Astm stp 617 1977

CARLYLE 153 Specimen Design and Fabrication 155 Experimental Facilities and Procedures 156 Mechanical Property Results 157 Composite Resuhs 159 Acoustic Emission Response 160 Analysis a

Trang 2

TESTING AND DESIGN

(FOURTH CONFERENCE)

A conference sponsored by the AMERICAN SOCIETY FOR TESTING AND MATERIALS Valley Forge, Pa, 3-4 May 1976

ASTM SPECIAL TECHNICAL PUBLICATION 617

J G Davis, Jr., conference chairman

List price$51.75 04-617000-33

#

AMERICAN SOCIETY FOR TESTING AND MATERIALS

1916 Race Street, Philadelphia, Pa 19103

Trang 3

Library of Congress Catalog Card Number: 76-40796

NOTE The Society is not responsible, as a body, for the statements and opinions advanced in this publication

Trang 4

The Fourth Conference on Composite Materials: Testing and Design was held 3-4 May 1976 at Valley Forge, Pa The American Society for Testing and Materials' Committee D-30 on High Modulus Fibers and Their Composites sponsored the conference J G Davis, Jr., National Aeronautics and Space Administration-Langley Research Center, served

as conference chairman Most of the papers presented at the eight sessions are included in this volume which complements the first, second, and

third conference publications—>lSrM STP 460, ASTM STP 497, and ASTM STP 546, Composite Materials: Testing and Design

Trang 5

Related ASTM Publications

Composite Reliability, STP 580 (1975), $49.75 (04-580000-33)

Fracture Mechanics of Composites, STP 593 (1976), $23.50 (04-593000-33)

Environmental Effects on Advanced Composite Materials, STP 602

Trang 6

to Reviewers

This publication is made possible by the authors and, also, the

un-heralded efforts of the reviewers This body of technical experts whose

dedication, sacrifice of time and effort, and collective wisdom in

review-ing the papers must be acknowledged The quality level of ASTM

publica-tions in a direct function of their respected opinions On behalf of ASTM

we acknowledge their contribution with appreciation

ASTM Committee on Publications

Trang 7

Editorial Staff

Jane B Wheeler, Managing Editor Helen M Hoersch, Associate Editor Ellen J McGlinchey, Assistant Editor Kathleen P Turner, Assistant Editor Sheila G Pulver, Assistant Editor

Downloaded/printed by

University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized.

Trang 8

Introduction

FRACTURE AND FATIGUE

Fracture Resistance Characterization of Graphite/Epoxy Composites—

D H MORRIS AND H T HAHN 5

Experimental Program 6

Results 7

Conclusions 15

An Experimental Study of tlie Fracture Behavior of Laminated

Graphite/Epoxy Composites—H F. BRINSON AND Y T YEOW 18

Materials and Test Procedures 22

Experimental Results 22

Discussion 34

Effect of Time at Load on Fatigue Response of [(0/±45/90) J ^

T300/5208 Graphite-Epoxy Laminate—G P. SENDECKYJ AND

H D STALNAKER 39

Analysis of Test Results 46

Conclusions 51

Preliminary Development of a Fundamental Analysis Model for

Crack Growth in a Fiber Reinforced Composite Material—

M F KANNINEN, E F RYBICKI, AND W I GRIFFITH 53

Analysis Procedure 54

Example Computational Results and Discussion 62

Fatigue of Notched Fiber Composite Laminates: Analytical and

Experimental Evaluation—S V. KULKARNI, P V. MCLAUGHLIN,

J R , R B PIPES, AND B W ROSEN 70

Static Failure Model 72

Fatigue Analysis 75

Analysis/Experiment Correlation Study 84

Concluding Remarks 91

Trang 9

Delamination in Quasi-Isotropic Graphite-Epoxy Laminates—

K L REIFSNIDER, E G HENNEKE II, AND W W STINCHCOMB 93

Results 96 Discussion and Conclusions 103

Structural Design Significance of Tension-Tension Fatigue Data on

MATERIALS AND PROCESSING

Evaluation of Selected High-Temperature Thermoplastic Polymers

for Advanced Composite and Adhesive Applications—

Development of Multidirectional Fiber-Reinforced Plastics—

Y SUEZAWA, M TAKEMOTO, ANDS TAKAHASHI 137

Fabrication Method of Multidirectional Glass-Fiber Reinforced

Acoustic Emission Response Characteristics of Metal Matrix

Composites—R B. PIPES, N J. BALLINTYN, W R SCOTT, AND

J M CARLYLE 153

Specimen Design and Fabrication 155

Experimental Facilities and Procedures 156

Mechanical Property Results 157

Composite Resuhs 159

Acoustic Emission Response 160

Analysis and Conclusions 163

Trang 10

Compression Testing Procedure 172

Experimental Verification 177

Summary and Conclusions 188

Nondestructive Tests for Sliear Strength Degradation of a

Graphite-Epoxy Composite—D H KAEBLE AND P J DYNES 190

Experimental 191 Results 191 Summary 199

Failure Analysis of tlie Split-D Test Method—C E. KNIGHT, J R 201

Finite Element Model and Analysis 202

Results of Analysis 206

Conclusions and Recommendations 214

Longitudinal Residual Stresses in Boron Fibers—D R. BEHRENDT 215

Experimental Test Apparatus 216

Specimen Description 218

Analysis of the Data 218

Discussion 222

DESIGN AND ANALYSIS

Effect of Stacking Sequence on the Notched Strength of Laminated

Data Reduction 234

Discussion and Conclusions 238

An Analysis Model for Spatially Oriented Fiber Composites—

B W ROSEN, S N CHATTERJEE, AND J J KIBLER 243

Background 244 Description of the Model 246

Method of Analysis 248

Property Predictions 251

Empirical Crippling Analysis of Graphite/Epoxy Laminated

Experimental Procedure 257

Trang 11

Orthotropic Theoretical Elastic Buckling Equations 259

Theoretical Elastic Buckling of A-S/3501 Graphite/Epoxy 264

Orthotropic Nondimensional Empirical Crippling Equations 264

Crippling Test Program 265

Empirical Crippling Curves 266

Conclusions and Recommendations 270

Reliability Prediction for Composites Under Periodic Proof

Tests in Service—J N YANG 272

Statistical Distribution of Residual Strength Under Service Loads

and Periodic Proof Tests 274

Service Loads and Failure Rate 277

Probability of Failure Under Periodic Proof Tests In Service 279

Numerical Examples 284

Conclusion 290

A Perturbation Solution for Interlaminar Stresses in Bidirectional

Laminates—P W Hsu AND C T HERAKOVICH 296

Formulation 297

Conclusion 315

Evaluation of Composite Curing Stresses—N J PAG AND AND H T

HAHN 317 Analytical Approach 318

Stress-Free Temperature 320

Curing Stress Experiment 321

Influence of Curing Stresses on Laminate Strength 324

Lamination Residual Strains and Stresses in Hybrid Laminates—

I M DANIEL AND T LIBER 330

Experimental Procedure 331

Results and Discussion 332

Tensile and Compressive Behavior of Borsic/Aluminum—

C T HERAKOVICH, J G DAVIS, J R , AND C N VISWANATHAN 344

Trang 12

Tension Tests 363

Compression Tests 363

In-Plane Shear Tests 365

Interlaminar Shear Tests 365

Bolt Bearing Tests 366

Tension Fatigue Tests 366

Composite Preparation and Tests 377

Results and Discussion 379

Impact Damage in Graphite-Fiber-Reinforced Composites—

L B GRESZCZUK AND H CHAD 389

Theoretical Considerations 390

Theory Application 395

Experimental Studies 401

Discussion and Conclusions 403

Impact Response of Polymer-Matrix Composite Materials—

An Analytical Method for Evaluation of Impact Damage Energy of

Laminated Composites—C T SUN 427

Trang 13

Effects of Tliermal Cycling on tlie Properties of Grapliite-Epoxy

Thermally Induced Failure Mechanisms 467

Experimental Work 468

Conclusions 480

Moisture Effects in Epoxy Matrix Composites—C E. BROWNING,

G E HusMAN, AND J M WHITNEY 481

Experimental Procedures 482

Effect of Absorbed Moisture on Glass Transition Temperature 484

Prediction of Moisture Diffusion 486

Discussion of Mechanical Properties 488

Moisture Absorption and Desorption in Epoxy Composite Laminates—

C D SHIRRELL AND J HALPIN 514

Theory of Diffusion 515

Diffusion of Water in Composite Laminates 517

Effects of Moisture Absorption 522

Trang 14

Introduction

The American Society for Testing and Materials held the Fourth

Con-ference on Composite Materials: Testing and Design on 3-4 May 1976 in

Valley Forge, Pa The objectives of this conference were the same as

those of its organizing group (ASTM Committee D-30), that is, to

stimu-late research and promote the understanding of the behavior of fibers and

their composites, including reexamination of conventional tests in the

light of structural design requirements and composite material properties

Because the field of advanced composites is rapidly growing and

chang-ing, it is possible to meet such broad objectives only to the extent the

technology has progressed to date—and this the Fourth Conference has

done successfully The previous three similar conferences were held in

New Orleans in 1969 {ASTM STP 460), Anaheim in 1971 (ASTM STP

497), and Williamsburg in 1973 {ASTM STP 546), and succeeding

confer-ences will continue to be held as long as encouragement of new

develop-ments continue to be needed This volume includes most of the papers

presented at the conference, and, since its eight sessions (two on fracture

and fatigue, two on design and analysis, and one on materials and

pro-cessing, test methods, impact, and environment, respectively) cover the

total subject adequately in depth and breadth, it will make a valuable

ad-dition to the library of the scientist, analyst, designer, or testing engineer

who is seeking a better understanding of the behavior of advanced

com-posite materials

The papers in this volume cover a wide range of topics—from

investi-gation of a single filament to the design and fabrication of flight

hard-ware for acommerical transport All papers deal with subjects which may

affect the apphcation of advanced composites to industrial, military, and

consumer products Contributions in the areas of fracture and fatigue

phenomena, evaluation of resin matrices for advanced composites and

adhesives, processing for multidirectional fiber-reinforced composites,

test methods (including nondestructive), impact phenomena,

environ-mental effects, and the design and analysis of advanced composite

mate-rial are included Both theoretical and experimental approaches are

described and useful data are presented It is hoped that dissemination

of the results of recent advancements and successes will encourage

appli-cation of composites to new industrial, military, and consumer areas

Special thanks are due to Dr S Y Elliott, symposium chairman of the

third conference, for his advice and guidance in organizing and

Trang 15

schedul-2 COMPOSITE MATERIALS (FOURTH CONFERENCE)

ing this conference Recognition is also due the authors, session chairmen,

reviewers, and ASTM staff who responded in a timely and professional

manner to make this conference a success

J G Davis, Jr

National Aeronautics and Space tration-Langley Research Center, Hampton, Va 23665;

Trang 17

D H Morris' and H T Hahn'

Fracture Resistance Characterization

of Graphite/Epoxy Composites

REFERENCE: Morris, D H and Hahn, H T., "Fracture Resistance

Characteriza-tion of Grapliite/Epoxy Composites," Composite Materials: Testing and Design

(Fourth Conference), ASTM STP 617 American Society for Testing and Materials,

1977, pp 5-17

ABSTRACT: The resistance method has been applied to graphite/epoxy composites

The method is based on the assumption that the damage growth at the crack tip can

be modeled as a self-similar crack extension through compUance matching

Experi-mental data for center-cracked tension specimens reveal a Unear relationship between

crack-growth resistance and initial crack length For the [0/±45], laminate, the

effective increment of crack length at fracture and the corresponding crack-growth

resistance essentially are independent of initial crack length The average amount of

this crack extension in the [0/±45]2;, and [0/±45], laminates is higher than the values

obtained from a best fit of fracture strength data reported in the literature However,

the present method results in an improved prediction of fracture strength for the

[0/90/±45], laminate

KEY WORDS: composite materials, laminates, fracture tests, resistance method

A great deal of effort has been expended on resistance curve (Ajj-curve)

determination of metals [/].' However, there have been but a few attempts

to extend this method to advanced composites Gaggar and Broutman [2]

generated crack-growth resistance curves for epoxy and polyester

com-posites randomly reinforced with discontinuous fibers Their results

in-dicate that the ^^R-curve is independent of initial crack length They

con-clude from their study that the KR-CUIVC concept can be a useful approach

to study the crack-growth phenomena in random fiber composites

Eftis et al [3] state the basic concept of the resistance curve as follows:

as the rate of energy available for crack extension, G, is increased during

specimen loading, it is opposed by an increasing resistance to crack

exten-sion, R, such that G and R remain in equilibrium up to the point of crack

instabiUty The resistance curve represents the rate of energy absorption

' Associate professor, Mississippi State University, Mississippi State, Miss 39762

^ Research engineer University of Dayton Research Institute, Dayton Ohio 45469

' The italic numbers in brackets refer to the list of references appended to this paper

Trang 18

in the creation of new surfaces and plastic deformation throughout the

border region of the crack

The mechanism of energy absorption for composite materials is not

the same as that of metals In metals, slow, stable crack growth often is

observed prior to catastrophic failure In testing composites, it was found

that there is no visible self-similar crack growth The damages at crack

tips typically occur in the form of cracking along the fiber directions

within plies and delamination Frequently, these damages cannot be seen

with the naked eye; however, they are amenable to some of the

non-destructive examination techniques such as X-ray [4], The effect of these

differences in damage mode on constructing resistance curves will be

discussed later

The objective of this paper is to consider the possibility of using the

resistance method as a means of characterizing the fracture resistance of

graphite/epoxy composites The materials tested have different laminate

thicknesses and ply orientations

Experimental Program

The material used in the experimental program consisted of Thornel

300 graphite fibers in Narmco 5208 epoxy resin A total of 35

center-cracked tension specimens were tested All specimens were 2 in wide,

12 in long (9 in between end tabs), with crack lengths 0.2 to 1.0 in., in

increments of 0.2 in Cracks were produced by first drilling a small hole

in a specimen, followed by a final lengthening with a 5 mil diamond wire

No attempt was made to further sharpen the crack tips

The laminate orientations and number of specimens may be summarized

as

[0/90/±45]s: two specimens of each crack length [0/ ± 45],: two specimens of each crack length

[ 0 / ± 4 5 ] 2 J : three specimens of each crack length

The unnotched tensile strength was determined by testing six tensile

cou-pons of the [0/90/±45]s laminate and four coucou-pons of the [ 0 / ± 4 5 ] 2 J

laminate

All specimens were loaded by friction grips and tested in a closed loop

MTS machine at a constant cross-head rate of 0.04 in./min During each

test, the applied load and a pseudocrack opening displacement (COD)

were monitored and recorded continuously The COD was measured by a

double cantilever clip gage of the type used in fracture testing of metals

[5] The clip gage was attached to aluminum tabs which were bonded to

the specimen with epoxy cement 0.3 in apart

Trang 19

MORRIS AND HAHN ON FRACTURE RESISTANCE 7

Results

A comparison of three test records of load versus COD where each

specimen has the same initial crack length is seen in Fig 1 The load-COD

Crack Opening Displacement

FIG 1—Comparison of toad-crack opening displacement records

records are initially linear, followed by rapid changes in COD similar to

the pop-in effect seen in metals The rapid changes in COD were

accom-panied by audible levels of acoustic emission; however, no attempt was

made to record acoustic emission or to correlate it with load-COD data

Figure 1 also indicates that the load-COD relationship remains linear

even between loads where there is a rapid increase in COD Using random

fiber composites, Gaggar and Broutman [2] found the load-COD records

to be initially Unear followed by a deviation in lineeirity that is practically

continuous

As previously mentioned, the composites tested did not exhibit any

visible self-similar crack growth such as occurs in metals Hence, in order

to construct resistance curves, an effective crack length may be defined by

matching the compliance based on the COD

Trang 20

Compliance calibration (based on COD), as a function of initial crack

length, was obtained from the initial straight portion of a load-COD

record Figure 2 shows calibration curves for the three laminates tested

These curves are used to determine the effective crack lengths

0.3 0.4 0.5 0.6 0.7 OB 0.9 1.0

Initial Crack Length , 2 a ( I n )

FIG 2—Compliance curves for three laminates

Figure 3 illustrates the method of calculating the effective crack length

First, a straight line is drawn from the origin to the loading curve at

selected intervals of load or COD (shown as dashed Unes); the inverse of

the slope is the compliance This value of compUance, together with the

calibration curve shown in Fig 2, gives an effective crack length The

effective crack length is not a preexisting crack, but rather a crack-like

region developing prior to the commencement of uhimate failure [2,6\

Continuing in this manner, additional values of effective crack length are

found from Figs 2 and 3

Crack growth resistance, which is a function of crack length, is

cal-culated from

where

<T = nominal stress based on increasing load levels and unnotched area,

a = effective crack half-length at the corresponding load level, and

Y = finite width correction factor based on effective crack half-length

Trang 21

MORRIS AND HAHN ON FRACTURE RESISTANCE 9

Crock Opening Displocemeni

FIG i—Schematic of compliance determination

The finite width correction factor for the [0/±45]2j and [0/±45]s

lam-inates is slightly different from the isotropic value However, the difference

is less than 4 percent in the entire range of crack sizes considered [7]

Therefore, Y is determined from the equation for isotropic materials [J]

Y = I + 0.1282 (2a/H^) - 0.2881 (2a/Wy + 1.5254 (2a/W^)' (2)

Figure 4 depicts the relationship between crack-growth resistance and

effective crack half-length for the quasi-isotropic laminate There is no

effective crack growth for a specimen with an initial crack length (2ao) of

0.2 in When 2oo = 0.4 in., three straight Unes are shown in Fig 4, the

dashed Unes are the results of two different tests, the solid line is an

"eye-ball" best fit of the two tests For the other two initial crack lengths, only

the soUd line is shown This figure illustrates that the ^g-effective

crack-length relationship is linear

The results shown in Figs 5 and 6 also indicate a linear relationship

between KR and effective crack length Superposition of the figures reveals

Trang 22

Effective Crack Half-length (in.)

FIG 4—Crack-growth resistance for [0/90/±45J s laminate

that the straight lines for the same 2ao almost are identical, indicating that

crack-growth resistance should be independent of laminate thickness

However, more data are needed to substantiate this statement

If the crack-growth resistance curve has a unique shape and is

inde-pendent of initial crack length, specimen geometry, and boundary loading

conditions, it can be considered a material property Figure 7 represents

the crack-growth resistance KR as a function of crack extension (Aa =

a - flo) for the [0/±45]2s laminate Due to data scatter, no conclusive

statement can be made as to whether KR is a material property

Once the A^R-curve is obtained, the ultimate failure stress can be

deter-mined by the point of tangency between KR, as found from Eq 1, and

^-curves defined by

Trang 23

FIG 5—Crack-growth resistance for [0/±45]2^ laminate

with (T as a parameter (Fig 8) The results indicate no point of tangency

Thus, the critical value of K is the maximum value on the KR effective

crack-length curve

Figure 5 shows that the maximum value of KR is practically constant

for the [ 0 / ± 4 5 ] 2 J laminate, where three specimens of each crack length

were tested However, such a statement cannot be made for the [0/ ± 45]^

and [0/90/±45]J laminates, where only two specimens of each crack

length were tested Another interesting feature of the results is that the

value of KR at initiation of crack growth is independent of initial crack

length except for the smallest cracks in the [0/±45]25 and [0/±45]s

lam-inates

In all the laminates tested, the amount of effective crack growth Ac at

Trang 24

0 , 2 0.3 0,4 O.e

Effective Crock Half-length (in)

FIG 6—Crack-growth resistance for [0/±45Js laminate

fracture depends on initial crack length as seen in Fig 9 This dependence

is seen to be least for the [0/ ± 45] 2^ laminate and most for the [0/90/ + 45J,

laminate However, the average amount is almost the same for both

[0/±45]2s and [0/±45]j laminates, indicating negligible effect of

thick-ness Note that the straight lines represent the average values

Several models have been proposed in the literature [8.9] for the

pre-diction of fracture strength In the case of cracks, the average stress

model [9] becomes identical with the inherent flaw model [8] as discussed

in Ref 6 It should be noted that the inherent flaw model also follows

from the present resistance method if ^^ and Aa at fracture are independent

of initial crack size

According to the preceding models, the ratio of the (notched) fracture

strength (T„ to the (unnotched) ultimate strength ffui, is given by

Trang 25

Crack Extension, Aa (in.)

FIG 7—Crack-growth resistance as a function of crack extension for [0/±45]2s laminate

where Co is the dimension of the damage zone at crack tips Note that Y is

calculated for the original crack length 2ao The average strengths required

in the foregoing equation are listed in Table 1 together with the raw data

Trang 26

0.1 0.2 0.3 0.4 CRACK - H A L F LENGTH (in.)

[0/±45]j

0.1 0.2 0.3 0.4 CRACK -HALF LENGTH (in.)

[O/90/t 45J5

0 0.1 0.2 0.3 0.4 CRACK-HALF LENGTH (in.)

FIG 9—Crack growth at fracture versus initial crack half-length

TABLE 1—Ultimate strengths

Laminate

[ 0 / ± 4 5 ] , ,

Avg

CV, % [0/90/±45],

Thickness,

in

0.065 0.065 0.065 0.065 0.065

0 0.044 0.044 0.044 0.044 0.043 0.044 0.044 0.86

Strength, 10' psi 80.06 82.40 67.50 83.78 78.44 9.50 65.66 64.54 68.25 66.26 65.02 65.59 65.89 1.97 NOTE—CV = Coefficient of variation

Trang 27

The Strengths of [0/±45]j and [0/90/±45]^ laminates are slightly lower

than those reported for a [0/±45]j laminate [7\ and for a [0/±45/90]2j

FIG 10—Prediction of fracture strength

each laminate, Co was taken to be the average amount of crack growth at

fracture The experimental data are shown in Fig 10, and specimen

dimensions are listed in Table 2 Thickness does not seem to affect the

fracture strength, as can be seen from the data for the [0/±45]2s and

[0/±45]j laminates

For the [0/±45]2i and [0/±45]j laminates, the values of Co obtained by

using the present method of compliance matching yield results higher than

the experimental data These values of Co are higher than the one (0.075

in.) for the [0/±45]j laminate reported [70], where Co was determined

from the best fit of the data This latter value was found to result in lower

than actual strengths for the [0/90±45]2^ laminate [9] However, the

present value of Co, which is higher than 0.075 in., for the [0/90/±45]^

laminate leads to a good agreement between the theory and data

Conclusions

The resistance method has been applied to graphite/epoxy composites

The method is based on the assumption that damage growth at the crack

tip can be modeled as a self-similar crack extension through compliance

matching The ^^-curve thus obtained provides full information on the

fracture resistance of the material up to final fracture In the case of

Trang 28

TABLE 2—Fracture strengths

[0/±45]j

[0/±45]2, [0/±45]j

[0/±45]

[0/±45L [0/±45]

[0/±45]

[0/±45L [0/±45], [0/±45L [0/±451, [0/±45]

[0/90/±45]

[0/90/±45], [0/90/±45]

[0/90/±45], [0/90/±45], [0/90/±45], [0/90/±45], [0/90/±45], [0/90/±45],

W, in

2.00 2.00 1.99 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 1.99 2.00 2.00 1.99 2.00 1.99 2.00 1.99 1.99 1.99 1.99 1.99 2.00 1.99 2.01 2.00 1.99 1.99 1.99 1.99 1.99 1.99 1.99 1.99 2.00 2.00

t, in

0.0679 0.0677 0.0670 0.0683 0.0674 0.0675 0.0682 0.0676 0.0674 0.0654 0.0676 0.0666 0.0676 0.0667 0.0677 0.0345 0.0346 0.0350 0.0346 0.0345 0.0345 0.0349 0.0340 0.0329 0.0347 0.0333 0.0331 0.0462 0.0460 0.0469 0.0447 0.0466 0.0466 0.0470 0.0471 0.0466 0.0470

2ao in

0.20 0.19 0.19 0.40 0.40 0.39 0.59 0.59 0.59 0.78 0.81 0.79 0.99 0.99 0.99 0.20 0.19 0.40 0.40 0.59 0.60 0.80 0.79 1.00 0.99 1.18 1.19 0.20 0.20 0.39 0.40 0.60 0.60 0.79 0.79 0.99 0.99

0.332 0.257 0.700 0.607 0.765 0.810 1.057 1.062

0.762 0.508 0.683 0.707 1.035 1.043

NOTE—I-c02-l,2; linear to fracture

graphite/epwxy composites studied, the relationship between KR and

effec-tive crack length is linear The value of KR at initiation of crack growth

is fairly independent of initial crack length In addition, the effective

increment of crack length at fracture and the corresponding KR essentially

are independent of initial crack length, at least for one of the laminates

tested For the [0/±45]2j and [0/±45]j laminates, the effective increment

of crack length at fracture determined by the compliance matching is

higher than the values resulting from a best fit of experimental strength

data [70] However, the present method leads to an improved prediction

of fracture strength for the [0/90/±45]^ laminate

Trang 29

Acknowledgments

The first author would Uke to acknowledge the support of the Air Force

Office of Scientific Research for providing a fellowship through the

United States Air Force—American Society for Engineering Education

Summer Faculty Research Program The second author's work was

spon-sored by the Nonmetallic Materials Division of the Air Force Materials

Laboratory under Contract No F33615-75-C-5093 The authors would

also Uke to thank Dr R Kim for performing the tests

References

[/] Fracture Toughness Evaluation by R-Curve Methods, ASTM STP 527, American

Society for Testing and Materials, 1973

[2] Gaggar, S and Broutman, L J., Journal of Composite Materials, Vol 9, 1975, pp

216-227

[JJ Eftis, J., Jones, D L and Liebowitz, H., Fracture Mechanics of Aircraft Structures,

H Liebowitz, Ed., AGARD-AG-176, North Atlantic Treaty Organization, 1974, pp

32-73

[4\ Chang, F H., Couchman, J C , Eisenmann, J R., and Yee, B G W., in

Com-posite Reliability, ASTM STP 580, American Society for Testing and Materials, 1975,

pp 176-190

[5] Brown, W F and Srawley, J E., Plane Strain Crack Toughness Testing of High

Strength Metallic Materials, ASTM STP 410, American Society for Testing and

Mate-rials, 1966

[6] Tsai, S W and Hahn, H T in Inelastic Behavior of Composite Materials, AMD Vol

13, American Society of Mechanical Engineers, 1975, pp 73-96

[7\ Cruse, T A and Osias, J R., "Exploratory Development on Fracture Mechanics of

Composite Materials," AFML-TR-74-111, Air Force Materials Laboratory, April 1974

[8] Waddoiips, M E., Eisenmann, J R., and Kaminski, B E., Journal of Composite

Materials, Vol 5, 1971, pp 446-454

[P] Nuismer, R J and Whitney, J M in Fracture Mechanics of Composites, ASTM STP

593, American Society for Testing and Materials, 1975, pp 117-142

[70] Whitney, J M and Nuismer, R J., Journal of Composite Materials, Vol 8, 1974, pp

Trang 30

An Experimental Study of the

Fracture Behavior of Laminated

Graphite/Epoxy Composites

REFERENCE: Brinson, H F and Yeow, Y T., "An Experimental Study of the

Fracture Behavior of Laminated Graphite/Epoxy Composites," Composite Materials:

Testing and Design (Fourth Conference), ASTM STP 617, American Society for

Testing and Materials, 1977, pp 18-38

ABSTRACT: Tlie results of an experimental investigation on the fracture behavior of

unidirectional and multidirectional laminated graphite/epoxy composites is reported

Critical tensile fracture stresses for constant head rate uniaxial specimens containing

single-edge notches, double-edge notches, and centrally located circular holes are

presented Results are reported for loads and notches at various angles to the fiber

direction(s) Evidence of notch sensitivity and stable crack growth is presented

Self-similar crack growth is shown to occur for only a limited set of circumstances

Critical stresses are compared to the theories of Waddoups et al and Whitney et al

These comparisons are presented using isotropic and orthotropic stress concentration

factors together with a finite width correction factor The results tend to show that

use of only isotropic correction factors allow good correlation between theory and

experiment

KEY WORDS: composite materials, fracturing, graphite composites, epoxy laminates

The mathematical theory of Hnear elastic fracture mechanics (LEFM) is

well established for homogeneous isotropic and anisotropic materials

[1,2\} However, there remain many fundamental questions in regard to

the experimental determination of stress intensity factors {K) or strain

energy release rates (G) for particular crack geometries For example,

LEFM assumes a perfect crack of zero width and zero crack root radius

Obviously, such perfection is not possible in the laboratory As a result,

there is still some concern for isotropic materials as to what effects finite

crack tip radii have on G or A" and, especially, how close to the finite

' Professor and research associate, respectively Department of Engineering Science and

Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, Va 24061

^The italic numbers in brackets refer to the list of references appended to this paper

Trang 31

BRINSON AND YEOW ON GRAPHITE/EPOXY COMPOSITES 19

crack tip data can be collected and still be correlated to LEFM Even if

near perfect crack tip geometries are generated using fatigue to grow or

enlarge a small crack, a small region near the crack tip cannot be modeled

well by LEFM because of finite deformation and plasticity effects Thus,

for isotropic as well as anisotropic but homogeneous materials, a core

region adjacent to the crack tip, on the order of the size of the crack root

radius, must be excluded in any analysis using LEFM

In composite materials, the picture is much more complex These

materials are nonhomogeneous as well as anisotropic, and various

frac-ture mechanisms with separate but perhaps coupled fracfrac-ture energies must

be accounted for However, perhaps the single most complicating feature

of composite fracture is that self-similar crack growth is not likely to

occur even for unidirectional or symmetric angle-ply laminates In general,

without self-similar growth the usual methods of LEFM are not

appli-cable to any material

The early fracture theories of Waddoups et al [3], Cruse [4], and

Whit-ney et al [5,6] consider only self-similar crack growth Each of these

in-vestigators found that in order to use various fracture solutions for either

holes or cracks the crack length had to be adjusted to include an intense

energy region at each crack tip The size of the intense energy region had

to be found from experimental data

The more recent theories of Wu [7,8] and Sih [9,10] not only can be

used to predict critical load levels for crack growth, but they will predict

also the direction of crack propagation Wu's technique performs this

function by locating the intersection of the stress vector surface and the

failure surface (determined from unnotched biaxial tests) This calculation

must be made at some distance away from the crack tip to avoid singular

stress fields Sih's technique employs a strain energy density concept The

strain energy density and its derivative also must be found at some

dis-tance away from the crack tip to avoid singular stress fields Thus, while

each of these theories give non-self-similar crack growth predictions, the

size of an intense region must be known a priori or found from

experi-mental data

An approach due to Kulkarni and Rosen [11] uses a material science

approach to model crack growth normal to the crack plane Such crack

growth has been observed for both unidirectional and general laminates

[12] Without going into details, the size of a critical intense energy region

in the direction of the crack must be assumed In addition, the damage

zone normal to the crack is found from the analysis The approach does

attempt to incorporate material heterogenity into the analysis

Currently, other numerical approaches are being developed to include

material heterogenity One such example is that of Kanninen et al [73]

which is included in this publication

It is worth noting that each of the fracture theories mentioned require

Trang 32

experimentally determined moduli, failure stresses or strains, or fracture

information Thus, additional test programs are required to utilize the

various theories over and above those which are required normally for

LEFM This is due to the fact that current fracture approaches to

com-posites represent models containing at least two arbitrary parameters as

opposed to the usual one arbitrary parameter model of LEFM

Obviously, all the questions regarding the size of actual crack tip

geometries as opposed to assumed ideal crack tip geometries used in

frac-ture analyses are even more important for composite materials than for

other engineering materials This is reinforced by the fact that it is not

clear if laminated composite materials are notch sensitive as are metallic

and polymeric materials

From the preceding comments, it is clear that test programs must be

conducted to determine accurate properties and fracture information for

composite materials This investigation represents an effort to obtain

some of the required information The specific objective of this

investiga-tion was to measure critical fracture loads for both unidirecinvestiga-tional and

multidirectional notched composites with the load and the notch at various

orientations to the principal fiber direction In the process, it was

antici-pated that information would be obtained regarding notch sensitivity,

self-similar crack growth, stable crack growth, and fracture mechanisms

Further, comparison between experimental results and some fracture

theories was desired For this reason and for later reference, the theories

of Waddoups, Eisenmann, and Kaminski [3] and Whitney and Nuismer

[5,6] will be outlined briefly

In Ref 3, Waddoups et al modeled a circular flaw in a composite as

having two slits or cracks emanating symmetrically from either side of

the hole perpendicular to the load direction Even though the slits were

defined only as intense energy regions, they were modeled mathematically

as cracks using the Bowie crack solution [14] The latter can be written as

Kic = <r, sfl^fia/f) (1)

where

/Tic = opening mode critical stress intensity factor,

(T^ = critical remote load,

a = length of the intense energy region (or crack adjacent to the

hole), and

f(a/f) = function of the hole radius r

A table for f{a/f) values for an infinite plate for different hole sizes is

given in Ref 14 For a specimen with no hole,/(o/r) = 1.0 Therefore

- = Ka/r) (2)

Trang 33

where ffo is the critical remote load for an unnotched tension specimen

Thus, given ao and tr,, for one size hole, critical stress intensity factors

can be calculated for other size holes using Eq 1 provided a/r values can

be found The a/r values were found using the elliptical hole analysis of

Griffith [75] which essentially determines the size of the intense energy

region or the value a

The fundamental idea is that using the results from one unnotched

tension test and one notched tension test, critical stresses for other size

holes can be calculated assuming K\<, and o remain constant An identical

procedure was used for slits For the case of holes, the size of the intense

energy region was found to be ^ 0 0 4 in.)

Whitney and Nuismer \5,6\ used quite a different technique to explain

the hole size effect in composites Their argument was that, while

dif-ferent size holes in an infinite plate have the same stress concentration

factor, the stress gradient is quite different for each That is, large stresses

are localized more closely to the edge of a small hole than a large hole As

a result, a critical defect is more likely to occur in a region of high stress

for a large hole Both a point stress and an average stress technique were

used The point stress criterion was given by

The quantity/(A^r°° /?) is a function of the hole size and the orthotropic

stress concentration factor for an infinite sheet, KT" The average stress

criterion was given by

<T 2(1 - R)

— = (4)

[2 - R' - R* + fiKr'',R)]

where R = r/r + Oo, Oo is the size of the damage zone and tr,., ao, and

fiKT°°,R) are as defined previously

The same technique was used identically for cracks except the stress

state in front of a crack was used instead of the stress state in front of a

hole Good correlation between theory and experiment was shown for a

variety of quasi-isotropic laminates [5,6]

Trang 34

Materials and Test Procedures

The materials studied in this investigation were manufactured by

Lock-heed (Sunnyvale, Calif.) from prepreg tapes composed of Hercules

(Magna, Utah) graphite AS fibers and epoxy resin 3501 The fundamental

properties of the fibers were 380 to 400 ksi tensile strength, 30 to 40 x

10' ksi elastic modulus, and 10 000 fibers/tow The resin was a hot-melt

1(X) percent soHds epoxy No properties of the resin were available The

resulting [0]ss and [0/±30/0]25 laminates were medium strength and

medium modulus composite materials Large 0.80-in thick plates were

received from which individual specimens were machined

Some effort was made to determine the best procedures for machining

specimens Diamond saws, tungsten carbide cutting tools, and ultrasonic

machining techniques were attempted Diamond saws were selected to

give the best surface for the amount of machine time required Surfaces

machined by the various techniques were examined with a scanning

elec-tron microscope (SEM) and various inherent flaws were found Figures la

and b are SEM photographs of a diamond and an ultrasonically machined

surface, respectively Also shown in Fig 1 are examples of typical flaws

which were found Figure la shows a near cyhndrical void, while Fig lb

shows a flaw which appears to be in a single ply and extending at an angle

to the interface between laminae

Uniaxial tension tests were performed on specimens with and without

flaws using an Instron testing machine After machining, all specimens

were stored in a desiccator until tested Specimens were allowed to sit and

stabilize to the test environment for at least 1 h prior to testing Test

temperatures were generally at a room temperature of approximately

75 °F, and the relative humidity was generally less than 60 percent

Specimens (1 in wide with ^^4.5 in between grips) with single-edge

notches, double-edge notches, and circular cutouts were tested Notched

specimens were tested generally at a head rate of 0.01 in./min Edge

notches were used as opposed to center notches, because notch widths

and notch tip geometries could be made much smaller using diamond

saws as opposed to end mills The notches were made with a 0.006-in

diamond saw with the resulting notch width of 0.0075 in The tip of the

notch was reasonably flat but with rounded corners One corner

consis-tently appeared to have a smaller radius than the other

All tests were conducted without tabs, using sandpaper between

epoxy-coated wedge grips, to minimize penetration of grip serrations into the

graphite/epoxy materials Unnotched data collected in this manner

corre-lated well with data collected by NASA-Ames using tabs [76]

Experimental Results

Uniaxial tension tests were performed on specimens containing

Trang 35

single-BRINSON AND YEOW ON GRAPHITE/EPOXY COMPOSITES 23

(o) [OJs material—diamond machined surface at ^^5 deg to fibers, x 950

(b) [0/ ± 30/0]i, material—ultrasonically machined at >^^ to 0-deg fibers, x 200

(Arrows denote flaw tips and laminae interfaces.)

FIG 1—Inherent flaws in graphite/epoxy laminates

Trang 36

edge notches (SEN), inclined single-edge notches (ISEN), double-edge

notches (DEN), and centrally located holes Various aspect ratios, that is,

crack length or hole radius to plate width ratio, were used In the SEN

and DEN tests, the load was at various angles to the fiber direction(s)

with the notches at right angles to the load direction In the ISEN tests,

the load was similarly at various angles to the fiber direction(s), and the

notches were also at various angles to the applied load (All angle

designa-tions, henceforth, are measured from the load direction.)

Fracture planes for all tests on unidirectional laminates were in the

fiber direction In other words, fracture was primarily in the matrix

Figure 2 shows failure planes for two ISEN specimens Thus, in general

FIG 2—ISEN fracture planes for [45]2s specimens

non-self-similar fracture occurred for unidirectional laminates unless the

crack was machined to be in the fiber direction It might be noted that

longitudinal splitting was the fracture mode for all [0\is tests That is,

when the load was in the fiber direction of the zero fiber with the crack

normal to the fiber direction, fracture occurred parallel to the load in

every case This was due most likely to thickness variations and gripping

conditions The fracture loads are not thought, at this time, to represent

realistic material values

Fracture planes for all notched multidirectional laminates were generally

in the principal fiber direction except for the [0/ ± 30/0] tests For example,

in Fig 3 the fracture plane for a [90/± 60/90]2s specimen is shown to be

at right angles to the load and in the direction of the principal fibers

Fracture planes for the [0/ ± 30/0]2s specimen are shown in Fig 4, and it

can be seen that in these cases crack propagation was erratic but generally

normal to the load and principal fiber direction

In most cases, fracture appeared to occur at the smaller notch tip radii

Also, in nearly all general laminate tests, audible noise could be heard

substantially before fracture Also, in these cases, and in some

Trang 37

unidirec-BRINSON AND YEOW ON GRAPHITE/EPOXY COMPOSITES 25

FIG i—Stable crock growth for [90/±60/90]2^ specimen

Trang 38

FIG A—Fracture planes for [0/ ±30/0)2^ DEN specimens

tional tests, visible and stable crack growth was observed That stable

growth was observed is evident from examination of successive 35-mm

photographs taken during fracture and shown in Figs 3 and 5 for a

[90/ ± 60/9O]2J S E N and DEN test, respectively Similar observations were

made in other tests Note that the stable growth shown by the

photomi-crograph of Fig 5 can be seen only in the outer ply Further note the

additional cracks somewhat above and below the notch tip and the jagged

appearance of the fracture surface Apparently, fracture occurred in inner

and outer plies at different times and directions While the general

ap-pearance of fracture is self-similar in a gross sense, and especially for the

outer plies, self-similar behavior was not the fracture mode on a local

level for the inner plies

The audible noise mentioned for the general-ply tests appeared to occur

in many cases in conjunction with a load reduction That is, at some point

prior to complete separation, load reduction would occur instantaneously

After a delay time, the load would again increase to its previous or a

higher value Repeated load reductions were observed in some cases as

typified by Fig 6

Trang 39

The [90/±60/90]2 DEN specimen containing a 0.05-in length notch

on one side is shown in Fig 7 As may be observed, fracture occurred

at a considerable distance from the site of the machined notch In this

particular case, the specimen thickness at the crack tip was ^^.085 in.,

while its minimum value was 0.075 in at the fracture site Thus, the

aver-age areas at each location were about the same, that is, ^^.075 in.^ Thus,

it would appear that an inherent flaw existed at the minimum section

which was more critical than the machined notch One might infer from

this case that the material is not notch insensitive Obviously this is not

necessarily the case as the material is not a continuum and, as such, the

converse is likely to be true The real question is only the size of a critical

inherent flaw if one existed

Tests were performed on both types of laminated specimens

contain-ing circular holes of varycontain-ing sizes For unidirectional laminates, fracture

originated at the edge of the hole and propagated in the direction of the

fibers in each case For general laminates, fracture originated (in most

cases) at the edge of the hole and propagated in various directions

de-pending on the layup Figure 8 gives typical examples of fracture planes

for various [0/±30/0]2„ [45/15/75/45]2„ and [90/±60/90]2 specimens

Also note the [90/±60/90]!, specimen which separated at a location other

than the hole In this case, the thickness at the edge of the hole was

0.079 in and 0.074 in at one location where fracture occurred Thus,

even though the net area was smallest at the minimum section, fracture

occurred at the point where the specimen was the thinnest Again,

pre-sumably an inherent flaw at the fracture site was more critical than the

machined hole

The gross fracture stresses obtained in the various tests are shown in

Figs 9 through 12 and plotted as a function of aspect ratio The data

appear to be quite consistent except for the [OJss SEN and ISEN fracture

strengths Likely errors for the latter cases were discussed previously

From an examination of these results, it is apparent that the graphite/

epoxy laminates tested were notch sensitive Further, it is not unreasonable

to infer that some type of singular stress field (or extreme stress gradient)

does exist at the notch tip Critical gross stresses found for the [0]8s and

[0/±30/0]2s specimens containing holes are quite similar to those found

for double-edge notches Less similarities exist for the other cases

The ISEN data shown in Fig 10 indicate only a small variation of gross

failure stress with the angle of incHnation of the crack All the inclined

cracks were machined such that their horizontal projection was half the

plate width Thus, the results of Fig 10 tend to indicate that only the

horizontal projection of the inclined crack is of importance when

con-sidering angle cracks That is, the length and inclination of the crack is

relatively unimportant, and the length of the horizontal projection of the

crack tends to govern the fracture behavior

Tiêu đề	Testing and Design
Tác giả	J. G. Davis, Jr.
Trường học	University of Washington
Chuyên ngành	Composite Materials
Thể loại	Bài báo
Năm xuất bản	1977
Thành phố	Philadelphia

Định dạng
Số trang	534
Dung lượng	8,34 MB