage causes 
redistribution of the stresses in the laminate making the 
stress
 

analysis of the undamaged laminate of little value in predicting strength [9]. Static strength'models for notched
 

laminates- have been developed that do not require a stress
 

analysis of the damaged laminate. Instead, the strength of
 

the notched and the 
unnotched laminates are compared. In
 

1974 Whitney and Nuismer [10] suggested a failure criterion
 

that predicts the uniaxial tensile strength and is based on
 

a simple consideration of the isbtropic 
stress distribution
 

rather than on the actual state of laminate stresses. Their
 

failure criterion features two versions: the first one pre-'
 

dicts failure if the material is critically stressed over 
a
 

certain distance from the hole; the second one predicts that
 
6
 

a laminate will fail if the average stress over some other
 

distance away from the hole exceeds a certain value.
 

However; their models determine the ratio of the notched
 

strength to the unnotched strength of a laminate so that the
 

latter must be known; moreover, they are dealing with the
 

different mechanisms of straight edge driven versus notch
 

initiated failure simply by adjusting the materfal dependent
 

parameters. After collecting data for both unnotched and
 

notched laminates, failure loads for various notch sizes can
 

be predicted.
 

Three years later Whitney and Kim [11] published the
 

results of a test series which exhibit that notched failure
 

mechanisms 
differ from those in the unnotched situation.
 

They investigated the influence of laminates with two different stacking sequences, one of them producing tensile,
 

the other producing compressive, interlaminar normal stress
 

througout the thickness of the straight edge on both notched
 

and unnotched specimens.
 

The data indicate that unnotched tensile strength is
 

reduced by tensile interlaminar stresses along the straight
 

edge and is strongly dependent on the stacking sequence;
 

while the strength of notched specimens is independent of
 

the straight edge effects since tensile failure is initiated
 

by the locally high stress at the notch before straight edge
 
7
 

delamination comes into effect. 
Other investigations of the
 

fatigue behaviour of notched specimens were conducted by
 

Sendeckyj [3], Stinchcomb, and co-workers 
[21, and Whitcomb
 

[9]. The work most comparable to the present one is that of
 

Whitcomb, who described the damage state and -the mechanical
 

response of four different notched laminates after fatigue
 

loading and related delamination onset to the results of a
 

FEM stress analysis. 
 The load levels of two-thirds of the
 

initial strength of the laminates correspond to fatigue
 

lives greater than ten million cycles. At this point, the
 

damaged specimens were investigated using destructive and
 

nondestructive methods. 
 The residual strength of all laminates was equal to or
 higher than the initial strength of
 

the specimens. Stiffness degradations were found to be in
 

the range from zero 
to,1O percent. Whitcomb also presented
 

figures comparing initial stress distributions with delaminations at different locations through the thickness on the
 

hole edge that suggest that interlaminar normal stress and
 

shear stress distributions govern the locations of first
 

fatigue delaminations. 
 Later in the lifetime, the direction
 

of delamination growth can be changed by an 
altered stress
 

distribution.
 

Sendeckyj's work is ,mainly concerned with the introduction of stereo X-ray radiography and describes the damage
 
8
 

that is made visible on X-ray stereo pairs. The emphasis of
 

the paper of Stinchcomb and co-workers is on the investigation of constraint effects on the development of initial 

damage. Notches were introduced in specimens by cutting 

notches out of single plies before lamination. The surface 

plies of the laminates to be produced were left undamaged.
 

The results of their work can be partially related to damage-pattern characteristics found in the present work which
 

are dependent on the stacking sequence.
 

In the first phase of the present study, the fatigue damage pattern was observed in laminates with four different
 

stacking sequences. For further investigations, two of the
 

laminates with relatively little straight edge initiated
 

damage were chosen in order to isolate notch related damage
 

from straight edge driven damage as much as possible.
 

-The damage induced by static and by fatigue loading was
 

observed by nondestructive inspection and other methods.
 

Cyclic and monotonic tests' were performed to-compare the
 

development of damage under cyclic loading with that under
 

static loading. Residual tensile strength tests were conducted on damaged specimens to determine the relationship
 

between loading history, damage state, and strength.
 
II
 

2.0 EXPERIMENTAL PROCEDURES
 

2.1 MATERIAL AND SPECIMENS
 

The material used in this 
study was T300-5208 graphite
 

epoxy. The, specimens for the preliminary study were ten
 

inches long, 1.5 inches wide 
and had a 0.25 inch diameter
 

hole in the center. The four stacking sequences were:
 

0,+45,-45, 90]
 

0, 90,+45,-45]
 

45, 0,-45, 90]s
 

[+45,-45, 0, 90]
s
 

From the results of mechanical and nondestructive tests on
 

these laminates, two stacking sequences were chosen for further investigation of notch related damage. They were:
 

0, 90,+45,-45]s type A
 

[+45, 90,-45, 0]s type B.
 

9
 
10
 

The new specimens had a 0.375 inch diameter center hole
 

machined using an ultrasonic drilling machine. A third
 

stacking sequence,
 

[+45,-45,0,90] s type C
 

was used to determine the critical strain energy release rate
 

for delaminations in the batch of material used for this
 

study. These specimens had no hole.
 

2.2 	 MECHANICAL TESTS
 

All mechanical tests were conducted in load control on a
 

20 kip servo hydraulic, closed loop MTS testing machine.
 

Mechanical tests were performed to obtain strength and
 

stiffness data for the undamaged and damaged specimens and to
 

impose cyclic loading histories on the specimens.
 

The test machine was equipped with MTS hydraulic grips.
 

The ends of the specimens seated in the grips were wrapped
 

with a double layer of sandpaper folded around the upper and
 

the lower edge such that the vertical edges of the specimens
 

remained uncovered. This is merely a precaution to avoid
 

slipping of the grips under high tensile loading. The sandpaper should be replaced regularly. Alignment plates fill­
ing in the gaps between the specimen edges and the inner
 

surface of the grip housing helped to align and position the
 

specimen and thereby reduce unintentional load components
 

like bending moments. Correcting a relative twist between
 

the upper and the lower grip avoided unintentional twisting
 

moments acting on the specimens. Any relative twist was minimized by placing alignment bars between the grips and
 

rotating the lower grip until the pointer and the crossmark
 

on the alignment bars matched. The specimen, equipped with
 

sandpaper and the alignment plates, was placed in the lower
 

grip, and the 
gripping pressure was adjusted so that the
 

specimen was still moveable against friction. Then the lower
 

grip and specimen were moved up by hydraulic pressure until
 

the upper part of the specimen and the alignment plates were
 

in the right position within the upper grips. While the
 

control set point was adjusted such that the lower grip was
 

moving down at 
a very low time rate, both grips were slowly
 

tightened. This procedure guarantees an 
almost buckle free
 

positioning of the specimen under a slight 'tensile 
load.
 

However; it was necessary to clean the grip housing and the
 

wedges periodically because 
dirt on their contacting surfaces can cause unintentional relative twists of the wedges
 

while tightening.
 
12
 

2.3 	 MONOTONIC LOADING TESTS
 

The specimens were loaded at time rates between 25 lbs/
 

sec and 50 lbs/sec using the ramp function of the MTS
 

function generator.
 

Each of the four laminates used in the preliminary study
 

was loaded until failure occurred in order to obtain the
 

stiffnesses and strengths of these laminates.
 

Strain was measured by a 1.0 inch extensometer attached
 

by rubber bands to the specimen. Slippingof the extensometer was prevented by pressing the knife edges into strips of
 

double adhesive tape attached to the specimens. The extensometer was centered with respect to the notch and oriented
 

for measuring the longitudinal strain only.
 

Stiffness curves were recorded on an X-Y plotter. Some
 

tests were performed on damaged specimens to obtain changes
 

of stiffness and strength dependent on the loading history.
 

Five specimens of each of the new laminate types A, B and
 

C were subjected to strength tests with stiffness and acoustic emission recording to obtain the tensile strength, initial stiffness and information on damage events during the
 

loading process. Monotonic tests were also performed on damaged specimens to measure the effects of cycling loading on
 

strength and stiffness. Stiffness was measured during several tests with a 1.0 inch extensometer and a 3.625 inch
 
13
 

extensometer 
to obtain information on the strain values
 

around the hole based on short and long gauge length.
 

2.4 SEQUENTIAL LOADING TESTS 

Valuable information about a typical fatigue effected 

damage- state distinguished from a damage state caused by 

monotonic loads was 
obtained from sequential loading tests.
 

Two specimens, A22 and Bi6, 
were loaded in tension to a low
 

load, treated with zinc iodide (a medium nearly opaque 
to


X-rays) unloaded, X-rayed, and 
loaded again to a greater
 

load. This procedure was repeated until failure. 
For each
 

loading procedure, a stress-strain curve was recorded. The
 

specimens were instrumented with the 
3.625 inch extensometer. Beginning at a very low load level, 
the specimens were
 

sequentially loaded in increments 
bf 10 percent of the mean
 

tensile strength until a stress. equal 
 to the tensile
 

strength of the virgin specimens was reached. Then the
 

increment was lowered to 5 percent of the tensile strength
 

and the sequential loading was continued until the specimen
 

failed.
 
14
 

2.5 	 FATIGUE TESTS
 

All fatigue tests were run in the tension-tension mode
 

with a load ratio of R=0.1 and a frequency of 10 Hertz.
 

Specimens were tested at. several different load levels
 

designated as percentages of the mean tensile strength of
 

five samples. The load levels spanned the range from 70 to
 

95 	percent; i.e. from long-life-load levels to short-lifeload levels.
 

Several specimens were run to failure to obtain S-N
 

curves, others were monotonically loaded to failure after a
 

certain number of cycles to obtain the strength-versus-loading-history curves. Many of these specimens were subjected
 

to nondestructive inspections such as X-ray radiography or
 

moire tests at selected numbers of cycles.
 

Continuous stiffness degradation curves were produced
 

using a Z-80 microprocessor and a peak-detector program.
 

The inputs for the microprocessor were load and strain signals from the MTS load cell and strain amplifier, respectively. The microprocessor evaluated the average load range
 

and strain range during a time period of one second (10
 

cycles). These data were used as the input for a peak detector program. The initial load and strain range data 
were
 

used to define an initial stiffness value based on the
 

unnotched cross-sectional area. All subsequent stiffness
 
15
 

data were referred to as percentages of the initial stiffness. Results 
were printed at each 0.5 percent stiffness
 

loss. Additionally the continuously updated stiffness-cycles
 

curve was displayed on the terminal screen and 
could be
 

plotted'
on paper. The printed results 
were used to produce
 

stiffness degradation • plots on both real and logarithmic
 

lifetime scales. However, it was not possible to record the
 

values 
of stiffness degradation during approximately the
 

first 100 cycles since the peak detector program is not
 

started until the desired loading conditions are imposed on
 

the specimen.
 

2.6 X-RAY RADIOGRAPHY
 

The X-ray photographs were taken using a Hewlett Packard
 

N Faxitron X-ray system, using the voltage of 25 Kv for all
 

exposures.
 

The specimens were held by 
a device which allowed the
 

specimens to be tilted from zero to about 45 deg with
 

respect to the horizontal plane. The distance of the film
 

from the beam source was about 18 inches.
 

Stereoscopic investigation is possible by taking two
 

radiographs of the same 
specimen, each at a different angular position with respect to the direction of the X-ray
 

. -beam. For the stereo negatives Kodak-R-film was exposed for
 
16
 

0.6 minutes. If a 3-D investigation was not intended, Kodak
 

M-film was exposed for 0.3 minutes.
 

To make damage, especially matrix cracks but also delaminations, visible on X-ray photographs, the specimen must be
 

prepared by filling the openings of the damage zone with a
 

contrast medium. In the present study the specimens were
 

moisturized at the edges 
of the hole and at the straight
 

edges with zinc iodide which is nearly opaque to X-rays. The
 

zinc iodide was applied shortly before the end of a cyclic
 

test so that the relative movement of material adjacent to
 

cracks helped it penetrate into the damage zone; however,
 

the time of cyclic loading with contrast medium in the specimen was kept short to avoid effects of zinc iodide on the
 

fatigue behavior. For monotonic test conditions, the zinc
 

iodide was allowed to soak in under load for 
some minutes.
 

Load levels for the purpose of letting the contrast medium
 

penetrate were the maximum load applied during the test or a
 

somewhat lower load in cases where 
the testing load
 

approached or exceeded the tensile strength of a specimen.
 

The excess zinc iodide on the surface had to be washed
 

out carefully using acetone in order to avoid concealing the
 

damage pattern by the image of the surface. Although this
 

method of detecting damage within a specimen gives highly
 

precise information about the location and the size of 
even
 
17
 

single matrix cracks, it must be critically mentioned that
 

only 
those cracks which are penetrated by the contrast
 

medium are visible; 
on the other hand, the zinc iodide can
 

only penetrate along cracks which are 
connected with a surface. Therefore, those cracks which are not connected with
 

the surface where 
the zinc iodide was applied can not be
 

made visible on X-ray photographs. There is, however, an
 

advantage in this weakness: applying the contrast medium
 

only at the edge of the hole gives good information on what
 

part of the damage initiates there. 
Similar observation can
 

be made for the damage associated with the straight edges.
 

Using the moire test device, specimens could be loaded during X-ray exposure; however, only few photographs of.loaded
 

specimens could be taken.
 

In agreement with Sendeckyj's observations [3], delaminations 
appear as dark regions with diffuse edges and sometimes have lighter areas embedded which are sharply distinguished from the surrounding spot. As in the present study,
 

the light areas usually appear on X-rays of highly damaged
 

specimens. It 
is believed that the variations in darkness
 

are formed by mechanisms illustrated in Figure 1.
 

At the periphere of a delaminated area, the gap between
 

the delaminated plies is 
small, offering space for only a'
 

thin layer of penetrant that slightly reduces theintensity
 
18 

Penetrant Distribution-


Effect on X-Ray Photograph 

Figure 1: Penetrant Distribution in a Delaminated Area 
19
 

of passing X-ray beams 
and leads to the effect of diffuse
 

edges. With increasing distance from the periphere, 
the
 

thickness of the penetrant layer increases up to the point
 

where the bond between the fluid and the 
solid material is
 

no longer sufficient to form an uninterrupted layer. This
 

transition phase is 
small and gives the distinct limits of
 

the light spots. Thus, the 
light areas indicate a minimum
 

gap width between delaminated plies.
 

2.7 DEPLY TECHNIQUE
 

The deply technique gives information on the location and
 

extent of delaminations 
and fiber cracks. The specimens
 

were kept at a temperature of 785 deg Fahrenheit for 30 to
 

50 min. in an electrically heated oven with controlled air
 

exchange. This 
process effects the destruction of the
 

resin-rich layer between the 
fiber carrying plies (the ply
 

interface), which could then be separated and filed on paper
 

cards for investigations such as photography or microscopy.
 

Applying gold chloride solution to specimens before the heat
 

treatment helps identify regions of delaminations and fiber
 

cracking. 
Layers to be deplied were first fixed by applying
 

sticky tape and then disconnected from the remaining laminate by using a knife edge to systematically enlarge already
 

present gaps.
 
20
 

As a general result of the experimental part of this
 

study, the. interlaminar surface patterns of deplied specimens consist of four elements. A surface showing exposed
 

fibers looks typically silky or shiny-and-covers-the~largest
 

part of the area. The ply surface contains evenly distributed spots of residual resin that are oriented in the fiber
 

direction of the adjacent layer of the intact
 laminate.
 

More significant for damage studies are the spots colored by
 

gold chloride and characteristic dark blue areas. These are
 

often accompanied by a concentration of resin-rest spots and
 

match the locations of the previously mentioned dark areas
 

on X-ray photos. It is believed that the blue color arises
 

from zinc iodide since the deplied specimen underwent X-ray
 

radiography before deplying. However, the contrast on the
 

deplied surfaces was so poor that, instead of a photographic
 

documentation, sketches of the damaged zone were drawn.
 

2.8 MOIRE TECHNIQUE
 

2.8.1 Purposes
 

The moire technique can be used as an accurate tool to 

obtain the complete two-dimensional displacement field on
 

the plane surface of loaded elastic bodies. Because of its
 

accuracy it is widely used to experimentally obtain elasticity solutions that cannot be determined analytically or to
 
21
 

judge the validity of approximate solutions. Another important feature of the technique is its ability to show the
 

effects of structural damage within 
a body on its elastic
 

behavior. In other words, using the moire technique, it is
 

possible to obtain the stiffness changes in damage zones.
 

2.8.2 'Theoretical Background
 

Mechanical interference or coarse moire produces the same
 

fringe pattern as moire interferometry. Here the test setup
 

consists simply 
of two coarse gratings with frequencies
 

between 1 line/mm and 40 lines/mm. One is fixed in space
 

and is called the reference grating; the other undergoes
 

in-plane deformations and is called an active 
grating. In
 

practice, the active grating is attached to a body whose
 

deformations 
under certain loading conditions-are to be
 

measured.
 

If for instance the active grating is uniformly
 

stretched, a fringe pattern of equidistant light and dark
 

zones appears. Any of these fringes is the location of equal
 

displacements of points 
on the active grating. The moire
 

fringe orders Nx and Ny are the number of subsequent changes
 

of intensity experienced at a certain point during the loading process from zero to the final value. 
The corresponding
 

displacements u and v can be calculated by:
 
22
 

u = gN x
 

(2.1) 

v = gNy 

where g is the pitch of the reference grating. 

The same principle of using a fringe pattern to measure inplane displacements is used for moire interferometry, which
 

uses much finer gratings with pitches on the order of
 

magnitude of the wavelength of light and therefore involves
 

the effects of diffraction and interference of light.
 

Figure 2 illustrates the principle of a transmissive moire
 

test setup as it can be used in practice for an investigation
 

of the elastic behavior of a transparent body. In Figure 2a
 

the beam of coherent parallel directed light is diffracted at
 

the reference grating into only two symmetrically oriented
 

beams of diffraction order 0 and 1. The conditions for this
 

arrangement can be calculated using the grating equation:
 

sinem = mxf + sinz (2.2)
 

and implementing the condition of symmetry of the diffraction
 

orders 0 and 1.
 

Xf (2.3) 

with= 

with 
23
 

Reference Frequency = f 

a) Active Frequency f 

f 

b) Active Frequency =2(I+EFigure 2: Transmissive Moire Test Set Up
 
24
 

c = angle-of incidence
 

Om = direction of the diffracted light
 

m = diffraction order, counted counter clockwise
 

X = wavelength of the coherent light
 

f = frequency'of the optical grating
 

Two, and only two, diffraction order are produced if
 

2 32 (2.4)
 

x 3X
 

The beams of the diffracted light are diffracted again at the
 

active grating. Since the strain is zero, both grating
 

frequencies are equal and the beams of the diffraction order
 

1,0 and 0,1 are parallel, thus having parallel wavefronts.
 

If the active grating is deformed, however,-the angles of
 

the beams of diffraction order 1,0 and 0,1 are different
 

according to the grating equation. The angle orientations of
 

their wavefronts differ by the same value and produce a fringe
 

pattern in space as is depicted in Figure 3.
 

An important improvement of this setup is to choose an
 

active grating with an undeformed frequency being one-half the
 

value of the reference -grating so the beams of the order 1,-i
 

and 0,1 emerge perpendicularly from the plane and allow an
 

unforeshortened view of the fringe pattern, Figure 2b.
 
25
 

'/l ig ht 

Wave Train I dark 

2a light 

Wave dark Train 2 

light 

x 

Figure 3: Interference of Two Wavefronts of Coherent Light
 
26
 

Another effect of decreasing the pitch of the reference
 

grating by even multiples is called moire fringe multiplication. For a given active grating frequency there are 5 times 

as many fringes produced if the reference grating frequency
 

is R times higher than the active grating frequency.
 

Another modification is inevitable if the body to 
be


investigated is opaque. Without changing the theory or the
 

resulting fringe pattern the transparent active grating is
 

replaced by a reflecting grating, and the effect of the reference grating has to be achieved by a so called virtual
 

grating. A virtual grating produces two beams of coherent
 

light just as the reference grating did, as is illustrated
 

in Figure 4.
 

2.8.3 Loading Fixture
 

The size of the graphite epoxy specimens required the
 

construction of a new loading fixture for.making moire measurements under load. The design, although kept as simple as
 

possible, allows 
stresses as great as the tensile strength
 

of the specimens to be applied. At the same time the creation of any out-of-plane effects is eliminated by, making
 

all forces colinear. The actual applied load can be measured through strain gages attached to a calibrated bolt,
 

which is designed for undergoing suitable strains within the
 

load levels in question.
 
Loser
 

N, 

Observer 

Mirror Specimen 

Figure 4: Reflective Moire Test Set Up with Virtual Grating
 
28
 

For the moire test, the device is being attached to a
 

vertical surface and held by only one screw whose axis
 

passes through the hole in the specimen. This allows the
 

device to be turned around the axis to obtain displacement
 

fields in both the X-direction and the Y-direction of the
 

laminate. The device consists of the framd, the 
carriage,
 

the load cell, the torsion eliminator, the back plate, and
 

two holders, Figure 5. The frame contains the lower grip
 

for the specimen and guides the movable carriage and the
 

torsion eliminator. The back plate is fixed to the end of
 

the frame and holds the loading screw. The force, applied by
 

turning the screw, is transmitted on the specimen through
 

the torsion eliminator, the load cell, and the carriage. The 
-

torsion eliminator interrupts the transmission of the torsional moment from the screw on the load -cell.-For simplicity, the load is transmitted on the specimens not by friction but mainly through two pins in the center of each grip.
 

The specimen ends are reinforced by glass epoxy laminates.
 

All parts are dimensioned such that the forces in them have
 

the same centerline, thus avoiding bending moments and other
 

out-of-plane effects. As a result, the load cell, consisting of a steel rod with threads and attached strain gauges
 

is free of torsional and bending moments. The four strain
 

gauges are attached such that the first two measure the
 
29
 

positive longitudinal strain on each side of the rod, giving
 

a positive signal, while the second two measures the negative transverse strain (Poisson strain) on each side, also
 

giving a positive signal. The sensitivity of the device is
 

thereby increased by the factor 2(1+v) (v is Poisson's
 

Ratio), while at the same time the effect of thermal expansion is eliminated. The load measuring device was calibrated
 

by using an Instron-test machine. The applied loads were
 

measured and plotted against the corresponding strain
 

recorded by the load cell.
 

2.8.4 Preparation of Specimens for Moire Tests
 

During a moire test the load is transmitted to the specimen through the pin and the edge of the holes drilled at the
 

ends of each specimen. Since the magnitude of the load may
 

come close to the static strength of specimens the ends were
 

reinforced to prevent their breakage. The reinforcements
 

consist of [0, 45,-45] glass-epoxy plates which are glued
 

to both sides of each specimen, using a two-component epoxy
 

adhesive.
 

To produce high quality moire fringe patterns, the specimen plane, with the grating, and the surface planes of the 

reinforced ends must be parallel. If those surfaces are not 

parallel to each other, bending will be introduced during a
 
30 ORIGINAL PAGE IS 

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a 

EL 

Fig 

Figure 5: Loading Fixture
 
31
 

test and the result will be falsified. All surfaces to be
 

glued together were sanded and cleaned with acetone. A thin
 

layer of adhesive was spread onto the prepared surfaces,
 

then the pieces were put together so that the reinforcement
 

plates were attached to one side of the specimen at a time.
 

The specimen was then placed on a thick glass plate, another
 

plate was set on the middle of the specimen, and a heavy
 

weight with a plane surface was set on top of the specimen,
 

thus improving the adhesive bond and ensuring the parallelism of reinforcement plates and specimen surfaces. 
 The
 

plate on the middle of the specimen helped eliminate bending
 

during the curing time of the epoxy.
 

The holes in the tabs were machined to provide a press
 

fit with the loading pins to achieve a symmetric distribution of pressure at the edge of the holes.
 

During the specimen fabrication process, the pattern of
 

the curing, cloth was 
formed in the matrix material on the
 

specimen surface. To provide a surface that is plane and
 

smooth enough to support an optical grating two different
 

approaches can be taken. The first method is to polish the
 

surface down until the curing cloth pattern is removed and a
 

smooth surface is left. This method has two disadvantages. 

The first one is that some of the pattern might remain 

while, at the same time, the outside layer of fibers is 
32
 

exposed. Damaged 
fibers on the surface of the specimen
 

reduce the adhesibility of the grating, may cause local distortion of the displacement fields, and may reduce strength.
 

The other disadvantage is that removing of matrix material
 

from the surface disturbs the balance of' residual stresses
 

within the laminate, thus leading to its, bending in the
 

unloaded state. This has probably only little effect on the
 

specimen behavior during moire tests but makes proper
 

attachment of the grating more difficult.
 

In the second method, the holes of the surface pattern
 

are filled with 
epoxy material rather then removing the
 

embossed parts. For this purpose epoxy adhesive is spread
 

onto the surface and then covered by a teflon strip under
 

firm pressure. Shrinkage of the hardening epoxy then leads
 

to a less coarse reproduction of the original pattern rather
 

than to its complete removal.
 

Therefore, a combination of. the two methods seems 
to be


recommendable. Instead of polishing down the whole pattern,
 

fine sandpaper was used to remove the coarsest 
uneven
 

patches only. The epoxy adhesive method was then applied.
 

This avoids disturbing the balance of residual stresses
 

while at the same time the surface is fine enough to apply
 

the epoxy technique successfully.
 
33
 

The optical grating 
was produced by exposing a photographic plate to two interferential beams of coherent light.
 

After developing, the photo layer bears 
a pattern of equidistant bars and furrows. The furrows are at locations where
 

the light sensitivity was lower and the remaining unreacted
 

silver particles were 
washed out to, a higher extend. The
 

surface of the photolayer was then treated with photoflo,
 

what lessens the adhesibility to the coating to be attached
 

later. 
Using a vacuum chamber in order to minimize oxygeneous reactions, an aluminum layer was produced by evaporating
 

this metal using electrically heated wire. The photographic
 

plate was later glued to the prepared surface of the specimens. After hardening of the glue, the glass plate bearing
 

the photographic layer was removed and the very thin metal
 

foil with the imprinted negative image of the grating 
was
 

left; thus, the specimen was ready for the moire test.
 

2.8.5 Test Matrix
 

Moire. tests were run for an A-specimen and a B-specimen
 

at logarithmically distributed stages of lifetime from I0 0
 

to 105 cycles or to 6x105 cycles. Fringe patterns of the
 

displacement fields in both the x- and the y-directions were
 

recorded. The specimens were tested under 
loads varying
 

from a nominal load of 50 lbs to a load of 1550 lbs, which
 

is about 60 percent of the static strength.
 
34
 

For stiffness measurements, the effect of frequency
 

mismatch- is eliminated if there are two fringe patterns
 

under different loads available. In this case, the difference in fringe order and the load increment can be used to
 

obtain a correct stiffness value. It also must be determined if the actual reference frequency is lower or higher
 

than the theoretically desired one. In the latter case, the
 

null-field-fringe order must be counted negative in order to
 

obtain a proper correction.
 
III
 

3.0 DISCUSSION OF TEST DATA
 

3.1 X-RAY PHOTOGRAPHY
 

During the following discussion cracks that are initiated
 

at the hole boundary or the straight edge will be called
 

primary cracks. Other, usually smaller cracks, which initiate along the primary cracks are located in adjacent plies
 

and will be called secondary cracks. For locating the angular position of damage around the hole, 
a reference axis,
 

coincident with the loading 
direction and the direction of
 

zero deg plies, is defined. Positive angles (8) are measured counter- clockwise from the reference axis.
 

3.1.1 A-Specimens
 

3.1.1.1 	 Quasistatic Damage Patterns
 

The radiographs of quasistatic tests 
with repeated and
 

increasing load applications give some data about the initiation of damage.
 

The first visible cracks for specimen A-22 appear at 60
 

percent of the average initial strength for A-laminates,
 

Figure 6a. They are zero-deg cracks on both sides of the
 

hole, having equal extensions in both directions, and
 

shorter, 90-deg cracks also 
on 	both sides of the hole,
 

35
 
ORIGINAL PAGE IS 

36 OF POOR QUALITY 

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Figure ,_rusg-ttc ~ ~ f Damgein-a ALaminate
37
 

extending along the 90-deg direction less than one-fifth of
 

the hole diameter. This very early pattern of damage in 
zerodeg and 90-deg plies is completed by matrix cracks in the
 

45-deg plies.
 

The 70 percent radiograph of the same specimen shows
 very 

well defined +45-deg cracks along a line passing through thecenter of the hole. The cracks tangent to the hole are much 

smaller. Very small secondary -45-deg cracks develop along
 

the other cracks, Figure 6b.
 

In the radiographs following the 80 percent and 90 percent
 

steps, the tangent zero-deg cracks appear darker but do not
 

increase in length very much. The density and then the length
 

of the 90-deg cracks, still confined to the area governed by
 

the zero-deg cracks, increase considerably. The +45-deg
 

cracks tangent to the hole grow rapidly into the area which is
 

already occupied by the 90-deg cracks.
 

The first delaminations were stereo-optically detected in
 

the 90/45 interface after loading to the 80 percent level and
 

are more clearly observed in the radiograph made after the 90
 

percent load level. Figures 6c and 6d show the 
 initial 

delaminations bounded by matrix cracks and the edge of the 

hole in the regions e = 60-deg and 0 = 120-deg. 

The highest load levels are characterized by a greater 

number and increased length of -45-deg cracks and by a 
38
 

butterfly pattern of delamination around the hole. The
 

observations suggest that the onset 
of- delamination is at
 

least assisted by, if not 
caused by, the existing matrix
 

crack pattern.
 

3.1.1.2 Fatigue Damage Patterns
 

The damage patterns discussed in this section belong to
 

several type A specimens.which were subjected to different
 

numbers of cycles at the 80-percent load level. The X-radiograph of A-14, Figure 7a, shows damage after 10 cycles at
 

the 80 percent load that is very similar to that shown in
 

Figure 6c. A low penetration with zinc iodide is the probable cause for the 90 deg cracks not showing up clearly in
 

this figure. The matrix crack pattern after IK cycles shown
 

in Figure 7b shows an increase in length of all cracks.
 

Additionally,. the specimen developed 
delaminations at the
 

edge of the hole 8 = 135 deg and 8= -45 deg. After 10K
 

cycles these delaminations are more developed and new delaminations in the B = 45 
deg and 8 = -135 deg regions are
 

initiated. The zero-deg tangent cracks now extend
 beyond
 

the area of the hole while cracks in the other plies are
 

also longer. The damage in specimen A-4 with 10K cycles of
 

fatigue loading, Figure 7c, prevents a generalization of the
 

delamination development shown in the previous photographs.
 
39
 

Namely, the delaminations at the -45/135-deg locations are
 

less developed than in A-4. 
The delaminations are now following the path of the tangent cracks which are&40 percent
 

longer than the hole diameter. Cracks in the 45-deg direction are longer than 
those in the -45-deg direction. A
 

large number of 90-deg cracks have developed; many of them
 

initiate at the tangent zero-deg cracks, 
and some approach
 

the straight edge.
 

The damage state after lOOK cycles in A-39 is 
shown in
 

Figure 7d. 
 The zero-deg cracks have an extension of 190
 

percent of 
the hole diameter and are still accompanied by
 

delaminations, mostly on the side facing the straight edge.
 

Delaminations also developed along the hole edge between the
 

tangent cracks.
 

Figure 8 shows a.highly developed damage state after 600K
 

cycles in specimen A-39. Other specimens cycled at the
 

80-percent load level survived 900K 
to 1300K cycles. The
 

damage zone includes large delaminations of an obviously
 

complex distribution and the tangent zero-deg matrix cracks
 

passing through it, matching its extension. New zero-deg
 

cracks of a large size have formed in the middle between the
 

tangent cracks, and one is seen between the hole and the
 

straight edge. The +45-deg and the 90-deg 
cracks extend
 

from the edge of the hole to the straight edges. Some
 
ORIGINAL PAGE IS
 

40 OF POOR QUALIY
 

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-M t•A~ .t k ", A. ..­n 

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Figure -7: Fatigue Damage in an A-Laminate 
41
 

ORIGINAL PAGE 13
 

-OF POOR QUALITY
 

Figure 8: 
 A-39 after 600K Cycles at 80 Percent Load Level
 
42
 

matrix cracks and a delamination initiate on the straight
 

edge.
 

It is mentioned here that this specimen at this stage of 

fatigue loading had a residual strength of 122 percent of 

themean strength of undamaged specimens, and the 1.0-inch 

extensometer measured a stiffness of approximately 65 percent 

of the mean stiffness of undamaged specimens. 

3.1.2 B-Specimens 

3.1.2.1 Quasi-static Damage Pattern 

The radiographs taken during the quasi-static test on 

specimen B-16 show the first matrix cracks in the +45-deg 

plies on lines which pass through or near the center of the
 

hole at the 50 percent load level, Fig. 9a. The next picture,
 

Fig. 9b, taken after application of a 60 percent load, shows
 

cracks in all plies. While the previous cracks grew only a
 

small amount, new cracks in the +45-deg direction are added.
 

These follow lines that pass through the hole but closer to
 

the periphery than to the center, and extend away from the
 

boundary of the hole. The new cracks in the +45-deg direction
 

have the same size as, the initial ones. Cracks in the zerodeg plies initiate tangent to the hole and extend into the
 

region containing cracks in the +45-deg plies. Along the new
 

+45-deg cracks, equidistantly distributed small, 90-deg cracks
 
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44
 

appear, while the tangent zero-deg cracks are accompanied by
 

similar cracks -in the -45-deg direction. The spacing of the
 

cracks in the -45-deg plies is less than that of cracks in the
 

90-deg plies. Observing the radiographs recorded at the 60
 

percent load level through a stereo-microscope reveals very
 

small delaminations in regions where matrix 'cracks have
 

formed. These delaminations are more apparent in subsequent
 

radiographs made at greater loads.
 

The 80 percent load level radiograph, Fig. 9c, shows some
 

additional +45-deg cracks located in the area between the very
 

first cracks and those which followed, and the zero-deg cracks
 

are longer. The delaminations are on the 45/90 interface in
 

the region a = 100-deg and 0 = -80-deg. Delaminations also 

occur on the 90/-45 interface. 

Loading to 90 and 95 percent causes continued growth of the
 

tangent zero-deg cracks away from the delaminated region and
 

increases the intensity and size of the shadowed area. The
 

number and extent of cracks in the 90- and -45-deg plies also
 

increases. At the same time only one of the straight edges
 

develops +45-deg cracks, Figure 9d.
 

Until the 110 percent load level is reached, all primary
 

+45-deg cracks increase in number and length with respect to
 

their associated secondary 90-deg cracks. At a load level
 
45
 

of 115 percent of the mean tensile strength, the first pair
 

of cracks, one developing from the hole, the other from the
 

straight edge, grow together and form 
a single, continuous
 

crack, Figure 10a.
 

Cracks in the 90-deg plies initiate along the edge of the
 

specimen at locations such that, in a plan view, they shape
 

triangles defined by themselves, the free edge and the
 

already present +45-deg cracks in the adjacent ply.
 

In the radiographs for the 125 percent and the 130 percent loads, Figure 10b, edge initiated damage, consisting of
 

90- and +45-deg ply cracks, can be seen.
 

The specimen broke while applying a 135 percent load 

level. Until then, the damage pattern consisted of matrix 

cracks with a major extent only in the zero-deg and the 

+45-deg plies and in the 90-deg plies only -where +45-deg
 

cracks did not develop. The delaminations extended as far as
 

the two tangent zero-deg matrix cracks.
 

We may suspect an interaction between these zero-deg
 

cracks, the delaminations, and the plus 45-deg matrix cracks
 

which were seen on the 60 percent radiograph.
 

3.1.2.2 Fatigue Damage Patterns
 

First, consider fatigue damage due to the low load level
 

of 70 percent, applied to specimen B-Il. Comparing the radi­
46
 

RMIGINAL PAGE IS 

OF POOR QUALITY 

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47
 

ographs of B-lI 
with that of B-16 after applying the 50 percent load level (Fig. 10a) it is noted that the only visible
 

damage in B-16 does not occur in the B-l1 
during its whole
 

life.
 

The damage states of B-16 after the 70 percent load level
 

and B-il after 100 cycles (Figure Ila) at that load level
 

are similar. Although the major or primary cracks 
in the
 

zero-deg and plus 45-deg directions are comparable in number
 

and length, the fatigued specimen developed more and longer
 

secondary cracks than the quasistatically loaded specimen,
 

and the delaminations are more distinct. 
After one thousand
 

cycles, all previous damage modes are increased, but there
 

are no new damage modes (Figure llb).
 

The radiograph taken after ten thousand cycles shows the
 

two symmetric, zero-deg cracks now having the length of the
 

hole diameter. The tips of the primary plus 45-deg cracks
 

extend as far along the longitudinal direction of the specimen as the zero-deg cracks. The secondary cracks in the
 

minus 45-deg and 90-deg directions now form a dense mesh.
 

The four original delamination areas grew together, extending from the hole edge along the zero-deg cracks and the
 

darkest and longest 45-deg cracks. One of the two edges has
 

a damage pattern consisting of 45-deg/90-deg crack combinations, each forming a little triangle, Figure lc.
 
POOR QUALITY 48 OF 

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49
 

After one hundred thousand cycles the primary plus 45-deg
 

cracks doubled in length while the tangent zero-deg cracks
 

extend into the direction of advancement 'of the cracks in
 

the 45-deg plies. Delamination now fills the region between
 

the hole edge and the zero-deg cracks and, between these.
 

cracks 
and the straight edges, follows them very precisely.
 

Delamination extends in the direction of the plus 45-deg
 

cracks which are nearly tangent to the hole edge. At the
 

previously damaged straight 
edge, the plus 45-deg cracks
 

became longer, as shown in Figure lld.
 

The last recorded state of damage at one million cycles
 

shows the primary plus 45-deg cracks connecting the hole and
 

the straight edges. The zero-deg cracks 
have a length of
 

twice the hole diameter and form a boundary for one set of
 

delaminations. Another delamination follows-the path 
of
 

the plus 45-deg cracks as described previously, now covering
 

about two thirds of the distance to the straight edge, Figure 12.
 

The strength test performed on the damaged specimen gave
 

a very high residual strength of 137 percent of the mean
 

initial strength of B-specimen, thus indicating that this
 

radiograph shows a very advanced state of matrix damage and
 

delamination 
while most of the load carrying fibers are
 

still intact.
 
50
 

§WINAL PAGE IS 0 POOR QUALITY 

+gI1 . r g

Figure 12: Fatigue Damage after 1 Million cycles in B-li 
51
 

3.1.3 Fatigue Damage at High Load Level
 

The state of damage in B-6 cycled ten times at 95 percent
 

of the initial strength value is shown in Figure 13a. The
 

damage state is very similar to that of B-16 after reaching
 

the 95 percent load step. The only notable difference is the
 

greater extent of the secondary 90-deg matrix cracks into
 

areas of the cyclically loaded specimen which-appear free of
 

other cracks. Some of those cracks nearly reach the straight
 

edge.
 

After one hundred cycles all cracks grew only a little
 

while the delaminations spread out following 
the pattern
 

indicated previously, as shown in Figure 13b.
 

The following nine hundred cycles produced an increase.in
 

the length of plus 45-deg cracks and an increase in number
 

and length of the secondary 90-deg cracks, which reach the
 

straight edges. Little damage initiates on these edges, 
as
 

can be seen in Figure 13c.
 

Comparing the damage in the late stage of life of B-6 and
 

B-I (see Figure 11 and Figure 13d), the similarities consist of a nearly identical delamination pattern and the
 

arrangement of the primary plus 45-deg and zero-deg matrix
 

cracks. Although B-lI shows many straight edge induced
 

matrix cracks in plus 45-deg, 90-deg, and minus 45-deg
 

plies, B-6 has only a few of these cracks - an effect that 
52- OF POORI QUALITYr~a,-~- -___ 

,.-.~ W- z­ fl ~ ~* -4* 

~z TR--­

~ - ~-*-* 

±g 'ng'-t- i4tw -

44Z~s M4--W-Hg 

___ 

Fiue13 atgeDmg 

Laminate~ __

a ihLa Lvli1aB 
53
 

is hard to explain due to the load levels. A possible cause
 

of the difference might be a less careful finish (polish) of
 

the B-I edges, thus introducing additional local stress
 

concentrations.
 

An additional effect in B-6 is the well developed pattern
 

of secondary 90-deg cracks, most of which are near 
the


straight edges. Another effect is the presence of large plus
 

45-deg cracks that neither belong to the primary cracks nor
 

are initiated by them. This damage is probably a 'third
 

order effect' in 
the sense that the new plus 45-deg cracks
 

are initiated by the secondary 90-deg or minus 45-deg cracks
 

or by the combined effect of these. Recalling that the plus
 

45-deg ply and the minus 45-deg ply are separated by the
 

90-deg ply, it is noted that interactive effects between
 

cracks in separated plies may exist.
 

3.2 	 DEPLY TECHNIQUE
 

The deplied specimens A35 and B35 contain a maximum of
 

damage. Both underwent continuous stiffness monitoring
 

tests that were halted late in the fatigue life just prior
 

to failure, see Figure 27. 
 Figure 14 depicts the essential
 

delamination pattern highlighted by stained 
areas on the
 

interfaces 
 of adjacent plies whose fiber orientation is
 

indicated by the crossed lines. Since the 
stain comes from
 
54
 

zinc iodide concentrations, the outer limits of these areas
 

mark the extent of delaminations as well as the position of
 

matrix cracks containing a relatively large amount of zinc
 

iodide. Experience shows that it is difficult to deply two
 

adjacent layers of the 
same fiber direction. It seems
 

likely that there is no significant delamination between the
 

layers adjacent to the laminate midplane since, because of
 

the symmetry of both the loading and the geometry, -interlaminar shear stresses are zero in this plane.
 

3.2.1 A-Specimen
 

The characteristic 'spider'-shape defined by the stained
 

areas on the zero-deg/90-deg interface of 
the A-specimen
 

marks the extent of delaminations. The central stripes
 

between the tangent cracks are not locations of delamination
 

growth since delamination has fully taken place already (see
 

X-rays, Figure 7 and Figure 8). 
 They are probably caused by
 

the zinc iodide in the middle zero-deg cracks. The tangent
 

zero-deg cracks did not leave such a trace. 
This seemingly
 

inconsistent observation may be rationalized using the previously mentioned model based on 
the adhesive relations
 

between the fluid and the solid material. The width of the
 

tangent zero-deg cracks is larger 
than that, of the middle
 

cracks so that 
the fluid is not kept in the wider cracks.
 
55
 

+ x
 

,Figure 14: Delaminations on A-Laminate Interfaces
 
56
 

The interface between the '90-deg and the 45-deg layer shows
 

a shadowed area resembling a 'Z'. This pattern can also be
 

found on the X-ray in Figure 8. The typical pattern between
 

the 45-deg and -45-deg plies is sketched in Figure 14.
 

3.2.2 B-Specimen
 

In contrast to the A-specimen, B35 was not treated with
 

zinc iodide but was more thoroughly penetrated with gold
 

chloride. However, delaminations can be identified and are
 

sketched in Figure 15. 
 Straight edge delaminations developed on the 90-deg/-45-deg interface. The larger extent of
 

delaminations on the 45-deg/90-deg interface, compared with
 

those on the 90-deg/-45-deg interface, indicates interactive
 

effects between delaminations and matrix cracks. 
The shapes
 

of delaminations on 45-deg/90-deg interfaces in the A- and
 

the B-specimen, respectively, are quite different. While
 

the larger extent of the 
cracks towards the straight edges
 

in the B-specimen can be explained by the influence of
 

matrix cracks in the outer layer, the larger extent of the
 

delaminations in the A-specimen along the loading axis of
 

the laminate could be related to buckling effects in this
 

specimen. These buckling 
effects were visually observed
 

during fatigue loading and are discussed in Section 4.4.2 on
 

continuous stiffness monitoring tests. 
At the late stage of
 
57
 

lifetime of these deplied specimens, the delaminations cannot
 

be related to the initial distribution of interlaminarstresses in the laminates.
 

3.3 MOIRE INTERFEROMETRY
 

All moire-fringe patterns show damage to the surface layer
 

in detail and show the effect of damage on the surface
 

displacement field. Although damage in the inner layers
 

cannot be measured directly, its collective effect on the
 

overall laminate response is included on the surface
 

displacement. In other words, the moire technique is much
 

more sensitive to damage in the surface layer than to damage
 

anywhere else. For this reason, the fringe patterns of the
 

damaged A-specimen and the B-specimen, respectively, look 

quite different. None of the photographs shows a perfectly 

undamaged laminate -- not even those taken under a 550 lb. 

load. - Due to an error in the experimental procedure, the 

calibrated loading fixture was tested by loading specimens up 

to more than 1000 lbs. As a check on the accuracy and 

sensitivity of the experiments, the mean stiffness value from 

a series of static stiffness tests performed using a 1.0 inch 

extensometer was compared with an equivalent stiffness 

calculated from the fringe pattern. Two points, 1.0 inch
 

apart, located symmetrically with respect to the transverse
 
58
 

Figure 15: Delaminations on B-Laminate Interfaces
 
59
 

axis of the specimen were taken and the number of included
 

fringes was counted. This number was corrected by a low-load
 

fringe order and gave a stiffness of 53.3 msi and 51.8 msi for
 

the A- and B-specimens, respectively. Both values lie within
 

the range of 'the 1.0 inch extensometer measurements but areabout 6 percent and 4 percent greater than the mean value of 

these measurements, respectively. There is an agreement 

between the results of the two methods in that the initial 

stiffness of an A-specimen is slightly higher than that of a
 

B-specimen. Since the part of the specimen reproduced on the
 

moire negative is small, it was not possible to compare the
 

2.0 inch and the 3.625 inch extensometer measurements with
 

values obtained from the fringe pattern. At a distlnce from
 

the hole edge of less than two diameters, the longitudinal
 

displacement field appears to be almost uniform. Another
 

demonstration shows that the 1.0 inch extensometer stiffness
 

measurement is almost insensitive to eccentricities of the
 

extensometer with respect to the hole. For the A-specimen,
 

for instance, a shift of 0.1 inches led to a fringe order
 

deviation of 2 from the correct value of 97.
 
60
 

3.3.1 A-Specimen
 

3.3.1.1 Fringe Pattern of the Undamaged Specimen
 

The fringes for the longitudinal (u) and for the transverse (v) displacements are shown in Figure 16a and b,
 

respectively. One of the four matrix cracks tangent to the
 

hole is not yet fully developed and in this area the highly
 

increased density of the u-displacement fringes can be studied. On the opposite side of the hole, along the zero-deg
 

matrix crack, the fringes are less dense than in the area
 

spoken of above. At a distance from the hole edge of less
 

than two diameters, the u-displacement field appears to be
 

almost uniform.
 

3.3.1.2 Onset of Fatigue Damage
 

Figures 17a and b show 'the damage state of the specimen
 

under 1050 lbs load before the load is cycled and that of
 

the specimen after 10 cycles at 1550 lbs- maximum load,
 

respectively. After 10 cycles of fatigue loading, the crack
 

that was not fully formed in the specimen before cyclic
 

loading has grown, and its immediate effect on the stress
 

field close to the hole edge can be studied. Apparently the
 

crack redistributes and relaxes the strain field and lowers
 

the strain concentration. From the results of an elastic
 

analysis of an isotropic plate with a circular hole under
 
0?" POOR QUAEIy 61 

Figure 16: Fringe Patterns of an,Undamaged A-Laminate
 
62
 

ORIGINAL PAGE IS
 

OF POOR QUALTY.
 

Figure 17: Fringe Patterns for an Undamaged and Slightly
 

Damaged A-Laminate 
63
 

uniaxial tension, a strain concentration of three for sx may
 

be assumed for an idealized, undamaged situation and compared with the new strain concentration along the crack. It
 

is difficult to determine the maximum fringe density at the
 

crack. Therefore, fringes emerging from the crack tips 
are
 

traced to a straight edge where the distance between them is
 

measured. This value, in comparison to the crack length,
 

serves 
as an averaged strain concentration, although the
 

actual value of strain concentration at the crack tip may be
 

greater. The 
relation between the relaxation of strain at
 

the tangent cracks and the strain distribution along the
 

straight edge can be determined by relating the length a
 

chosen segment to the number of fringes within this segment.
 

This procedure should lead to correct numbers even under the
 

condition of frequency mismatch by subtracting the nullfield fringes.
 

3.3.1.3 Fringe Pattern of the Highly Damaged Specimen
 

Figures 18a and b clearly show the areas of delaminations
 

between the zero-deg matrix cracks and the influence of the
 

damage on the lamina behavior. The former complete symmetry
 

of the fringe pattern is now reduced to a mere point symmetry with respect to the specimen center. Looking at the
 

photograph, the crack above the hole is 
shifted toward the
 
64 ORIGINAL PAGE IS OF POOR QUALITY 

u displacement
 

A 

v displacement
 

qf 

Figure 18: Fringe Pattern of the Highly Damaged A-Laminate
 
65
 

negative x-direction (loading direction) while the areas of
 

low strain are shifted clockwise, possibly an effect of damage
 

in the 45-deg plies. The tongue shaped areas bounded by the
 

hole edges and the tangent cracks undergo a relative
 

displacement to the delaminated areas outside the cracks.
 

Although the edge of the hole appears somewhat diffuse, it can
 

be seen that the strain concentration factor for s x is


approximately uniformly distributed over the whole length of
 

the cracks with only slight additional concentrations at the
 

tips of the cracks. As an estimate, the average strain
 

concentration along the cracks is 1.46 and that at the tips is
 

not determinable. Considering a fringe-order difference of
 

149 between the idealized 1.0 inch extensometer measurement
 

points minus 24 fringes of residual deformation found on the
 

null-field pattern and an applied load of 550 lbs., a 

stiffness value of 79.5 percent of the value calculated for 

the undamaged specimen is determined. 

3.3.2 B-Specimen
 

3.3.2.1 Fringe Pattern of the Undamaged Specimen
 

The initial fringe pattern of the B-specimen is almost
 

undisturbed by cracks as Figures 19a and b show. It seems
 

that at this stage only the tangential +45-deg cracks (here
 

depicted in -45-deg direction) lead to a significant reduction
 

of the strain component sx at the hole edge.
 
66 

Su displacement ' 

v displacement 

Figure 19± Fringe Pattern of an Undamaged B-Laminate 
67
 

3.3.2.2 Onset of Damage
 

Figures 20a and b indicate that the displacement field is
 

heavily changed at locations where cracks are almost perpendicular to fringes and only slightly changed where cracks
 

are almost parallel to the fringes. The displacement field
 

is most changed by the cracks tangent to the hole. A
 

greater change in the displacement field corresponds to a
 

greater stress relaxation and, going one step further, to a
 

greater reduction of the elastic energy due to the regional
 

stiffness of the laminate. In this context, the X-ray photos document a more rapid growth of the tangent +45-deg
 

cracks than of the other +45-deg cracks after the onset of
 

damage.
 

3.3.2.3 Fringe Pattern of the Highly Damaged-Specimen
 

Figures 21a and b show the delaminated areas along the
 

tangent +45-deg cracks. It is difficult to obtain a 1.0
 

inch extensometer equivalent stiffness since the large
 

+45-deg cracks make it impossible to count fringes through
 

this area. Particularly in Figure 21b, the fringes have
 

curvatures regularly placed along the +45-deg direction. A
 

possible interpretation is that along these lines cracks are
 

impending but not yet fully formed. Such regularly distributed fringe shifts appear also between the hole and the
 
Figure 20: Fringe Patterns for an Undamaged and Slightly
 

Damaged B-Laminate
 
ORIGINAL PAGE rs OF POOR QUALITY 

I Mm 

!7* ,-
 t* '

F-I--it 
 o-tFigure'21i 
 Fringe Pat,ternof-the Highly Damaged B-Laminate
 
70
 

straight edge in the 90-deg direction. It is possible that
 

this fringe pattern shows a local displacement which precedes
 

crack initiation or, in the case of a fringe shift along a 90­

deg direction, the pattern is due to a crack in the adjacent
 

layer. Unlike the fringe pattern of the A-specimen, fringe
 

patterns of the B-specimens do not provide data to .make
 

quantified estimates on the residual strain concentration,
 

since the strength governing zero-deg layers is located at the
 

midplane of this laminate.
 
IV
 

4.0 RESULTS
 

4.1 INITIAL TENSILE STRENGTH
 

Tensile strength tests were performed on five specimens
 

of each type of laminate, including the unnotched laminate.
 

In Figure 22, the failure load of each specimen is represented by the length of a vertical line. The mean failure
 

loads of A,B and C specimens were 2620, 2240, and 4680 lbs.,
 

respectively, as indicated by the solid horizontal lines.
 

The lower, dashed horizontal lines indicate the mean load
 

levels for which major discontinuities in the load-strain
 

curves, as well as 
the first strong acoustic emissions during the loading process, occurred. The percentages refer to
 

the mean failure load of each type of laminate. The C-specimens typically had edge induced delaminations accompanied by
 

strong acoustic emissions at approximately 0.66 percent
 

strain. The correlation between the onset of acoustic emission activity and this' strain value was 
much better than
 

that with load values. The root of the sum of the squared
 

deviations is 2.54 for the strains and 5.59 
for the corresponding loads.
 

After the delamination point, indicated by an increase in
 

strain for nearly constant load on the load-strain curve,
 

71
 
72
 

7.0­

- mean failure load
 

mean load at first strong
 

6.0 acoustic emission event 

0 

0 

50 theoretical -o- -- 5.15 

actual 4.68 

maximum measured 

-4.0 residual failure load 

LI 

- -D 3.55 . ---- 3.25 

U3.0- (63%) 

2.62 

2.44 

I­

--- - 1.59 ------ l.45


1.0, (61%) (60%)
 

0 

A B C 

Figure 22: Static Tensile Strength
 
73
 

the stiffness was reduced. Both the 
step in the curve and
 

the reduced slope after the step suggested the idea of predicting strength values for the 'no delamination' situation
 

by simply multiplying the mean stiffness value taken from
 

the initial part of the load-strain curve by-. the failure
 

strain of each specimen. These values, indicated by the open
 

circles, average to 5150 lbs. or 110 percent 
of the actual
 

mean strength as indicated in the figure. Considering the
 

critical, net cross sections, which are the notched sections
 

for the A and B specimens, the average failure stresses are
 

52.8, 48.6 and 71.5 ksi for A-, B-, and C-specimens, respectively. The large difference between the strength values of
 

notched and unnotched specimens is due to the stress concentrating effect of the hole. Yet, it must be noted, that the
 

strength of the C-specimens is also reduced by straight,
 

free edge effects. However, the strength values indicate
 

that a strength reduction factor for the hole must be much
 

larger than that for the straight edge.
 

Furthermore, since edge effects 
in general (whether for
 

curved 
or straight edges) decrease rapidly with increasing
 

distance from the edge, the effects of the straight and the
 

curved edges on the notched laminates are independent. In
 

other words, we may assume that for the notched specimens
 

used in this study, the effects of the straight edge do not
 
74
 

yield an additional contribution to the reduction of static
 

strength caused by the hole.
 

It is important to note that the greatest measured residual strengths, related to the notched cross section, of A­

(66.5 ksi) and B- (71.4 ksi) specimens approach the tensile
 

strengths of C-specimens, thus indicating that fatigue damage redistributes local stresses to the extent of reducing
 

the stress concentration due to the hole.
 

4.2 	 INITIAL STIFFNESS
 

Stiffness data were taken from the linear part of the
 

load-strain curves recorded during the tensile strength
 

tests by means of a 1.0 in. extensometer centered with
 

respect to the hole. Each vertical line in Figure 23 represents the stiffness of a specimen. Mean stiffness values,
 

based on the area of the unnotched section, are indicated by
 

the horizontal lines. The stiffness values of A- and
 

B-specimens, based on the unnotched cross-sectional area,
 

are lower than the stiffness values determined for unnotched
 

C type specimens. This demonstrates the large, local deformation field associated with the local stresses due to the
 

hole.
 
75
 

8.0 

7.0­

6.0 

1.0 in. gage length 

notched cross section 

6.7 

66 

unnotched cross section 

E 5.0-

,,Eci 

z 

5.0 

4.9 

5.0 

2.0 

1.0­

0 

A B C 

Figure 23: Static Stiffness 
76
 

4.3 S-N DATA
 

A lifetime of more 6
 than 10 cycles under the condition of 

a sinusoidal load with a ratio amin/max = 0.1 and a frequency of 10 Hz can be expected at an 80 percent load level
 

(2095 kips) for A-specimens and a 70 percent load level
 

(1710 kips) for B-specimens. Load-log life curves for the
 

two 
laminates are shown in Figure 24. A-specimens, cycled
 

at a 95 percent load level (2485 kips), and B-specimens,
 

cycled on an 85 percent load level (2075 kips) will survive
 

105 cycles.
 

Two A-specimens had an average lifetime of l.lxlO6 cycles
 

at the 80 percent load level while the B-specimen, cycled at
 

the 70 percent level, had a residual strength of 137 percent
 

of the virgin strength after 106 cycles. The residual
 

strength data for type B laminates suggest that residual
 

strength values of this magnitude occur during the final
 

decade of logarithmic life.
 

4.4 STIFFNESS DEGRADATION
 

4.4.1 	 Interrupted Stiffness Recording
 

Stiffness data for type B laminates cycled at the 85 percent level are shown in Figure 25. The two stiffness curves
 

show the effect of gage length on the stiffness values. A
 

clip type strain gage extensometer centered over the hole
 
77
 

50­

4041­

U)d w 

I 

x 

30­

20 

I0 

-

Specimen Monotonic 

A 

B 

frequency I0Hz 

R=O.I 

-3 

Cyclic 

o0­

00 

0a 

0 0.2 

I I 

0.4 0.6 

LIFE, MILLIONS 

I 

0.8 

OF CYCLES 

I 

1.0 

I 

1.2 

Figure 24: S-N Curves 
78
 

Strength Stiffness 

0-85 % test level amm- 3.6 in.gage length 

140 0-low test level &- 1.0 in. gage length iiImi 

II3 ]I. ! I ' l 

1t0 

a0 a.

I=I
 

EJ
 

II
 

I\1
 10 Fatigue 

ailure/' -
 ,I"8 test level ( 85F 

11 M I 

0 I 2 3 4 5 6 

LOG CYCLES 

Figure 25: Stiffness and Residual Strength Versus Life
 
79
 

was used to measure displacement over a 1.0 inch gage
 

length. A DCDT extensometer centered over the hole measured
 

displacement over a 3.625 inch gage length. The stiffness
 

change values based on the short extensometer data are
 

larger. However, if the damage zone spreads outside the 1.0
 

inch gage length, the stiffness change values determined'
 

from the short extensometer are inaccurate.
 

The process of damage development around the hole of 
a
 

type B laminate is indicated by the stiffness curves shown
 

in Figure 25. The limits of regions I, II, and III are somewhat arbitrary, but are chosen to reflect transitions in the
 F 

damage growth process as represented by stiffness change.
 

In region I, the stiffness decreases at a decreasing rate.as
 

small matrix cracks develop near the hole. In region II,
 

the stiffness degrades linearly with log cycles as-. the
 

matrix cracks in the zero and 45 deg plies extend away from
 

the hole and delaminations form in the region damaged by
 

matrix cracks. Region III begins as the stiffness degradation rate increases. In this region, the sharp decrease in
 

stiffness is associated with further extension of the cracks
 

in the zero and 45 deg plies, an increase in the density of
 

the cracks in the 45 
deg. plies, and growth of delamination
 

along the- 45 deg. matrix cracks. Early in the life of the
 

laminate (region I) the damage is confined to the approxi­
80
 

mate zone of stress concentration around the hole. In later
 

stages of life, the stresses around the hole are redistributed and the stress concentration around the hole changes
 

due to the growth of the damage zone .away from the hole.
 

Radiographs of damaged type B specimens at several intervals
 

in the loading history are shown in Figure 11 and Figure 13.
 

The data in Figure 25 are presented in terms of percent
 

change in stiffness because the exact yalues of stiffness
 

are not repeatable in situations where the cyclic test is
 

stopped, the extensometer is removed from the specimen, and
 

the specimen is removed from the grips for nondestructive
 

evaluation at various cyclic intervals. However, if the
 

stiffness values are determined at the beginning and end of
 

each cyclic interval, or are recorded throughout a cyclic
 

interval by the data aquisition system, the change in stiffness during the cyclic interval can be determined. The total
 

change is then computed as the sum of the stiffness changes
 

for all intervals.
 

4.4.2 Continuous Stiffness Recording
 

The plots of the results of the peak detector program on
 

a logarithmic lifetime scale confirm the estimated stiffness
 

curves based on quasi-static tests. The suggestion of a
 

five percent stiffness loss after 100 cycles at a 90 percent
 
81
 

cyclic load for both laminates was taken into account by
 

multiplying the first stiffness value received by the 
peak
 

detector after 200 cycles, by the factor 0.95.
 

Figure 26 shows regions II and III of the stiffness degradation due to fatigue loading at the 90 ;percent load 

level. The time axis is logarithmically scaled. In this 

representation, region II appears as an almost linear line 

leading into a sharp knee 
which connects region II with
 

region III. Immediately beyond the knee, 
the degradation
 

rate appears to be highly increased. At the end of region
 

III, the stiffness decay accelerates again until failure.
 

Comparing the two curves 
shown in Figure 26, the B-laminate shows less stiffness degradation before the knee, a
 

later and more distinct knee, and a higher degradation rate
 

after the knee than the A-laminate. The stiffness loss at
 

the end of fatigue life is 18 percent for the B-specimen and
 

40 percent for the A-specimen. The data have been replotted
 

using a linear scale for the life axis, Figure 27. Throughout the lifetime, the A-specimen has a lower stiffness than
 

the B-specimen. Between 10 K and 50 K cycles, the degradation rates of both 
curves are similar; after that the
 

A-specimen looses stiffness 
more rapidly than the B-specimen. 
 Although the total stiffness loss during its lifetime
 

is lower for the B-specimen, its degradation rate shortly
 
82
 

.100- B-SPECIMEN 

Li)

w 

z 

w_90-

It
 

80A 

A-SPECIMEN 

1= 

l70 

U0
1-o-60­

z

w 

w 5 00 I I I I I I I I I I I I a_ 1.0 2.0 3.0 4.0 5.0 6.0 

LOG CYCLES
 

Figure 26: Sti-ffness Degradation Versus Logarithmic Cycles
 
83
 

o_ IO0,
 

IL 

_j 

LL-70 A-SPECIMEN 

0
 

z 

U'
 

0 20 40 60 80 100 120 140 160 180 200 

KILO CYCLES 

Figure 27: Stiffness Degradation Versus Linear Cycles
 
84
 

before failure is very great. Both laminates exhibit three
 

sudden stiffness changes during the fatigue life,: the first
 

one 
occurs during the very first few cycles of loading, the
 

second one 
occurs within the first half of the lifetime for
 

the A-specimen and well before failure for the B-specimen,
 

and the third, sudden stiffness loss leads to the failure
 

of the specimens. The A-specimen has its second sudden
 

stiffness loss at 70 k cycles and the corresponding event in
 

the B-specimen occurs at 157 K cycles. Both events coincide
 

with the onset of the knee in the logarithmically scale 

stiffness representation and are generally followed by an 

increased degradation rate. 

It should be mentioned here that locally confined buckling effects were seen during cyclic loading of the A-specimen. On both sides of the specimen, the zero-and 90-deg
 

sublaminate delaminated from the inner [45,-45]s group at
 

locations governed by compressive circumferential stresses
 

and buckled outwards. It could be hypothesized that the
 

forming of these delaminations and the attendant stiffness
 

degradation are rapidly accelerated after reaching a critical delamination size which facilitates'buckling. The sudden stiffness change at 70 K for the A-specimen could then
 

be related to the observed buckling effects. By visual
 

inspection, no buckling effects were visible for the B-spec­
85
 

imen. However, at the end-of fatigue life, it seemed to be
 

apparent by visual observation that the surface 45-deg ply
 

contributed little 
or nothing to the load transfer, since
 

around the hole, matrix cracks were formed and some of the
 

surface material confined by those cracks 
was almost completely delaminated. 
The matrix cracks prevent the in-plane
 

load transfer and the delaminations make load transfer
 

through interlaminar shear 
 stresses impossible. These
 

effects were visible at the end of the
 lifetime of the
 

B-specimen, thus suggesting the possibility of a relationship between them and the sudden stiffness change at 157 K
 

cycles. Finally it should be recalled that the 90 percent
 

load levels for the A- and the B-specimens are represented
 

by the maximum load values of 2354 lbs and 2195 ibs, respectively.
 

4.5 RESIDUAL STRENGTH
 

A number of the cyclic tests were halted at various
 

stages of the loading history for nondestructive inspection
 

of the damage zone and residual strength measurements. This
 

series of tests provided a characteristic and repeatable
 

curve of the 
change in residual strength throughout the
 

loading history, Figures 25 and 28.
 
86
 

130­

w
 

,,oo _ I-00 --. U)4 

W0 

(D 

CL 

90­

2 fatigue

failure 

80 

II 

A test level 

I (80%) I I 

lur 

0 I 2 3 4 5 6 7 

LOG CYCLES 

Figure 28: Residual Strength of an A-Laminate
 
87
 

During the first few 
(ten) cycles, the damage, primarily
 

matrix cracks, reduces the effect of 
the stress concentration at the hole and the residual strength increase is on
 

the order of ten percent. The actual strength increase does
 

depend on the cyclic stress level, with the higher stress
 

levels corresponding to 
slightly higher strength increases
 

than the lower stress levels.
 

Stiffness change and residual strength data for 
a type B
 

laminate after 100 cycles at a low cyclic 
stress amplitude
 

are also shown in Figure 25. Both the increase in residual
 

strength and the decrease in stiffness are less than those
 

for the same type specimen cycled at the 85 percent 
stress
 

level. The second 
region of the residual strength curve,
 

approximately ten percent of the fatigue life, is characterized by a gradual, but constant rate of increase in residual
 

strength over a logarithmic cycles scale. At the end of the
 

second region, the increase in residual strength is 115 to
 

120 percent. The limits of regions I and II for ..
 residual
 

strength are approximately the same as observed for 
stiffness change.
 

The third region of the residual strength curve is marked
 

by a further increase in residual strength. Although the
 

data in this regiron are incomplete, it appears that the maximum residual strength is reached between 50 and 80 percent
 
88
 

of 	the lifetime. The largest residual strengths are 126 and
 

142 percent of the initial strength for the type A and B
 

laminates, respectively. During the final region of the
 

fatigue life, the residual strength decreases until the
 

strength equals the level of maximum cyclic stress, as 
shown
 

in Figures 25 and 28. The last two regions of the residual
 

strength-log cycles curve correspond to the third region of
 

the stiffness reduction curve where the' stiffness change
 

shows a sharp decrease on the log cycles plot. The logarithmic scale used to represent the lifetime may cause some
 

confusion in interpreting these results. The residual
 

strength data have been replotted in Figure 29 using a linear scale to represent cycles.
 

4.6 	 DAMAGE PATTERNS 

Static damage starts with matrix cracks usually in the 

surface plies at 1570 lbs load for the A-laminate and 1220
 

lbs load for the B-laminate. At higher load levels, cracks
 

appear in all directions. The A-laminate develops more well
 

defined zero-deg cracks tangent to the hole while the B-laminate develops more well defined 45-deg cracks. Note that
 

these are the directions of the surface layers, respectively. In both laminates, 45-deg and zero-deg cracks are
 

more well defined than -45-deg and 90-deg cracks. The lat­
89
 

130­

120 

.Jo
 

LU 0A specimen 

-Dt 0 B specimen - Fatigue (D Failure 

B test level (85 %) 

80 A test lev'el (80 %) xi--

B? 

A I 

Of2 0.2 0.4 04 0.60.6 q.8 0.8 I10 1.0I 

.L1.2I _ 1.14 X 1.4I 2l44 26x 10I 

CYCLES 

Figure 29: Residual Strength Versus Linear Cycles
 
90
 

ter cracks are often secondary cracks in the sense that they
 

are initiated at locations where 45-deg and zero-deg*cracks
 

already exist. Zero-deg cracks in the A-laminate grow to a
 

length of more than five hole diameters. When- the tangent
 

zero-deg cracks approach their maximum length, cracks in
 

45-deg and 90-deg direction are also initiated on the
 

straight edge. In the final stages of lifetime, a regular
 

pattern of matrix cracks is formed between the tangent
 

zero-deg cracks and the straight edges. The uniformity of
 

these 
cracks is similar to damage patterns of unnotched
 

laminates, so-called characteristic damage states (CDS).
 

The delamination zone visible on an X-ray photo consists
 

of the superimposed images of the delaminations on the various laminate interfaces. It seems as if the tangent zero
 

deg cracks in both the A- and B-laminates are associated
 

with delaminations on adjacent interfaces. Those delaminations have the largest continuously connected area of all
 

delaminations in the laminates. Intgeneral, while the A-laminate develops a much larger delamination along its tangent
 

zero-deg cracks,' the more confined delaminations of the
 

B-laminate spread along the 45-deg direction and reach the
 

straight edge. It is emphasized that Figure 14 and Figure
 

15 give the spatial distributions and the characteristic
 

shapes as well as the proper magnitude of the delamination
 

C)
 
91
 

zones. Noting that the area of delaminations on all interfaces is higher for the A-laminate than for the B-laminate,
 

we recall that the A-specimens experienced much higher
 

stiffness losses during their fatigue life than the B-specimens.
 

The observations on the locations of initial delaminations in type A and B laminates presented in Sections
 

3.1.1.1 and 3.1.2.1 agree with the analysis of O'Brien and
 

Raju [12]. However, the 
stress levels at which the delaminations initiated were lower than those predicted by the
 

strain energy release rate analysis which considered delainination as the only damage mode. Experimental data for
 

unnotched T300/5208 quasi-isotropic laminates by O'Brien
 

[13] show that delaminations initiate in the laminates with
 

matrix cracks at lower critical strain energy release rates
 

than in laminates without matrix cracks. 
 This observation
 

is supported by the results 
of Jamison and Reifsnider [6]
 

and Wang [14]. The fact that the measured strains at initiation of delamination in type A and B laminates, 
in which
 

matrix cracking was the first damage mode, were lower than
 

the initiation strains predicted by the analysis considering
 

only delamination is consistent with other reported results.
 

Matrix cracking is an important phase of the damage development process. Although matrix cracks, 
by themselves, may
 
92
 

not significantly affect the strength and life of structural
 

laminates, they do act as catalysts to initiate
 other
 

strength and life-limiting damage modes such as delamination
 

and fiber fracture [6].
 

4.7 DAMAGE AND MECHANICAL RESPONSE
 

Figure 17 shows that the tangent zero-deg cracks have a
 

strong redistributing effect on the strain field near the
 

hole, reducing the maximum strain concentration in the longitudinal direction. Except at the crack tips, the strain
 

distribution along the cracks is almost uniform. 
Figure 30
 

presents the average strain concentrations as a function of
 

the length of the tangent cracks at various fatigue stages
 

for the A-specimen. After 600K cycles, which is estimated
 

as being 50 percent of the expected lifetime the strain concentration is reduced to K =1.46.
 

Figure 31 shows the decrease of strain concentration versus the logarithmically scaled number of cycles. The rate
 

of decrease is very high during the first cycles of fatigue
 

loading. Recalling that the rate of increase of residual
 

strength of both laminates is very high in the early stages
 

of fatigue life, it seems very likely that the tangent 

zero-deg cracks are a main factor influencing residual 

strength. 
93
 

3,.0­

0@2.5­

002.0-

U_
 

1.5­

1 .0 1 0.2 0.4 0.6
 

Crack Length ,(in.) 

Figure 30: 	 Strain Concentration Versus Crack Length for an
 

A-Laminate
 
94
 

3.0
 

2.5­

a 2.0­

1.5­

1.0 

0 1 

I 

2 3 

Log Cycles 

4 5 6 

Figure 31: Strain Concentration Versus Cycles for an ALaminate 
95
 

Figure 32 shows the results of two strength tests performed on an k-specimen and a B-specimen versus the length
 

of the tangential cracks obtained from X-ray photos taken 

after applying the fatigue load. Cracks of equal.length in
 

A- and B-specimens seem to influence the strength increases
 

of A- and B-specimens differently. As a result of a linear
 

curve fit for the data points, the increase in strength rate
 

is 44 percent per inch for the B- and 23 percent Per inch
 

for the A-laminate.
 

A residual-strength versus strain-concentration curve
 

(Figure 33) was ,constructed from the data used in Figure 30
 

and Figure 32 by eliminating the crack length. Figure 34
 

and Figure 35 show the increase in length of cracks in the
 

-zero-deg plies with the number of cycles under fatigue load.
 

The crack lengths are the average values of the length of
 

the two cracks visible on X-ray photos. For two reasons it
 

is difficult,: however, to measure average crack length
 

exactly. First, the length of the dark line on a X-ray
 

matches the actual crack length only in the case of completepenetration with zinc 
iodide. Second, it is difficult to
 

decide what the length of a crack is since a dark line on a
 

X-ray is the superimposed image of actually two cracks on
 

each side of the laminate midplane. If these two actual
 

cracks are shifted longitudinally, one might measure a
 
96
 

30- p 

/ 

0
 

-

15 

~~~ r0ASpecimens a0 

10 0OB- Specimens 

C : 


5
 

O0 I]1 1 1I 1I F 

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 

Crack Length, (in.) 

Figure 32: Residual ,Strength Versus Crack Length
 
97
 

120 

-11 

a 

I001
 

23
 

Strain Concentration 

Figure 33: Strain Concentration Versus Residual Strength
 
98
 

1.4 

1.2 

- 1.0 _ 

CP:0.8-

A- Specimens 

_.. 0.6­

0 04J

040.2F 

0 I 2 3 

Log Cycles 

4 5 6 

Figure 34: Zero-Deg Crack Length Versus Number of Cycles
 

for an A-Laminate
 
0.8- B - Specimens 

o 70 percent 

1-7* A 80 percent 

0.6 E 90 percent 

c04-

U0 

02­

0 I II II 

0 I 2 3 4 5 6 

L~g Cycles 

Figure'35: ,Zero-Deg Crack Length Versus Number of Cycles for B-Laminates
 
100
 

longer crack length than actually exists. Since the data for
 

the B-laminate is more complete, Figure 35 provides
 

information on. the influence of the load parameter on the
 

growth rate of those cracks. Figure 34 takes into account the
 

initial crack length due to static load.
 

The appearance of the- fracture surfaces depends on the
 

subcritical damage in the specimens and the loading history.
 

Several failed type A and type B specimens are shown in
 

Figures 36 and 37, respectively. A typical fracture due to
 

monotonic tensile loading is located along a straight line
 

passing through the center of the hole as shown in Figures 36a
 

and 37a. During cyclic loading, the damage zones, consisting 

of matrix cracks and delaminations, are larger and less 

localized than the concentrated damage zones caused by a 

monotonic tensile load. Failures due- to monotonic loading 

after a period of cyclic loading are shown in Figures 36b and
 

37b. and are less regular than those due to only monotonic
 

loading. Cyclic loading to fracture causes the damage zones
 

to extend away from the region of the hole, creating a highly
 

irregular fracture pattern as shown in Figures 36c and 37c.
 

The phenomenon of irregular fracture surfaces, as~shown in
 

Figures 36 'and -37, for specimens with long loading histories,
 

can be related to the shift of high strain concentrations away
 

from the hole. Since those strain concentrations are
 
101
 

_W7 

Figure 36: Fracture Surtfaces of Type A Laminates:
 

(a) monotonic tension,no prior damage; (b) monotonic
 

tension after 500,000 cycles at &max = 0.8 cult; and
 

(c) fatigue failure after 1.3 million cycles at
 

max = 0.8 %It"
 
102ORIGINAL PAGE IS 

OF POOR QUALITY 

I-


Figure 37: Fracture Surfaces of Type B Laminates:
 

(a) monotonic tension, no prior damage; (b) monotonic
 tension after 200,000 cycles at amax = 0.8 cult; and
 

(c) fatigue failure after 220,000 cycles at dmax = 0.8 ault
 
103
 

presumably highest at the tips of the cracks, we conclude that
 

catastrophic failure can be initiated there. Specimen A-6
 

underwent a fatigue life test at the 80 percent load level and
 

its fracture surface is shown in Figure 36c. Many zero-deg
 

fibers broke at a distance from the hole of 6 to 7 hole
 

diameters or from 2.2- inches to 2.6 inches. As for the
 

phenomenon of stiffness degradation, we note that the Alaminate exhibits much larger delaminations than the Blaminate. These delaminations and also the buckling described
 

in the section on continuous stiffness recording contribute to
 

higher stiffness losses in the A-laminate than in the Blaminata.
 
V
 

5.0 CONCLUSIONS
 

1. 	 Enhanced X-ray radiography gives detailed information on
 

matrix cracks that can be used to establish relations
 

between the location and length of the cracks and the
 

fatigue response of laminates.
 

2. 	 In conjunction with X-ray radiography, the deply
 

technique gives the shape, size, and spatial distribution
 

of delaminations.
 

3. 	 The moire technique can be used to detect damage in the
 

surface layer and related effects in the displacement
 

field. Local stiffness can be measured for various
 

damage situations. These results are in good agreement
 

with extensometer measurements. The moire patterns of
 

the laminate with the zero-deg surface layer (type A)
 

gave more evidence about relations between damage and
 

response than those of the B-laminate. All possibilities
 

of the moire technique were not completely used in this
 

work. More sophisticated data processing methods could
 

help to take full advantage of this technique.
 

104
 
105
 

4. 	 Stiffness losses during the lifetime are dependent on
 

load levels and reached 20 percent for the B-laminate and
 

40 percent for the A-laminate. Stiffness-change versus
 

number-of-cycles curves are typical for each laminate.
 

5. 	 Residual strength exceeds initial ,strength until the
 

final stages of lifetime are reached. Increases may
 

reach levels of at least 26 percent for the A- and 42
 

percent for the B-laminate. Laminates with the higher
 

initial strength are not necessarily those with higher
 

residual values.
 

6. 	 The pre-failure damage patterns, consisting of matrix
 

cracks and delaminations are characteristic for each
 

laminate. In general, surface layer matrix cracks
 

associated with the hole develop sooner and extend
 

further than the matrix cracks in the other layers.
 

Delaminations can be caused by certain stress situations
 

in the undamaged or low damaged specimen as well as by
 

stresses which are due to the presence of matrix
 

cracks. Delaminations between the surface layer and the
 

adjacent layer followed major cracks in the surface
 

layer. Moreover, tangent zero-deg cracks are well
 

defined in both laminates and are associated with
 
lO6
 

delaminations on adjacent interfaces. In the A-specimen,
 

these delaminations cover a larger area than the other
 

delaminations. In the B-specimen, the wing-like
 

delaminations between the 45-deg surface layer and the
 

adjacent 90-deg layer extend further but do not
 

necessarily cover a larger area than the delaminations
 

between the zero-deg and the adjacent -45-deg layer.
 

Since the zero-deg ply is a surface layer in the Alaminate, it has longer zero-deg cracks than the Blaminate and consequently the area covered by the
 

delaminations initiated by these cracks is much larger
 

than 	that for the B-specimen.
 

7. 	 Zero-deg matrix cracks tangent to the hole have a major
 

influence on residual strength via relaxation of strain
 

concentrations near the hole. The relationship between
 

crack length and residual strength is dependent on the
 

stacking sequence. It appears that the length of zerodeg matrix cracks has a major influence on delamination
 

size and attendant stiffness change. Further work could
 

better quantify these relations.
 
id7
 

8. 	 The matrix cracks and delaminations which develop at the
 

hole due to cyclic tension-tension loads change the
 

geometry of the notch and reduce the strain concentration
 

at the hole during the first 50 to 80 percent of the
 

fatigue life. During this period, the residual tensile
 

strength, of the laminate increases. Throughout the
 

remaining portion of the fatigue life, damage continues
 

to grow in the ligaments of material adjacent to the hole
 

and reduces the strength of the ligaments. Fatigue
 

failure occurs when the damaged ligaments cannot support
 

the maximum cyclic load; i.e., when the strength is
 

reduced to a value equal to the maximum applied cyclic
 

tensile stress.
 
VI
 

6.0 REFERENCES
 

1. 	W. W. Stinchcomb and K. L. Reifsnider, "Fatigue Damage
 

Mechanisms in Composite Materials: A Review," Fatigue
 

Mechanisms, J. T. Fong, Ed., ASTM STP 675, American
 

Society for Testing and Materials, 1979, pp. 762-787.
 

2. 	W. W. Stinchcomb, K. L. Reifsnider, P. Yeung, and
 

J. Masters, "Effect of Ply Constraint on Fatigue Damage
 

Development in Composite Material Laminates," Fatigue of
 

Fibrous Composite Materials, ASTM STP 723, American
 

Society for Testing and Materials, 1981, pp. 64-84.
 

3. 	G. P. Sendeckyj, G. E. Maddux, and E. Porter, "Damage
 

Documentation in Composites by Stereo Radiography,"
 

Damage in Composite Materials, ASTM STP 775,
 

K. L. Reifsnider, Ed., American Society for Testing and
 

Materials, 1982, pp. 16-26.
 

4. 	S. M. Freeman, "Damage Progression in Graphite-Epoxy by a
 

Deplying Technique," AFWAL-TR-81-3157, Wright Patterson
 

Air Force Base, OH, Dec. 1981.
 

5. 	Daniel Post, "Optical Interference for Deformation
 

Measurements -- Classical Holographic and Moire
 

Interferometry," Mechanics of Nondestructive Testing,
 

W. W. Stinchcomb, Ed., Plenum Press, New York, 1980.
 

6. 	R. D. Jamison and K. L. Reifsnider, "Advanced Fatigue
 

Damage Development in Graphite Epoxy Laminates,"
 

AFWAL-TR-82-3103, Dec. 1982.
 

7. 	T. K. O'Brien, "Stiffness Change as a Nondestructive
 

Damage Measurement," Mechanics of Nondestructive Testing,
 

W. W. Stinchcomb, Ed., Plenum Press, New York, 1980.
 

8. 	E. T. Camponeschi and W. W. Stinchcomb, "Stiffness
 

Reduction as an Indicator of Damage in Graphite/Epoxy
 

Laminates," Composite Materials: Testing and Design
 

(Sixth Conf.), ASTM STP 787, I. M. Daniel, Ed., American
 

Society for Testing and Materials, 1982, pp. 225-246.
 

108
 
109
 

9. 	J. D. Whitcomb, "Experimental and Analytical Study of
 

Fatigue Damage in Notched Graphite/Epoxy Laminates,"
 

Fatigue of Fibrous Composite Materials, ASTM STP 723,
 

American Society for Testing and Mterials, 1981,
 

pp. 48-63.
 

10. 	 J. M. Whitney and R. J. Nuismer, "Stress Fracture
 

Criteria for Laminated Composites Containing Stress
 

Concentrations," J. Composite Materials, Vol. 8,
 

July 1974.
 

11. 	 J. M. Whitney and R. Y. Kim, "Effect of Stacking Sequence
 

on the Notched Strength of Laminated Composites,"
 

Composite Materials: Testing and Design (Fourth Conf.),
 

ASTM STP 617, American Society for Testing and Materials,
 

1977, pp. 22%-242.
 

12. 	 T. K. O'Brien and I. S. Raju, "Strain Energy Release Rate
 

Analysis of Delamination Around an Open Hole in Composite
 

Laminates," presented at the 25th AIAA/ASME/ASCE/AHS
 

Structures, Structural Dynamics, and Materials
 

Conference, Palm Springs, CA, May 1984.
 

13. 	 T. K. O'Brien, "Mixed-Mode Strain Energy Release Rate
 

Effects on Edge Delamination of Composites," Effects of
 

Defects in Composite Materials, ASTM STP 836, D. Wilkins,
 

Ed., American Society for Testing and Materials, 1984.
 

14. 	 A. S. D. Wang, N. N. Kishore, and C. A. Li, "On Crack
 

Development in Graphite-Epoxy [02/90n]s Laminates Under
 

Uniaxial Tension," to be presented at the International
 

Symposium on Composites, Materials and Engineering,


University of Delaware, Newark, DE, 1984.
 
VIRGINIA TECH CENTER FOR
 

COMPOSITE MATERIALS AND STRUCTURES
 

The Center for Composite Materials and Research is conducted in a wide variety of 

Structures is a coordinating organization for areas including design and analysis of comporesearch and educational activity at Virginia site materials and composite structures, 

Tech. The Center was formed in 1982 to chemistry of materials and surfaces, characteriencourage and promote continued advances in zation of material properties, development of 

composite materials and composite structures. new material systems, and relations between 

Those advances will be made from the base of damage and response of composites. Extensive 

individual accomplishments of the thirty-four laboratories are available for mechanical 

founding members who represent ten different testing, nondestructive testing and evaluation, 

departments in two colleges. stress analysis, polymer synthesis and characterization, material surface characterization, 

The Center functions by means of an component fabrication and other specialties. 

Administrative Board which is elected yearly. The general purposes of the Center include: Educational activities include eight formal 

courses offered at the undergraduate and 

* 	 collection and dissemination of informa, graduate levels dealing with the physics, 

tion about composites activities at Virginia . chemistry, mechanics, and design of composite 

Tech, materials and structures. As of 1982, some 33 

* 	 contact point for other organizations and Doctoral and 37 Master's students have 

individuals, completed graduate programs and several 

* 	 mechanism for collective educational and hundred Bachelor-level students have been 

research pursuits, trained in various aspects of composite 

* 	forum and mechanism for internal inter- materials and structures. A significant number 

actions at Virginia Tech. of graduates are now active in industry and 

government. 

The Center for Composite Materials ahd 

Structures is supported by a vigorous program Various Center faculty are internationally 

of activity at Virginia Tech that has developed recognized for their leadership in composite 

since 1963. Research expenditures for investiga- materials and composite structures through 

tions of composite materials and structures total books, lectures, workshops, professional society 

well over five million dollars with yearly activities, and research papers. 

expenditures presently approaching two million 

dollars. 

FOUNDING MEMBERS OF THE CENTER 

Aerospace and Ocean Engineering Science and Industrial Engineering 

Engineering Mechanics 	 and Operations Research 

Raphael T. Haftka Hal F.Brinson 	 Joel A. Nachlas 

William L. Hallauer, Jr. John C. Duke, Jr. 	 Materials Engineering 

Eric R.Johnson 	 Daniel Frederick David W. Dwight 

Chemical Engineering Robert A. Heller 	 D. P. H. Hasselman 

Donald G. Baird 	 Edmund G. Henneke, 11 Charles R.Houska Carl T. Herakovich 	 M. R.Louthan, Jr. chemistry Michael W. HlyerMahmtc 

James E. McGrath Robert M. Jones Mathematics 

Thomas C. Ward Manohar P. Kamat Werner E. Kohler 

James P. Wightman Alfred C. Loos Mechanical Engineering 

Civil Engineering Don H. Morris Norman S. Eiss, Jr. 

Raymond H. Plaut Daniel Post Chades E. Knight 

Electrical Engineering J. N. Reddy S. W. Zewari 

loannis M. Besieris Kenneth L. Reifsnider 

Richard o. Claus C. W. Smith 

Wayne W. Stinchcomb 

Inquiries should be directed to:
 

Center for Composite Materials & Structures
 

College of Engineering
 

Virginia Tech
 

Blacksburg, VA 24061
 

Phone: (703) 961-4969
 
EC
 

PROS 

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