Contractor Report ""178&66

DELAMINATION GROWTH IN COMPOSITE MATERIALS

John W. Gillespie, Jr., Leif A. Carlsson,

R. Byron Pipes, Robert Rothschilds,

Bruce Trethewey, and Anthony Smiley

UNIVERSITY OF DELAWARE

Center for Composite Materials

College of Engineering

Newark, Delaware

Grant NAG1-475

February 1986

{NASA-CB-178Q66) DELAHINATIO N GfiOHTH IN

COMPOSITE MATEBIA1S (Delaware Univ.)/ 212, p

HC A10/HF A01 - CSCL 1"1D

NASA

National Aeronautics and

Space Administration

Langley Research Center

Hampton,Virginia 23665

G3/24

N86-21618

Onclas

05655
Table of Contents

Page

1. INTRODUCTION 1

2 . EXPERIMENTAL 9

2 .1 Materials Processing 9

2 .2 Basic Materials Characterization 14

2.3 Determination of Interlaminar Fracture Toughness 14

2.4 Imbedded Through-Width Delamination Specimen Testing..23

3 . ANALYSIS 31

3.1 Finite Element Analysis of the ENF Specimen 31

3.1.1 Compliance of an Orthotropic Beam 36

3.1.2 Compliance of the ENF Specimen 39

3.1.3 Strain Energy Release Rate of the ENF Specimen 45

3.1.4 Sensitivity of ENF Strain Energy Release Rate on

Crack Offset 55

3.1.5 Finite Element/Beam Theory-Based Data Reduction

Schemes for the ENF Specimen 57

3.1.6 Influence of Friction on the Compliance and Strain

Energy Release Rate of the ENF Specimen 60

3.1.7 Discussion of ENF Data Reduction Scheme 66

4 . INTERLAMINAR FRACTURE TEST RESULTS 72

4 .1 DCB Test Results 77

4 . 2 ENF Test Results 85

4.3 Rate Effects in Mode I and Mode II Fracture 91

4 . 4 ITWD Test Results 108

5 . CONCLUSIONS 118

6 . FUTURE WORK 120

REFERENCES 121
Appendices

Page

APPENDIX 1

APPENXIX 2

APPENDIX 3

APPENDIX 4

APPENDIX 5

APPENDIX 6

APPENDIX 7

Data Reduction Schemes for the DCB, ENF

and CLS Specimens 125

Stability of Crack Growth for the ENF

Specimen 136

Design Considerations for the DCB, ENF and

CLS Specimens 139

Influence of Shear Deformation on the ENF

Compliance and Strain Energy Release Rate 150

Influence of Friction on the ENF Strain

Energy Release Rate 156

Stress-strain curves for APC-2 and

CYCOM 982 161

Mode I and II Interlaminar Fracture

Test Data 168

PRECEDING PAGE BLANK NOT FILMED

iii
1. INTRODUCTION

Delaminations represent a common and characteristic flaw in

composite laminates that may be introduced during processing or

subsequent service conditions. The local instability of

composite laminates in the vicinity of interlaminar defects and

the potential for delamination initiation and growth may induce

significant strength reductions under compressive loadings

[1-8]. Therefore, a fundamental understanding of the mechanisms

governing delamination initiation and growth is required to

develop appropriate failure criteria to assess defect

criticality. In composite structures, impact damage may result

in multiple delaminations of various planforms interacting with

intraply cracks. Analysis of delamination growth including the

interaction of the various flaws would be complex and require a

three dimensional stress analysis. Consequently, most studies to

date have considered delamination growth of imbedded defects in

simple configurations. Perhaps the simplest geometry is the

imbedded through-width delamination imbedded in a laminate

subjected to compressive loads, see Fig. 1. Delamination

growth models for this geometry based upon fracture mechanics

have been reported by a host of researchers [1,4,5,9-12]. Strain

energy release rate formulations have been based upon both

analytic formulations [1,4,5,10] and finite element analysis

[9,11,12]. The Mode I component of the strain energy release

rate, Gj, for a compressively loaded laminate with an ITWD

monotonically increases, attains a global maximum and diminishes

to zero with increasing load [1,9,13]. The Mode II component
Fig. 1 Local Buckling of ITWD in a compressively loaded laminate

[9],
(GIJ) , however, is a monotonically increasing function of the

applied compressive load. This phenomenon is attribute d to

geometric non-linearity and the reduction in axial stiffness

exhibited by the buckled sublaminate in particular.

Trends based upon existing models and fracture criteria,

however, appear contradictory and are in all probability only

applicable for specific combinations of material systems and

delamination geometries. Whitcomb [13] clearly highlights the

need for an experimentally verified mixed-mode failure criteria

by presenting, in Fig. 2, large differences in predicted loads

for the onset of delamination growth for a variety of typical

growth criteria employed in the analysis of ITWD specimens. In

genera l terms, short deeply imbedded delaminations or

delaminations in materials exhibiting low Mode I fractur e

toughness should be predicted accurately by Gj = Gjc. For this

combination of ITWD geometry and GJC, the Mode II component GJJ

is negligible and all three failure criteria converge for short

delaminations, see Fig. 2. Conversely, long near surface

delaminations or materials exhibiting large GJC values exhibit

reduced axial stiffness resulting in a dominately Mode II state

of deformation since Gj tends to zero. Consequently for this

bound on ITWD geometry, the appropriate failure criteria would be

GH

 = GIIC- *n

 this regime , only the mixed-mode failur e

criterion attempts to include the dominate Mode II contribution.

Therefore, the critical loads for delamination onset diverge

significantly as shown in Fig. 2 for the three failure criteria

considered. For intermediate combinations of ITWD geometries and
PT. kN

100

80

60

40

20 BUCKLING CURVE

10 20 30 40 50

DELAMINATION LENGTH, mm

Fig. 2 Critical load for delamination growth using three

growth criteria [13].
fracture toughnesses falling within the two limiting bounds

»

mentioned above, the Mode I and Mode II components of strain

energy release rate may be equally important for predicting

delamination growth. In this situation, only an appropriate

mixed-mode failur e criterion will incorporate the actual

mechanisms of delamination growth and include both bounds

discussed above.

In the present study, a comprehensive investigation of

instability related delamination growth is underway through the

following research objectives:

• Experimenta l investigation of instability-related

delamination growth for two graphite fiber composites

exhibitin g significantl y differen t fractur e

toughnesses. Various delamination lengths and depths

are considered to provide a wide range of mixed-mode

response.

• Correlate experimental data (pre and postbuckling

strain s an d deformations) wit h analyti c an d

geometrically non-linear finite element results.

• Establish a mixed-mode interlaminar fracture criteria

by direct correlation with experimental data for the

onset of delamination growth in the ITWD test specimen.

The validity of any mixed-mode failure criterion, however,

is strongly dependent upon the accuracy of independent critical

strain energy release rate measurements. Fracture tests employed

in the present study consist of the Double Cantilever Beam (DCS),

Cracked Lap Shear (CLS) and the relatively new End Notched
Flexural (ENF) test specimens. The DCB specimen is a viable

pure Mode I test for measuring GJC. Stable crack growth is

achievable enabling the compliance method to be employed in the

straightforward data reduction scheme summarized in Appendix 1 .

The CLS fracture specimen is a mixed-mode test as quantified by

finite element analysis in conjunction with crack closure

techniques [14,15], The approach employed in a previous study

[15] to estimate GJJC f°r a material system of interest is

possible only by assuming a mixed-mode failure criterion. GJJC

is then back calculated employing finite element results for mode

separation. Obviously, this is not the ideal procedure for

deriving an appropriate mixed mode failure criterion. The CLS

fracture specimen, however, provides stable crack growth

resulting in the straightforward data reduction scheme for

reliable measurement of the total critical strain energy release

rate, GQ. Consequently, the CLS specimen, in addition to the

ITWD specimen, is included in the present study to assess the

validity of various failure criteria based upon independent

measurements of GJC and GUQ.

Recently, Russell and Street [16], introduced the End

Notched Flexural fracture specimen as a viable pure Mode II

test. The test specimen is essentially a three point flexure

specimen with an ITWD placed at the laminate mid-surface where

interlaminar shear stresses are greatest. The delamination is

also placed at one end to accommodate the sliding deformation

resulting from the bending of the delaminated region. The

analysis of the ENF fracture specimen reported to date has been
limited to simple isotropic beam theory for deriving expressions

for compliance and strain energy release rate. Since an

independent measurement of Gjig is required to evaluate mixed

mode failure criteria for the ITWD specimen, additional analysis

of the ENF fracture specimen has been performed. In Chapter 3, a

more accurate beam theory formulation including interlaminar

shear deformation is summarized. In addition, a closed form

expression for GJJ to quantify frictional effects opposing

sliding deformation along the crack interface is derived. A nondimensional parameter relating geometry and the coefficient of

sliding friction to the reduction in strain energy release rate

is identified which enables frictional effects to be minimized

through the judicious choice of test specimen geometry.

Furthermore, linear elastic two-dimensional finite element

analysis of the ENF test specimen is performed to assess the

accuracy of beam theory expressions for GJJ. The contact problem

is included in the finite element model and frictional effects

are evaluated. Strain energy release rates are evaluated

numerically using the virtual crack closure technique which

enables mode separation. Gj is found to be identically zero.

The compliance method for calculating the total strain energy

release rate is also utilized and yields identical results with

the crack closure approach. Consequently, both numerical

techniques allow GU to be evaluated straightforwardly. The ENF

fracture specimen is thus shown to be a pure Mode II test within

the constraints of small deflection theory. Finite element

results show that data reduction schemes based upon linear beam
theory underestimate GJJ significantly for typical unidirectional

graphite fiber composite test specimen geometries. Consequently,

data reduction for the ENF fracture specimen will be based on a

combination of finite element and beam theory results.
2. EXPERIMENTAL

An outline of the experimental program is presented in

Table 1. The program includes processing of thermoset composites

[ Graphite/Epox y (CYCO M 982) ] and thermoplastic composites

[Graphite/PEEK (APC-2) ] in order to obtain unidirectiona l

laminates. The basic materials characterization aims to provide

the lamina elastic and failure properties and the fractur e

characterization will determine the interlaminar fracture

toughness under pure Mode I or Mode II loading and under mixedmode loading. Through-width delamination testing will be

performed in order to investigate the applicability of the

interlamina r fractur e data for the instability related

delamination growth observed for this specimen.

2.1 Materials Processing

The thermoset material, Graphite/CYCOM 982, was processed in

an autoclave according to the prepreg manufacturer's recommended

cure cycle. The processing of the thermoplastic material,

Graphite/PEEK (APC-2) required the development of new processing

techniques due to the high temperatures and pressures needed for

this material. In Figs. 3, 4 and 5, details for the compression

molding of APC-2 panels at the Center for Composite Materials are

summarized. The processing closely follows ICI recommended

procedures except that a single press is employed for both the

heating and cooling phases shown in Fig. 4. Post consolidation

cooling should be rapid and ICI achieves acceptable cooling rates

by transferring the APC-2 panels to a second cool press at about

190°C. The Wabash Press employed in the current processing cools
Table 1 Outline of the Experimental Program

• Materials: Graphite/PEEK: APC-2

Graphite/Epoxy: CYCOM 982

Unidirectional lay-ups

• Basic Materials Characterization

Tension, Compression, Flexure, Thermal

• Delamination Fracture Characterization

DCB - Mode I

ENF - Mode II

CLS - Mode I & II (Mixed Mode)

• Through-Width Delamination Testing

Shadow Moire

Dial Gages

Strain Gages

10
ARC 2 PROCESSING

Wabash Press

Max Temp. = 427 °C (800°F)

Max. Load = 150 ton

Cooling: Air/Water ,

JL

Press Platen

i Glazing Plate

Aluminum Foil

W APC

I Picture Frame L

APC 2 Panel: L x W x t I

L = 30 5 cm (1 2 in)

W = 20.3 cm (8 in.)

t = laminate

thickness ^

Glazing Plate (Stainless)

t,= 4 8 mm (0.1 675 in.)

Aluminum Foil

(Release Agent Required)

t2= O.lmm (0.004 in.)

Picture Frame

0.0254 mm (0 I0in.)< t - t3 < 038 mm (0.015 in.)

1

Fig. 3 APC-2 Picture Frame Molding

11
ARC 2 PROCESSING

Press Temperature

Cooling Rate

« 40°C/min

N = Number of plies

-<T < 3 0 mi n

u

382 ~

l_

200 |

a

T+5 T+10 T+15 Time

(min)

Cooling Pressure

Consolidation Pressure

Contact Pressure

T T+5 T-HO T+15 Time

(min)

Fig. 4 APC-2 Heating/Cooling Cycle

12
COOLING RATES FOR APC 2 PROCESSING

i.o

I

0)

O

0_

0.8 -

0.6 -

0.4 -

0.2 -

0.0

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1C I Recommended Cooling

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Wabash Press Cooling

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•Water Cooling-

• Thermocouple Imbedded at

Midplane of [0]lfi Laminate

i i *° i

4 6 8

Time (minutes)

10 12

Fig. 5 Experimental Cooling Rates for APC-2 [0]-]g Panels

13
the press platens with an air/water mixture which provides an

adequate cooling rate of approximately 40°C/min over the critical

temperature range of 380°C to 200°C) see Fig. 5.

2.2 Basic Materials Characterization

The test matrix for the basic materials characterization is

summarized in Table 2. Experimental results based upon five

replicates/test are presented in Tables 3, 4 and 5 for APC-2 and

CYCOM 982. Stress-strain curves are given in Appendix 6. In

Tables 3-5, material properties taken from the ICI Provisional

Data Sheet (APC PD2) are also included for direct comparison with

results that correspond to the process conditions mentioned

above. In all cases, excellent agreement is obtained and

confidence is generated in the processing condition employed in

the present study.

2.3 Determination of Interlaminar Fracture Toughness

Fracture characterization for the two graphit e fibe r

composite materials will consist of the Double Cantilever Beam

(DCB) [4,14 ] and the End Notched Flexure (ENF) [16] specimens for

measuring Gjc and GJJC respectively. The Cracked Lap Shear (CLS)

specimen will also be included to investigate mixed-mode

fracture. The data reduction procedures are based on compliance

measurements and are presented in Appendix 1. As shown

schematically in Fig. 6, the compliance measurements will be

made directly with an LVDT to minimize the potential source of

error induced by machine and load cell compliance.

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CIS

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Fig. 6 Interlaminar Fracture Tests,

19
Unstable crack growth is a common occurrence in ENF fracture

testing [15, 16]. Consequently, the data reduction scheme based

upon measuring dC/da experimentally cannot be utilized and

approximate beam theory expressions or a finite element based

crack closure calculation has to be used. The stability analysis

of crack growth for the ENF specimen presented in Appendix 2,

however, indicates that stable crack growth may be attainable

under fixed displacement conditions for a/L — 0.7 where a is the

crack length and L is the half span. This will be investigated

experimentally in the present project. Interestingly, most

results in the literature [15, 17 ] have been for a/L ty, 0.5 and

unstable crack growth has been reported.

It is anticipated that the APC-2 thermoplastic will exhibit

an order of magnitude greater fracture toughness than the typical

graphite thermosets Els 1 • Consequently, design and sizing of the

various fracture tests to avoid tensile or flexure failures and

to guarantee crack growth is an important consideration in the

present study. In Table 6, the design considerations for sizing

the DCS, ENF and CLS specimens are summarized. Details are

presented in Appendix 3.

In Fig. 7, the number of plies required to keep the DCB

specimen in the linear regime is presented as a function of G^CResults indicate that the standard 24 ply unidirectional laminate

should be thick enough to avoid large deflection response even

for the APC-2 material. However, processing constraints require

26 ply APC-2 specimens.

20
Table 6 Design considerations for Sizing the Fracture Specimens

Specimen Constraints

DCS Maintain linear behavior

ENF Avoid flexural failure, maintain linear behavior

CLS Avoid strap tensile failure

21
SIZING OF THE DCB SPECIMEN

(MAINTAIN LINEAR RESPONSE)

0

GIC, in.lb./in?

6 8 10

o>

CL a = 152.4 mm (6 in.)

= l38GPa(20xl06psi)

GIC, kJ/m'

Fig. 7 Sizing the DCB Specimen to maintain linear behavior

22
In Fig. 8, the number of plies for the CLS specimen required to

avoid tensile strap failure is presented. A six ply laminate

will be employed for both materials. In Fig. 9, the number of

plies for the ENF specimen required to maintain linear response

and to avoid flexural failure is presented as a function of

GIIc- In ttle range °f GIIc values expected for the CYCOM 982

thermoset material ( 2kJ/m2), the small deflection behavior

dictates the number of plies required for the ENF specimen. In

the present study, twenty-four plies will be employed for the

thermoset material which is consistent with the geometry used for

data published earlier [16,17]. APC-2, on the other hand, may

have high GJJC values and flexural failure may occur prior to

crack propagation. Consequently, ENF specimens fabricated from

APC-2 will be 40 plies as well as the .standard 26 ply

laminate. A summary of the fracture test based upon the above

considerations is presented in Table 7.

2.4 Imbedded Through-Wdith Delamination Specimen Testing

The experimental evaluation of delamination growth for the

ITWD specimen will initially be limited to imbedded single

delaminations and unidirectional lay-ups. Unidirectional

laminates are chosen so that direct correlation can be

established with the unidirectional DCB, ENF and CLS test

results. Also, the Mode III component of the strain energy

release rate will be absent when the implanted defect is located

between the plies in a unidirectional laminate. This results in

considerable simplication of the problem. Strain gages mounted

at the center of the surface of the delamination are being used

to monitor the onset of buckling and to allow for comparison

23
SIZING OF THE CLS SPECIMEN

(AVOID TENSILE STRAP FAILURE)

20

10

15

0>

I0

CLS

Gc, in.

20

2

30 40

T I

E = l38GPa(20xl06psi)

x= 2100 MPa (0.3 x!06psi)

8

Gc, kJ/m'

Fig. 8 Sizing the CLS Specimen to avoid strap failure

50

24
GIC, in. lb,/in.

20 30

Small Deflections

L = 50.8m 38.lmm

Linear Material Behavior

or Flexural Failure

8

GIC, kJ/nV

Fig. 9 Sizing the ENF Specimen to maintain linear elastic

response E-] =13 8 GPa, a/L = 0.5 and y\ = 0.2

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betweeen analysis and experiment. Dial gages are used to detect

the magnitude of the out-of-plane displacements at the center of

the delaminated region. The loads and the out-of-plane

displacements will be compared to finite element and strength of

materials predictions. It must be confirmed that there is a

close correlation between predicted and experimentally determined

loads and out-of-plane displacements because these parameters are

vitally important to the modelling of instablity related

delamination growth.

In order to determine the shape of the post-buckled region,

the shadow moire technique, Fig. 10, will be employed. These

results will be used to verify the expected one-dimensional

nature of the ITWD problem.

The mechanical properties data along with the Mode I and

Mode II fracture toughnesses have been established first in order

to design the ITWD specimen. The design of the ITWD specimen

with near surface delaminations will be guided by the

superposition analysis of Whitcomb [13] summarized in Figures 11

and 12. Analysis developed for this program along with the

analysis by Ashizawa [4] and Chai [19] is used to study ITWD

specimens with deeply imbedded delaminations.

27
SHADOW MOIRE OPTICAL SET UP FOR THE

THROUGH-WIDTH DELAMINATION SPECIMEN

Master Grid

lines/in.

Collimating

Lens

Light Source

(with a laser beam expander)

r'ig. 1 0 Shadow iMoire optical set up for the through-width

delamination specimen.

28
3000

2500

2000

0

2(SA+SD)

GT 1500 1 §

1000

500

i •

-1012345 6

Fig. 11 Normalized Plot of Gj vs. Applied Load [13]

29
10X10

8X10*

6X104

4X104

2X104

Fig. 12 Normalized Plot of GH vs. Applied Load [13]

30
3. ANALYSIS

3.1. Finite Element Analysis of the ENF Specimen

Since unstable crack growth is a common occurrence in ENF

fracture testing, the data reduction based upon experimentally

measuring dC/da (Appendix 1) may not be utilized. To assess the

accuracy of the linear beam theory expression currently used to

determine GU (see Appendix 1), finite element analysis based on

crack closure techniques have been performed.

Linear elastic two dimensional finite element stress

analysis of the ENF test specimen was performed by using a fournode plane stress element in the finite element code, ADINA

[20]. The finite element model with an exploded view of the

crack tip mesh is presented in Figures 13 to 15. The frictionless contact problem was incorporated into the finite element

model by connecting duplicate nodes (actually separated by 2.5 x

10~3 mm) across the crack interface with non-linear truss

elements. The constitutive model employed for the truss elements

exhibits zero tensile stiffness and infinite stiffness in

compression as shown in Fig. 16.

In all geometries investigated to date, the non-linear truss

elements tension release along the entire crack interface except

in the vicinity of the support in the three-point bend fixture.

Consequently, employing constraint equations for the vertical

component of deformation to simulate frictionless contact is not

correct, since in this modelling technique, implicit is the

assumption that the contact area extends along the entire crack

length.

31
t

o

4_>

<u

tn c 2 1

4>4LU

.22O•O)

CO

CO

o2

<D £ £ w oj OJ

«>

at

CO

"• en

_' CD

CO "O

I § o b 3 § tn — «_, a) <_. o o> vo re Q> fe ^* =

 M

 « c * 13

^ < «- 2 - £

ii Stsli

5 Q s r i 0

Iro

OcJ 010)C4J0) •HMZCOa01O•He0wrH) 4JC•H•H

_l

Cn

•H

32
Crack

Interface

..J

Pig. 14 Finite Element Model in the Vicinity of the Crack Tip

33
i

Q.H

\

i

oh

i

~r

1

HI

^X

- \ —

1L

f ^

j

x^

^^ ^

1

^ Crack Tip

(y-displacement fixed)

^^^ Non-linear Truss

Elements Along

Crack Interface

<- Aa(l.27xlO"2mm)

Fig. 15 Deformed shape of Finite Element Model in the vicinity

of the crack tip

34
Compression

a

Tension

Fig. 16 Constitutive Model for Nonlinear Truss Elements

35
Material properties employed in the Finite Element modelling

are given in Table 8. In Figure 17, the contact force

distribution as a function of E-|/G-| 3 is presented which shows

that the contact area is less than 4h (two laminate thicknesses)

in length and centered about the point of load introduction in

the fixture. Summation of the contact forces within the contact

area verifies that each beam carries an equal load.

3.1.1. Compliance of an orthotropic beam

To assess the accuracy of the finite element model shown in

Figures 13 to 15, the compliance for an orthotropic beam with no

delamination, loaded in three-point bending is correlated with

beam theory expressions derived in Appendix 4. The crack is

eliminated from the model by replacing truss element with

appropriate two-dimensional elements. The following beam theory

expressions are obtained by setting the crack length equal to

zero in Equations (10) and (14) of Appendix 4.

\ 9

(1) C

SH

 (a=0) =

L

3

4E1wh3

, , / EiY hN-

 2

1 1 1 • 2 I „ 1' V " ' 1

 13A y

 -

7

CBT ( <i 0)

 L

a — \J I — ^ (2)

Table 9 shows that finite element results agree within 3.5

percent of the simple beam theory expression in Equation (2).

The discrepancy, however, is reduced to 0.1 percent by the

analytical solution with shear deformation included (Equation 1)

as shown in Table 9.

36
Table 8 Material Properties investigated in the Finite Element

Modeling. (V12 » V23 =

 V13 = °-3>

Material 1 Material 2 Material 3

E-| GPa 137.8 126.1 115.1

£2 GPa 10.0 9.7 9.7

E3 GPa 10.0 9.7 9.7

33.3

Ei/Gn

18.3

26.9

122.0

183.0

12.8

25.7

51.4

Table 9 Compliance of an Orthotropic Beam under Three Point

Bending. Material 1, Ei/G-|3 = 33. L = 50.8 mm,

h = 1.52 mm/ w = 25.4 mm.

CBT CSH CBT

1.035 0.999 1.035

37
0.14

Load Introduction

(P/2)

-1.2 0.8 -0.4 0.0 0.4 0.8

Fig. 17 Contact Normal Force distribution (Material 2)

38
3.1.2. Compliance of the ENF Specimen

In Appendix 4, the contribution of shear deformation to the

ENF complianc e has been derived yielding the followin g

expression:

,T3 . ~ 3 2(1. 2L + 0.9a)h2E1

ZL| + 3a

SE^ir (2L + 3a)G 1 3

The parametri c study investigates the influence of -shear

deformation (£1/613) with the material properties presented in

Table 8 as well as the influence of span, (L), crack length (a)

and laminate thickness (2h) on specimen compliance.

The results, displayed in Tables 10-13, show that in

general, finite elements results are more compliant than the

simple beam theory expression for CBT«

 CBT appears to converge

to finite element results for small E-| /G-| 3 ratios.

Equation (2) for ENF compliance with shear deformation

included provides excellent agreement (less than 4 percent

difference) with finite element results in all cases investigated

in the parametric study. Experimental results reported in

[15] have been for 24 ply unidirectional graphite epoxy laminates

(h = 1.52 - 1.70 mm) with a = 19.3 mm, L = 38.1 or 50.8 mm and

E

1 /G1 3 = 26. For this particular configuration, finite element

results are within two and seven percent of CSH

 anc* CBT

respectively. Reasonable agreement between experimenta l

compliance and beam theory has been observed [16], see Fig. 18,

which generates confidence in the finite element model as an

accurate description of the ENF fracture specimen.

39
Table 10 Compliance of the ENF Specimen

Comparison of Finite Element Results with Beam Theory

Results, Material 3, L = 38.1 mm, a = 12.7 mm.

EJL

G1 3 C

BT

C

SH

h = 1 .70 mm 12.8

25.7

51.4

1 .037

1.071

1.134

1 .001

0.998

0.990

h = 2.62 mm

25.7

51.4

1 .084

1.158

1.301

0.998

0.988

0.968

40
Table 11 Compliance of the ENF Specimen.

Comparison of Finite Element Results with Beam

Theory Results. L = 38.1 mm, a = 19.3 mm.

El

G13 CBT

.

CSH

Material 2

h = 1.52 mm

h = 1. 70 mm

18.3

26.9

122.0

183.0

26.9

1 .049

1 .067

1 .246

1 .353

1.081

1.008

1 .007

0.981

0.963

1.007

Material 3

h = 1.70 mm

12.8

25.7

51.4

1.043

1 .078

1 .140

1 .008

1 .006

0.999

Material 3

h = 2.62 mm

12.8

25.7

51.4

1 .092

1.165

1.301

1 .008

0.997

0.974

41
Table 12 Compliance of the ENF Specimen.

Comparison of Finite Element Results with Beam

Theory Results. L = 38.1 mm, a = 25.4 mm

Si

G13 CBT

CSH

Material 2

h = 1.52 mm

18.3

26.9

122.0

183.0

1.052

1 .070

1.235

1 .330

1 .015

1 .016

0.994

0.974

Material 3

h = 1.70 mm

12.8

25.7

51.4

1.047

1.081

1 .140

1.015

1 .016

1 .011

Material 3

h = 2.62 mm

12.8

25.7

51 .4

1 .094

1 .162

1 .285

1 .018

1.010

0.987

42
Table 13 Compliance of the ENF Specimen.

Comparison of Finite Element Results with Beam

Theory Results. L = 50.8 mm, a = 25.4 mm

E_L

C

BT

CSH

Material 2

h = 1 .52 mm

18.3

26.9

122.0

183.0

1.031

1 .042

1.149

1.212

1.008

1 .008

0.997

0.987

Material 3

h = 1.70 mm

12.8

25.7

51.4

1.028

1.049

1.087

1.007

1.009

1.006

Material 3

h = 2.62 mm

12.8

25.7

51.4

1.059

1.103

1.184

1.011

1.008

0.996

43
S- -u.CUZi C4JoP

>- (0ocl c(0cu4J •Hocu

 c

t>3 01

•H e

rH -H

o, u

•H

0/0 '
3.1.3. Strain Energy Release Rate of the ENF Specimen

One of the objectives with the finite element analysis of

the ENF specimen was to evaluate the strain energy release rate.

Two approaches, the crack closure and compliance techniques, have

been investigated numerically. Fig. 19 shows the finite element

mesh close to the crack tip. With the crack closure technique

[21 ] the components Gj and GU of the strain energy release rate

may be determined,

G

I - la+0 2*1 WV <4>

where Fc and Tc are the normal and tangential forces required to

hold nodes c and d together. Analogously, the quantities (VC-V&)

and (Uc-U(j) are the normal and tangential deformations

corresponding to Mode I and Mode II crack propagation. Two

finite element computations are required for each strain energy

release rate calculation.

In all cases investigated to date, the quantity (VC-V<3) in

Equation (4) is identically zero for the finite element mesh

presented in Figure 15. Consequently, the ENF fracture specimen

is a pure Mode II test within the constraints of small deflection

theory.

45
hAa-

-Ar~

Fig. 19 Finite Element Mesh Near Crack Tip.

46
In finite element representation, the compliance method

yields the following expression for the total strain energy

release rate,

lim P. (Cya+Aa) - Ci(a))

G

 ~ Aa+0 2^7 Si

 (6)

where C^ = VI/PI. Vj^ is the vertical component of deformation

resulting from the applied load, P^, at node i. This technique

also requires two finite element computations.

The compliance technique (Equation 6) yields identical

results with the crack closure technique (Equations 4 and 5)

confirming that Gj = 0 and that the ENF specimen is a viable Mode

II Specimen.

In Fig. 20, the stress state in the vicinity of the crack

tip is presented. Stresses for each element are extrapolated

from the Gauss points to nodal points lying along the crack

interface. An individual node has, in general, stress output

from four adjacent elements. Minimal stress discontinuities

between element output indicated that the model has sufficient

mesh refinement. The results presented in Fig. 20 correspond

to the average nodal stress components.

The flexure and interlaminar normal stresses are identically

zero (Kj = 0) and the interlaminar shear stress exhibits the

expected singularity. Consequently, the ENF fracture specimen is

a pure Mode II test in agreement with the strain energy release

rate calculations.

47
Geometry

L=50.8 mm (2.0 inches)

= 25.4 mm (1.0 inches)

2h= 3.05 mm (0.12 inches)

0-,/a,

BT

-1.25 0.25

Fig. 20 Stress Distribution Ahead of the Crack Tip for the ENF

Specimen

48
In Appendix 4, the influence of shear deformation on the

strain energy release rate, GJJ, for the ENF specimen has been

derived from beam theory yielding the following expressions:

2 ? CU Oa P "7

GII = 2 3 [l + 0-2(E1/G13)(h/a)^] (7)

16E..W h

= 9a2P

2

/(16ElW

2

h

3

) (8)

SH

where G^ is the strain energy release rate including shear

BT

deformation and G^ is the same quantity where shear deformation

is neglected.

In Tables 14 to 17, finite element strain energy release

rate calculations are compared with beam theory results. In

general, the finite element results diverge significantly from

orn ^H

J-J- and G^ for any combination of specimen geometry and

material properties which enhances shear deformation. Inspection

of the results presented in Tables 14 to 17 indicates that errors

approaching 200 percent are typical for these extreme cases.

Although the inclusion of shear deformation in the derivation of

CU

JJ reduces the discrepancy between beam theory and finite

element results, 20 to 40 percent errors are still realized for

the typical graphite fiber composite (E-|/G-| 3 «* 26 ).

The beam theory solution presented in Appendix 4 which

provides reasonable estimates of global specimen compliance are

49
Table 14 Strain Energy Release Rate for the ENF Specimen.

Comparison of Finite Element Results with Beam

Theory Results. Material 3, L = 38.1 mm, a = 12.7 mm

_ __ _

13

FE

ll

FE

h = 1 .70 mm 12.8

25.7

51.4

1 .068

1.263

1.604

1.021

1.156

1.354

2.62 mm 12.8

25.7

51.4

1 .324

1.576

2.025

1.194

1.294

1.410

50
Table 15 Strain Energy Release Rate for the ENF Specimen,

Comparison of Finite Element Results with Beam

Theory Results. L = 38.1 mm, a = 19.3 mm

rFE _FE

E, fll

 GII

i om CU

7» r°L fjn G13

 GII GII

Material 2

h = 1 . 52 mm

18.3

26.9

122.0

183.0

1 .232

1 .342

2.311

2.835

1 .205

1 .298

2.006

2.308

h = 1.70 mm 26.9 1.402 1.346

Material 3 12.8 1.198 1.175

h = 1.70 mm 25.7 1.375 1.322

51.4 1.682 1.558

Material 3 12.8 1.342 1.282

h = 2.62 mm 25.7 1.554 1.420

51.4 1.926 1.620

51
Table 16 Strain Energy Release Rate for the ENF Specimen.

Comparison of Finite Element Results with Beam

Theory Results. L = 38.1 mm, a = 25.4 mm

'13

,FE

,BT

'II

,FE

,SH

Material

h = 1.52

Material

h = 1 .70

Material

h = 2.62

2

nun

3

nun

3

mm

18.

26.

122.

183.

12.

25.

51.

12.

25.

51 .

3

9

0

0

8

7

4

8

7

4

1

1

2

2

1

1

1

1

1

1

.342

.448

.368

.860

.290

.455

.750

.366

.559

.890

1.

1 .

2.

2.

1 .

1 .

1 .

1 .

1 .

1 .

324

420

177

527

275

422

673

330

478

704

52
Table 17 Strain Energy Release Rate for the ENF Specimen.

Comparison of Finite Element Results with Beam

Theory Results. L = 50.8 mm, a = 25.4 mm

r>FE ,,FE

SH

Material

h = 1 .52

Material

h = 1 .70

Material

h = 2.62

2

mm

3

mm

3

mm

18.

26.

122.

183.

12.

25.

51.

12.

25.

51 .

3

9

0

0

8

7

4

8

7

4

1 .

1.

2.

2.

1 .

1.

1 .

1 .

1 .

1.

138

237

122

607

1 13

277

558

269

460

790

1

1

1

2

1

1

1

1

1

1

.123

.214

.950

.303

.100

.248

.489

.255

.427

.614

53
simply first order approximations to an elasticity solution (not

presently available) for the calculation of strain energy release

rates. The derivation of the beam theory expressions in Appendix

4 makes no attempt to include the intense shear deformation

occuring at the crack tip. Consequently, it should not be

surprising that beam theory provides conservative estimates of

the strain energy release rate. This will be further discussed

in Section 3.1.7. .

An experimental observation reported by Murri and O'Brien

[ 17] which appears to support the finite element results

presented herein, is an absolute dependence of Pcr, the load at

delamination onset, on span (L). For a given crack length,

finite element results predict an absolute span dependence which

is not predicted by beam theory. For example (Material 3, E-J /G-| 3

«25.7, h = 1 .70 mm),

rFE

II

-±i = 1.28 (L = 50.8 mm, a = 25. 4. mm) (9)

r°i

G

II

and

rFE

II

-|± = 1.46 (L = 38.1 mm, a = 25.4 mm) (10)

Since GUC ^s assumed to be a material property, the critical

load at the onset of crack propagation would be approximately

seven percent greater for the longer span since,

Pcr(L = 50.8 mm)

Pcr(L = 38.1 mm)

1.46

1.28

1/2

= 1.07 (11)

54
Murri and O'Brien [17] have reported a 13 percent increase of Pcr

for the two spans investigated although their results are for a

different crack length (a«19 mm) and material system (T300/5208

graphite/epoxy). In any event, finite element results are in

qualitative agreement with experimental observations that cannot

be predicted by beam theory.

3.1.4. Sensitivity of ENF Strain Energy Release Rate on Crack

Offset

In the fabrication of the ENF fracture specimen, implanted

defects of Teflon, Kapton or Aluminum are placed at the laminate

midsurface to provide a starter crack for subsequent testing.

As a consequence of processing, however, the implanted defect is

not likely to remain at the laminate midsurface. In Table 18,

the sensitivity of the ENF strain energy release rate on the

crack offset from the specimen midplane is presented for a

typical 24 ply unidirectional graphite/epoxy laminate. The

maximum realistic offset investigated in the present study is

assumed to be one nominal ply thickness where the delamination is

displaced toward both the tensile and compressive faces of the

flexural specimen. Finite element results indicate that the ENF

fracture specimen remains a pure Mode II test (Gj = 0). The

J?T?

strain energy release rate, G^ , decreases by less than three

percent of the midplane value for the offset and geometry

investigated. Consequently, the ENF fracture specimen appears to

be relatively insensitive to delamination offset and remains a

pure Mode II test.

55
Table 18 Sensitivity of ENF Strain Energy Release Rate on Crack

Offset From Laminate Midplane, Material 3, L = 50.8 mm,

a = 25.4 mm and h = 1.70 mm

z/h*

+0.075

-0.075

C

FE(z)

C

FE(0)

0.997

0.997

G

FE(z)

G

FE(0)

0.976

0.976

*z/h = ±0.075 corresponds to the delamination displaced one ply

thickness in the compressive ( + ) or tensile (-)

direction in the ENF specimen.

56
3.1.5. Finite Element/Beam Theory-based data reduction schemes

for the ENF Specimen

In an attempt to generalize finite elements results, nondimensional expressions for the strain energy release rate are

identified to accommodate slight variations in geometry or lamina

properties that will inevitably arise in an experimental program

to characterize GJJC- Finite element results are assumed to be

of the non-dimensional form derived in Appendix 4,

where

II

,BT

'II

,BT

a+3 (12)

9aV

16E1w

2

h

2

(13)

a and $ are parameters determined by a least squares fit to the

numerical results presented in Tables 15 to 17 for spans of 38.1

and 50.8 mm (a/L = 0.5) to more accurately reflect the influence

of shear deformation. In Fig. 21 , GT^/G^ is indeed found to be

a linear function of (E-j /G-j 3) (h/a) 2 for a 24 ply laminate.

Consequently, for a/L = 0.5,

c!!5/G?T = fl.045 + 1.657 (E, /G. ) (h/a) H L = 38.1 mm (14) ,L ^ ^ ^ L J»^ O j

and _

T = [o.967 -f- 2.644 (Ej/G^) (h/a)2] L = 50.8 mm (15)

Equations (14) and (15) accurately predict strain energy

release rates for a broad range of the flexural modulus (E-) ) and

57
Ei/G-)3 ratios as shown in Figure 21. These equations, however,

are restricted to slight perturbation in a/L and laminat e

thickness. Subject to these constraints, the utility of

Equations (14 ) and (15) cannot be overstated since the

experimentalist does not need to perform a finite element

analysis of each ENF specimen exhibiting slight variations in

geometry to calculate GUQ.

In most instances, specimen compliance will be measured

during the fracture test directly by the crosshead displacement

or appropriat e instrumentatio n such as the LVDT shown

schematically in Figure 6. In this situation, it is convenient

to express E-] in terms of the specimen compliance, C, instead of

the absolute flexural modulus which requires an independent

test. Assuming C = Cgjj, E^ can be expressed as a function of C

by using Equation (3) for CSH:

- - -

t(2LJ + 3aJ) + 2(1.2L + 0 .9a)

The E-| /G-) 3 value needed in the right hand side of Equation (16)

may be obtained from literature data for the actual material

system. As a first order approximation E-j and G-j 3 may be set

equal to the tensile modulus and the in-plane shear modulus (G-|2)

respectively.

Equation (16) may then be substituted into Equation (Q) for

yielding the desired expression:

-BT _ 9a2P

2

C

VJ

11

 2w[(2L3 + 3a3) + 2(1.2L + 0.9a)h2 (E/G ) } (17)

58
2.50

2.25 -

2.00 -

1.75 -

1.50 -

1.25 -

0.15 0.30 0.45 0.60 0.75 0.90

'is

Fig. 21 Influence of Shear Deformation on Strain Energy Release

Rate (a/L = 0.5).

59
Note that by neglecting the contribution of shear deformation,

Equation (17) simplifies to the expressions reported in [16],

BT _ 9a2P

2C

II 3 3~~

 ( ' 2w(2LJ + 3aJ)

Consequently, an improved data reduction scheme which retains the

simplicity of beam theory and includes the accuracy of the finite

element strain energy release rate calculations is presented.

PP RT

The procedure utilizes Equation (14) or (15) for G^/G^ in

RT

conjunction with Equation (17) where G,. is expressed in terms

of the experimental compliance of the ENF test specimen.

3.1.6. Influence of friction on the Compliance and Strain

Energy Release Rate of the ENF Specimen.

In general, an incremental formulation must be employed to

investigate contact problems with friction [22, 23]. Linear

elastic behavior and quasi-static application of the load are

basic assumptions. The solution is based upon the minimization

of the total incremental potential energy satisfying displacement

constraints and the constitutive relations governing friction in

the contact region where sticking, slipping and tension release

are possible between two bodies in contact [23].

Non-conservative frictional forces are treated as known piecewise

conservative tangential nodal forces calculated from the previous

iteration. In a general problem, the size of the contact region

cannot be predicted a priori and in all likelihood will vary with

the applied load. Consequently, most contact algorithms consist

of an iterative procedure within each load increment to find the

contact area.

60
In the present investigation of the ENF fracture specimen,

Coulomb's law of friction is utilized. The coefficient of static

friction corresponds to sticking of the crack surfaces so that no

relative sliding in the contact area is permissable. Sticking

effects, due to static friction however, are not observed during

loading and unloading of the test specimen. Consequently, static

friction is neglected in the present model. The coefficient of

sliding friction, y , however, would reduce the specimen

compliance upon loading and may be difficult to detect in an

experiment.

Frictional forces, T^, opposing the sliding deformation, are

evaluated from the nodal normal forces, P^, in the contact area

from the frictionless solution, see Fig. 22,

Ti = UPi (19)

Frictional forces are then applied as horizontal nodal forces as

shown schematically in Figure 22. Inspection of finite element

results show that the normal forces and contact area remain

unchanged in the presence of the tangential loads. Consequently,

no further iterations are required and the problem is solved

within the constraints of small deflection theory.

In Table 19, the influence of sliding friction on the ENF

compliance and strain energy release rate is presented. Two

coefficients of sliding friction (y= 0.25, 0.50) are investigated

in the finite element model for a variety of crack lengths and

laminate thicknesses to evaluate the validity of the

non-dimensional parameter derived in Appendix 5 (Equation (11)).

Results presented in Table 19, non-dimensionalized by the

corresponding frictionless solution, show that CPE(U) and

61
S-u<Uinl -p(UwiHQJ 0)C4J10 •HCO

1-1

•HU

4->

•HOC2OTJ

fc, oc<NCMPu•HC•Hn •H

62
<D

en

5J x:| <d <N m

Q) (N ^r

rj 3. o o o

<l> . .

OS rr|n o o

01

0)

^

•H

c

u

c

 'S.

4J -*

V3 W M

fa M

tJ O

C 1

03 -— *

o

U W~M

C fa M

(0 U

00 M

<— t n

o o o

EH M

CO M O O

0

E

•H

 —

O ru . ^

in 3.

fa CM ^

Z U M

U II fa M

a

^— .

f^ ^5 (^ vO

*~~ o oo r~

td M O Cf^ Cft

fa M • • •

O rH O O

C d

O -I

c ^-

O -H

•H W -*

JfJ -J_

u -

•H ro u

M fa

fa H o

^-v

o o r- ^r

*~* O C^ ON

U O O> O>

f a .. .

U t-( O O

(0

U-l -H

O t-l

0)

0) 4-> in o

U (0 3. CM in

C 2 o • •

0) — ' O O

H (I)

4-1 4-1

C HJ

M K

g E 6

»TMi

oo ^r o

0) • . rr-i o m .

X) m IN •-)

(0 II II II

6" J (0 X3

T a\

n vo

o o o

0 O

o m *-i

o (N in

o o o

• • *

•-too

o on in

O CO VO

O CTN ^

.. .

•H O O

O vO <N

CO CT\ O^

C5 CT^ O^

.. .

t-H O O

m o

IN m

o . •

0 0

§ 1

e

00 'S

1

 fM

. . vO

o m «

m (N (N

n n u

^ (0 .C

*3

in

"

o

r

n

o

 o

o

0 0

•

tro»

CO Cf

.

^

o

o o

o ON

o &*

9 *

r-l 0

in

o >

o

c c p

Si t

<H ^ O

. • p""

co m •

n f\i tH

n n u

tj fO XC

cr>

00

o

ro

 o

l

vo

o o

.

0

O (N

o m

^3 ON

t •

<-t 0

O vO

^3 ON

O <T>

• •

t-l

m

 O

o •

o

<-i r^

. .

00 (N

n <-t

n n

J (0

63
ITT?

G

jj(y ) decrease wit h y as expected. For the geometrie s

FE

considered, Cpg( y ) and G (y)ar e reduced by no more than one and

five percent, respectively. In Fig. 23, finite element results

are correlated with the non-dimensional parameter derived in

Appendix 5,

GII( ,=O) - GII(M )

rBT 3a

G

II

Numerical results exhibit linear behavior over the entire domain

and the analytical results are shown to provide a conservative

upper bound on the effects of friction on GJJ. The magnitude of

BT

the sliding deformation, Au , employed in the derivation of the

non-dimensional parameter is also presented in Table 19. It is

observed that the finite element results show larger degree of

sliding than the beam theory results which must be due to the

intense stress field at the crack tip. Furthermore, the amount

of sliding decreases with increased coefficient of friction.

64
0.10

0.08

0.06

BT

0.04

0.02

0.00

0.00 0.02 0.04 0.06 0.08 0.10

4_

3

Fig. 23 Influence of Friction on ENF Strain Energy Release Rate

65
3.1.7. Discussion of ENF Data Reduction Scheme

It may appear contradictory that even if excellent agreement

between compliance calculated from beam theory with shear

deformations included and finite element is noted there is such a

large discrepancy between the strain energy release rate

calculated from the two methods. However, the strain energy

is determined uniqued by dC/da not by the absolute specimen

compliance, C. In an experimental program, dC/da should be

ideally approximated by

dC lim AC ,_„.

da Aa-*0 Aa

 { '

Unfortunately, Aa must be chosen sufficiently large so that Ac

can be measured accurately. The minimum Aa is limited by the

sensitivity and experimental error induced by the instrumentation

employed to measure specimen compliance. Consequently, most

experimental approaches consist of measuring compliance for a

variety of crack lengths where Aa is typically 6 to 1 3 mm.

Experimental results are then curve fitted to a function based

upon simple beam theory (Appendix 4) assumed to accurately model

the compliance-crack length response,

c =

 2Ij3 + 3fl3 (21) RBT

T 1 * '

 8ElWh

3

This experimental approach is illustrated in Figure 18 where

dC/da is determined from the average slope of compliance versus

a^, (see Appendix 1). The onset of delamination growth, however,

is governed by the pointwise variation in dC/da not the averaged

response over a large range of crack lengths. Consequently, the

validity of this approach is determined solely by the accuracy of

66
the solution to predict the pointwise variation in dC/da.

On the average, the experimental data appear to fit the

assumed form quite well over the range of a/L = 0 to 1 . In

practice, ENF fracture testing is limited to delamination lengths

in the range of 0.5 < a/L < 0.75 to minimize load introduction

effects. In this region, however, the experimental rate of

change of compliance with crack length, is significantly

different than the beam theory prediction as shown in Figure 18,

even though the absolute compliance is adequately predicted by

the beam theory expression. Admittedly, the response exhibited

by the data in Figure 18 may be simply attributed to experimental

errors in compliance measurements. Finite element results,

however, substantiate the trend observed in Figure 18 and the

beam theory data reduction schemes provide an average value which

is too conservative in the determination of the fracture

toughness.

To further emphasize this point, finite element compliance

(CFE) minus the beam theory compliance (CSH) normalized with the

simple beam theory compliance (Co) is plotted in Figs. 24 and

25. The results clearly illustrate that dCpg/da (and therefore

FE

Gj ) is significantly greater than dCsn/^a even though CFE/CSH

< 1 .04 for all cases investigated in the parametric study (see

Tables 10 to 13). A logical extension of the present work would

be to analyze larger crack lengths to further examine the

validity of the beam theory results and relate the finite element

compliance to experimental compliance over a range of crack

lengths and ENF geometries.

67
a/L

0.2 04 0.5 06

0.02

0.01

0.00

-0.01

-0.02

-0.03

-0.04

-0.05

Fig. 24 ENF Compliance as a. function of Crack Length

(Material 3, h = 2.62 mm) Co = L3/(4E-|wh3).

0.00 0.05 0.10 0.15 0.20 0.25 0.30

(a/L)3

68
(o/L)

C

FE"CSH

Co

oozol00151-

0.010 I0.005 I0.05 0.10 0.15 0.20 0.25 0.30

(a/L)3

Fig. 25 ENF Compliance as a function of Crack Length

(Material 3, h = 2.62 mm) Co = L3/( 4E-| wh3).

69
Finally, strain energy release rate calculations are further

substantiated by exhibiting good agreement with results presented

by Barrett and Foschi who evaluated Mode II stress-intensity

factors for cracked wood beams [24] . The stress intensity factors

in their analysis of the ENF geometry were determined by the finite

element method, using singular, orthotropic, isoparametric elements

which incorporated the exact displacement field in the region

surrounding the crack tip. Strain energy release rates were

calculated from the stress intensity by the following relationship:

1/2

The correlation of results are presented in Table 20 for ENF

geometries exhibiting similar span/thickness ratios.

70
Table 20 Correlation of Strain Energy Release Rates

with the Results of Barrett and Foshi (Gjj

(h=2.62 mm, L=38.1 mm, Material 3)

a/L E /G,., rFE/rBT rSI/rBT

a/Ll bl/C313 G TT/G

TT

 G TT/ G

TT

0

0

0

0

0

0

0

0

0

.33

.33

.33

.50

.50

.50

.67

.67

.67

12

25

51

12

25

51

12

25

51

.8

.7

.4

.8

.7

.7

.8

.7

.4

1

1

2

1

1

1

1

1

1

.32

.58

.03

.34

.55

.93

.37

.56

.87

1.

1.

2.

1.

1.

2.

1.

1.

2.

26

62

18

19

54

07

16

50

01

71
4. INTERLAMINAR FRACTURE TEST RESULTS

One of the objectives in this investigation is to evaluate

mixed-mode fracture criteria for the prediction of delamination

growth in the ITWD test specimen geometry. Two graphite fiber

composite materials (APC-2 and CYCOM 982) having significantly

different fracture toughnesses are included in the experimental

effort to provide additional insight into instability related

delamination growth as a function of Gj^ and GJJQ. The validity

of any mixed-mode fracture criterion, however, is strongly

dependent on the accuracy of indepedent critical strain energy

release rate measurements. Consequently, a detailed experimental

study characterizing the Mode I and Mode II fracture toughness is

conducted in conjunction with preliminary testing of the ITWD test

specimen geometry (see Section 4.4).

Initial testing was conducted at room temperature and at a

cross-head rate of 1.25 mm/min (0.05 in/min) for both the DCB and

ENF fracture tests. The original intent of the DCB testing was to

straightforwardly characterize GJQ at initiation and during

propagation using the compliance and area method data reduction

schemes summarized in Appendix 1. The ENF test matrix was designed

to investigate the influence of span and laminate thickness on GIIC

to complement the analysis presented in Chapter 3 in additon to the

basic materials characterization. Furthermore, the sensitivity of

C*IIC on precracking technique (Mode I, Mode II or none) is also

72
investigated. This is an important issue to resolve since selfconsistent precracking of the ITWD specimen is desired. Test

results are discussed in subsequent sections and summarized in

Appendix 7.

Initial testing, however, revealed fundamental differences in

the fracture behavior between the thermoset and thermoplastic

unidirectional graphite fiber composite materials. In general, the

CYCOM 982 thermoset material exhibits linear load-deflection

response and data reduction schemes based upon linear elastic

fracture mechanics are appropriate for both the Mode I and Mode II

tests. The APC-2 thermoplastic, however, exhibits significant nonlinear behavior, particularly evident for the Mode II loading. In

Figure 26, a characteristic load-deflection response is presented

for an ENF test of the APC-2 material. The degree of non-linearity

is quantified in subsequent discussions by the strain energy

release rates based upon the initial compliance and the load at the

onset of non-linearity (GISC or GjjgC) and the initial compliance

and the maximum load (Gj£ or GJJQ), respectively, as defined in

Figure 26.

In Figure 27, the test fixture utilized for ENF testing is

presented. A travelling microscope is employed to monitor the

crack tip during the test. Unstable crack growth is observed for

both the thermoset and thermoplastic materials (a/L=0.5). The

APC-2 material, however, exhibits subcritical crack growth prior to

the unstable growth to the center load pin. The response is shown

73
•o

CO

o

G

Initial Modulus, Compliance

Displacement

Figure 26. Strain energy release rate definitions to

characterize non-linear behavior.

74
ORIGINAL PAGE IS

OF POOR QUALITY

Fig. 27 ENF Test Fixture

75
Crack

Size

Load

Slow

Crack

Extension Crack

Propagation

Load

Time

Fig. 28 Influence of Subcritical Crack Growth on Load

76
schematically in Figure 28. The onset of non-linearity in loaddisplacement response corresponds approximately with the onset of

subcritical crack growth as detected with the travelling

microscope. This observation does not eliminate the possibilty

that matrix yielding and viscoelastic effect may contribute

significantly to the non-linear response observed experimentally.

In all probability, crack extension in a ductile resin such as PEEK

may be proceeded by the development of a process zone, constrained

by the elastic fibers, where extensive deformation and

microcracking may occur [25] . The subcritical crack growth may

therefore correspond to the coalescence of microcracks within the

process zone prior to unstable crack growth.

4 .1 DCS Test Results

The minimum number of plies required to maintain linear

reponse for the largest crack length tested is based on the

analysis presented in Appendix 3 and summarized in Figure 7.

Measured GIC values confirm that [0]2g APC-2 and [0]24 CYCOM 982

provide adequate thickness to minimize errors induced by geometric

non-linearites. Hinges are employed for load introduction into the

delaminated beams for both materials. Hinges were adhesively

bonded to the CYCOM 982 specimens and crack lengths were measured

from the center of the hinge pivot pin. Due to an initial weak

bonding of the hinges to the APC-2 specimens, hinges were fastened

with small screws. Crack lengths in this situation were measured

77
from the center of the screw. Subsequently, hinges were

sucessfully bonded to the APC-2 samples. Test results showed no

change in GJQ values due to different hinge fastening or crack

length definitions. Furthermore, crack length definitions were

consistent with compliance versus crack length measurements.

The compliance and area method data reduction schemes

summarized in Appendix 1 are employed in the present investigation.

In Figure 29, typical load-deflection curves for a CYCOM 982 DCB

specimen is presented. Linear elastic response is observed and

stable, slow growth initiates at the highest load level for all

rates tested. Further imposed deflection yields additonal stable

crack growth and a monotonic decrease in load. From the loading

and unloading curves, the compliance versus crack length and

critical load versus crack length is obtained as shown in Figure 30

(see Appendix 7). The compliance method yields an initiation

energy of GIC = 0.25 ± 0.02 kJ/m2. The area method yields a

slightly greater propagation interlaminar fracture tougness of

GIC = 0.26 ± 0.02 kJ/m2.

In contrast to the stable crack growth observed in the epoxy

specimens, the Mode I crack growth in the APC-2 was often unstable.

This 'stick-slip1 phenomenon has been documented previously by

other researchers [26]. In Figure 31, typical load-deflection

curves for a cross-head speed of 25mm/min are presented to

illustrate the variety of crack growth mechanisms observed during

78
the Mode I testing of APC-2. In general, stable, unstable and

subcritical crack growth are possible as shown in Figure 31. Rate

effects to be further discussed in Section 4.3, indicates that

stable growth is achievable as crosshead speeds diminish. As shown

in Figure 32, linear elastic, stable crack growth is realized for a

crosshead speed of 0.5 nun/min.

The area method was employed to characterize the average

fracture energy consumed during unstable and stable delamination

growth, respectively. An average value of GIC = 1.50 ± 0.20 kJ/m2

was measured for the unstable crack growth mechanism in APC-2.

Stable crack growth data analyzed using the area method yielded a

significantly higher toughness of GIC = 2.00 ± 0.10 kJ/m2. The GIC

value for stable growth of APC-2 (Vf = 0.62) is in good agreement

with earlier published results as shown in Figure 33, where GJQ is

found

to diminish with increasing fiber volume fraction. The initiation

energy based on the compliance method and maximum load yields

GIC = 1>75 * 0-13 kJ/m2, an intermediate value falling between the

two area method measurements. The DCB test results discussed in

this section are summarized in Table 21.

79
40 -

Crossheod Speed

25.4mm/min.

20 40 60

Crosshead Displacement (mm)

Fig. 29 Typical Load vs. Displacement Curves for CYCOM 982

DCB Test.

80
gOTX

T 681

9

V G 2

QV01 1V3I1IUO

CJ

Isx

OTX; cuCMOJ 03COJ CJ enK cu 01

•*-•aoo

O03m3CnOJ

OJauncum.

CaJ

•-»

to

voi X

8-O

W

 8

8 s

30NVIldW03

,tCJD 2

OW

S- (Cl 0u3UOfC

•rH

-P

•r

S-Hl

(1cTDU3c-o; ^ C

O

u cr>

OJ U

U

 O

cn >H

> U 0) <4-l U O (Cc

 O"

1

•H C

rH -H

04 -P

e w 0 0) U EH rH CQ (0 U 0 Q nO•H

81
175

o

o

25

Crosshead Speed

25.4 mm/min.

onset of

subcritical

crack growth

critical crack growth

20 40 60

Crosshead Displacement (mm)

80

Fig. 31 Load vs. Displacement Curves For APC-2 DCS Test

(Crosshead speed = 25iran/min) .

82
Crosshead Speed

0.508 mm/min.

T>

o

o

20 40 60 80

Crosshead Displacement (mm)

Fig. 32 Load vs Displacement Curves for APC-2 DCB Test

(Crosshead speed = 0.5mm/min).

83
3.01-

Fracture

Energy 2.2

(kJ/m2)

Mode I

0.60 0.62 0.64 0.66

Fiber Volume Fraction

0.68

Figure 33. Mode I fracture toughness versus fiber volume

fraction for APC-2.

84
Table 21. DCB Test Results: GTr (kJ/m2

1C

)

Material Compliance Method* Area Method

Stable Unstable

APC-2

CYCOM 982

1.75 ± 0.13

0.25 ± 0.02

2.00 ± 0.09

0.26 ± 0.02

1.50 ± 0.20

NONE

*Averaged results based on maximum load.

Instron rate: 1.25 to 2.5 mm/min (0.05 to 0.10 in/min)

4.2 ENF Test Results

In this section the influence of precracking on the Mode II

fracture toughness will be discussed. Furthermore, finite element

based data reduction will be illustrated on the CYCOM 982 material

which essentially behaves in a linear elastic manner.

Three techniques of precracking were studied. The first

technique, illustrated in Figure 34, was to wedge the crack

surfaces open with a razor to propagate the crack away from the

Kapton insert film. The crack was allowed to propagate a distance

of about 5 mm until it was arrested at the clamp, see Figure 34. In

this way a Mode I precrack was achieved which produces a distinct

85
OcJ0u•H)tIHOCWCP0UM•H)0HM)0o•d) •CMH

86
mark on the fracture surface at the Mode II initiation line.

The second way of introducing a precrack was to load the

specimen in the TPB fixture. Based upon the stability analysis

presented in Appendix 2, a/L > 0.7 was chosen to propagate the

crack slowly in a stable manner to the center load pin. This

produced a Mode II precrack. By carefully wedging the crack open

the crack tip was marked on both sides with a fine pencil. The

third technique was to use the Kapton insert as a starter crack (no

precrack) .

Table 22 shows the results in terms of GIISC and GIIC defined

in Figure 26. It is observed that the CYCOM 982 material behaves

essentially in a linear elastic manner reflected in the closeness

of the GUSC

 an<* ^IIC values

- Furthermore, compared to the Mode I

precracking, the Mode II precracking results in larger fracture

toughness values and brings GUSC

 anc* ^nc cl°ser

- However, the

most striking effect is the high toughness values for the case

where no precracking was used. This effect is evidently a result of

the blunted crack tip at the end of the Kapton insert film (two

plies of nominal thickness 0.025 mm) .

For the APC-2 material significant nonlinear behavior was

observed manifested in the large difference in the GHSC

 anci GIIC

values presented in Table 22. The Mode I precracking produced

consistent G values at different thicknesses and spans. The Mode

II precracking resulted in a higher GHQ value and decreased the

87
percentage difference between GIISc

 and Gnc- As for tne CYCOM

 982

material, however/ the largest

precrack situation.

va^ue was

 obtained for the no

Table 22 Mode II test results. Influence of precracking.

Five replicates. a/L=0.5. Displacement rate is

1.25 mm/mih (0:05 in/min.). Data reduction is

based oh simple beam theory.

Material/No. Precrack

of Plies

Half Span/ L

mm

GIISC

kJ/m2

GIIC

kJ/m2

CYCOM 982/24

CYCOM 982/24

CYCOM 982/24

CYCOM 982/24

CYCOM 982/24

Mode I

Mode II

ti

No precrack

51

51

38

51

38

0.61±0.04

0.75±0.07

0.6510.09

0.68±0.02

0.77±0.07

0.68±0.11

1.45+0.16

1.40±0.18

APC-2/26

APC-2/40

APC-2/26

APC-2/40

APC-2/26

APC-2/26

Mode I

Mode II

No precrack

51

51

38

38

51

51

1.37±0.20

1.63±0.28

1.84±0.07

1.7810.11

1.8710.11

1.8910.16

1.8410.07

1.9310.28

2.7310.33

88
The nonlinearities observed before unstable crack growth appear to

be due to inelastic material behavior (viscoelastic or plastic

yield), in the vicinity of crack tip combined with some amount of

stable crack growth, here denoted by subcritical crack growth as

detected with the travelling microscope. Crack propagation in a

ductile resin has been found to be preceeded by the development of

a process zone, constrained by the rigid, elastic fibers, where

extensive deformation and microcracking may occur [25]. The

subcritical crack growth may therefore correspond to the

coalescence of microcracks within the process zone prior to

unstable crack growth. In the context of this mechanism, the Mode I

precracking appears to produce an initially sharper crack leading

to larger amount of subcritical crack growth before unstable Mode

II crack growth initiates. The Mode II precracking, on the'other

hand, creates a precrack which is more conditioned for shear

loading resulting in less amount of subcritical crack growth or

inelastic material behavior prior to unstable growth evidenced by

the relative closeness of GIISC and GJJQ for this situation. For

the no precrack situation the blunted precrack amplifies the extent

of inelastic material behavior in the vicinity of the crack tip and

increases the apparent fracture toughness.

89
To illustrate the finite element (EE) based data reduction

scheme for the ENF specimen discussed in Chapter 3, the CYCOM 982

data in Table 22, which essentially fullfill the linear elastic

assumptions made in the finite element analysis, were employed. In

particular the data for a/L=0.5 at two different half spans L=38 mm

and 51 mm, respectively, for Mode II precracks were used to obtain

a consistent comparison of the results. Table 23 shows that the FE

based data reduction scheme results in more consistent values of

the fracture toughness in Mode II.

Table 23 Finite element based data reduction for CYCOM 982

ENF specimens with Mode II precracks. See Tables 15

and 17 for material 3: (E1/G13 = 25.7)

Half Span

mm

51

38

rBT

,

G

IIC

kJ/m2

0.7710.07

0.68±0.11

rFE

G

IIC

kJ/m2

0.98±0.09

0.94±0.15

90
4.3 Rate Effects in Mode I and II Fracture

In this section the influence of rate on the Mode I and II

fracture behavior is examined over a range of Instron crosshead

rates for the APC-2 material. The following crosshead rates were

used ; 0.25, 2.5, 25 and 250 mm/min (0.01, 0.10, 1.00 and 10.0

in/min). ,

Typical load-displacement curves for the DCB test (Mode I) are

shown in Figure 35. At low rates the response may be characterized

as linear elastic-stable while at higher rates a deviation from

linearity is noted at some point before critical crack growth

occurs. The knee point in the load-displacement record appears to

be related to subcritical crack growth as discussed in Section 4.2

for the Mode II testing. A significant difference, however, between

Mode I and II loading is that in Mode II the subcritical crack

i

growth is associated with some degree of inelastic material

behavior, while the deviation from linearity in the Mode I case

almost entirely is related to subcritical crack growth with

negligible inelastic material behavior observed, see Figure 31 for

more detail. At low rates the critical crack growth (crack growth

that leads to a load drop) is stable but becomes unstable,

"stick-slip", at higher rates. The "stick-slip" phenomenon

apparently reflects strain rate effects occuring in the process

zone. Before further discussing the rate effects the

load-displacement behavior for Mode II loading will be outlined.

Figure 36 shows typical load-displacement curves for the APC-2 ENF

91
T8O

§ = 0.25 mm/min

= 25 mm/min

5 = 2.5 mm/min

0 « 250 mm/min

Displacement, 8

Figure 35. Typical load-displacement response for APC-2

DCB specimen at various crosshead rates.

92
tests at various displacement rates. At low rates significant

nonlinear response was observed before the initiation of unstable

crack growth. As mentioned earlier in this section, the

nonlinearities are attributed to subcritical crack growth in

combination with crack front inelastic material behavior. The

tracing of the subcritical crack growth prior to the onset of rapid

fracture, based on surface measurements by the travelling

microscope is not entirely satisfactory due to the possibility of

tunneling which may obscure the true tip of the crack [28] and the

possible influence of edge effects. However, qualitatively, the

subcritical crack growth observed here appears to be similar to

what has been observed in metals [28], namely, a slow stable crack

growth sometimes associated with small "pop-ins" in the

load-displacement record. At higher displacement rates, the

load-displacement response becomes more linear and at the highest

rate tested (250 mm/min) negligible nonlinearities are observed,

see Figure 36.

Apparently the nonlinear response in both Mode I and II is

higly rate dependent indicating that the development of the process

zone and the subcritical crack growth are viscoelastic in nature.

To gain further insight into the rate dependency it is useful to

discuss rate effects more locally, i.e. in the crack tip region.

For the DCB specimen, Smiley [29] derived the following expression

*

for the rate of crack opening displacement, 8CT , at any instant

preceeding crack propagation,

93
C

O

0c)QCDE

.

(AQ

QO•H£0)C-P-Hoa) U0) a-uIW2ena) cnaoc

ITo) Cm-POMC

S-§Nl

M-l cn

)70) •H>0(0C(N)

d '

06) aMQJ roo(3aiH(0O

cnCD

4->

(0

S-l

EL,

94
6CT = 1.58S2

 (23)

where 5 is the displacement rate at the point of load introduction

and ^ is a nondimensional distance, x/a, measured from the crack

tip (x/a « 1).

Prior to the onset of crack propagation, at the crack tip,

t

£ = 0 and 5CT = 0. Therefore, the crack tip velocity is defined at

an arbitrarily small distance/ in this case about two ply

thicknesses (x=0.25 mm), away from the crack tip. Defining a local

displacement rate is particularly important in quantifying rate

effects in the DCB specimen where the crack tip velocity diminishes

with the square of crack length, see equation (23).

For the Mode II specimen the corresponding expression for the

relative sliding rate, UCT, at a distance £ from the crack tip is,

24 ha2 5 e <24)

U

 CTCT

 = 3 3~ ' (2L + 3a )

Ten DCB specimens (72 crack lengths) and 20 ENF specimens (20

crack lengths) were included in the experimental study of rate

effects in Mode I and II fracture. The response was studied over

four decades of Instron rates, viz. 0.25, 2.5, 25 and 250 mm/min.

95
Average results for the DCB and ENF specimens are summarized in

Tables 24 and 25, respectively. In Mode I the toughness for onset

of subcritical crack growth, GISC, decreases somewhat with

increased displacement rate while the toughness for critical crack

growth, GIC, peaks at an intermediate displacement rate. For the

Mode II situation, Table 25, Gjjg^ is relatively constant up to the

highest rate where an increase is noted. To relate the rate effects

to local crack tip behavior the crack tip velocities for the DCB

and ENF specimens were calculated from equations (23) and (24),

respectively.

Table 24 Rate dependency of APC-2 Mode I fracture toughness

Data reduction is based on beam theory, GIx =

3A1Px^a^/2w where x = SC and C respectively

(Fig. 31) and A^ is an initial compliance

coefficient defined in Appendix 1.

Displacement Rate 5pm

mm/min m/s x 1010

0.25 0.02-1.6

2.5 1-10

25 8-118

250 108-1102

GISC

kJ/m2

1

1

1

1

.56±0

.60±0

.41±0

.37±0

.05

.26

.21

.15

1

1

1

1

G

IC

kJ/m2

.56±0

,75±0

.98±0

.71±0

.05

.13

.13

.16

96
Table 25 Rate dependency of APC-2 Mode II fracture

toughness. Data reduction is based on beam theory

(initial compliance) and load at onset of

nonlinearity, PgC'

 and load at

 critical crack

growth, Pc (Fig. 26).

Displacement Rate SCT

mm/min

0.25

2.5

25

250

m/s x 109

2.86

28.6

286

2860

G

IISC

JcJ/m2

0

1

0

1

.95±0

.01±0

. 98±0

.40±0

.18

.09

.16

.13

1

1

1

1

G

IIC

kJ/m2

.84±0

.82±0

.40±0

.40±0

.27

.20

.13

.13

Figure 37 shows the toughness values plotted versus crack tip

displacement rate. It is observed that GJQ goes through a maximum

and GISC goes through a slight minimum as the crack tip opening

rate increases. GIIC and GIISC, on the other hand, remain fairly

constant at all crack tip velocities up to the highest velocity

where GIIC decreases and GIISC increases. At the highest rate the

response in both Mode I and II loading is approximately linear

elastic resulting in,

97
2.5

APC-2, [0]26

2.0

2

CD

C

JC

D)

O

§

f>

2LJL

1.5

1.0

O G

0.5

0.0

-11

lc

lsc

llsc

-10 -9

I I

-8 -7

log 6CT

-6 -5 -4

Figure 37. Rate dependence of Mode I and II fracture

toughness.

98
G

ISC ~

 GIC

G

IISC

 = GIIC

To further illustrate the rate dependency of toughness the

difference between the toughnesses for critical crack growth and

subcritical crack growth in Mode I and II, respectively, was

calculated,

AGIC = GIC - GISC (26)

AGIIC = GIIC ~ GIISC (27)

Figure 38 shows that AGjQ peaks "at an intermediate crack tip

velocity that is achieved at a displacement rate of about 25

mm/min. At the highest crack tip velocities negligible subcritical

crack growth is observed as reflected in the small AGj,-. values. For

Mode II loading AGIIC decreases slowly initially and drops to a

small magnitude at the highest rate tested.

Discussion

The rate effects on interlaminar fracture of APC-2 observed

99
•COO) o

UIc4Ju

r-OO•Hal -

S- rUUHl

s-en3WUi 0MHU)U

rtj CMO

— I <

o0no) ki

•CDn •H

100
herein appear to be viscoelastic in nature. Based on insitu

scanning electron microscopic examination of the fracture process,

it has been found that a significant process zone develops around

the crack tip [25] . The process zone is assumed, in the present

discussion, to contain all inelastic behavior such as matrix

plasticity, viscoelasticity and microcracking as well as fiber

debonding. The discussion of rate effects is based on the following

premises:

On a micromechanics level, the plastic zone surrounding the

crack tip will develop instantaneouesly relative to the loading

rate when the yield stress in the matrix is exceeded. The plastic

zone will continue to grow with increased load until an.equilibrium

geometry of the zone is established. In this situation, the size of

the plastic zone will be determined by the yield stress of the

matrix in conjunction with the stress redistribution to adjacent

elastic fibers. The constraint imposed by the fibers will clearly

diminish the plastic zone size relative to the neat polymer

response [25] . Furthermore, the yield stress for most glassy

polymers increases in direct proportion to the logarithm of strain

rate [30] . It is therefore anticipated that the size of the plastic

zone in the vicinity of the crack tip will be inversely

proportional to the crack tip displacement rate.

The second premise in the discussion addresses the influence

of rate on the material response within the process zone external

to the plastic zone where viscoelastic effects may dominate. At low

rates, viscoelastic effects will be prevalent yielding an upper

101
bound on the size of the process zone. At the highest rates,

viscoelastic effects will be negligible and the process zone will

tend to be coincident with the developing plastic zone.

Intermediate rates will yield intermediate process zone sizes.

In Figure 38, the influence of rate on the degree of

nonlinearity in the load displacement response is quantified for

the APC-2 material by AGIC and AGIIC defined in equations (26) and

(27) for Mode I and Mode II loading, respectively. In Mode II

loading the polymer in the process zone is subjected to an intense

shear stress. Polymers are known to be more viscoelastic and to

yield more easily in pure shear than in dilatation (Mode I) [30].

The degree of nonlinearity in the load-displacement response is

significantly greater than for the Mode I situation evidenced by

AGjjQ > AGjQ as shown in Figure 38. This indicates that the

process zone in the ENF specimen is significantly larger than in

the DCB specimen.

At the lowest rates tested, linear elastic load deflection

response and stable crack growth is observed in Mode I where

AGIC = 0, see Figure 38. In this situation, the yield stress

exhibit a minimum value which corresponds to maximum plastic zone

and process zone sizes. It is hypothesized that the stable crack

growth corresponds to a slow drawing of the polymer and the

coalescence of microcracks within the process zone. More

102
importantly, however, the loading rate is sufficiently low so that

the crack growth rate and the process zone growth rate are the same

order of magnitude.

Crack growth occuring entirely within the evolving process

zone is the mechanism associated with subcritical crack growth. The

above scenario is analogous to the Crack Layer Theory [31,32] where

this type of behavior is observed in metals and polymers. It is

interesting to note that on a macroscopic level, linear elastic

load-displacement response is observed for a rate where

viscoelastic and plastic 'response dominate crack growth.

As crack tip displacement rates increase, however, the Mode I

fracture toughness, GJQ, increases prior to attaining a maximum

value while GISC is relatively rate independent. The increase in

GIC is attribated qualitatively to an increase in the matrix yield

stress within the plastic zone. Similar trends in the fracture

toughness of neat polymers have been reported [30]. It has also

been observed that the "stick-slip" phenomen and subcritical crack

growth occurs over this range of displacement rate in Mode I

loading, it is hypothesized that the subcritical crack growth rate

is greater than the growth of the evolving process zone. When the

crack is contained within the process zone, stable growth occurs as

noted for the lowest rates tested. When the crack grows to the

boundary of the evolving process zone, unstable growth occurs.

Since the size of the process zone diminishes with increased rate,

?

it is anticipated that an increasing amount of unstable crack

103
growth occurs as rates increase. This is substantiated by trends

exhibited by experimental data presented herein.

Further increase in displacement rate results in a

ductile/brittle transition and a reduction in GIC as shown in

Figures 37 and 38. The transition is evident from the inspection of

the SEM fracture surfaces shown in Figures 39 and 40, where plastic

deformation of the matrix normal to the plane of crack growth is

significantly reduced.

With respect to the Mode II loading, similar mechanisms as

discussed for the Mode I situation are proposed to explain the

influence of rate on fracture toughness. Significant nonlinearity

in the load-displacement curves is observed for all but the highest

rate tested. This response is shown schematically in Figure 36 and

quantified by AG^JQ in Figure 38. The nonlinearity is attributed to

inelastic material response and subcritical crack growth within the

process zone.

In contrast to the Mode I loading, AGIIC does not tend to zero

for the lowest rate tested, see Figure 38 . Although the lowest rate

tested for the ENF specimen results in a crack tip velocity that is

two decades higher than the corresponding rate for the DCB

specimen, it is not anticipated that AGjjQ will tend to zero with

diminishing rate for the following reasons : Multiple crack lengths

are routinely tested in the DCB test . After the first crack growth

104
ORIGINAL PAGE .s

*** QU4UTY

640 X

2500 X

Figure 39. Mode I fracture surface of APC-2 loaded at

a low displacement rate showing ductile behavior,

105
2500 X

Figure 40. Mode I fracture surface of APC-2 loaded at a

high displacement rate showing brittle behavior.

106
increment the process zone, if fully developed, would not

significantly contribute to a nonlinear load deflection response in

subsequent loading cycles. In the Mode II test, only a single crack

length is tested. The onset of nonlinearity is therefore associated

with the development of the process zone. As stated previously, the

size of the process zone will tend to increase with diminishing

rate. The process zone in the Mode II situation will also be

significantly larger than in the Mode I case since inelastic

effects are more pronounced in shear. Furthermore, crack lengths

are 2-6 times smaller than those in the DCB fracture specimen. A

larger process zone in conjunction with shorter crack lengths will

certainly contribute to the macroscopic nonlinearity in the

load-deflection response observed. Based on the above discussion,

one might expect AGjj^ to increase prior to reaching a plateau

value with diminishing rate. This trend is observed experimentally

as shown in Figure 38.

The second reason which precludes the possibility of AGjj^

tending to zero with decreasing crack tip displacement rate is the

fundamental difference between the DCB and ENF fracture tests.

Under fixed grip conditions, the Mode II specimen yields unstable

crack growth (see Appendix 2) while the Mode I specimen is

inherently stable. The mechanism of subcritical crack growth due to

coalescence of microcracks within the process zone also occurs and

contributes to the nonlinear load-deflection response. Since the

strain energy release rate increases with crack length, subcritical

107
crack growth initiating in the developing process zone will be

accelerated as shown schematically in Figure 28. In contrast to the

DCB response at low rates, the growth of the process zone will not

match the subcritical crack growth rate. Consequently, the crack

will growth towards the boundary of the process zone resulting in

unstable crack growth.

At the highest rate tested, linear elastic behavior is

observed and a reduction in GJJQ corresponds to a ductile/brittle

transition in the fracture process. The transition is evident from

the inspection of the fracture surfaces of the APC-2 material shown

in Figures 41 and 42. A significant reduction in plastic

deformation associated with the formation of hackles,

characteristic of the shear loading, is noted.

4.4 ITWD Test Results

Fabrication of the ITWD specimen is accomplished by implanting

2 layers 0.025 mm thick Kapton film betwen plies at various depths.

64 plies was chosen as the laminate thickness in order to study a

wide range of delamination depths. Furthermore, a thick laminate

minimizes global bending of the 100 mm test section.

Experience gained during compression testing reported in

Section 2.2 clearly demonstrated that the IITRI compression fixture

would not be suitable for the 64 ply ITWD specimen since end tab

shear failures would occur for the high loads required to propagate

108
2500 X

Figure 41. Mode II fracture surface of APC-2 loaded at a

low displacement rate showing ductile behavior

109
640 X

2500 X

Figure 42. Mode II fracture surface of APC-2 loaded at a high

displacement rate showing brittle behavior.

110
the delamination. A new fixture was designed which successfully end

loads the specimen without initiating damage to the load

introduction surfaces, see Figure 43. This is achieved by clamping

the specimen over a 38 mm distance from either end. To assess the

uniformity in load introduction, strain gages were mounted on all

four sides of a no defect sample at the center of the gage section.

Minimal strain gradients were observed indicating a uniform loading

of the specimen.

Cylindrical clamps were developed, see Figures 43 and 44, to

arrest the potentially unstable crack growth at specified lines

before the delamination propagates to the end of the test section.

In this manner, precracking to obtain a natural crack tip is

achieved. Precracking is essential because the resin pockets

created at the ends of the implanted delamination would

significantly increase the apparent fracture toughness. This effect

was verified through testing of ENF specimens that where not

precracked, see Section 4.2. Clamping just beyond the crack front

may also provide a means to test one specimen with multiple crack

lengths. Additional testing and analysis of the influence of the

clamped crack arrest is in progress. Figure 44 shows a specimen

with a delamination of an initial length of 38 mm arrested with

clamps at 54 mm. Compressive loading of the specimen shown in

Figure 44 maintains the post-buckled shape of the delaminated

region. Close examination of Figure 44 also reveals the presence of

global bending due to the reduction in stiffness of the buckled

sublaminate.

Ill
ORIGINAL PAGE IS

OF POOR QUALITY

Figure 43. End loading compression fixture

112
ORIGINAL PAGE IS

OF POOR QUALITY

Figure 44. 64 ply ITWD specimen with postbuckled subleminate

(at 110 KN load.)

113
The compresive strengths and failure modes of 64 ply laminates

without implanted delaminations have been investigated. Preliminary

tests of [0]g4 APC-2 and CYCOM 982 specimens indicate compressive

strengths of about 900 and 650 MPa, respectively. The basic

mechanical properties characterization showed that [0]16 APC-2 and

CYCOM 982 specimens have compressive strengths of 1250 and 1300 MPa

respectively, for the brooming failure mode. The difference appears

to be related to a change in the mode of failure in compression.

Shear type of failures through the width of the [0]64 CYCOM

982 may be responsible for the loss 50% in compressive strength.

However, the shear mode of failure of [OJg^ APC-2 laminates

decreased the strength by only 28%. Figure 45 shows a through the

width shear type of failure of a CYCOM 982 specimen after buckling

of the 38 mm long, 12 plies thick, delaminated region.

Consequently, the reduction in compressive strain to failure

must be incorporated into the sizing of the ITWD specimen. Based

upon the superposition analysis of Whitcomb [13], delamination

lengths and depths will be chosen in conjunction with the

appropriate fracture toughness values to guarantee crack growth at

desired Gj/Gjj ratios prior to compressive failure. In this manner,

the ITWD test specimen geometry can be employed to assess the

validity of various mixed-mode failure criteria for the onset of

delamination growth.

Preliminary results have been obtained for the out-of-plane

114
ORIGINAL PAGE |S

OF POOR QUALITY

Figure 45. Shear type failure in an ITWD specimen,

115
displacement of the delaminated region. When the load is removed

after precracking a finite out-of-plane displacement of the

delaminated region remains. Upon reloading, the out-of-plane

deformation increases monotonically from zero load as expected.

Figure 46 shows measured and predicted out-of-plane deformation for

an ITWD specimen with an initial displacement of the delaminated

region. The predictions by Whitcomb [13], Ashizawa [4] and

Gillespie [I] underestimate the out-of-plane deformation in the

upper region of the loading curve. This discrepancy may possibly be

caused by global bending of the test section. An analytical

prediction for the out-of-plane deformation as a function of the

applied load, including global bending, is underway for this

program. Nonlinear finite element results will also be compared to

the analytical and experimental data.

116
o

o

DELAM. THICKNESS=0.51mm

SPECIMEN THICKNESS=8.29mm

INITIAL IMPERFECTIONS.34mm

0.00 40.00 80.00 120.00 160.00 200.00

LOAD (kN)

Figure 46. Comparison of measured and predicted out-of-plane

displacement as a function of the applied load.

(APC-2, Delamination length =54.1 mm)

117
5. CONCLUSIONS

Based on the results presented in this report the following

conclusions may be drawn:

Processing techniques developed for thermoplastic

graphite/PEEK composites appear to produce high quality

laminates.

Sizing of fracture specimens is important in order to achieve

crack growth prior to geometric nonlinearities or material

failure.

Interlaminar shear deformation may have to be considered for

certain ENF specimen geometries.

Friction between the crack surfaces can be minimized through

suitable design of the ENF specimen based on beam theory

analysis.

- For ENF geometries commonly in use friction reduces GJJ by 2

to 4 percent.

- Finite element analysis confirms that the ENF specimen is a

pure Mode II test.

118
Finite element analysis of the ENF specimen reveals that beam

theory underestimates GJJ by 20 to 40 percent depending on the

crack length to span ratio.

- ENF specimen insensitive to delamination offset from laminate

midsurface.

Data reduction scheme for ENF specimen may have to rely on a

combination of beam theory and finite elements.

Precracking essential for the ENF specimen.

Nonlinear response observed for the DCB and ENF specimen is

• attributed to subcritical crack growth and/or inelastic

material behavior.

- Nonlinear effects are highly rate dependent.

- Stick-slip behavior in Mode I testing of APC-2 is a rate

effect.

- Preliminary ITWD testing reveals that test fixture is

appropriate.

119
6. FUTURE WORK

Future work related to this project consists of:

Sizing the ITWD specimen to achieve crack growth prior to

global buckling or compressive failure.

- Defining a test matrix for ITWD specimens.

Implement the shodow moire technique to characterize full

field out-of-plane displacements of the delaminated region as

well as global bending.

- Beam theory analysis of ITWD specimen including global

bending.

- Finite element analysis of the ITWD specimen to assess beam

theory results.

- Prediction of the onset of delamination growth for CYCOM 982

and APC-2 via mixed-mode fracture criteria.

- Assessment of nonlinear effects in interlaminar fracture.

120
REFERENCES

1. J. W. Gillespie and R. B. Pipes, "Compressive Strength of

Composite laminates with Interlaminar Defects," Composite

Structures, Vol. 2, 1984, p. 49.

2. J. W. Gillespie and R. B. Pipes, "Compressive Strength of

Composite Laminates with Interlaminar Defects," CCM-79-17,

Center for Composite Materials, University of Delaware,

1979.

3. J. D. Webster, "Flaw Criticality of Circular Disbond Defects

in Composite Laminates," CCM-81-03, Center for Composite

Materials, University of Delaware, 1981.

4. M. Ashizawa, "Fast Interlaminar Fracture of a Compressively

Loaded Composite Containing a Defect," Douglas Paper 6994,

January 1981.

5. M. Ashizawa, "Improving Damage Tolerance of Laminated

Composites Through the Use of New Tough Resins," Douglas

Paper 7250, January 1983.

. B. Pipes, "Definition

ir-iVi-il-o PT Hoi- PoH nfr^ffort

Epox y Resin Matri x Composite

Development Center Report No. NADC

7. S. N. Chatterjee, Z. Hashin, and R. B. Pipes, "Definition

and Modeling of Critical Flaws in Graphite Fiber Reinforced

Resin Matrix Composite Materials," Naval Air Development

Center Report No. NADC 77278-30, August 1979.

8. S. N. Chatterje e and R. B. Pipes, "Composite Defec t

Significance," Proceedings of the Mechanics of Composites

Review Meeting, Dayton, Ohio, October 1982.

9. J. D. Whitcomb, "Finite Element Analysis of Instability

Related Delamination Growth," J. Composite Materials,

Vol. 15, Sept. 1981, pp. 403.

10. J. D. Whitcomb, "Approximate Analysis of Postbuckled

Through-Width Delaminations," NASA Technical Memorandum

83167, June 1981 .

11. J. D. Whitcomb, "Strain Energy Release Rate Analysis of

Cyclic Delaminatio n Growth in Compressively Loaded

Laminates," NASA Technical Memorandum 84598, January 1983.

121
12. J. D. Whitcomb, "Delamination Growth in Compressively Loaded

Laminates," Presented at the ASTM Symposium on Effects of

Defects in Composite Materials, San Francisco, California,

December 1982.

13. J. D. Whitcomb, "Parametric Analytical Study of InstabilityRelated Delamination Growth," paper presented at the CCM

Symposium 24-25 Sept. 1984.

14. D. J. Wilkins, J. R. Eisenmann, R. A. Camin, W. S. Margolis,

and R. A. Benson, "Characterizing Delamination Growth in

Graphite/Epoxy," Damage in Composite Materials, ASTM STP 775,

1982, p. 168.

15. R. L. Ramkumar, "Performance of a Quantitative Study of

Instability-Related Delamination Growth," NASA Contract

Report No. NASA-16727, March 1983.

16. A. J. Russell and K. N. Street, "Factors Affecting the

Interlaminar Fracture Energy of Graphite/Epoxy Laminates,"

Hayashi, T. et. al. ed., ICCM-IV, Tokyo, 1982.

17. G. B. Murri and T. K. O'Brien, "Interlaminar Gllc evaluation

of Toughened Resin Matrix Composites Using the End-Notched

Flexure Test," 26th AIAA/ASME/ASCE/AHS Structures, Structural

Dynamics and Materials Conference, Orlando, April 15, 1985.

18. D. R. Carlile and D. C. Leach, "Damage and Notch Sensitivity

of Graphite-PEEK Composites," Sampe Conference, Cincinnati,

(USA), October 2-3, 1983.

19. H. Chai, "The Growth of Impact Damage in Compressively

Loaded Laminates," Ph.D. Thesis, CalTech, March, (1982).

20. ADINA: A Finite Element Program for Automatic Dynamic

Incremental Nonlinear Analysis, Report AE81-ADINA Engineering

INC., September 1981.

21. E. F. Rybicki and M. F. Kanninen, "A Finite Element

Calculation of Stress Intensity Factors By a Modified Crack

Closure Integral," Eng. Fracture Mechanics, Vol. 9, 1977,

p. 931.

22. B. Torstenfelt, "Finite Elements in Contact and Friction

Applications, " Ph.D. Dissertation No. 103, Linkoping

University, Sweden (1983).

23. K. R. Bathe and A. Chandhany, "A Solution Method for Planar

and Axisymmetric Contact Problems," Int. J. Num. Meth. Eng.

in Press, (1985).

122
24. J. D. Barrett and R. O. Foshi, "Mode II Stress Intensity

Factors for Cracked Wood Beams," Eng. Fracture Mechanics,

Vol. 9, (1977), p. 371.

25. W. L. Bradley and R. N. Cohen, "Matrix Deformation and

Fracture in Graphite-Reinforced Epoxies," Delamination and

Debonding of Materials, ASTM STP 876, (1985), p. 389.

26. D. C. Leach and D. R. Moore, "Toughness of Aromatic Polymer

Composites," presented at a Symposium at University of

Delaware, September, 1984, to be published in Composites

Science and Technology.

27. A. J. Russell and K. N. Street, "The Effect of Matrix

Toughness on Delamination: Static and Fatigue Fracture Under

Mode II Shear Loading of Graphite Fiber Composites,"

presented at NASA/ASTM Symposium on Toughened Composites,

Houston, TX, March, 1985.

28. R. W Boyle, "A Method for Determining Crack Growth in Notched

Sheet Specimens," Mater. Res. Stand., 2, (1968), p. 646.

29. A. Smiley, "Rate Sensitivity of Interlaminar Fracture

Toughness," MSc. Thesis, University of Delaware,(1985).

30. A. J. Kinloch and R. J. Young," Fracture Behavior of

Polymers," Applied Sci. Publishers Ltd., (1983).

31. A. Chudnovsky, "Crack Layer Theory", NASA Report NAG-3-23,

Dec. 1983, NASA Lewis Research Center.

32. A. Chudnovsky, A. Dolgopolsky and M. Cachanov, "On Stress

Analysis of a Crack Layer", NASA Report NAG-3-223, Oct. 1984,

NASA Lewis Research Center.

123
APPENDIX 1

Data Reduction schemes for

DCB, ENF and CLS Specimens

PRECEDING PAGE BLANK NOT FUMED

125
1. DCB DATA REDUCTION

1.1 Coropliance Method [1]

El

El

6 = 2Pa /3EI

C = 6/P = 2a/3EI -

(1)

where AI =

The energy release rate G is obtained from

P

2 dC G

. _f" *****

-*• -*"^TM

 Li- -

2w da

(2)

127

"****""*»«****„
Eq. (1) in (2) gives

G = 3A,P2a

2/2w

(3)

G = GC for P = PC gives

P a/2W = GC (4

> /

c

 =

c •*

2w G_ 1.

a

(5)

consequently

Pc = A2/a 6)

Experimentally the C-a and P -a relations are

measured giving the constants A, and A~

log C log Pc

log A

-I

log a log a

The critical energy release rate G is obtainer by

substituting Equation (6) into Equation (4).

128
(7)

1.2. Area Method 12]

For linear elastic behavior and the case where the

load deflection curve during crack propagation can be

approximated by a straight line, the energy release rate can

be determined from,

G = (8)

This quantity is equal to the area between the

loading and unloading curves. An average G_c value may be

obtained from a series of loading and unloading curves.

129
2. CLS DATA REDUCTION

shear ply

(flap)

Strength of materials analysis gives:

6 = P(L-a) + -Pa_ (9)

(L-a) ^ a

wEhn wEh,h_

(10)

P'

c

2w

dC

da

(11)

From Equation (10), C nay be expressed as a linear

function of a,

130
C = (12)

Equations (11) and (12) give

G

 ' -

 A (13)

cr

131
3. ENF DATA REDUCTION [3]

El

P/2

P/2

For the undelaninated regions BC and CD the displacements

are,

P[2L3 - 3aL2 + a3]/8Ewh3(14)

PL3/4Ewh3

(15)

The deflection of the delaminated region due to the slope at

B is:

~ a3l/8Ewh3 (16)

The deflection of the delaninated region due to bending is,

132
A AB,B

 = Pa /Ewh (17 )

Total deflection of the delaminated part is then:

3P(aL2-a 3) L 8Pa3

AB AB,S AB,B IS U Wll UUW11

(18)

= P[aL2

+ 5a3]

8Ewh3

For small deflections the total deflection 6 is:

6 = - £-_ [ 2L + 3a ] ( 20 )

8Ewh

The compliance C may thus be expressed

c = 1 = I 2tj-f 3a (21)

P

 8Ewh3

dC = 9a2

 = 9a2C (22 )

da

 8Ewh3 [2L3+ 3a3j

2 2 2

dC 9a*Pz

C =

 2L

 + ^ = A,a3 + Afi (24 )

8Ewh 8Ewh

133
da- 25!

log Pc

log A7

-1

log a

Gc - 2w

(26)

IST a = Va

(27)

(28)

In many cases unstable crack growth occurs with this specimen. For that case G is calculated directly from Eg. (22),

G

c - 2w(2L3+3a3)

(29)

where C is the measured compliance (corrected for the

machine compliance).

134
REFERENCES

[ij D. J. Wilkins, J. R. Eisenmann, R. A. Catnin, W. S.

Margolis and R. A. Benson, "Characterizing

Delamination Growth in Graphite/Epoxy", Damage in

Composite Materials, ASTM STP 775,(1982), p. 168

[2\ J. M. Whitney, C. E. Browning and Hoogsteden, W.,"A

Double Cantilevier Bean Test for Characterizing Mode

I Delamination of Composite Materials", J. Reinforced

Plastics and Composites, vol. 1, (1982),p. 297

|3j A. J. Russell and K. N. Street, "Moisture and

Temperature effects on the mixed-mode delanination

fracture of unidirectional Graphite/Epoxy" Paper presented at an ASTM Symposium on Delamination and

debonding of Materials, Nov. 8-10, (1983)

Pittsburgh, Pennsylvania

135
APPENDIX 2

Stability of Crack Growth For the ENF Specimen [11

The stability of crack growth may be judged from the

sign of dG-./da. If dG-,j/da is positive unstable crack

growth will occur, while stable crack growth occur if dGTT/da

is zero or negative. Gj is obtained from the general

expression:

_ P2 dC

~ It da"

For fixed load conditions dG,.,./da is directly obtained from

eq. (22), Appendix 1,

9aP2

da

 " SEwV

This quantity is always positive, hence the crack growth is

unstable.

For fixed grip conditions, which is more common in

testing G is expressed by

136
- _ _

11

 2»C2

Differentiation of this expression yields:

dGH _ 62 |d2C _ 2 ,dC.2| , .

da

 " 2wC2 Lda2 C'da J (4>

If the influence of shear is neglected, Eq. (22)/Appendix 1,

gives,

dGII _ 96 2a . 9a3 .

j — o -3 S II ~ T T 1 V J )

da

 8Ew2h

3C2 2L3

 + 3a3

For stable crack growth, a ,is thus required to be:

a > L/~~3 « 0.7L (6)

Consequently for the commonly used a/L = 0.5, the crack

growth is unstable under fixed grip conditions.

137
REFERENCE

[1] L.A. Carlsson, J.W. Gillespie and R.B. Pipes,

"On the Analysis of the End Notched Flexure (ENF)

Specimen for Mode II Testing", Submitted for

Publication.

/

138
APPENDIX 3

Design Considerations for DCB, ENF and CLS Specimens

1. DCB Specimen Design

The main requirement on the DCB specimen is that the

beams act as linear elastic beans. An investigation by

Dewitt et. al [l] shows that geometric nonlinearities occur

in the DCB specimen for

6_

2a

15.30 Figur e I.

( 1 )

fsl

El

4 -

2 -

0.4 0.6 0.8

Fi.j. I rtonch

 -nens iona.l load vs. nondineosional displacement

11]

139
At 6/2a = 0.3, i.e. 6/a = 0.6 the error induced in the load

by assuming linear behaviour is approximately 10%. This is

also the error in G [ij.

Relation between the thickness required to keep the beams in

_the linea _ r regim _e an c d G .

Equation (1) in Appendix 1 is

C = Aa3 ( 1)

2

in which A, = --

Here El is the flexural rigidity of each beam of the DCB

specimen. Consequently,

I = w(h/2)3/12 = wh3/96 (2)

This in Equation (1) yeilds,

Ewh

or

Ewh

The critical strain energy release rate may be expressed as

96P2a

2

G

c

 =

c

140
Substitution into Equation (4) gives

128G

To keep <5 /a less or equal to 0.6 requires;

fl28G

(7)

or

2

128G a'

f— < 0.36 (8)

3Eh

This is equivalent to,

h >4.9 (GE ) a2/3 (9)

Note that the required thickness increases with crack

length a. The longest crack length expected in the testing

is about 150 mm

2. CLb Specimen Design

The design of the CLS specimen has been discussed by

Mangalari and Johnson [2]. Based on the two possible

failure modes, viz. delamination and adherend failure, the

minimum thickness may be determined. Figure 2 shows the

geometry of the specimen.

141
t

Fig. 2 Geometry of the CLS specimen.

From Equations (10) and (11) in Appendix 1,

(10)

With h, = h, h~ = h/2 we get

G =

2w2Eh

i .e.

P_ = w / 2EhG

(11)

(12)

To avoid failure in the strap ply (if the stress

concentration at the crack tip and the rotation of the

specimen is neglected) we need

(13)

142
T

where X, is the uniaxial tensile strength,

Equations (12) and (13) yield

w / 2EhG < X^ wh/2 (14)

This yields:

T 2 *[) (15)

3. ENF Specimen Design [3]

The analysis of the ENF specimen presented here,

is based on small deflection theory. Large

deflection/rotations increase the complexities of the analysis and the data reduction scheme substantially. In this

section, an analysis based on beam theory, will be presented

which allows sizing of the ENF specimen to obtain crack

growth within the linear elastic regime. Influences of

interlaminar shear and friction are not considered in this

approximate analysis.

In linear beam theory the following expression for

the curvature:

d

2y/dx2

(dy/dx)J

143
is generally approximated with

1/R = d2y/dx2 (17)

since the square of the slope (dy/dx) is assumed to be much

less than unity.

The maximum slope occurs at the end of the. delaminated region. Neglecting influence of shear deformation it

may be calculated from the slope of the beam at the tip of

the delaminated crack

_ 3P(L2-a2)

" 8Ewh3

The slope due to bending of the delaminated beams is

obtained from the deflection curve for a cantilever beam

( see Appendix 4) .

<*2 -

The maximum slope occurs at x = 0 and is

,9V v _ Pa2 (21)

V9x '0 ~ 8EI

144
This leads to

. _ 3Pa2 (22)

° " 2Ewh3

The maximum slope is then approximately

(23)

vdx'm vdx' B x dx'O

Equations (18) and (22) give:

(dy_. 3P(L2+3a2) (24)

dx m " 8Ewh3

In terms of displacement, 6, the maximum slope is:

- 3(L2 + 3a2)6 (25)

dx m " 2L3

 + 3a3

For (dy/dx) < 0.2 the error in eq. (16) is approximately

6%. The integrated form of eq. (16) which should be

employed in a large deflection analysis would lead to less

than 6% error since the above estimate is based on the maximum slope, at a point.

Denoting the maximum allowable slope by y , the

maximum allowable displacement, <S , corresponding to y

a o

may be calculated from Eq. (25),

x ,

 ya (2L3+ 3a3) (26)

m

 3<L2+ 3a2)

145
Relation between 6 and G-,

9P a26

(27)

2w(2L

The critical load P may also be obtained from Eq. (20) of

Appendix 1,

Pc = 3 «c (28) C J J °

Substitution into Eq. (28) yields,

6 = (29)

c 5a

Combination of Eqs. (29) and (26) with the requirement

6

c

 < 6 m 9ives:

2 3

h

 (30)

(L2+ 3a2)

This relation shows that the small deflection regime may be

increased by increasing E and h or by decreasing L. For

example, if thickness is the controlling parameter,

G

3 x 2

4(yV&

146
Designing versus nonlinear material behavior or flexural

failure

Material nonlinearities or flexural failure may also

be avoided by proper sizing of the ENF specimen. For crack

lengths, a, less than or equal to L/2 the maximum bending

stress (disregarding the localized stress singularity at the

crack tip) occurs in the center of the beam.

The maximum bending moment is,

M = L (32)

The maximum bending stress is

om = Mh/I (33)

Combination of equations (32) and (33) gives

3PL

 (34)

m 2I

 4wh2

The maximum strain e is then,

_ 3PL (35)

em E ~ ,_ . 2 4Ewh

In terms of displacement this gives

147
6Lh6 (36)

2L3+3a3

where 6 is the displacement of the central loading pin. By

similar reasoning, a thickness requirement may be formulated

from the condition &„ < 6, where 6= is the maximum allowable

C 3 «

displacement related to the maximum allowable strain, e ,

m, a

to maintain linear material behavior. Calculations of the

required thickness yields:

h > , 0

IIC

 (37)

a Em,aE

148
REFERENCES

[1] D.F. Dewittr R. A. Shapery and W. L. Bradley,

"Method for determining the Mode I delanination

Fracture toughness of Elastic and Viscoelastic

Composite Materials", J. Compos. Material., Vol.

14, (1980), p. 270.

[2] P. D. Mangalgiri and W. S.. Johnson, "Design of CLS

Specimen for Different Resin Toughnesses", ASTM

Meeting Minutes D 30.02.02, test group on interlaminar fracture toughness, measurement, Dallas/Ft.

Worth, Oct. 24, (1984)

[3] L. A. Carlsson, J. W. Gillespie and R. B. Pipes, "On

the analysis of the End Notched Flexure (ENF)

Specimen for Mode II Testing", Submitted for publication.

149
APPENDIX 4

Influence of shear deformations on the ENF Compliance and

strain energy release rate [1]

In Figure 1, the ENF specimen geometry is defined

and modeled as three beams. For small deflections, the

deflection, <S, at the center (C) is simply the algebraic

sum,

where ACD, ABC, and AAB are the maximum deflections of the

three beams CD, BC and AB, respectively. Beams BC and CD

and modeled as the cantilever beam presented in Figure 2.

The deflection due to a point load at one end including

shear deformation [2] is,

150
T

2h

JL

P/2

Fig. 1 ENF Geometry

Fig. 2 Cantilever Bean

2L

\< a >

fv

i*- ^ Ay h II

rK r* x

h

T

P/2

151
where E, and G^^ are the flexural modulus and interlaminar

shear modulus, respectively, and I is the moment of inertia

of the beam. Implicit in the deriviation of Equation (2) is

the assumption that the built-in end does not warp under the

action of shearing stress. This appears to be a reasonable

assumption for beams CD and BC since the point of load

introduciton (Point C) in Figure 1 is an approximate line of

symmetry. Consequently,

G

13

For the delaminated region, AB, of the ENF

geometry, the ends of the parallel beams at point B in

Figure 1 are allowed to warp. For a beam of thickness h =

2c, the horizontal and vertical displacements (u,v),

according to Timoshenko [3], may be expressed with respect

to Figure 2 as

2 3 3 „ 2

p -x y v y y i y

u = — ( - + + ) (5)

152
where

H

The total deformation of the delaminated region has two

components. The bending and shearing deformation is defined

in Equation (6). The second component arises from the rotation of the built-in end for the delaminated region at point

B in Figure 1. The deflection, A._ ... due to the local

AD i o

slope is shown to be [1]

UL2-a3+ ah 2( E 1 /G,,)) (8 )

l 13

The total deflection of the delaminated region assuming

each beam carries an equal load of P/4 is obtained from the

summation of Equations (6) and (8),

(3aL2+5a3+6ah2(E./Gl7)) (9)

1 13

Substitution^of Equations (3), (4) and (9) into (1) yields

an expression for the displacement at the point of load

introduction.

153
. .

4G13h

The compliance including shear deformation is,

,. ~T3 3 2(1.2L + 0.9a)h2E

C = 1 =

 2L

 + 3a ( i + 11 * -i -i

'13

This equation with,

.SH _ P SH

gives,

cu Qa^t) ^1 h 9

G^" = *a W (1 + Qf2(7±-)(-)*) (13)

16E1w h G13

 a

Neglecting the contribution of shear deformation, Equations

(11) and (13) simplify to the expression reported in [4],

C = (14) RT 7.

 V ' BT 3

and

9a2P

2

154
REFERENCES

[1] L. A. Carlsson, J. W. Gillespie and R. B.

Pipes, "On the Analysis of the End Notched

Flexure (ENF) Specimen for Mode II Testing'

Submitted for publication.

[2] S. P. Timoshenko, "Strength of Materials",

Part 1, Krieger Publishing, (1984).

[31 S. P. Timoshenko and J. N. Goodier, "Theory of

Elasticity", Mc-Graw Hill (1970)

[4] A. J. Russell, and K. N. Street., "Moisture

and Temperature effects on the mixed-mode

delamination fracture of unidirectional

graphite/epoxy", Paper presented at an ASTM

Symposium on Delamination and Debonding of

Materials, Nov. 8-10, 1983, Pittsburgh,

Pennsylvania.

155
APPENDIX 5

Influence of friction on the ENF Strain Energy Release Rate

~m

A potential, energy absorbing mechanism in the ENF

specimen, is the friction between the crack surfaces.

Finite element results discussed in Section 3 show that the

contact area is located symmetrically over the outer support

pin and is less than 4h in length where h is the thickness

of each beam in the delaminated region. Summation of the

normal forces within the contact area verifies that each

beam carries an equal load.

With this insight/ an approximate expression to

quantify the work of friction during crack growth may be

obtained from beam theory[lj. The frictional work, Wp, can

be expressed as:

2h

/ uN(x)Au(x)dx (1)

-2h

where y is the coefficient of friction, N(x) is the normal

force distribution and Au(x) is the relative displacement

(sliding) of the crack surfaces. The integral is calculated

over the contact area.

156
The induced normal stress field may, as an

approximation, be represented by the Dirac delta function,

6(x),l2]

N(x) = -| 6(x) (2)

Substitution into Eq. (1) yields the following upper bound,

WF < P u(0)/4 (3)

The sliding, Au(0), may be calculated from the

expression given in Timoshenko and Goodier [3] for the

displacement of a cantilever beam:

Au(0) = 2 |u(0) | = ZL-^ [a2 + h2(E1/G13)/12J (4)

2E, wh

The frictional work is thus:

2

Wp =

 3P M

 ? [a2 -I- h2(E,/G1,)/12] (5)

f Z X 1J

The crack growth criterion nay be formulated by

considering the energy changes as the crack increases its

area by an amount dA:

dA ' dA

 > GIIc + dA~

157
where W is the work supplied by the movement of the external

load, U is the stored strain energy in the body and G,- is

the work required to create a unit new crack surface.

A resonable assumption is that the compliance of the

specimen is unaffected by friction. For this case Eqs. (6),

and (5) give:

3P2ua

4E l wh

SH

where G , given in Appendix 4 is,

2 2

9a P 2] (8)

The energy available for creating new crack surfaces,

may thus be expressed:

SH _ 3P2ua

._ 2, 2 4E,w h

or by using equation (8):

0.2(E1/G13)(h/a)

 2

 - 4y(h/a)/3j (10)

R T 2 2 2 2

where G°j = 9a P /( 16E,w h ) is the expression for G

where influences of interlaminar shear and friction are

neglected.

158
A non-dimensional strain energy release rate

parameter quantifying the influence of friction to the

reduction in strain energy release rate is defined in Eq.

(11),

G^yO) - GII(U) = 4y(h/a)/3 (11)

The results discussed in Chapter 3 show that Eq.(ll) indeed

provides an upper bound to the numerical finite element

results.

159
REFERENCES

[11 L. A, Carlsson, J. W. Gillespie and

R. B. Pipes, "On the Analysis of the

End Notched Flexure (ENF) Specimen

for Mode II Testing", Submitted for

publication.

[2] M.D. Greenberg, "Foundations of

Applied Mathematics", Prentice-Hall

(1978) .

[3] S. P. Timoshenko, and J. N. Goodier,

"Theory of elasticity", 3rd.ed.,

McGraw-Hill (1970) .

160
APPENDIX 6

Stress-Strain Curves5 to forr AP APr o C-2 and CYCOM 982

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167
Appendix 7

Interleuninar Fracture Test Data

Page

Mode I: Double Cantilever Beam

CYCOM 982* 43

APC-2** 50

Lower Bound: G__ 51

Intermediate Bound:GIC 61

Mode II: End Notched Flexure

CYCOM 982* 72

APC2** 76

APC2 Rate Deoendence 80

* Linear load-deflection response

** Non-linear load-deflection response

168
Mode I: Double Cantilever Beam

CYCOM 982*

2W**

Nomenclature

Al[Nm ] : Coefficient(Compliance C[m/N]: Initial Compliance

vs. Crack Length) Pc[N]: Critical Load

A2[Nm]: Coefficient(Critical w[m]: Width

load vs. Crack Length

Summary

Instron Cross Head Rate,6

— 6 [in/min] [10 m/s]

0.05 21

Overall Average

G

IC

[kj/m2]

0.26

0.27

0.25

0.23

0.22

0.26

0.25±0.02

* Linear elastic response and stable crack growth

** See Appendix 1

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Mode I: Double Cantilever Beam

APC-2 Lower Bound: G g

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Nomenclature

A[m]: Crack length DR[mm/s]: Instron Crosshead Speed

2

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Pc[N]: Load at the onset of Al [Nm ] : Coefficient

Nonlinear response

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Summary: Averaged Results

Instron Cross Head Crack Tip Opening*

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1

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1.60±0.26

1.41±0.21

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Overall Average 1.47

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Mode I: Double Cantilever Beam

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Nomenclature

A[m]: Crack length DR[mm/s] : Instron Cross Head Speed

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2 —1

Pc[N]: Maximum load Al [Nm ] : Coefficient

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Summary; Averaged Results

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. . CT

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1.98+0.13

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Mode II: End Notched Flexure

CYCOM 982*

BT 9a2Pc2C

2w(2L3+3a3)

Nomenclature

a[m]: crack length

L[m]: Half Span

W[m]: width

-2

(2.55+0.01x10 m)

Pc[N]:

C[m/N]

t[m] :

Maxium Load

Initial Compliance

Thickness

(3.51+0.03xlO~3m)

Summary

**

Precrack

No Precrack

Mode I

Mode II

Mode II

No Precrack

Half Span

[ml

0.051

0.051

0.051

0.038

0.038

G

n

[kj/m2]

1.45+0.16

0.68+0.02

0.77+0.07

0.68+0.11

1.40+0.18

FE***

1.85+0.20

0.87+0.03

0.98+0.09

0.94+0.15

1.93+0.25

*

**

***

Linear load deflection response

Instron Rate: 21x10 m/s [0.05 in/min]

See Tables 15 and 17 for Material 3 (E1/G13=25.7)

198
Mode II: End Notched Flexure

CYCOM 982

No Precrack

Sample

C4

C6

C7

C9

Cll

CIS

C20

C28

Cl

C2

C17

C5

C23

C3

C8

C26

L

[m]

0.051

0.051

0.051

0.051

0.051

0.051

0.051

0.051

0.038

0.038

0.038

0.038

0.038

0.038

0.038

0.038

a

L

0.52

0.51

0.51

0.50

0.51

0.51

0.50

0.51

0.37

0.37

0.36

0.57

0.54

0.69

0.68

0.68

c

[10~6m/N]

2.53

2.46

2.41

2.36

2.42

2.01

2.51

2.45

0.93

0.96

0.96

1.18

1.16

1.41

1.41

1.37

PC

[N]

1268

1321

1201

1357

1334

1277

1237

1201

2002

2037

2171

1503

1557

1179

1277

1179

_BT

Giic2

[kj/in

1.59

1.63

1.29

1.59

1.63

1.23

1.41

1.31

1.10

1.31

1.28

1.56

1.52

1.45

1.67

1.39

199
Mode II: End Notched Flexure

CYCOM 982

Mode I Precrack

Sample

C-2-12

C-2-15

C-2-16

02-17

C-2-2

C-2-18

C-2-32

C-2-31

C-2-21

C-2-13

C-2-11

C-2-10

C-2-14

L

Cm]

0.051

0.051

0.051

0.051

0.051

0.051

0.051

0.051

0.051

0.051

0.051

0.051

0.051

a

L

0.55

0.57

0.54

0.56

Mode

0.64

0.60

0.58

0.58

0.51

0.59

0.78

0.79

0.87

C

[10~6m/N]

2.59

2.66

2.67

2.81

II Precrack

2.85

2.66

2.66

2.57

2.48

2.45

3.19

3.62

3.79

PC

IN]

801

765

792

743

725

796

783

801

863

863

667

609

560

rBT

G

IIC

[kj/m2]

0.71

0.69

0.69

0.67

0.75

0.79

0.75

0.7 4

0.69

0.86

0.88

0.84

0.78

200
Mode II: End Notched Flexure

CYCOM 982

Mode II Freerack

Sample

C-2-3

C-2-5

C-2-7

C-2-29

C-2-25

C-2-26

C-2-27

C-2-28

C- 2- 30

C-2-1

C-2-6

C-2-20

C-2-24

L

[ml

0.038

0.038

0.038

0.038

0.038

0.038

0.038

0.038

0.038

0.038

0.038

0.038

0.038

a

L

0.54

0.44

0.44

0.42

0.45

0.54

0.47

0.62

0.70

0.57

0.82

0.82

0.87

C

[10~6m/N]

1.04

0.97

0.97

1.01

1.04

1.12

1.27

1.28

1.38

1.50

1.80

1.53

1.66

PC

lw]

1076

1348

1414

1334

1099

1054

947

899

899

810

681

752

729

rBT

G

IIC

[kj/m2]

0.65

0.70

0.78

0.65

0.51

0.69

0.51

0.68

0.83

0.58

0.71

0.73

0.78

201
Mode II: End Notched Flexure

APC-2*

BT 9a2Pc C

2w(2L3+3a3)

Nomenclature

a [m] : Crack length

L[m]: Half Span

W[m]: Width**

Pc[N]: Maxium Load

C[ro/N]: Initial Compliance

t[m]: Thickness**

Summary

***

Precrack

No Precrack

Mode I

Mode I

Mode II

Mode I

Mode I

Number of

Plies

26

26

40

26

26

40

Half Span

f i [m]

0.051

0.051

0.051

0.051

0.038

0.038

~ BT

GIIC

j

[kj/nT]

2.7310.33

1.7810.11

1.8710.11

1.9310.28

1.8910.16

1.8410.07

*

**

***

Non-linear load deflection response

_2

Average width: 2.54±0.01x10 m

Average Thickness: 3.37±0.02xlO m (26 ply)'

5.26±0.05xlO~3m (40 ply)

Instron Rate: 21xlO~ m/s [0.05 in/min]

202
Mode II: End Notched Flexure

APC-2

No Precrack (26 plies)

Sample

A- 2- 24

A- 2- 2

A- 2- 8

A- 2- 4

A- 2-1

A- 2- 20

A- 2- 14

A- 2- 13

A- 1-5

A- 1-17

A- 1-11

A- 1-3

A- 1-21

A-l-15

L

[m]

0.051

0.051

0.051

Mode

0.051

0.051

0.051

0.051

0.051

0.051

0.051

0.051

0.051

0.051

0.051

a

L

 [10

0.49

0.50

0.49

I Precrack

0.53

0.52

0.52

0.51

0.50

0.52

0.53

0.53

0.51

0.53

0.51

C PC

~

6

m/N] [N]

3.21

3.47

2.91

(26

3.89

3.56

2.81

3.02

2.78

2.64

3.02

2.57

2.57

2.92

2.62

1546

1368

1724

plies)

1079

1112

1257

1212

1301

1303

1268

1535

1303

1201

1414

1.80

1.70

1.74

1.66

1.72

1.76

1.93

2.01

1.68

1.67

1.99

203
Mode II: End Notched Flexure

APC-2

Mode I Precrack (40 plies)

Sample

A- 3-1

A- 3- 2

A- 3- 3

A- 3- 4

A- 3- 5

A- 3- 6

A- 3- 7

A- 3- 8

A- 3- 9

A- 3- 10

A- 3- 11

L

[m]

0.051

0.051

0.051

0.051

0.051

0.051

0.051

0.051

0.051

0.051

0.051

a

L

0.50

0.52

0.54

0.53

0.52

0.53

0.52

0.50

0.50

0.50

0.51

C

[10~6m/N]

0.73

0.67

0.69

0.71

0.67

0.77

0.83

0.74

0.73

0.76

0.76

PC

[N]

2630

2624

2489

2530

2677

2694

2483

2618

2778

2542

2483

rBT G

nc2

[kj/nT]

1.86

1.82

1.84

1.80

1.86

2.26

2.01

1.86

2.08

1.87

1.77

Mode II Precrack (26 plies)

A- 2- 5

A- 2- 9

A- 2- 18

0.051

0.051

0.051

0.51

0.49

0.52

4.78

2.77

3.07

1012

1546

1268

1.81

2.35

1.95

204
Mode II: End Notched Flexure

APC-2

Mode I Precrack (26 plies)

Sample

A- 1-6

A- 1-8

A- 1-7

A- 1-12

A- 1-24

A- 1-19

A- 1-20

A- 1-22

A-l-23

A- 1-2

A- 1-9

A- 1-1

A- 3- 12

A- 3-13

A- 3- 14

A- 3-15

A- 3- 16

L

0.038

0.038

0.038

0.038

0.038

0.038

0.038

0.038

0.038

0.038

0.038

0.038

Mode

0.038

0.038

0.038

0.038

0.038

a C PC

L

 [10"6m/N] [N]

0.68

0.66

0.68

0.65

0.53

0.52

0.51

0.48

0.52

0.32

0.34

0.35

I Precrack

0.54

0.51

0.58

0.51

0.56

1.36

1.35

1.30

1.35

1.09

1.03

1.16

1.12

1.26

0.95

1.00

0.96

(40

0.32

0.32

0.34

0.31

0.33

1312

1410

1423

1414

1801

1890

1922

1926

1766

2847

3069

2433

plies)

3203

3410

3114

3380

3084

G

IIC

[kj/m2]

1.69

1.88

1.94

1.86

1.96

1.88

2.15

1.90

2.05

1.83

2.08

1.56

1.79

1.86

1.98

1.79

1.77

205
Mode II: End Notched Flexure

APC-2 Rate Dependence*

orp 93. P C TIT

_ BT NL r.tii - - 9a2Pc2C

IISC

 2w(2LJ+aJ)

 IX

 2w(2L3-i-3a3)

a[m]

L[m]

w[m]

t[m]

Nomenclature

: Crack Length Pc[N]:

: Half Span (0.051m)

 P

NL

[N]:

: Width (2.5410.010"2)

: Thickness .,

(3.37 0.02x10'^) C[m/N]:

Averaged Results

Mode II Rate Dependence

Averaged Results

Instron Cross Head Crack Tip Shear

Rate, 6* Rate, 6 ^

[in/min] [10"6m/s] [10~10m/s]

0.01

0.05

0.10

1.00

10.00

* Mode I

** 5CT =

6

4 26

21 130

42 260

423

 2500

4233 25000

Overall Average

Precrack unless noted otherwise

<VL)3 E,

Maximum Load

Load at the onset on

nonlinear response

Initial compliance

: APC2*

rBT BT

IISC IIC

[kj/m

0.9510.18 1.8410.

1.0210.20 1.7310.

1.0H0.09 1.8210.

0.9810.16 1.8710.

1.4010.13 1.4010.

1.31 1.73

2!

27

20

20

24

13

!+!<!> ' >5T3

206
Mode II Rate Dependence: APC-2

Instron Cross Head Rate:4x10 m/s [0.01 in/min]

Sample

EP-.01-1

EP-.01-2

EP-.01-3

EP-.01-4

EP-.01-5

Instron

EP-.l-l

EP- . 1- 2

EP-.1-3

EP-.1-4

EP-.1-5

A- 2- 11

A- 2- 21

A- 2- 16

A- 2- 3

A- 2- 6

A- 2- 7

A- 2- 10

A- 2- 19

a

L

0.52

0.56

0.52

0.47

0.51

Cross

0.48

0.54

0.51

0.53

0.52

0.49

0.50

0.50

0.49

0.51

0.49

0.51

0.54

C PnL

[10~6m/N] [N]

2.63

2.72

2.84

2.02

3.45

Head Rate:

2.54

2.85

2.43

2.86

2.75

2.87

3.15

3.02

3.85

Mode II

'3.64

3.07

2.88

2.97

956

801

1001

1045

1001

42xlO~6m/s

1134

890

1001

956

979

1112

956

1023

945

Precrack

1212

1268

1290

1245

PC

[N]

1303

1130

1334

1619

1312

[0.10

1512

1210

1326

1228

1370

1312

1257

1257

1101

1323

1401

1446

1368

rBT

^IISC

[kj/m2]

0.91

0.75

1.10

0.74

1.29

in/min]

1.14

0.93

0.92

1.05

1.02

1.27

1.08

1.16

1.23

1.77

1.79

1.79

1.91

~BT

G

IIC

[kj/m2]

1.72

1.49

1.95

1.77

2.22

2.03

1.72

1.61

1.73

2.00

1.79

1.85

1.74

1.66

2.14

2.25

2.25

2.30

207
Mode II Rate Dependence: APC-2

Instron Cross Head Rate; 423x10 m/s [1.00 in/min]

Sample

EP-1-1

EP-1-2

EP- 1- 3

EP-1-4

EP- 1- 5

Instron

EP-10-1

EP-10-2

EP-10-3

EP-10-4

EP-10-5

a

L

0.53

0.53

0.52

0.53

0.51

Cross

0.51

0.52

0.52

0.53

0.53

C

no'6

2.92

2.55

3.06

2.99

2.58

Head Rate

2.59

3.11

2.82

3.42

3.16

PnL

m/N] [N]

1023

912

890

845

1001

: 4233xlO~6m/s

1210

1103

1192

939

1023

PC

[N]

1379

1379

1157

1214

1334

[10.0

1210

1103

1192

939

1023

rBT

G

IISC

[kj/m2]

1.24

0.85

0.96

0.86

0.99

in/min]

1.43

1.46

1.57

1.21

1.32

rBT

G

IIC

[kj/m2]

2.25

1.94

1.62

1.77

1.75

1.43

1.46

1.57

1.21

1.32

208
Standard Bibliographic Page

1. Report No.

NASA CR- 178066

4. Title and Subtitle

Del ami nation Growth in Composite

7. Author(s) John W. Gillespie, Jr.

Leif A. Carlsson

R. Byron Pipes

2. Government Accession No.

Materials

Robert Rothschilds

Bruce Trethewey

Anthony Smiley

9. Performing Organization Name and Address

University of Delaware

College of Engineering

Newark, Delaware 19716

12. Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Washington, DC 20546

3. Recipient's Catalog No.

5. Report Date

February 1986

6. Performing Organization Code

8. Performing Organization Report No.

10. Work Unit No.

11. Contract or Grant No.

NAG1-475

13. Type of Report and Period Covered

Contractor Report

14. Sponsoring Agency Code

506-43-11

15. Supplementary Notes

Langley technical monitor: J. D. Whitcomb

16 Abstract

The Double Cantilever Beam (DCB) and the End Notched Flexure (ENF) specimens are

employed to characterize MODE I and MODE II interlaminar fracture resistance of

graphite/epoxy (CYCOM 982) and graphite/PEEK (APC2) composites. Sizing of test

specimen geometries to achieve crack growth in the linear elastic regime is presented. Data reduction schemes based upon beam theory are derived for the ENF

specimen and include the effects of shear deformation and friction between crack

surfaces on compliance, C, and strain energy release rate, GTJ. Finite element

(FE) analyses of the ENF geometry including the contact problem with friction are

presented to assess the accuracy of beam theory expressions for C and GJJ.

Virtual crack closure techniques verify that the ENF specimen is a pure Mode II

test. Beam theory expressions are shown to be conservative by 20 to 40 percent

for typical unidirectional test specimen geometries. A FE parametric study investigating the influence of delamination length and depth, span, thickness and

material properties on GTJ is presented. Based upon these results, a more

accurate data reduction scheme is proposed. Mode I and II interlaminar fracture

test results are presented. Important experimental parameters are isolated, such

as precracking techniques, rate effects, and nonlinear load-deflection response.

It is found that subcritical crack growth and inelastic materials behavior, responsible for the observed nonlinearities, are highly rate-dependent phenomena

with high rates generally leading to linear elastic response.

17. Key Words (Suggested by Authors(s))

Delamination

Fracture Toughness

Composites

Compression

Analysis

19. Security Classif.(of this report)

Unclassified

18. Distribution Statement

Unclassified-Unlimited

Subject Category 24

20. Security Classif.(of this page)

Unclassified

21. No. of Pages

212

22. Price

A 10

For sale by the National Technical Information Service, Springfield, Virginia 22161

NASA Langley Form 63 (June 1985)