NASA-CR-176416 

19860004845 
.~ 

DELAMINATION GROWTH 

IN COMPOSITE MATERIALS 

John W. Gillespie, Jr. 

Leif A. Carlsson 

R. Byron Pipes 

Robert Rothschilds 

Bruce Trethewey 

and 

Anthony Smiley 

r - -- - - r -

CENTER FOR COMPOSITE MATERIALS 

College of Engineering 

University of Delaware 

Newark, Delaware 19716 

, , 

! I.' l... I r'{' I I • I -. , .!. .... 

NASA Grant Number NAG-1-475 

Program Monitor: John D. Whitcomb 
ABSTRACT 

In this report research related to growth of an imbedded 

through-width delamination (ITWD) in a compression loaded composite 

structural element is presented. In the experimental part of the 

study, composites with widely different interlaminar fracture 

resistance were examined, viz., graphite/epoxy (CYCOM 982) and 

graphite/PEEK (APC-2). 

The initial part of the program consisted of characterizing 

the material in tension, compression and shear mainly to obtain 

consistent material properties for analysis, but also as a check of 

the processing method developed for the thermoplastic APC-2 

material. 

The characterization of the delamination growth in the ITWD 

specimen, which for the unidirectional case is essentially a mixed 

Mode I and II geometry, requires verified mixed-mode growth 

criteria for the two materials involved. For this purpose the main 

emphasis during this part of the investigation has been on Mode I 

and II fracture specimens, namely the Double Cantilever Beam (DCB) 

and End Notched Flexure (ENF) specimens. Data reduction schemes and 

sizing to achieve crack growth in the linear elastic regime are 

discussed. Moreover, beam theory expressions for the ENF specimen 

including the influence of inter laminar shear deformation for the 

compliance, C, and strain energy release rate, GII has been 

derived. The results indicate that for certain combinations of 

material properties and geometry interlaminar shear may indeed need 

i 
!"" 

to be accounted for in the data reduction scheme. Furthermore, the 

influence of friction between the crack surfaces was addressed by 

beam theory where the decrease in strain energy release rate due to 

friction was quantified by a non-dimensional strain energy release 

rate parameter. This parameter provides means to minimize the 

influence of friction by suitable specimen design. Results for 

commonly used ENF geometries indicate that neglecting friction, 

results in an overestimate of the strain energy release rate of 

only 2 to 4 percent for the friction coefficients investigated. 

Finite element (FE) analysis was performed to investigate 

whether the ENF geometry is a pure Mode II test and to assess the 

accuracy of the beam theory expressions for C and GIl· The contact 

problem was investigated by introducing nonlinear truss elements 

along the crack interface. Frictional effects were also evaluated. 

GI and GIl were numerically determined using the virtual closure 

technique which enables mode separation. GI was found to be 

identically zero. The compliance method for calculating the total 

strain energy release rate was also utilized and gave identical 

results with the crack closure approach. Consequently, both 

numerical techniques allow GIl to be evaluated straightforwardly. 

Comparison with beam theory expressions including inter laminar 

shear revealed that although good agreement in global compliance 

was obtained, beam theory expressions for GIl may be conservative 

by 20 to 40 percent for a typical unidirectional graphite fiber 

ii 
composite and test specimen geometry. 

A parametric study based upon the finite element analysis of 

the frictionless contact problem is presented. The influence of 

delamination length and depth, span, laminate thickness and 

material properties on GIl are presented and correlated with beam 

theory results. In an attempt to generalize finite element results, 

non-dimensional quantities for compliance and GIl are identified 

from the parametric study to accommodate sligth variations in 

geometry or material properties that will inevitably arise in an 

experimental program to characterize GIIC . Based upon these results 

a more accurate data reduction scheme is proposed. 

The numerical results on friction effects bear out that 

analytical beam theory provides a conservative upper bound on the 

decrease in GIl due to friction. Thus, for reasonable coefficients 

of friction, frictional effects are negligible for commonly used 

ENF geometries. 

In Chapter 4, 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 

material behavior, responsible for the observed nonlinearities, are 

highly rate dependent phenomena with high rates generally leading 

to linear elastic type of behavior. Moreover, unstable crack growth 

in APC-2 during Mode I loading was found to be highly rate 

iii 
dependent. At all rates, except at the lowest rates, stick-slip 

behavior or unstable crack growth was observed in DeB testing of 

APC-2. Finally, preliminary ITWD test results on 64 ply 

unidirectional laminates are presented. 

iv 
Table of Contents 

ABSTRACT 

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 

r 3.1. 6 

Schemes for the ENF Specimen .......................... 57 

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 

REFERENCE S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 121 

v 
APpendices 

APPENDIX 1 Data Reduction Schemes for the DCB, ENF 

and CLS Specimens ................................. 1 

APPENXIX 2 Stability of Crack Growth for the ENF 

Specimen ......................................... 10 

APPENDIX 3 Design Considerations for the DCB, ENF and 

CLS Specimens .................................... 13 

APPENDIX 4 Influence of Shear Deformation on the ENF 

Compliance and Strain Energy Release Rate ........ 24 

APPENDIX 5 Influence of Friction on the ENF Strain 

Energy Release Rate .............................. 30 

APPENDIX 6 Stress-strain curves for APC-2 and 

CYCOM 982 ........................................ 35 

APPENDIX 7 Mode I and II Interlaminar Fracture 

Test Data ........................................ 42 

vi 
1. INTRODUCTION 

Delaminations represent a common and characteristic flaw ~n 

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 load~ngs 

[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 stud~es 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, GI, for a compressively loaded laminate with an ITWD 

monotonically increases, attains a global maximum and dim~nishes 

to zero with increasing load [1,9,13]. The Mode II component 

1 

(GII), however, is a monotonically increasing function of the 

applied compressive load. This phenomenon is attributed 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 

general terms, short deeply imbedded delaminations or 

delaminations in materials exhibiting low Mode I fracture 

toughness should be predicted accurately by GI = GIC. For this 

combination of ITWD geometry and GIC, the Mode II component GII 

is negligible and all three failure criteria converge for short 

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

delaminations or materials exhibiting large GIC values exhibit 

reduced axial stiffness resulting in a dominately Mode II state 

of deformation since GI tends to zero. Consequently for this 

bound on ITWD geometry, the appropriate failure criteria would be 

GII = GIIC. In this regime, only the mixed-mode failure 

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 

3 
Fig. 2 

100 

80 

60 

40 

20 

~ 

~ 

\ 

\ 

\ 

, 

, 

BUCKLING CURVE / "' " 

" ..... ..... -----. %~----~10~--~2~O~----3~O------4~O----~50 

DELAMINATION LENGTH, mm 

Critical load for delamination growth us~ng three 

growth criteria [13]. 

4 
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 pred~cting 

delamination growth. In this situation, only an appropriate 

mixed-mode failure 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: 

• Experimental investigation of instability-related 

delamination growth for two graphite fiber composites 

exhibiting significantly different fracture 

toughnesses. Various delamination lengths and depths 

are considered to provide a wide range of mixed-mode 

response. 

• Correlate experimental data (pre and postbuckling 

strains and deformations) with analytic and 

geometrically non-linear finite element results. 

• Establish a mixed-mode interlaminar fracture cr~teria 

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 (DCB), 

I 

~ Cracked Lap Shear (CLS) and the relatively new End Notched 

5 
Flexural (ENF) test specimens. The DCB specimen is a viable 

pure Mode I test for measuring GIC' Stable crack growth is 

achievable enabling the compliance method to be employed in the 

straightforward data reduction scheme summarized in Append~x 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 

{IS] to estimate GIIC for a material system of interest is 

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

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, GC' 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 GIC and GIIC' 

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 

inter laminar 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 

6 
limited to simple isotropic beam theory for deriving express~ons 

for compliance and strain energy release rate. S~nce an 

independent measurement of GIIC 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 GII 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 GII. 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. GI 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 GII 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 

7 
theory underestimate GIl signif~cantly 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. 

8 
2. EXPERIMENTAL 

An outline of the experimental program is presented in 

Table 1. The program includes processing of thermoset composites 

[Graphite/Epoxy (CYCOM 982)] and thermoplastic composites 

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

laminates. The.basic materials characterization aims to provide 

the lamina elastic and failure properties and the fracture 

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 

interlaminar fracture 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 consol~dation 

cooling should be rapid and ICI achieves acceptable cooling rates 

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

190oC. The Wabash Press employed in the current processing cools 

9 
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 
APC 2 PROCESSING 

WZJbZJsh Press 

MZJx. Temp. = 427°C (800°F) 

MZJx. lOZJd = 150 ton 

Cooling: Alr/WZJter 

t2 

APC 2 PZJnel: l x W x t r ~======:;:X::; l = 30.5 em ( 12 in.) 

W = 20.3 cm (8 inJ 

t = IZJminZJte 

thickness 

Glgzing Plqte (Stginless) 

t 1 = 4.8 mm (0 1875 in.) 

Aluminum FOIl 

(Release Agent Required) 

t 2 = 0.1 mm (0.004 in.) 

Picture FrZJme 

Press P1ZJten 

0.0254 mm (010 in) ~ t - t3 ~ 0.38 mm (0.015 in.) 

Fig. 3 APC-2 Picture Frame Molding 

11 
APC 2 PROCESSING 

- Press Temperature LI. 

0 

- 720 ~ 

L. 

::;, 

~ 

a 

L. 400 ~ 

Q. 

E 

~ 

... T+1S Time 

(min) 

.--

en Cooling Pressure 

Q. 

- 340 ~ 

~ 250 

en 

en 

~ 

d: 85 t--I--.... 

Contact Pressure 

Fig. 4 APC-2 Heating/Cooling Cycle 

12 

Time 

(min) 

u 

382 0 

-~ 

'-

::;, 

~ 

200 10 

'-

~ 

Q. 

E 

~ 

... 
COOLING RATES FOR APC 2 PROCESSING 

1.0 

ICI Recommended Cooling 

0.8 Rate ~36° C/ Minute 

Wabash Press Cooling 

Q) 

~ Rate::=: 38°C/Minute 

:::::J 

-0 06 ~ Water Cooling 8. -.. E E 

~ ~ 

r-. 0.4 Q) 

c: 

0 Air/Water 

a.. 

Cooling 

0.2 T melt = 380° C 

• Thermocouple Imbedded at 

0.0 

Midplane of [0]16 Laminate 

0 2 4 6 8 10 12 

Time (minutes) 

Fig. 5 Experimental Cooling Rates for APC-2 [0]16 Panels 

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

adequate cooling rate of approximately 40oC/min over the critical 

temperature range of 3800 C to 200oC, 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 graphite fiber 

composite materials will consist of the Double Cantilever Beam 

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

measuring Glc and Gllc 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. 

14 
) ) ') 

Table 2 Bas~c Materials Characterizat~on 

No. of 

Load~ng Lay-uEs Dimensions Gages ReElicas Obta~n 

Tens~on [0]8 12.7 x 229 mm 1 Axial-Transv. 5 E1 ' 

T T,ult v 12 ,X1 ,e: l , 

[90]16 25.4 x 229 mm II 5 T T,ult E2'V21,X2,e:2 

[±45]2S 25.4 x 229 mm II 5 G12 ,S6' 

ult 

y 12 

I-' 

U1 EC XC &C,ult Compr. [0]16 6.4 x 127 mm 2 Axial-Transv. 5 l' l' 1 

[90]40 12.7 x 127 mm II 5 EC xC e:C,ult 

l' l' 2 

Flex. [0]16 6.4 x 102 mm 2 Ax~al (Top/bottom) 5 f f 

E1 ,Xl 

Thermal [0]8 50.8 x 50.8 mm Axial-Transv. 2 a 1 ,a2 (CTE) 
I-' 

0\ 

') 

I ') 

Table 3 Tens11e and Shear Test Results 

Property units APC-2 APC-2/ICI 2 Graphite/CYCOM 982 

El GPa (Msi) 129.0 (18.7i 1.0) 

E2 GPa (Msi) 9.4 (1.37±0.02) 

v 12 0.310±0.020 

v 21 0.023±0.003 

G12 GPa (Msi) 4.5 (0.65±0.02) 

xT 

1 MPa (Ksi) 2140 (310±8) 

xT 

2 MPa (Ksi) 76 (11±1) 

S6 MPa 141 (21:!:1)3 

£T,ult % 1. 60±0. 04 1 

e;T,ult 

2 % 0.94±0.05 

r-F1ve Rep11cates 

2 Prov1s1onal Data Sheet APe PD2 

3 [±4512S Lam1nate Strength 

134.0 (19.4) 

8.9 (1.29) 

5.1 (0.74) 

2130 (309) 

80 (11.6) 

150 (22 

1.45 

1.00 

136.0 (19.7±0.1) 

10.0 (1.53±0.1) 

0.300±0.020 

0.023±0.003 

4.7 (0.68±0.002) 

2170 (315:!:6) 

47 (6.8:!:0.6) 

78 + n1.3-0.2 ) 

1. 60±0 .10 

0.45±0.04 
') -) ') 

Table 4 Compress1ve Test Results 

Property Units APC-2 APC-2/ICI Graph1te/CYCOM 982 

E1 GPa (Msi) 117 (17.0:!:1.0) 131 (19.0±1.0) 

E2 GPa (Msi) + 9.2 (1.33-0.05) 9.3 (1.35±0.07) 

C 

Xl MPa (KS1) 1254 (182±5) 1100 (160) 1295 (188±5) 

XC 

2 MPa (Ksi) 214 (31±1) 193 (28±1) 

..... 

...... e:c,ult 

1 % 1.1±0.1 1.0±0.1 

e:c,ult % 2.3±0.1 2.7±0.1 2 

1 F1ve Replicates 

2 Prov1s10nal Data Sheet APC PD2 
') 

.... 

00 

Table 5 

') 

Fiber Volume Fractlon, Coefficient of Thermal Expanslon and 

Flexure Test Results 

Property Units APC-2 APC-2/ICI 2 Graphite/CYCOM 982 

Vf 0.62 0.62 0.67 

<Xl \.u:/ o C (}.I£/OF) 3.4 (1.9) 

().2 }.l£/o C (}.I£/oF) 34.1 (18.9) 

Ef 

1 GPa (MS1) 115.1 (16.7±0.5) 126 (18.3±0.7) 

xf 

1 MPa (Ksi) 1632 (237±6) 1729 (251±8) 

f,ult 

£1 % 1.4±0.1 1.3±0.1 

1 Five Replicates 

2 Provlsional Data Sheet APC PD2 

) 
DCB t 

ENF 

LV Dr 

ClS 

LVDr 

Fig. 6 Inter1aminar 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 aiL ~ 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 aiL ~ 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 [1S]. 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 DCB, 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 GIC. 

Results 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 

DCB Maintain linear behavior 

ENF Avoid flexural failure, maintain linear behavior 

CLS Avoid strap tensile failure 

21 
30 

tJ) 20 

Q) 

a.. 

~ 10 

SIZING OF THE DCB SPECIMEN 

(MAINTAIN LINEAR RESPONSE) 

GIC , in.lb./in~ 

o 6 8 10 

o = 152.4 mm (6 in.) 

E = 138 GPo (20 x 106 psi) 

o~ ____ ~ ____ ~ ____ ~ __ ~~ __ ~ 

o 0.5 1.0 1.5 2.0 

Gtc , kJ/m2 

Fig. 7 Sizing the DeB 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 lam~nate 

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 

In the range of 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 GIIc 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 

de1aminations 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) 

Gc , in.lb.lin.2 

o 10 20 30 40 50 20~------------------------~-----

en 

cv 

15 

( a... 10 

~ 

5 

CLS 

E = 138 GPa (20 x 106 psi) 

xT = 2100 MPa (0.3 x 106 psj) 

2 

Fig. 8 Sizing the CLS Specimen to avoid strap failure 

24 

8 
en 

Q) 

GlIC , in. Ib./in.2 

400~ _____ 1~0 ______ 2~0 ______ 3~0 ______ ~4~0 ____ ~50 

ENF 

30 Small Deflections 

a.. 20 

~ 

10 1'---Linear Material Behavior 

2 

or Flexural Failure 

€ma=O.OI 

4 

2 GlIc, kJ/m 

6 8 

Fig. 9 Sizing the ENF Specimen to maintain linear elast~c 

response E1 = 138 GPa, aiL = 0.5 and y1 = 0.2 

25 
N 

C'I 

) 

Table 7 

SEec1men 

DCB 

ENF 

CLS 

') 

Details of Interlam1nar Fracture Test1ng 

Compl1ance 

APC-2 CYCOM 982 Dimensions Determination Data Reduction 

[0)26 [0)24 25.4 x 254 mm crosshead Compliance and 

movement Area Methods 

[0)26,r O)40 [0)24 25.4 x 279 mm LVDT,crosshead FE/Beam Theory 

[0)6 [0)6 25.4 x 254 mm LVDT,crosshead Compliance 

* All spec1mens have a 25.4 mm long starter crack cons1sting 

of a 0.025 mm th1ck Kepton film. 

) 

Obta1n 

Glc 

Gllc 

G I, IIc 
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 

I ..... ~f-------~4 in·------I~~I 

p-~ 

Master Grid ~ 100 lines/in. 

Collimating 

Lens 

~--p 

Grid Shadow 

Light Source 

(with a laser beam expander) 

.t"~g. 1 J Shauow Moire optical set up for the through-width 

delamination specimen. 

28 
3000 

I 

2500 

I 

2000 

a·SAsO 

G1 • 

1500 

02 (SA +SO) 

m- 1 

1000 

500 

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

29 
Fig. 12 Normalized Plot of GII 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 GII (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, impl~cit is the 

assumption that the contact area extends along the ent~re crack 

length. 

31 
W 

N 

'\ 

) ) 

Finite Element Model 

• Two-dImensional, plane stress 

• ADINA, 3611 nodes, 3318 elements 

• Linear elastic 

• Frlcttonless crack Interface 

• Non-linear truss elements Included 

to tdenttfy contact area 

Crack Tip Mesh 

·1· L • I,x 

I. a .1 

L .1 

F1g. 13 Finite Element Model of ENF Specimen. 

) 
+--_+-1 _---4 I 

·~I-~ I I 

tt§~£=E1 =:::J=t ___ Crack 5F Interface 

Fig. 14 Finite Element Model in the Vicinity of the Crack T~p 

33 
! 

L V 

/ 

O.16h 

I 

i 

./ V ~Cr ack Tip 

(y -displacement fixed) 

Non-linear Truss 

Elements Along 

Crack Interface 

Fig. 15 Deformed shape of Fin~te Element Model ~n the vicin~ty 

of the crack tip 

34 
(J 

Tension 

Compression 

F~g. 16 Constitutive Model for Nonlinear Truss Elements 

35 
Material properties employed in the F~nite Element modelling 

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

distribution as a function of E1/G13 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 ( 1 0 ) and (14) of Appendix 4. 

CSH (a=O) 

L3 [1 + 1. 2 ( Ell h \ J = 

4E G13 , \!0' l Wh3 

( 1 ) 

CBT (a=O) 

L3 

= 3 4El wh 

( 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 
,---- I 

Table 8 Material Properties investigated in the Finite Element 

Modeling. (\112 = "23 = ')13 = 0.3) 

Material 1 

137.8 

10.0 

10.0 

33.3 

Material 

126.1 

9.7 

9.7 

Ej/G13 

18.3 

26.9 

122.0 

183.0 

2 Material 3 

115.1 

9.7 

9.7 

12.8 

25.7 

51.4 

Table 9 Compliance of an Orthotropic Beam under Three Point 

Bending. Material 1, E1/G13 = 33. L = 50.8 mm, 

h = 1.52 mm, w = 25.4 mm. 

~ 

CBT 

1.035 

£EE. 

CSH 

0.999 

£slL. 

CBT 

1.035 

37 
(-

r 

a. 

Q) A 

e "C 

If 8 

~ 

(j "C 

!2 Q) 

c: 

0 c. 

u c. 

« 

014 ~-----r------r------r----~r------.-----,----~ 

0.12 

0.10 

0.08 

0.06 Contact Area s 4h 

0.04 

002 

E,/G'3 

• 183 

0 27 x 18 

Load Introduction 

(P/2) 

0.0 ~~~n-~~~L-~~~L-~~~~~~~~ ____ ~ 

-1.2 -0.8 -0.4 00 0.4 0.8 I 2 1 4 

x/2h 

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 compliance has been derived yielding the following 

expression: 

= [1 + 

2 2(1.2L + 0.9a}h El 

33] (2L + 3a }G13 

( 3 ) 

The parametric study investigates the influence of shear 

deformation (E1/G13) 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 E1/G13 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 ~n 

[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 

E1/G13 = 26. For this particular configuration, finite element 

results are within two and seven percent of CSH and CBT 

respectively. Reasonable agreement between experimental 

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 

h = 

h = 

Comparison of Finite Element Results with Beam Theory 

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

!1 £EE. £EE.. 

G13 CBT CSH 

1.70 mm 12.8 1.037 1.001 

25.7 1 .071 0.998 

51 .4 1.134 0.990 

2.62 mm 12.8 1.084 0.998 

25.7 1.158 0.988 

51.4 1 .301 0.968 

40 
Table 11 Compliance of the ENF Specimen. 

Material 

h = 1.52 

h = 1.70 

Material 

h = 1.70 

Material 

h = 2.62 

Comparison of Finite Element Results with Beam 

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

2 18.3 1.049 1.008 

mm 26.9 1.067 1.007 

122.0 1.246 0.981 

183.0 1.353 0.963 

mm 26.9 1.081 1.007 

3 12.8 1.043 1.008 

mm 25.7 1.078 1.006 

51.4 1.140 0.999 

3 12.8 1.092 1.008 

mm 25.7 1.165 0.997 

51 .4 1.301 0.974 

41 
Table 12 Compliance of the ENF Specimen. 

Comparison of Finite Element Results with Beam 

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

!1. SEE. SEE. 

G13 CBT CSH 

Material 2 18.3 1.052 1. 015 

h = 1.52 mrn 26.9 1.070 1 .016 

122.0 1.235 0.994 

183.0 1.330 0.974 

Material 3 12.8 1.047 1. 015 

h = 1.70 mrn 25.7 1 .081 1 .016 

51 .4 1.140 1 .011 

Material 3 12.8 1.094 1.018 

h = 2.62 mrn 25.7 1.162 1. 010 

51.4 1.285 0.987 

r' 

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 

!t £EE.. £EE. 

G13 CBT CSH 

Material 2 18.3 1 .031 1.008 

h = 1.52 mm 26.9 1.042 1.008 

122.0 1 .149 0.997 

183.0 1 .212 0.987 

Material 3 12.8 1.028 1.007 

h = 1.70 mm 25.7 1.049 1.009 

51.4 1.087 1.006 

Material 3 12.8 1.059 1. 011 

h = 2.62 mm 25.7 1.103 1.008 

51.4 1.184 0.996 

,~ 

43 
0 

u 

"-

u 

.. Cl) 

0 

c 

0 

-

a. 

E 

0 

U 

"U 

Cl) 

~ N or .. -

0 

E 

~ 

0 

z 

') 

(all) 

0 0.5 0.6 0.7 0.8 0.9 

3 

2 

Ir C/CO :: 1+ ~ (o/l)3 

0 

L3 C - 0- 4E Wh3 

I 

0.2 0.4 0.6 0.8 

(a/l)3 

11y. lu Comp11ance as a ¥unction of Crack Length for the ENF 

Specimen [16] 

) 

1.0 

1.0 
3.1.3. strain Energy Release Rate of the ENF Specimen 

One of the objectives with the finite element analys~s 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 GI and GIl of the strain energy release rate 

may be determined, 

G - lim 

I - Lla~ 

lim 

= Lla+O 

1 

2iia ( 4 ) 

( 5 ) 

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

hold nodes c and d together. Analogously, the quantities (Vc-Vd) 

and (Uc-Ud) 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-Vd) 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 
a c e ; 

b J d 

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, 

G = 

lim 

~a-+O 

P~ l. 

2w 

(Ci(a+~a) - ci(a)) 

~a (6) 

where Ci = Vl./Pi. Vi is the vertical component of deformation 

resulting from the applied load, Pi' 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 GI = 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 inter laminar normal stresses are identically 

zero (KI = 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 
50 ~----~----~----~----~,-----~----, 5 

40 Geometry 4 

L=50.8 mm (2.0 inches) 

a = 25.4 mm (1.0 inches) 

30 2h=3.05 mm (0.12 inches) 3 

I BT • TI3 BT 

lj3 TI3 • 0"1 

0"1/0"1 

20 BT_~ 2 

TI3 - 8wh 

O'BT = ~ 

10 I Whz 

0~----~ __ -A~~~ __ 4-~~~~~~~ __ ~ 0 

-1.25 -1.00 -0.75 -0.50 -0.25 0.00 0.25 

x/2h 

F~g. 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, GII, for the ENF specimen has been 

derived from beam theory yielding the following expressions: 

= ( 7 ) 

( 8 ) 

SH where GII is the strain energy release rate including shear 

deformation and G~i 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 

G~i 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 

G~~ reduces the discrepancy between beam theory and finite 

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

the typical graphite fiber composite (E1 /G13 ~ 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 

El 

GFE GFE 

II II 

G13 GBT GSH 

II II 

h = 1.70 mm 12.8 1.068 1 .021 

25.7 1.263 1 .156 

51.4 1.604 1.354 

h = 2.62 mm 12.8 1.324 1.194 

25.7 1.576 1.294 

51 .4 2.025 1 .410 

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

Material 

h = 1.52 

h = 1.70 

Material 

h = 1.70 

Material 

h = 2.62 

Comparison of Finite Element Results with Beam 

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

GFE GFE 

E1 II II 

~ GBT GSH 

13 II II 

2 18.3 1.232 1.205 

mm 26.9 1.342 1.298 

122.0 2.311 2.006 

183.0 2.835 2.308 

mm 26.9 1.402 1.346 

3 12.8 1.198 1.175 

mm 25.7 1.375 1.322 

51 .4 1.682 1.558 

3 12.8 1.342 1.282 

mm 25.7 1.554 1.420 

51.4 1.926 1.620 

51 
,~ 

Table 16 Stra~n Energy Release Rate for the ENF Specimen. 

Material 

h = 1.52 

Material 

h = 1.70 

Material 

h = 2.62 

Comparison of Finite Element Results with Beam 

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

2 18.3 1.342 1.324 

mm 26.9 1.448 1.420 

122.0 2.368 2.177 

183.0 2.860 2.527 

3 12.8 1.290 1.275 

mm 25.7 1.455 1.422 

51.4 1.750 1.673 

3 12.8 1.366 1.330 

mm 25.7 1.559 1.478 

51.4 1.890 1.704 

52 
r", 

, 

Table 17 Strain Energy Release Rate for the ENF Specimen. 

Material 

h = 1.52 

Material 

h = 1.70 

Material 

h = 2.62 

Comparison of Finite Element Results with Beam 

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

2 18.3 

mm 26.9 

122.0 

183.0 

3 12.8 

mm 25.7 

51.4 

3 12.8 

mm 25.7 

51 .4 

53 

GFE 

II 

GBT 

II 

1 .138 

1.237 

2.122 

2.607 

1.113 

1.277 

1.558 

1.269 

1.460 

1.790 

GFE 

II 

GSH 

II 

1.123 

1.214 

1 .950 

2.303 

1.100 

1.248 

1.489 

1.255 

1.427 

1. 614 
I~ 

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, E1/G13 

=25.7, h = 1. 70 mm) , 

GFE 

II 1.28 (L 50.8 mm, 25.4,mm) ( 9 ) 

GBT = = a = 

II 

and 

GFE 

II 1.46 (L 38.1 mm, 25.4 mm) (10) 

GBT = = a = 

II 

Since GIIC is 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) flo 461

1

/

2 

Pcr(L 38.1 mm) = = 1. 07 ( 11) = 1.28J 

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 (GI = 0) •. The 

FE strain energy release rate, GIl ' 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 0.997 0.976 

-0.075 0.997 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 Spec1men 

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 GIIC. Finite element results are assumed to be 

of the non-dimensional form derived in Appendix 4, 

:~~ = [a+6 ~ G:~)( ~)J (12 ) 

where 

= (13 ) 

a. and 8 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 

. FE BT of shear deformation. In F1g. 21, GIl/GIl is indeed found to be 

a linear function of (E1/G13)(h/a)2 for a 24 ply laminate. 

Consequently, for aiL = 0.5, 

GFE/GBT 

= [1.045 + 1.657 (El /G13 ) (h/a) j II II L = 38.1 mm (14) 

and 

2.644 (E1 /G13 GFE/GBT = [0.967 + ) (h/a)j 

II II 

L = 50.8 mm (15) 

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

release rates for a broad range of the flexural modulus (E1) and 

57 
E1/G13 ratios as shown in Figure 21. These equations, however, 

are restricted to slight perturbation in aiL and laminate 

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 GIIC. 

In most instances, specimen compliance will be measured 

during the fracture test directly by the crosshead displacement 

or appropriate instrumentation such as the LVDT shown 

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

to express E1 in terms of the specimen compliance, C, instead of 

the absolute flexural modulus which requires an independent 

~ test. Assuming C = CSH, E1 can be expressed as a function of C 

by using Equation (3) for CSH: 

8wh3C 

= 

[(2L3 + 3a3) + 2(1.2L + O.9a)h2 (E1/G13 )] 

(16) 

The E1/G13 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 E1 and G13 may be set 

equal to the tensile modulus and the in-plane shear modulus (G12) 

respectively. 

Equation (16) may then be substituted into Equation (8) for 

yielding the desired expression: 

(17) 

58 
2.50 r-------------~,.........-----"""'7"1 

2.25 

L=50.8 mm (2.0 in) 

2.00 

L=38.1 mm (I 5 In) 

175 

L EI 

(mm) (GPo) 

1.50 

• 38.1 1261 

• 38.1 1151 

1.25 4 381 126.1 

50.8 126.1 

50.8 115 I 

508 689 10 ~ ____ ~ ______ ~ ____ ~ ______ ~ ______ ~ ____ _ 

000 0.15 030 045 060 075 090 

~ {.!!...)2 GI3 0 

Fig. 21 Influence of Shear Deformation on Strain Energy Release 

Rate (aiL = 0.5). 

59 
Note that by neglecting the contribution of shear deformation, 

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

(18) 

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. 

FE BT The procedure utilizes Equation (14) or (15) for GIl/GIl in 

conjunction with Equation (17) where G~i 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 piecew~se 

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 f~nd 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, ll, however, would reduce the specimen 

compliance upon loading and may be difficult to detect in an 

experiment. 

Frictional forces, Ti' opposing the sliding deformation, are 

evaluated from the nodal normal forces, Pi' in the contact area 

from the frictionless solution, see Fig. 22, 

Ti = llPi ( 1 9 ) 

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 (ll= 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 ». 

r- Results presented in Table 19, non-dimensionalized by the 

corresponding frictionless solution, show that CFE(ll) and 

61 
en 

N 

') 

Tangential Frictional Forces 

T· = II p. I r I 

') 

I... Contact Area ~I 

------l 

I 

, 

----C~c;No~~~IF;~~~-p.- 7----------;p;. --------- --- --- ---- - - • ' 1 (Nonlinear Truss Elements) 

Fig. 22 Flnlte Element Analysis of Frlction: Nodal Forces 

) 
0'1 

W 

) ') 

Table 19 Influence of Fr1ct10n on ENF Compl1ance and Strain Energy Release 

Rate (Material 3, E1 /G13 = 25.7) 

L=50.8 mm 

a=25.4 mm 

h=1. 70 mm 

L=50.8 mm 

a=25.4 mm 

h=2.62 mm 

L=38.1 mm 

a=25.4 mm 

h=1.70 mm 

L=38.1 mm 

a=12.7 mm 

1J 

o 

0.25 

0.50 

o 

0.25 

0.50 

o 

0.5 

o 

0.5 

CFE (ll ) 

CFE(O) 

1.000 

0.997 

0.994 

1.000 

0.996 

0.992 

1.000 

0.990 

1.000 

0.996 

GFE ( II ) II 

GFE(O) 

II 

1.000 

0.986 

0.976 

1.000 

0.983 

0.965 

o 

0.977 

1.000 

0.952 

FE FE 

G1I(0)-GII(1l) 

GBT 

II 

o 

0.018 

0.031 

1.000 

0.025 

0.051 

o 

0.033 

o 

0.061 

4 h 

"3 II a 

o 

0.022 

0.045 

o 

0.034 

0.069 

o 

0.045 

o 

0.089 

lluFE 

lluBT 

1. 075 

1. 051 

1. 028 

1.075 

1. 033 

1.028 

1.039 

) 
FE 

GII (lod dec rease wi th j..I as expected. For the geometries 

FE considered, CFE( j..1 ) and GII(j..I) are 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, 

= 4j..1h 

3a 

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 GII. The magnitude of 

the sliding deformation, ~uBT , 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 
010~------------------------------~ 

L a h 

(mm) (mm) (mm) 

• 508 008 • 50.8 

25.4 170 

25.4 2.62 

25.4 1.70 

12.7 1.70 

006 

G~{O)-G~{JL) 

G~ 004 

002 

• 38.1 

• 38.1 

Beam Theory 

Fimte Element 

0.00 ~ ____ -L... ____ --L. _____ .l...-____ -'-____ ---I 

000 002 004 0.06 008 010 

~ LL{l!.) 3 r a 

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 ~f excellent agreement 

between compliance calculated from beam theory w~th 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 

da = 

lim 

~a~ (20) 

Unfortunately, ~a must be chosen sufficiently large so that ~C 

can be measured accurately. The minimum ~a 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 ~a is typically 6 to 13 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, 

2L3 + 3a3 

CBT = 3 

8E1wh 

(21) 

This experimental approach is illustrated in Figure 18 where 

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

a 3 , (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 aIL = 0 to 1. In 

practice, ENF fracture testing is limited to delamination lengths 

in the range of 0.5 < aIL < O. 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 theQry 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 dCFE/da (and therefore 

Gi~ is significantly greater than dCSH/da 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 
all 

02 04 05 06 

CFE-CSH -0.01 EI/G I3 

Fig. 24 

CO 

• 128 

• 257 

-0.02 • 51 4 

L=38.1 mm 

-003 

-0.04 

-0.05~----~------~----~----~~----~----~ 

000 005 0.10 0.15 020 025 

(01 l)3 

ENF Compliance as a function of Crack Length 

(Material 3, h = 2.62 mm) Co = L3/(4E1Wh3). 

68 

030 
I 

~ 

/' 

I 

Fig. 25 

(all) 

04 0.5 06 

0020 

0015 

0010 

-0005 

• 12.8 

• 25.7 

• 514 -0010 

L=38.1 mm 

-0.015 L--L-_..l-__ --L ___ l...-__ ....L __ --l. __ ---J 

0.00 0.05 0.10 0.15 

(o/l)3 

0.20 0.25 

ENF Compliance as a function of Crack Length 

(Material 3, h = 2.62 mm) Co = L3/(4E1Wh3). 

69 

030 
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 

V 13)] (22) 

The correlation of results are presented in Table 20 for ENF 

geometries exhibiting similar span/thickness ratios. 

70 
;--, 

~ 

( 

Table 20 

aiL 

0.33 

0.33 

0.3,3 

0.50 

0.50 

0.50 

0.67 

0.67 

0.67 

Correlation of Strain Energy Release Rates (Grr

FE ) 

with the Results of Barrett and Foshi (Grr

sr) 

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

E1 /G13 FE ~T GIll II Gsr/GBT 

II II 

12.8 1.32 1.26 

25.7 1.58 1. 62 

51.4 2.03 2.18 

12.8 1.34 1.19 

25.7 1.55 1.54 

51.7 1. 93 2.07 

12.8 1.37 1.16 

25.7 1.56 1.50 

51.4 1.87 2.01 

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 GIC and GIIC . 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 GIC 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 

GIIC 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, particulariy 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 GIISC) and the initial compliance 

and the maximum load (GIC or GIIC) , 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=O.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 
"C 

ca 

o 

...J 

Initial Modulus, Compliance 

Displacement 

Figure 26. Strain energy release rate def~nit~ons to 

characterize non-linear behav~or. 

74 
Fig. 27 ENF Test Fixture 

75 
Crack 

Size 

I 

I 

Slow I 

Crack I 

Exten~on(: 

I 

Time 

Crack 

Propagation 

Load 

Fig. 28 Influence of Subcr1tical 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 preceeded 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 DCB 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]26 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 GIC 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 inter laminar 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-slip' phenomenon has been documented previously by 

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

curves for a cross-head speed of 2Smm/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 mm/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 GIC 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 

30 

-

z 

-

~ 20 

c 

o 

...J 

10 

o 

Crosshead Speed 

25.4 mm/min. 

o 20 40 60 

Crosshead Displacement (mm) 

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

DCB Test. 

80 
) 

ex:> 

~ 

,. 

0 

..t 

X :1 

~j 

cu w, 

U o Z..t 

«x 

H..t 

.....J m a.. 

::E 

O~ U 

cu 

1 

o 

..t 

I-

) 

N 

0 

..t 

X 

..t 

SPECIMEN: CYCOM 982-2 

WIDTH- 0.019 (m) co 

~ 

C - 0.74788HAMM3 (mIN) CJ 

« Ooq' 

.....J 

Pc a 2.13270MAMM-1 (N) .....J «('I) 

U 

GIC a 0.27 (KJ/mMM2) H 

lH 

CI: cu U 

... 

C) 

..t 

~~~~~-rr'M'i~in"--~~-rriMii"i~" ~~r-~-'-rTiTin'im"~-'-'~TTi~"m" 

1X10 -2 1X10 -I 1X10 0 1X10 -2 1X10 -I 

CRACK LENGTH CRACK LENGTH 

F1g. 30 Typical Comp11ance vs Crack Length and Critical Load vs. Crack Length 

for DCB Testing of CYCOM 982. 

1X10 0 

) 
175 

125 

Z 100 

-

"'0 

o 

o 

-I 75 

50 

25 

Crosshead Speed 

25.4 mm/min. 

onset of 

subcritical 

crack growth 

cntlcal crack growth 

O~~~-L ______ ~ ____ ~L-____ -L_ 

o 20 40 60 80 

Cross head Displacement (mm) 

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

(Crosshead speed = 25mm/m~n). 

82 
-

z 

-

80 

60 

Crosshead Speed 

0.508 mm/min. 

-c 40 

c 

o 

~ 

Fig. 32 

20 

o~ ______ ~ ________ ~ ________ ~ ______ ~ ________ ~ 

o 20 40 60 80 100 

Crosshead Displacement (mm) 

Load vs Displacement Curves for APC-2 DCB Test 

(Crosshead speed = O.5mm/min). 

83 
3.0 

2.6 

Fracture 

Energy 2.2 

(kJ/m2) 

1.8 

Mode I 

1.4 =-_---:-':-:-__ --1... __ --1 ___ l-__ ...1 

0.58 0.60 0.62 0.64 0.66 0.68 

Fiber Volume Fraction 

F~gure 33. r.1ode I fracture toughness versus fiber volune 

fract~on for APC-2. 

84 
r 

Table 21. DCB Test Results: GIC (kJ/m2 ) 

Material Compliance Method* Area Method 

APC-2 

CYCOM 982 

1. 75 ± 0.13 

0.25 ± 0.02 

*Averaged results based on maximum load. 

Stable 

2.00 ± 0.09 

0.26 ± 0.02 

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

4.2 ENF Test Results 

Unstable 

1.50 ± 0.20 

NONE 

In this section the influence of pre cracking 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 rom until it was arrested at the clamp, see Figure 34. In 

this way a Mode I pre crack was achieved which produces a distinct 

85 
86 

. 

c 

~ .r-! 

() 

(J) 

0. 

til 

~ 

Z 

IJ::l 

C 

rtl 

lo-l 

o 

4-1 

tTl 

C 

.r-! 

.!t: 

rtl 

lo-l 

() 

(J) 

lo-l 

0. 

H 

(J) 

"d 

o 

:a: 
mark on the fracture surface at the Mode II initiation line. 

The second way of introducing a pre crack was to load the 

specimen in the TPB fixture. Based upon the stability analysis 

presented in Appendix 2, aiL> 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 GIIe defined 

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

essentially in a linear elastic manner reflected in the closeness 

of the GIISC and GrIC values. Furthermore, compared to the Mode I 

precracking, the Mode II precracking results in larger fracture 

toughness values and brings GIISe and GIIe closer. However, the 

most striking effect is the high toughness values for the case 

where no pre cracking 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 rnrn) . 

For the APC-2 material significant nonlinear behavior was 

observed manifested in the large difference in the GIISe and GIIe 

values presented in Table 22. The Mode I precracking produced 

consistent GIIe values at different thicknesses and spans. The Mode 

(~ II pre cracking resulted in a higher GIIC value and decreased the 

87 
(' 

percentage difference between GIISC and GIIC ' As for the CYCOM 982 

material, however, the largest GIIC value was obtained for the no 

precrack situation. 

Table 22 Mode II test results. Influence of precracking. 

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

1.25 mm/min (0.05 in/min.). Data reduction is 

based on simple beam theory. 

Material/No. Precrack Half Span, L GIISC 

kJ/m2 of Plies 

CYCOM 982/24 

CYCOM 982/24 

CYCOM 982/24 

CYCOM 982/24 

CYCOM 982/24 

APC-2/26 

APC-2/40 

APC-2/26 

APC-2/40 

APC-2/26 

APC-2/26 

Mode I 

Mode II 

" 

No precrack 

" 

Mode I 

" 

" 

" 

Mode II 

No pre crack 

mm 

51 

51 

38 

51 

38 

51 

51 

38 

38 

51 

51 

88 

0.61±0.04 

O.75±O.07 

O.65±0.09 

1. 37±0 .20 

1. 63±0. 28 

1. 84±O. 07 

0.68±0.02 

0.77±0.07 

0.68±0.11 

1. 45±0 .16 

1. 40±0 .18 

1. 78±0 .11 

1. 87±0 .11 

1. 89±O .16 

1.84±0.07 

1. 93±0. 28 

2.73±O.33 
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 pre cracking, 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 GIIC for this situation. For 

the no pre crack 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 (FE) 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=O.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 O.77±O.07 O.98±O.09 

38 0.68±O.11 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 DeB 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 

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 
Cl.. .. ~ o 

....J 

• • 3 = 0.25 mmlmin 3 = 2.5 mmlmin 

• • 3 =25 mmlmin 3 = 250 mmlmin 

Displacement, 8 

F~gure 35. Typ~cal load-d~splacement response for APC-2 

DCB spec~men at var~ous 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, 5CT ' at any instant 

(' preceeding crack propagation, 

93 
w 

"'" 

) 

a. 

--0 

CO 

a 

...J 

31 

') 

32 

• °3 

Displacement, () 

F1gure 36. Load displacement response for APC-2 ENF specimen at various crosshead 

rates, 0. 01<02<03. The range in ° is from 0.25 to 250 mm/min. 

) 
(23) 

• 

where a 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, 

• ~ = 0 and aCT = O. 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, 

U CT == 24 ha2 a 

3 3 ~ (2L + 3a ) 

(24) 

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 

r--\ 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, GIISC 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 = 

3A1Px2a2/2w where x = SC and C respectively 

(Fig. 31) and A1 is an initial compliance 

coefficient defined in Appendix 1. 

Displacement Rate GISC 

kJ/m2 

GIC 

mm/min kJ/m2 

0.25 

2.5 

25 

250 

0.02-1.6 

1-10 

8-118 

108-1102 

96 

1. 56±0. 05 1. 56±0. 05 

1. 60±0. 26 1. 75±0 .13 

1. 41±0. 21 1. 98±0 .13 

1. 37±0 .15 1.71±0.16 
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, PSC' and load at critical crack 

growth, Pc (Fig. 26). 

Displacement Rate GIISC 

mm/min kJ/m2 

0.25 

2.5 

25 

250 

m/s x 10 9 

2.86 

28.6 

286 

2860 

0.95±0.18 

1. 01±0. 09 

0.98±0.16 

1. 40±0 .13 

1.84±0.27 

1. 82±0 .20 

1. 40±0 .13 

1. 40±0 .13 

Figure 37 shows the toughness values plotted versus crack tip 

displacement rate. It is observed that GIC 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 

'E 2.0 

"'-

~ .. en 

en 1.5 

Q) 

c 

.c 

Cl 

::J 

0 

I- 1.0 

Q) 

'-

::J 

t5 0 Glc ttS 

'-

U. G1sc 0.5 • 

~ Guc 

A Gusc 

0.0 

-11 -10 -9 -8 -7 -6 -5 

• 

log OCT 

F~gure 37. Rate dependence of Mode I and II fracture 

toughness. 

98 

-4 
GISC = GIC 

GIISC = GIIC 

(25 ) 

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, 

(26) 

aGIIC = GIIC - GIISC (27) 

Figure 38 shows that aG1C peaks at an intermediate crack tip 

velocity that is achieved at a displacement rate of about 25 

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

crack growth is observed as reflected in the small aGIC values. For 

Mode II loading ~GIIC decreases slowly initially and drops to a 

small magnitude at the highest rate tested. 

Discussion 

The rate effects on inter laminar fracture of APC-2 observed 

99 
') ) ) 

1.21~-------r--------r--------r--------r--------r------~ 

1.0 

APC-2, [0]26 

...: 0.8 r ..L. ~ ~ Mode II II 

C\I -E 0.6 

~ ... Mode I ...... 0 0 

60.4 0 

<1 

0.2 

-8 -5 

• 

log ()CT 

Figure 38. 6G1C and 6G11C versus crack tip velocity for APC-2. 
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 
r"', 

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 

aGIIC > aGIC 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, GIC' 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 GlC 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 AGIlC 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, AGIlC 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 AGIIC 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 
640 X 

2500 X 

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

a low displacement rate showing ductile behavior. 

105 
640 X 

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 DeB 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 ~GIIe 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 ~Glle 

tending to zero with decreasing crack tip displacement rate is the 

fundamental difference between the DeB 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 GIIC 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 ITWO 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. 

III 
Figure 43. End loading compression fixture. 

112 
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]64 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 [0]64 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 rom 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 quarantee crack growth at 

desired GI/GII 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 
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 [1] 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 
r', 

I 

-E 

E 

-

. 

a.. 

en 

H 

Cl 

UJ 

Z 

< 

..J 

a.. 

I 

l1.. 

a 

I 

I--

=:l 

a 

. 

x 

< 

:E 

o 

o 

· 

0 

~ 

· C\J 

0 

CD 

~ · 

0 

C\J 

~ · 

0 

co 

· 0 

0 

0 

· 

0 0 . 00 40.00 

DELAM. THICKNESS=O.51mm 

SPECIMEN THICKNESS=8.29mm 

INITIAL IMPERFECTION=O.34mm 

80.00 120.00 160.00 200.00 

LOAD (kN) 

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

displacement as a functlon of the applied load. 

(APC-2, Delamination length = 54.1 rnrn) 

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 GIl 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 GIl 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 
1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11 • 

REFERENCES 

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

Composite laminates with Interlaminar Defects," Composite 

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

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. 

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

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

Materials, University of Delaware, 1981. 

M. Ashizawa, "Fast Interlaminar Fracture of a Compressively 

Loaded Composite Containing a Defect," Douglas Paper 6 9 9 4 , 

January 1981. 

M. Ashizawa, "Improving Damage Tolerance of Laminated 

Composites Through the Use of New Tough Resins," Douglas 

Paper 7250, January 1983. 

R. L. Ramkumar, S. V. Kulkarni, and R. B. Pipes, "Definition 

and Modeling of Critical Flaws in Graphite Fiber Reinforced 

Epoxy Resin Matrix Composite Materials," Naval Air 

Development Center Report No. NADC-76228-30, January 1978. 

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. 

S. N. Chatterjee and R. B. Pipes, "Composite Defect 

Significance," Proceedings of the Mechanics of Composites 

Review Meeting, Dayton, Ohio, October 1982. 

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

Related Delamination Growth," J. Composi te Ma terials, 

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

J. D. Whitcomb, "Approximate Analysis of Postbuckled 

Through-Width Delaminations," NASA Technical Memorandum 

83167, June 1981. 

J. D. Whi tcomb, "Strain Energy Release Rate Analysis of 

Cyclic Delamination 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 GIIc 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 
~ 

r ' 

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. Dolgopo1sky 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 
r'\ 

1. DCB DATA REDUCTION 

1.1 Compl1ance Method [1] 

where 

EI 

, 

a 

EI 

C = o/P 

2 

3EI 

p,a 

P 

The energy release rate G 1S obtained from 

1 

(1) 

( 2 ) 
Eq. (1) 1n (2) gives 

G = G

c 

for P = Pc gives 

consequently 

Experlmentally the C-a and pc-a relations are 

measured giving the constants Al and A2 • 

log C log Pc 

log II log II 

( 3 ) 

( 4 ) 

( 5 ) 

( 6 ) 

The cr1t1cal energy release rate G 1S obtalnpf' hy c 

subst1tut1ng Equat10n (6) 1nto Equatlon (4). 

2 
( 7 ) 

1.2. Area Method [2] 

p 

For 11near elastic behaV10r dnd the case where the 

load deflection curve during crack propagation can be 

approximated by a straight 11ne, the energy release rate can 

be determ1ned from, 

G = 1 2w6a 

This quant1ty is equal to the area between the 

( 8 ) 

loading and unloadlng curves. An average GIe value may be 

obtained from a serles of loading and unloading curves. 

3 
2. CLS DATA REDUCTION 

shear ply 

( flap) 

strap 

ply 

p 

Strength of materla1s analysls gives: 

C = i = (L-a) 

p wh1 E 

dC 

da 

( 9 ) 

( 10 ) 

( 11 ) 

From Equation (10), C may be expressed as a Ilnear 

functlon of a, 

4 
( 12) 

Equations (11) and (12) glve 

( 13 ) 

c c 

c c c 

c 

8 

5 
EI 

8" 

3. ENF DATA REDUCTION [3] 

P/2 

2h 

EI 

For the undelaninated regions BC and CD the displacements 

are, 

( 14 ) 

( 15) 

The deflection of the dela~inated region due to the slope at 

B 1.5: 

(16) 

The deflect10n of the delamInated reg10n due to bend1ng 1S, 

6 
Total deflection of the delam1nated part 15 then: 

= p[aL2

+ Sa3 ] 

8Ewh3 

8pa 3 

8Ewh3 

For small deflect10ns the total deflect10n 0 1S: 

o = 

P 

The compl1ance e may thus be expressed: 

e 

0 12L 3+ 3a 3] 

= = P 8Ewh3 

de 9a 2 9a 2e 

= = da 8Ewh3 l2L3+ 3a 3J 

G = 

p2 de 

= 

9a 2

p

2

e 

2w da 2w[ 2L 3+ 3a 3] 

e 

2L3 

+ 3a3 

ASa 

3 

= = + A6 

8Ewh 3 8Ewh3 

7 

( 17) 

( 18 ) 

( 19 ) 

( 20 ) 

( 21 ) 

( 22) 

( 23 ) 

( 24 ) 
c 

de 

da 

G = 

c 

2 = 3A ... a 

.J 

p = .J2WGc .!. 

c 3AS a 

( 25) 

log Pc 

log II 

( 26 ) 

( 27 ) 

( 28 ) 

In many cases unstable crack growth occurs wlth thlS speclmen. For that case GclS calculated dlrectly from Eq. (22), 

( 29) 

where C 1S the measured compliance (corrected for the 

machlne compllance). 

8 
REFERENCES 

llJ 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 

l21 J. M. Whltney, C. E. Browning and Hoogsteden, W.,"A 

Double Cantllevier Beam Test for Characterizing Mode 

I Delamination of Composite Materials", J. Reinforced 

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

l3J A. J. Russell and K. N. Street, "Moisture and 

Temperature effects on the mixed-mode delacination 

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

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

Pittsburgh, Pennsylvanla 

9 
APPENDIX 2 

Stabil1ty of Crack Growth For the ENF Spec1men [1] 

The stab1lity of crack growth may be Judged from the 

sign of dGII/da. If dGII/da 1S posit1ve unstable crack 

growth will occur, while stable crack growth occur 1f dGII/da 

is zero or negat1ve. GII 1S obtained from the general 

expression: 

( 1 ) 

For fixed load condltions dGII/da is directly obta1ned from 

eq. (22), Appendix 1, 

( 2 ) 

Th1S quant1ty 1S always pos1tive, hence the crack growth is 

unstable. 

For fixed g£iQ cond1t10ns, Wh1Ch 1S more common 1n 

testing GII 1S expressed by 

10 
r 

( 3 ) 

D1fferentiation of this expression yields: 

= ( 4 ) 

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

glves, 

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

a ) LiP == 0.7L 

Consequently for the commonly used aiL == 0.5, the crack 

growth 1S unstable under flxed gr1p conditions. 

11 

( 5 ) 

( 6 ) 
REFERENCE 

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

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

Specimen for Mode II Testing", Submltted for 

Publlcatlon. 

12 
APPENDIX 3 

Design Considerations for DCB, ENF and CLS Specimens 

1. DCB Speclmen Deslgn 

The maln requirement on the DCB specimen is that the 

beams act as Ilnear elastic beams. An lnvestlgation by 

Dewitt et. al [lJ shows that geometrlc nonllnearltles occur 

ln the DCB speclmen for 

IS ii ) 0.3 

6 

4 

2 

o ~~--~----~----~------

o 0.2 0.4 

8/20 

0.6 0.8 

(1) 

F 1'1. 1 (~ond 1 '.ens 1 )nal load vs. nond1nen::>lonal d lstJlacelaen c. 

[ 1 J 

13 
At o/2a = 0.3, l.e. o/a = 0.6 the error induced ln the load 

by assum1ng linear behaviour lS approximately 10%. Th1S is 

also the error 1n G l1J. 

Relation between the thickness required to keep the beaMs ln 

the llnear regime and G

c

• 

Equation (1) in Appendix 1 lS 

1n Wh1Ch Al = 2 

3EI 

Here EllS the flexural rigldlty of each beam of the DCB 

spec1men. Consequently, 

ThlS 1n Equat10n (1) ye1lds, 

64a3 

C = 

Ewh3 

or 

( 1 ) 

( 2 ) 

( 3 ) 

( 4 ) 

The cr1t1cal stra1n energy release rate may be expressed as 

G 

c 

14 

( 5 ) 
Substitutlon lnto Equation 

= aJ 128Gc 

a 

c -

a Eh3 

(4) gives 

To keep acla less or equal to 0.6 requires: 

J128G 

a c

3 

< 0.6 

3Eh 

or 

ThlS is equlvalent to, 

h )4.9 (GclE) 1/3 a 2/3 

( 6 ) 

( 7 ) 

( 8 ) 

( 9 ) 

Note that the requlred thickness increases with crack 

length a. The longest crack length expected ln the testlng 

is about 150 mm 

2. CL~ Speclmen Deslgn 

The design of the CLS specimen has been discussed by 

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

fallure modes, viz. delamination and adherend failure, the 

minlmum thickness may be determined. Figure 2 shows the 

geometry of the speclmen. 

15 
E, h/2 

E, h/2 I---~ P 

Flg. 2 Geometry of the CLS specimen. 

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

p2 (h1-h2 ) 

G = 

c 

c -2 Eh1h2 2w 

(10) 

With hI = h, h2 = h/2 we get 

-- p2 

G = 

c 

c 2w2Eh 

( 11 ) 

l.e. 

( 12) 

To avoid failure in the strap ply (If the stress 

concentration at the crack tip and the rotatlon of the 

specimen is neglected) we need 

Pc < xi wh 2 ( 13 ) 

16 
where xi lS the unlaxlal tenslle strength. 

Equatlons (12) and (13) yield 

w J 2EhGc <; xi wh/2 ( 14) 

ThlS yields: 

( 15) 

3. ENF Speclmen Deslgn [3] 

The analysis of the ENF specimen presented here, 

is based on small deflectlon theory. Large 

deflectlon/rotatlons increase the complexltles of the analysis and the data reduction scheme substantially. In thlS 

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

which allows slzlng of the ENF speclmen to obtain crack 

growth wlthin the linear elastlc regime. Influences of 

lnterlarnlnar shear and frlctlon are not considered ln thlS 

approximate analysls. 

In linear beam theory the following expression for 

the curvature: 

1 

R = II + (dy/dx) 213/2 

( 16 ) 

17 
1S generally approx1mated w1th 

( 17 ) 

since the square of the slope (dy/dx)2 is assumed to be much 

less than un1ty. 

The maX1mum slope occurs at the end of the delam1-

nated region. Neglecting 1nfluence of shear deformation 1t 

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

the delam1nated crack 

(18) 

The slope due to bending of the delaminated beams 1S 

obtained from the deflection curve for a cantilever beam 

(see Append1x 4). 

-p x3 2 

a

3 

a x 

y = 4I (6E -2E" +1E (19) 

2.Y = -p ( x2 - a

2 ) ax 8Er' ( 20) 

The maximum slope occurs at x = 0 and 1S 

av = Pa 2 (ax )0 8El ( 21 ) 

,~\ 

18 
This leads to 

(dX)O ~ 

The maximum slope lS then approximately 

Equations (18) and (22) give: 

(dx)m ~ = 3P(L2+3a 2 ) 

8Ewh3 

In terms of dlsplacement, 0, the maXlmum slope lS: 

(22) 

( 23) 

( 24) 

( 25) 

For (dy/dx)m (0.2 the error ln eq. (16) is approximately 

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

employed ln a large deflection analysis would lead to less 

than 6% error Slnce the above estimate lS based on the maxim~ slope, at a pOlnt. 

Denoting the maXlmum allowable slope by Y! ' the 

maximum allowable displacement, 0a' corresponding to Y! 

may be calculated from Eq. (25), 

1 

Ya (2L3+ 3a 3 ) 

3(L2+ 3a 2 ) 

19 

( 26 ) 
Relat10n between 0c and GIIc 

9P a

20 

c c 

2w(2L3+ 3a3 ) 

(27) 

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

Append1x 1, 

P = c 

subst1tutlon into Eq. (28) Ylelds, 

= 

Combination of Eqs. (29) and (26) wlth the requlrement 

0c .. 0 m gives: 

(28) 

( 29) 

(30) 

Th1S relation shows that the small deflectlon reglme may be 

1ncreased by increasing E and h or by decreaslng L. For 

example, 1f th1ckness is the controlling parameter, 

G (L2+3a 2 )2 IIc ( 31) 

20 
Des1gning versus nonl1near material behaV10r or flexural 

fa1lure 

Material nonl1near1ties or flexural fa1lure may also 

be avoided by proper sizing of the ENF spec1men. For crack 

lengths, a, less than or equal to L/2 the maX1mum bend1ng 

stress (d1sregard1ng the localized stress slngular1ty at the 

crack t1p) occurs 1n the center of the beam. 

The maximum bending moment is, 

P 

M = 2' L 

The maximum bending stress 1S 

am = Mh/I 

Comb1nat1on of equations (32) and (33) gives 

a = m 

PLh = 

2I 

3PL 

4wh 2 

The maximum strain €m 1S then, 

3PL 

4Ewh2 

In terms of displacement th1S glves 

21 

( 32) 

( 33 ) 

( 34 ) 

(35) 
e: 

rn 

(36) 

where ° is the dlsplacernent of the central loading pin. By 

similar reasoning, a thickness requirement may be formulated 

from the condltion 0c ( 0a where 0a is the maximum allowable 

dlsplacement related to the maximum allowable straln, e: , m,a 

to maintain linear material behavior. Calculations of the 

required thickness yields: 

h ;> (37) 

22 
• 

~ I 

REFERENCES 

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

"Method for determinlng the Mode I delarnlnatlon 

Fracture toughness of Elastic and Viscoelastic 

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

14, (1980), p. 270. 

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

Specimen for Dlfferent ReSln 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. Gillesple and R. B. Pipes, "On 

the analysis of the End Notched Flexure (ENF) 

Specimen for Mode II Testlng", Submitted for publlcation. 

23 
r, 

APPENDIX 4 

Influence of shear deformations on the ENF Compliance and 

strain energy release rate [1] 

In Figure 1, the ENF speclmen geometry 1S deflned 

and modeled as three beams. For small deflect10ns, the 

deflection, 0, at the center (C) is simply the algebraic 

sum, 

t:. CD + t:. BC + t:. AB 

o = 2 ( 1 ) 

where t:.CD ' t:. BC ' and t:.AB are the maximum deflect10ns of the 

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

and modeled as the cantllever beam presented 1n Flgure 2. 

The deflectlon due to a point load at one end including 

shear deformatlon [2] is, 

( 2 ) 

24 
10( 

2h 

h 

h 

T 

P/2 

~1~~------------2l------------~~ 

P/2 

~I 

Fig. 1 ENF Geometry 

p 

I----~X h 

to4---- J! ------:l)l1Jli1 

Y 

Flg. 2 Cantilever BeaM 

25 
---... 

-

where El and Gl3 are the flexural modulus and 1nterlam1nar 

shear modulus, respect1vely, and I 1S the moment of 1nert1a 

of the bean. Implic1t in the der1v1ation of Equat10n (2) is 

the assumpt10n that the built-in end does not warp under the 

action of shearing stress. Th1S appears to be a reasonable 

assumption for beams CD and BC since the p01nt of load 

1ntroduc1ton (Point C) 1n F1gure 1 1S an approximate llne of 

symmetry. Consequently, 

~CD PL3 

+ 0.3 PL = ( 3 ) 

4El Wh 3 Gl3wh 

P(2L3 - 3aL2 3 P~L - a) ~BC = + a ) + 0.3 ( 4 ) 

8El Wh 3 Gl3wh 

For the delam1nated region, AS, of the ENF 

geometry, the ends of the parallel beams at p01nt S in 

F1gure 1 are allowed to warp. For a beam of th1ckness h = 

2c, the hor1zontal and vert1cal displacements (u,v), 

accord1ng to T1moshenko [3], may be expressed w1th respect 

to Figure 2 as 

2 3 

-x Y \ll2Y 

u = P { ____ - + Y 2El 6E l 

( 5 ) 

26 
where 

dI 

P 

2 

P v 12xy 

v = Y(~2~E--

1 

3 

+ x + dI (x- n ) _ 6E P ~ 

1 

£,3 TE) 1 

The total deformation of the delaminated region has two 

( 6 ) 

( 7 ) 

components. The bendlng and shearlng deformatlon is deflned 

ln Equation (6). The second component arises from the rotatlon of the bUllt-ln end for the delarnlnated region at pOlnt 

B ln Flgure 1. The deflection, aAB,S due to the local 

slope lS shown to be [1] 

a AB,S = 

The total deflectlon of the delarnlnated reglon assumlng 

( 8 ) 

each beam carrles an equal load of P/4 is obtalned from the 

summatlon of Equatlons (6) and (8), 

/.}.AB = ( 9 ) 

Substltutlon of Equatlons (3), (4) and (9) lnto (1) Ylelds 

an expresslon for the displacement at the pOlnt of load 

lntroductlon. 

27 
r\ 

The cornpl1ance including shear deforrnat1on is, 

o 2L 3 + 3a 3 

= p = 8E

1

Wh 3 

This equat10n with, 

GSH 

= 

p2 dCSH 

II 2W da 

glves, 

GSH 9a 2p2 

= (1 + II 16E1W2h3 

(1 + 

2(1.2L + 0.9a)h2E1 

3 3 (2L +3a )G13 

E 

O.2(_l_)(h)2) G13 a 

(10 ) 

( 11) 

( 12) 

(13 ) 

Neglect1ng the contribution of shear deforrnat1on, Equat10ns 

(11) and (13) sirnpl1fy to the expression reported 1n [4], 

CST = 

2L3 + 3a3 

3 8E1wh 

( 14 ) 

and 

GBT 

= 

9a2p2 

II 16E1W2h3 ( 15) 

28 
r-, 

I 

REFERENCES 

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

Pipes, "On the Analysls of the End Notched 

Flexure (ENF) Specimen for Mode II Testlng", 

Submitted for publicatlon. 

[2] S. P. Timoshenko, "Strength of Mater1als", 

Part 1, Krleger Publ1shing, (1984). 

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

Elastlcity", Mc-Graw H1ll (1970) 

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

and Temperature effects on the mixed-mode 

delam1nation fracture of unldlrectlonal 

graphite/epoxy", Paper presented at an ASTM 

Symposlum on Delaminatlon and Debondlng of 

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

Pennsylvania. 

29 
I 

~ 

APPENDIX 5 

Influence of friction on the ENF Strain Energy Release Rate 

(1) 

A potent1al, energy absorb1ng mechanis~ 1n the ENF 

specimen, 1S the fr1ction between the crack surfaces. 

F1nite element results discussed 1n Section 3 show that the 

contact area is located symmetrically over the outer support 

p1n and is less than 4h in length where h 1S the th1ckness 

of each bea~ 1n the delaminated reg10n. Summation of the 

normal forces with1n the contact area ver1f1es that each 

beam carr1es an equal load. 

With this insight, an approximate expression to 

quant1fy the work of fr1ction dur1ng crack growth may be 

obta1ned from beam theoryllJ. The frictional work, WF, can 

be expressed as: 

H = F 

2h 

f lJN(x)~u(x)dx 

-2h 

( 1 ) 

where lJ 1S the coeffic1ent of fr1ction, N(x) 1S the normal 

force d1stribut10n and ~u(x) 1S the relative displacement 

(slid1ng) of the crack surfaces. The 1ntegral 1S calculated 

over the contact area. 

30 
I 

~ 

The lnduced normal stress fleld may, as an 

approximatlon, be represented by the Dlrac delta functlon, 

cS(x), [2] 

N(x) = : cS(x) ( 2 ) 

Substitutlon lnto Eq. (1) yields the following upper bound, 

WF <; P u(O)/4 

The slidlng, 6u(O), may be calculated from the 

expresslon glven ln Timoshenko and Goodler [3] for the 

dlsplacement of a cantilever beam: 

6u(O) = 2Iu(O) I = 3P 

2 2El wh 

The frictlonal work is thus: 

3p2lJ 

2 8El wh 

2 2 [a +h(E/G 13)/l2j 

The crack growth crlterion nay be formulated by 

( 3 ) 

( 4 ) 

( 5 ) 

conslderlng the energy changes as the crack lncreases ltS 

area by an amount dA: 

dW dU dWF 

dA - dA > Grrc + dA ( 6 ) 

31 
where W lS the work supplied by the movement of the external 

load, U lS the stored strain energy in the body and Gllc lS 

the work required to create a unit new crack surface. 

A resonable assumptlon is that the compliance of the 

speclmen is unaffected by frlctlon. For thlS case Eqs. (6), 

and (5) give: 

( 7 ) 

SH where Glr ' glven in Appendix 4 lS, 

( 8 ) 

The energy avallable for creatlng new crack surfaces, 

may thus be expressed: 

( 9 ) 

or by using equatlon (8): 

where lS the expresslon for GIl 

where lnfluences of lnterlamlnar shear and frlctlon are 

neglected. 

32 
A non-dimensional straln energy release rate 

parameter quantifying the influence of frlction to the 

reduction in strain energy release rate is defined in Eq. 

( 11) , 

= 411(h/a)/3 ( 11) 

The results discussed in Chapter 3 show that Eq.(1l) indeed 

provides an upper bound to the numerical finlte element 

results. 

r--'" 

33 
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] 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). 

34 
APPENDIX 6 

Stress-Strain Curves for APC-2 and CYCOM 982 

35 
) 

.... 

0 

~ 

* 

w co 

O'l ll. 

2: 

U) 

U) 

w 

a: 

IU) 

0 

0 

0 

LD 

ru 

0 

0 

0 

0 

ru 

0 

0 

0 

LD 

~ 

0 

0 

~I 0 

~I 

0 1 

0 

~~ 

o 

o 

) 

TENSILE TEST 

LONGITUDINAL DIRECTION 

[0]8 

H IE~ (GPa) I x~ (MPa) I EJu (X) 

I"'/ o --CYCOM 982 136 2170 1.6 

~p o --APC2 129 2140 1.6 

/ All material properties are an average 

of five specimens 

__ --L. ____ ~ _________ ~ 

0'" 0.00 0.40 0.80 1.20 1.60 2.00 2.40 2.80 

STRAIN (,ri) 

') 
) 

co 

[L 

::E 

w 

....... U1 

U1 

W 

a: 

Im 

') 

TENSILE TEST 

TRANSVERSE DIRECTION 

0 

0 

0 

0 

...-1 

0 

0 

0 

CIJ 

0 

0 

0 

lD 

gl 

~r 

I 

0 

01 

oL 

cu 

o 

o 

lJ 

Jf# 

;:{r? 

/ rl-' 

df 

01F---- o . 0 0 I ___ ~_-~----i-_ 

0.20 0.40 

[90]16 

/' I E~ (GPa) I x~ (MPa) I E Iu (X) 

o --CYCOM 982 10.0 47 0.45 

o --APC2 9.4 76 0.94 

All material properties are an average 

of five specimens 

~ _____ --L_~ 

0.60 0.80 1.00 1.20 1.40 

STRAIN (%) 

) 
) 

... 

0 

...-t 

;:I< 

w m ex> CL 

2: 

U) 

U) 

W 

II 

IU) 

0 

0 

0 

0 

CUI 

gl 

§~ 

:l 

...-t 

0 

0 

0 

m 

0 

0 

0 

~ 

o 

o 

) 

COMPRESSION TEST 

LONGITUDINAL DIRECTION 

[01'6 

'Ef (GPa) xf (MPa) Efu (X) 

o --CYCOM 982 131 1295 1.0 

12541t1t Itlt 

o --APC2 117 1.1 

765 It 0.61t 

** Brooming failure mode--three specimens * Shear failure of specimen at end tabs 

Material properties are an average of five specimens except where noted . 

o - _____ ~ ____ ___L_ ______ _L___ _--L-_ -

0.00 0.20 0.40 0.60 0.80 1.00 1.20 

STRAIN (%) 

) 

1.40 
) 

CO 

D2: 

IN 

\0 UJ 

UJ 

W 

0: 

IUJ 

0 

0 

0 

~r 

0 

0 

0 

lD 

.... 

0 

0 

0 

ru 

.... 

0 

0 

0 

CD 

0 

0 

0 

~ 

o 

o 

I 

') 

COMPRESSION TEST 

TRANSVERSE DIRECTION 

[90]40 

......-

,.-

......-

E~ (GPa) I x~ (MPa) I E ~u (%) 

__ _ _____ ---1.... ______ ------1........_ __ _ __ ------Lo --CYCOM 982 

o --APC2 

9.3 

9.2 

193 

214 

2.7 

>3.0 

All material properties are an average 

of five specimens 

___ ~ _____ -----1- ____ -----J 

0 .... 

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 

STRAIN (%) 

') 
) .) } 

THREE POINT BENDING FLEXURE TEST 

MAX. BENDING STRESS VS MAX. BENDING STRAIN 

0 

0 [0]'6 

0 

0 

(\J 

0 

0 

0 

lO 

...-1 

0 

0 0 

...-1 

* 0 

(\J 

...-1 

~ 

0 co 0 

0.. 0 

L gr /# IEF (GPali XF (MPa) I Efu (X) 

U) 

U) 'p~ o --CYCOM 982 I 126 1729 1.3 

IU 

:~ IT 

l- cPrtt' o --APC2 115 1632 1.4 

U) 

,- All material properties are an average 

I of five specimens 

I 

! 

0 

0 

. Jff- _....L. _. _ J -.. ~-. - _ _ __ ---1 _______ -.J --- _-1 - _____ ----1 

0 0 00 O. LtO 0.80 1.20 1.60 2.00 2.40 2.80 

STRAIN (%) 
) -) ") 

SHEAR TEST 

0 [:1:45]25 laminate 

0 

0 

0 

..-t 

0 

0 

g~ ------- --- I ~ ~ 

0 

--

0 

0 

0 

ro LO 

Q-

~ 

~ 0 .... (f) 

(f) ~I Y I G (GPa) I S~ (MPa) I Yu (~) w 0 

a: "'f 

I- o --CYCOM 982 

(f) 

4.7 78 

0 o --APC2 4.5 141 

0 

0 All material properties are an average 

(\j of five specimens 

*Strength of [±45]2S Laminate 

I /iii 

0 

0 .1-- _____ ----1.. _____ ---L-. ____ ~ ______ ....J 

0 0 . 00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 

STRAIN (%) 
Appendix 7 

Interlaminar Fracture Test Data 

Mode I: Double Cantilever Beam 

CYCOM 982 * . . . . . . . . . . . . . . . . . . . . . . . . . .. 43 

APC- 2 * * . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 50 

Lower Bound: GISC •••...•••••• 51 

Intermediate Bound:GIC .•••••• 61 

Mode II: End Notched Flexure 

cr COM 9 8 2 * . . . . . . . . . . . . . . . . . . . . . . . . . .. 7 2 

APC2** .........................•..... 76 

APC2 Rate Dependence ••••.•••••••••••• 80 

* Linear load-deflection response 

** Non-linear load-deflection response 

42 
Mode I: Double Cantilever Beam 

CYCOM 982* 

GIC=3AIA22/2W** 

Nomenclature 

Al[Nm2 ]-1: Coeff1cient(Comp11ance 

vs. Crack Length) 

A2[Nm]: Coefficient(Critical 

C[m/N]: Initial Comp11ance 

Pc[N]: Critical Load 

w [m]: Width 

load vs. Crack Length 

Summary 

Instron Cross Head Rate,8 

[1n/min] [10-6m/ s ] 

0.05 21 

Overall Average 

GIC 

[kj /m2] 

0.26 

0.27 

0.25 

0.23 

0.22 

0.26 

o . 25± 0 .02 

* L1near elast1c response and stable crack growth 

** See Append1x 1 

43 
o 

o 

-

x 

-

:::c 

"I-- It!) 

SZ 

XL1J 

---1 

:=:c::: 

u N« ICC SU ~~~~-r--~--~--~------~-----------+-~ 

-I 

C\I 

en 

tn 

::E -E 

c 

t.l - >- en 

t.l 

-

c 

:Z . 

C 

w 

::E n 

H :J: 

t.l ~ 

w c 

a. .... en ~ 

9 ~ 8 G 

OVOl lV:JIIIH:J 

- - ........ 

z ~ 

E @ 

- -I * (7] * * E

* * ........ 

* < ~ < * ~ 

* -.:r 

C\I - r-... -

C\I CD 

en - C\I C C . en . c . C\I C n 

n 

II t.l 

Cl .... t.l a. U) 

G B- O~X~ 8 9 

38NVIldW08 

44 

J o~x~ 

o 

o 

-

x 

-
) 

U1 "'"

~ 

0 

"'I'"i 

X :1 

In-l 

ru 

Wcp 

U o Z"'I'"i 

«x 

H"'I'"i 

-1m 

0... 

:::E 

Oin U 

ru 

1 

o "'I'"i 

~~---r-r~inini~inil---r~~riini~inil 

iXiO -2 iXiO -1 iXiO 0 

CRACK LENGTH 

) 

SPECIMEN: CyeOM 982-2 

WIDTH'" 0.019 (m) 

C = 0.74788*A**3 (mIN) 

Pc = 2.13270*A**-1 (N) 

GIC ... 0.27 (KJ/m**2) 

N 

0 

-

X 

-m 

CD 

" 

CD 

In 

0 

« 

O'q' 

-I 

-I 

«co 

U 

H 

lH 

lIru U 

.. 

C) 

"'I'"i 

~-;--~~-rTiTiinimii~~-'-rTTiniimii 

iXiO -2 iXiO -1 iXiO 0 

CRACK LENGTH 

) 
('\ 

r, 

o 

o 

-

x 

-

I .... 1--

It!) 

~:z 

xUJ 

--1 

~ 

t.J N« 10: 

~t.J 

~I~I~~I~I--~I--~I--~I----~I------~I~----------+-~ 

2 OlXl 6 8 L 9 9 V 8 G J OlXl 

OVOl lV8I1Itf8 

('Il z -

3 I , 

C\I e @ 

en 

m - -I * * - ('Il * e 

% e * * ..... 0 - * < ~ 

u < * ~ 

>- en * U 

I"'- - - ~ 0 

0 CD I"'- 10 

:Z . CD 0 C\I 0 C\I 

- . UJ l"'- . 0 

% n . C\I .... :::I: 0 II 

U l- II 

UJ C II U 

0- ..... 0 ..... Ul ~ U 0- m 0 

0 

-

x 

-

I .... 1--

It!) 

~:z xUJ 

--1 

~ 

t.J N« 10: 

~t.J x 

G B- O~X~ 8 9 - 38NVIldW08 

46 
~ 

-...J 

) 

cu 

1 

o 

....-t 

X 

....-t 

m 

LD 

w'" C\J ~ U l I 

ZO 

«~ I-~....-t 

_I m 

0... 

L 

o 

U LD 

C\J 

, 

I ~ I . ~ i I 

3 -+--,-~ ---'-1 "'""T1---r11TTTTl 

1Y10 -2 1X10 -1 1X10 0 

CRACK LENGTH 

) 

SPECIMEN: CYCOM 982-4 

WIDTH= 0.019 (m) 

C = 0.74387*A**3 (miN) 

Pc = 1.97113*A**-1 (N) 

GIC = 0.23 (KJ/m**2) 

cu 

0 

....-t 

X 

....-t 

01 

m 

t--

CD 

LD 

0 

« 

~ :1 

I--i 

I-- ! 

H I 

5 rui 

! , 

I 

, 

, 

, .... , 

\ 

\ 

\ 

\ 

i 

~ I I I I JlJlII' I 11111111 

1X10 -2 1X10 -1 1X10 0 

CRACK LENGTH 

~) 
) 

C\I 

, 

a 

....-i 

x 

....-i 

CD 

m 

1 I 

luCfJ ru l I 

f u' 

~O 

/- .... 1 

~~l I 

I - J CD 

0... 

L / "'" Om I co U 

1 1 

I 

I I 7rul I 

a ., ....-i 

X 

....-i -r --,- I I I I I III -""--'--"TTlll 

1\ 10 -2 ~/1O -1 1/10 0 

CRACK ~EtIGTH 

) 

SPECIMEN: CYCOM 982-5 

WIDTH= 0.019 (m) 

C = 0.70209*A**3 (miN) 

Pc = 1. 97580*A**-1 (N) 

GIC = 0.22 (KJ/m**2) 

C\I 

a 

....-i 

x ...-1 

m 

CD 

r---

CD 

m 

0 

~ ~l I 

j Oll 

.-i . l- . H 

5 ru1 

..... 

o ...-1 

X ' 

~ \ 

\ 

\ 

\ 

\ 

~ 

...-1-r I 11111111 I 11111111 

1Xl0 -2 1X10 -1 1)'10 0 

CRACK LENGTH 

-) 
) ) -) 

N N • 

0 0 ..... ..... X X 

..... :1 m 

SPECIME~ CYCOM 9822-6 CD 

10-1 " 

WIDTH= 0.019 (m) CD 

tn 

C = 0.69028HAHH3 (m/N) C\I 0 

Wro « o.q- u' 

z~ --1 

«x Pc = 2.17113HAHH-1 (N) H ..... --1 

«ro --1m U ~ n.. 

GIC = 0.26 (KJ/mHH2) H \D ::E I- 010 H U a:C\1 

u 

C\I 

1 ... o o ~ ..... ~~r--'~~,.n.n.~.nll~-'~~~.rinini~1I ~~r--'-'~'i'iTi~ii~i---r~-rTiTinlimil 

1X10 -2 lX10 -1 lX10 0 lX10 -2 lX10 -1 lX10 0 

CRACK LENGTH CRACK LENGTH 
Mode I: Double Cant~lever Beam 

APC-2 Lower Bound: GISC 

Nomenclature 

A[m]: Crack length 

C[m/N]: Initial Compliance 

Pc[N]: Load at the onset of 

DR [mm/s] : Instron Crosshead Speed 

GIC [kj/m2 ]: Lower Bound 

Al[Nm2 ]-1: Coefficient 

Nonl~near response 

w [m] : Width 

Summary: Averaged Results 

Instron Cross Head 

Rate, 6 

[in/min] [10-6m/ s ] 

0.01 4 

0.10 42 

Crack Tip Opening* 

• CT Rate, 0I 

[lO-lOm/s] 

0.02 - 1.6 

1 - 10 

1. 00 

10.00 

423 8 - 118 

4233 108 - 1102 

Overall Average 

t= 2 ply thicknesses 

50 

1.56±0 .05 

1.60±0.26 

1. 4l±0. 21 

1. 37± 0.15 

1.47 
) ) ) 

N 

1 

0 

-

>< 

-, SPECIMEN: APC2-0.01-1 

A1=0.533 (1/N-m**2) 

WIDTH= 0.019 (m) 

'? 

-~l I A (m) C (m/N) Pc (N) DR (mm/5) GIC (KJ/m**2) 

2-

.......... 0.050 0.00007 122.3 0.004 1.57 

E 0.059 0.00011 104.5 0.004 1.62 

w 0.068 0.00017 87.6 0.004 1.48 

U1 u 

t-' 2"1' 0.085 0.00033 70.3 0.004 1.49 «I 

H~ 0.092 0.00040 65.8 0.004 1.55 

--1>< 

0...- 0.101 0.00054 60.5 0.004 1.56 

:E 

a 0.109 0.00071 56.0 0.004 1.57 

u 

0.117 0.00086 52.5 0.004 1.57 

~~ 

0.127 0.00110 48.0 0.004 1.56 

0.133 0.00124 46.3 0.004 1.58 

0.141 0.00150 44.5 0.004 1.65 I I I I 1111/ I I I I I 1111 

1X10 -2 1X10 -1 1X10 0 

CRACK LENGTH (m) 
) 

Ul 

I'J 

':' 

---

a 

~ 

x 

~ 

m 

10 

Zru 

............ 

E'P 

---- a 

~ 

W X U~ 

Zm 

<t: 

H 

--.J1O 

(L 

::::E 

0 

u 

ru 

"1 

Al;0.441 (1/N-m**2) 

I 

I 

: 

a . 

3 I I I II 11111 I I II Ii "I 

1X10 -2 1X10 -1 1X10 0 

CRACK LENGTH (m) 

) ) 

SPECIMEN: APC2-IO.l-l 

WIDTH= 0.019 (m) 

A (m) C (mIN) Pc (N) DR (mm/s) GIC (KJ/m**2) 

0.066 0.00014 106.8 0.042 1. 74 

0.080 0.00022 89.0 0.042 1. 74 

0.109 0.00059 48.9 0.042 0.98 

0.158 0.00197 34.7 0.042 1.05 

0.179 0.00228 40.0 0.042 1. 77 

0.192 0.00272 36.5 0.042 1. 70 
) 

VI 

w 

~ 

.......... 

o 

...-t 

X 

...-t 

m 

10 

2ru 

........... If) EI 

'--"'0 

...-t 

w~ 

U 

2m 

A1=0.484 (1/N-m**2) 

I 

~ ~ j -110 

0... 

::E 

0 

U 

ru 

1 

o 

...-t 

~-1--~~~rlrllnl~ilr-~-'~TITITlrnlll 

1X10 -2 1XiO -1 1X10 0 

CRACK LENGTH (m) 

) ) 

SPECIMEN: APC2-IO.1-2 

WIDTH= 0.019 (m) 

A (m) C (mIN) Pc (N) DR (mm/s) GIC (KJ/m**2) 

0.080 0.00026 73.0 0.042 1.31 

0.094 0.00039 71.2 0.042 1. 70 

0.122 0.00086 53.4 0.042 1.61 

0.136 0.00116 47.2 0.042 1.56 

0.167 0.00233 38.3 0.042 1.55 
) 

VI 

.t>. 

ru 

I 

a ...-i 

x ...-i 

00 

10 

Zru 

........... E7 

---- a 

... -t 

W x ...-i 

U 

Zoo 

<t 

H 

-110 

Q.. 

2: 

0 

U 

ru 

~ 

I 

A1=0.466 (1/N-m**2) 

, 

I 

f 

a 1 ...-i 

X 

...-i~I~I~I~I~II~II~II---~I~I~I~I~II~"I 

1 X 10 -2 1 X 10 -1 1 X 10 0 

CRACK LENGTH (m) 

) ) 

SPECIMEN: APC2-IO.1-3 

WIDTH= 0.019 (m) 

A (m) C (m/N) Pc (N) DR (mm/s) GIC (KJ/m**2) 

0.065 0.00014 104.5 0.042 1.881 

0.078 0.00023 89.0 0.042 1.753 

0.114 0.00075 55.8 0.042 1.481 

0.148 0.00148 48.7 0.042 1.754 

0.183 0.00190 42.7 0.042 1.772 

0.178 0.00224 41.4 0.042 1.983 
) ) ') 

N 

I 

a 

~ 

x 

~ 

CD SPECIMEN: APC2-I1-1 ~ 

A1=0.46B(1/N-m**2) 

Ul~ WIDTH:: 0.019 (m) 

• 

~ "" E'P I '-"" a 

A (m) C (m/N) Pc (N) DR (mm/s) GIC (KJ/m**2) 

0.072 O.OOO1B B6.7 0.423 1.44 

0.090 0.00035 72.5 0.423 1.57 ~ 

W X 

U1 U~ 

U1 ZCD 

0.110 0.00059 61.4 0.423 1.69 

0.129 0.000B9 4B.9 0.423 1.46 

<t: 

H 0.161 0.00184 40.9 0.423 1.60 

~ ~~ , 

I 

~ 

ru1 J 

O.1BO 0.00329 31.6 0.423 1.19 

I 

a 

~ 

x 

~ 

1 ..... ···1 . """" """I 

1X10 -2 1X10 -1 1X1O 0 

CRACK LENGTH (m) 
111 

0\ 

) 

---

'P 

a 

~ 

x 

~ 

m 

10 

z 

--.......C\I 

E'? 

--- a 

~ 

W x U~ 

2m 

<t 

H 

-110 

0.. 

~ 

0 

u 

C\I 

~ 

I 

a 

~ 

x 

A1=0.556(1/N~**2) 

~I I I I I 11111 I I I I 11111 

1X10 -2 1X10 -1 1X10 0 

CRACK LENGTH (m) 

) ) 

SPECIMEN: APC2-I1-2 

WIDTH= 0.019 (m) 

A (m) C (mIN) Pc (N) DR (mm/s) GIC (KJ/m**2) 

0.072 0.00020 83.8 0.423 0.92 

0.093 0.00046 54.3 0.423 1.12 

0.121 0.00098 40.8 0.423 1.08 

0.149 0.00184 34.7 0.423 1.18 

0.168 0.00439 34.3 0.423 1.46 

0.186 0.00308 33.4 0.423 1.68 

0.202 0.00389 29.B 0.423 1.58 

0.225 0.00544 25.4 0.423 1.42 
) ) ) 

N 

I 

0 

vi 

X ...-t -, 

SPECIMEN: APC2-I1-3 

A1=0.4B4(1/N-m**2) 

WIDTH= 0.019 (m) 

'P " 

-~l I A (m) C (m/N) Pc (N) DR (mm/s) SIC (KJ/m**2) 

Z...-t 

, 0.059 0.00009 10B.8 0.423 1.43 

E 0.073 0.00018 81.4 0.423 1.28 

w ~ 0.OB8 0.00029 73.4 0.423 1.45 U1 u 

-..J z,. 

J 

0.101 0.00048 60.5 0.423 1.37 

<{I 

I-t~ 0.128 0.00104 47.6 0.423 1.35 

-1x 

o......-t 0.154 0.00173 41.8 0.423 1.51 

::E 

0 0.164 0.00204 42.7 0.423 1. 78 

u 0.180 0.00259 36.0 0.423 1.53 

10 

I 

0 ...-t 

x 

...-tT- I I I 111111 I I I I 11111 

1X10 -2 1X10 -1 1X10 0 

CRACK LENGTH (m) 
) 

U1 

(Xl 

'P 

---

o 

~ 

>< 

~ 

eo 

10 

0 

~ 

w>< 

u~ 

Zeo 

<t: 

t--i 

-110 

(L 

::E 

0 

u 

C\1 ..., 

I 

0 

~ 

>< 

... i 

A1=0.514 (1/N-m**2) 

f 

j 

I 

, ........ , ........ , 

1X10 -2 1X10 -1 1X10 0 

CRACK LENGTH (m) 

) ') 

SPECIMEN: APC2-I10-1 

WIDTH= 0.019 (m) 

A (m) C (m/N) Pc (N) DR (mm/s) SIC (KJ/m**2) 

0.06B 0.00016 BO.1 4.233 1.21 

0.OB2 0.00029 66.7 4.233 1.21 

0.105 0.00062 47.2 4.233 0.99 

0.132 0.00124 41.B 4.233 1.23 

0.137 0.00136 41.B 4.233 1.33 

0.165 0.00233 35.6 4.233 1.40 

0.195 0.00336 31.6 4.233 1.53 
) ) ) 

N 

I 

a 

~ 

x 

~ 

m3 SPECIMEN: APC2-I10-2 

A1~0.520(1/N-m**2) 

1O~ WIDTH; 0.019 (m) 

..- A (m) C (m/N) Pc (N) DR (mm/s) 6IC (KJ/m**2) 

Zru 

.......... 0.081 0.00011 97.9 4.233 1.45 

E'P 0.084 0.00032 88.1 4.233 1.33 ---a 

,-t 

W X 0.106 0.00083 52.0 4.233 1.26 

U1 

u~ 

Zm 0.125 0.00110 48.9 4.233 1.54 V) 

<! 

H 0.148 0.00163 42.0 4.233 1.59 

-110 

D- 0.184 0.00233 34.7 4.233 1.32 

::E 

a 0.191 0.00338 32.5 4.233 1.58 

u 

ru 

~I 1 

, , , , "'I -'IIlTfTTJ 

1XiO -2 1X10 -1 1X10 0 

CRACK LENGTH (m) 
0'1 

o 

) 

'r 

..--.. 

o 

"" X 

"" 

CD 

10 

z 

........... ru 

E~ 

--- 0 

vi 

W X Uvi 

ZCD 

« 

H 

--110 

0... 

:::E 

0 

u 

ru 

'1 

A1=0.511 (1/N-m**2) 

~q I I I I 11111 I I I I 1111, 

1X10 -2 1X10 -i 1X10 0 

CRACK LENGTH (m) 

) ) 

SPECIMEN: APC2-I10-3 

WIDTH= 0.019 (m) 

A (m) C (m/N) Pc (N) DR (mm/s) GIC (KJ/m**2) 

0.073 0.00020 77.0 4.233 1.28 

0.086 0.00032 65.4 4.233 1.27 

0.098 0.00048 61.4 4.233 1.44 

0.105 0.00059 56.5 4.233 1.41 

0.114 0.00075 51.2 4.233 1.38 

0.125 0.00100 4B.0 4.233 1.44 

0.134 0.00127 45.4 4.233 1.49 

0.156 0.00184 40.0 4.233 1.56 
Mode I: Double Cantllever Beam 

APC-2 Intermediate Bound: GIC 

Nomenclature 

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

C[m/N]: Initial Compllance 

Pc[N]: Maximum load 

GIC [kj/m2]: Intermediate Bound 

Ai[Nm2]-1: Coefficient 

W [m]: Width 

Summary: Averaged Results 

Instron Cross Head Crack Tip Opening* 

• CT Rate, 6 Rate, <5 I 

[in/min] [lO-6m/ s ] [lO-lOm/s] 

0.01 4 0.02 - 1.6 

0.10 42 1 - 10 

1.00 423 B - 118 

10.00 4233 108 - 1102 

Overall Average 

t= 2 ply thlcknesses 

61 

1. 56± 0.05 

1. 75± 0.13 

1. 98± 0.13 

1. 7l± 0.16 

1. 75 
en 

I'J 

) 

'" 1 

o 

~ 

X 

... 1 

'P 

o 

~ 

,--...>< 

:~-.c"t 

.......... 

E 

LJJ 

U 

""- ., i 

::(1 1 

1--1 0 

__ J~ I 

rL~ 

2: 

o 

u 

'? 

... -\ 

A1=0.533 (1!N-m**2) 

I 

~ 

I 

¥I 

I 

, 

" 

o~ ~t -, 1 1"1111"'1 -, 1., '1"1] 

1>:10 -2 1>:10 -1 1X1O 0 

CHACK LI~tIG fH (m) 

) ') 

SPECIMEN: APC2-0.01-1 

WIDTH= 0.019 (m) 

A (m) C (mIN) Pc (N) DR (mm/s) GIC (KJ/m**2) 

0.050 0.00007 122.3 0.004 1.57 

0.059 0.00011 104.5 0.004 1.82 

0.068 0.00017 87.6 0.004 1.48 

0.085 0.00033 70.3 0.004 1.49 

0.092 0.000-10 65.B 0.004 1.55 

0.101 0.00054 60.5 0.004 1.56 

0.109 0.00071 56.0 0.004 1.57 

0.117 0.00086 52.5 0.004 1.57 

0.127 0.00110 48.0 0.004 1.56 

0.133 0.0012·1 48.3 0.00,1 1.58 

0.141 0.00150 '1'1. 5 0.004 1.6b 
-) 

0\ 

w 

'r 

-

o 

.... 

x 

"" 

Zru "-

sf 

"""'0 

W"" X 

u"" 

Zm 

« 

H 

~&n 

0.. 

::e:: 

0 

c..J 

ru 

1 

o II .... 

x 

..... 

Al-0.44i(1/N-IIHM2) 

f 

I 

I " ." ... "". " .""" " "". iXl0 -2 iXl0 -I lXl0 0 

CRACK LENGTH (m) 

) ) 

SPECIMEN: APC2-IO.i-1U 

WIDTHa 0.019 (ID) 

A (II) C (II/N) Pc (N) DR (all/s) 6IC (KJ/IIIMM2) 

0.OB8 0.0001~ 10B.8 0.042 1.739 

O.OBO 0.00022 89.0 0.042 1.737 

0.109 0.00059 81.8 0.000 1.6B9 

0.168 0.00197 ~1.8 0.042 1.520 

0.179 0.0022B 40.5 0.042 1.B14 

0.192 0.00272 37.4 0.042 1.787 
C'\ 

~ 

) 

'}I 

o 

..-t 

X 

..-t 

eo 

tn 

--- 2 

,ru 

E'P 

"--" o 

..-t 

W X 

U..-t 

2eo 

« 

H 

-.l tn 

0... 

~ 

o 

u 

ru 

"1 

o 

..-t 

Al=0.484 (1/N-m**2) 

~-1~~~~~i~i~ii~i--~~-rTTiTirniii 

1X10 -2 1X10 -1 1X10 0 

CRACK LENGTH (m) 

') 

SPECIMEN: APC2-IO.1-2U 

WIDTH= 0.019 (m) 

A (m) 

0.080 

0.094 

0.122 

0.136 

0.167 

C (mIN) 

0.00026 

0.00039 

0.00086 

0.00116 

0.00233 

Pc (N) 

83.6 

73.4 

54.3 

4B.5 

40.9 

') 

DR (mm/s) SIC (KJ/m**2) 

0.042 1.718 

0.042 1.804 

0.042 1.669 

0.042 1.649 

0.042 1.773 
0\ 

UI 

-) 

N 

I 

o 

~ 

x 

~ 

m 

1.0 

........... 

2 

,ru 

E7 

.......... o 

~ 

W x U~ 

2m 

<! 

H 

---11.0 

0.. 

:::E 

o 

U 

ru 

1 

o 

~ 

Al=0.466 (1/N-m**2) 

X 

~--t----r--r-~lilrrlinl~I----'-~~-rITITITlnli 

1X10 -2 1X10 -1 1X10 0 

CRACK LENGTH (m) 

) 

SPECIMEN: APC2-IO.1-3U 

WIDTH= 0.019 (m) 

A (m) 

0.065 

0.078 

0.114 

0.148 

0.163 

0.178 

C (m/N) 

0.00014 

0.00023 

0.00075 

0.00146 

0.00190 

0.00224 

Pc (N) 

104.5 

69.0 

59.6 

48.9 

43.1 

41.6 

') 

DR (mm/5) GIC (KJ/m**2) 

0.042 1.681 

0.042 1.753 

0.042 1.702 

0.042 1.925 

0.042 1.609 

0.042 2.026 
0"1 

0"1 

) 

N 

I 

o 

~ 

x 

~ 

m 

LO 

--- Z 

,ru 

E'l' 

---o 

~ 

W X U~ 

Zm 

<t: 

H 

--1LO 

(L 

2 

o 

U 

ru 

.., 

o 

~ 

Al=0.468 (1/N-mHH2) 

• 

~-4--~-T~~iini~"r-~~~TTi~ii~iI 

lXl0 -2 lXl0 -1 lXl0 0 

CRACK LENGTH (m) 

') 

SPECIMEN: APC2-Il-1U 

WIDTH= 0.019 (m) 

A (m) 

0.072 

0.090 

0.110 

0.129 

0.161 

0.180 

C (m/N) 

0.00018 

0.00035 

0.00059 

0.00089 

0.00184 

0.00329 

Pc (N) 

105.4 

86.7 

71.8 

66.3 

53.8 

38.3 

-) 

DR (mm/s) GIC (KJ/mHH2) 

0.423 2.130 

0.423 2.253 

0.423 2.295 

0.423 2.872 

0.423 2.766 

0.423 1.743 
') 

0'1 

-....J 

'r 

..--.. 

a 

~ 

>< 

~ 

CD 

10 

Zru 

............ 

E'P ........, a 

~ 

w>< 

u~ 

ZCD 

<{ 

H 

-110 

0... 

:::;E 

0 

u 

ru 

1 

a 

~ 

>< 

~ 

)Uf2) 

, ........ , - _ .. ----, 

1X10 -2 1X10 -1 1X10 0 

CRACK LENGTH (m) 

) -j 

SPECIMEN: APC2-I1-2U 

WIOTH= 0.019 (m) 

A (m) C (mIN) Pc (N) OR (mm/s) GIC (KJ/mHH2) 

0.072 0.00020 81.0 0.423 1.493 

0.093 0.00046 67.2 0.423 1.716 

0.121 0.0009B 51.2 0.423 1.6B2 

0.149 0.001B4 43.6 0.423 1.856 

0.168 0.00439 41.4 0.423 2.125 

0.186 0.00306 36.5 0.423 2.00B 

0.202 0.00389 33.4 0.423 1.982 

0.225 0.00544 2B.0 0.423 1.734 
) ) ) 

N 

1 

0 

..-t 

X 

..-t -, 

SPECIMEN: APC2-I1-3U 

A1~0.484(1/N-m**2) 

WIDTH~ 0.018 (m) 

'P " 

-~l I A (m) C (mIN) Pc (N) DR (mm/s) GIC (KJ/m**2) 

Z..-t 0.058 0.00008 120.5 0.423 1.827 ""'-

E 0.073 0.00018 84.7 0.423 1.730 

w / 

0.088 0.00028 81.8 0.423 1.803 

u 

z .. 0.101 0.00048 71.2 0.423 1.881 m «I ex) 

H~ 0.128 0.00104 80.1 0.423 2.150 

-1x 

o.....-t 0.154 0.00173 44.8 0.423 1.747 

::£ 

0 0.184 0.00204 43.1 0.423 1.818 

u 0.180 0.00258 42.3 0.423 2.108 

f 

0 

..-t 

X 

..-t 

I ........• . """" """. 1X10 -2 1X10 -1 1X10 0 

CRACK LENGTH (m) 
) 

0\ 

1.0 

':' 

..--. 

o 

..-i 

X 

..-i 

m 

lC) 

Zru 

........... 

E'P 

-- 0 

..-i 

W X 

u..-i 

Zm 

« 

H 

--1lC) 

CL 

:E 

0 

u 

ru 

.... 

I 

Al=0.514 (1/N-m**2) 

81 I I I I 11111 I I I Ii llil 

lXlO -2 lX10 -1 lX10 0 

CRACK LENGTH (m) 

) ') 

SPECIMEN: APC2-II0-IU 

WIDTH= 0.019 (m) 

A (m) C (mIN) Pc (N) DR (mm/s) GIC (KJ/m**2) 

0.068 0.00018 89.0 4.233 1.494 

0.082 0.00029 78.7 4.233 1.602 

0.105 0.00082 82.3 4.233 1.734 

0.132 0.00124 41.8 4.233 1.229 

0.137 0.00136 45.4 4.233 1.572 

0.165 0.00233 39.1 4.233 1.689 

0.195 0.00338 31.8 4.233 1.527 
) 

....... 

0 

'}' 

,...--

o 

-

>< -

Zru 

........... 

E"P 

- 0 

lJ.Jx 

u--

Zeo 

<:t: 

H 

--1LO 

0.. 

:::::E 

0 

u 

ru 

.... 

I 

0 

-

>< -

Al~0.520(1/N-m**2) 

, ........ , ........ , 

lX10 -2 lXl0 -1 lXl0 0 

CRACK LENGTH (m) 

) ) 

SPECIMEN: APC2-10-2U 

WIDTH= 0.019 (m) 

A (m) C (mIN) Pc (N) DR (mm/s) GIC (KJ/m**2) 

0.081 0.00011 97.9 4.233 1.445 

0.084 0.00032 77.8 4.233 1.743 

0.108 0.00083 80.9 4.233 1.722 

0.125 O.OOUO 52.5 4.233 1.778 

0.148 0.00183 43.8 4.233 1.712 

0.184 0.00233 41.8 4.233 1.918 

0.191 0.00338 38.0 4.233 1.939 
) 

-..J 

I-' 

'P 

......... 

o 

-

x 

-

Zru 

........... 

E'P 

-0 

W -

x 

uzm 

« 

H 

.-IlC) 

0.. 

:::E 

0 

u 

ru 

1 

0 

-

x 

-

Al=0.511 (1/N-m**2) 

I ......... .... ····1 

1X10 -2 1X10 -1 1X10 0 

CRACK LENGTH (m) 

) ) 

SPECIMEN: APC2-II0-IU 

HIDTH= 0.019 (m) 

A (m) C (mIN) Pc (N) DR (mm/s) SIC (KJ/m**2) 

0.073 0.00020 89.0 4.233 1.704 

0.088 0.00032 75.8 4.233 1.698 

0.098 0.00048 81.4 4.233 1.443 

0.105 0.00059 58.3 4.233 1.504 

0.114 0.00075 56.5 4.233 1.678 

0.125 0.00100 48.9 4.233 1.498 

0.134 0.00127 51.2 4.233 1.894 

0.158 0.00184 48.3 4.233 2.088 
,---

Mode II: End Notched Flexure 

CYCOM 982* 

BT 9a2pc

2C 

G1IC= 2w(2L3+3a 3) 

Nomencluture 

a[m]: crack length 

L [m] : Half Span 

Pc[N]: Max~um Load 

C[m/N]: Initial Compliance 

W [m] : width -2 

(2.ss+0.01xlO m) 

Sununary 

Half Span 

Precrack [m] 

No Pre crack 0.051 

Mode I 0.051 

Mode II 0.051 

Mode II 0.038 

No Precrack 0.038 

t [m]: Thickness 

(3.s1+0.03xIO- 3m) 

** 

GBT FE*** 

II GIl 

[kj/m2 ] 

1. 45+0 .16 1. 85+0.20 

0.68+0.02 0.87+0.03 

0.77+0.07 0.98+0.09 

0.68+0.11 0.94+0.15 

1. 40+0.18 1. 93+0.25 

* 

** 

Linear load deflection response 

Instron Rate: 21xlO- 6m/s [0.05 in/min] 

*** See Tables 15 and 17 for Material 3 (El /G13=2s.7) 

72 
Mode II: End Notched Flexure 

CYCOM 982 

No Precrack 

Sample C Pc BT L a GIIC [m] L [10- 6m/tn [N] [kj/m2 ] 

C4 0.051 0.52 2.53 1268 1.59 

C6 0.051 0.51 2.46 1321 1.63 

C7 0.051 0.51 2.41 1201 1.29 

C9 0.051 0.50 2.36 1357 1.59 

C11 0.051 0.51 2.42 1334 1.63 

C18 0.051 0.51 2.01 1277 1.23 

C20 0.051 0.50 2.51 1237 1. 41 

C28 0.051 0.51 2.45 1201 1.31 

C1 0.038 0.37 0.93 2002 1.10 

C2 0.038 0.37 0.96 2037 1.31 

C17 0.038 0.36 0.96 2171 1.28 

C5 0.038 0.57 1.18 1503 1.56 

C23 0.038 0.54 1.16 1557 1.52 

C3 0.038 0.69 1.41 1179 1.45 

C8 0.038 0.68 1.41 1277 1.67. 

C26 0.038 0.68 1. 37 1179 1.39 

73 
Mode II: End Notched Flexure 

CYCOM 982 

Mode I Precrack 

Sample L C Pc BT a GIIC em] L [10- 6m/N] [N] [kJ/m2 ] 

C-2-12 0.051 0.55 2.59 801 0.71 

C-2-15 0.051 0.57 2.66 765 0.69 

C-2-16 0.051 0.54 2.67 792 0.69 

C-2-17 0.051 0.56 2.81 743 0.67 

Mode II Precrack 

C-2-2 0.051 0.64 2.85 725 0.75 

C-2-18 0.051 0.60 2.66 796 0.79 

C-2-32 0.051 0.58 2.66 783 0.75 

C-2-31 0.051 0.58 2.57 801 0.74 

C-2-21 0.051 0.51 2.48 863 0.69 

C-2-13 0.051 0.59 2.45 863 0.86 

C-2-11 0.051 0.78 3.19 667 0.88 

C-2-10 0.051 0.79 3.62 609 0.84 

C-2-14 0.051 0.87 3.79 560 0.78 

74 
Mode II: End Notched Flexure 

CYCOM 982 

Mode II Precrack 

Sample L C Pc BT 

a GIIC 

[m] L [10- 6m/N] [w] [kj/m2 ] 

C-2-3 0.038 0.54 1.04 1076 0.65 

C-2-5 0.038 0.44 0.97 1348 0.70 

C-2-7 0.038 0.44 0.97 1414 0.78 

C-2-29 0.038 0.42 1.01 1334 0.65 

C-2-25 0.038 0.45 1.04 1099 0.51 

C-2-26 0.038 0.54 1.12 1054 0.69 

C-2-27 0.038 0.47 1.27 947 0.51 

C-2-28 0.038 0.62 1.28 899 0.68 

C-2-30 0.038 0.70 1. 38 899 0.83 

C-2-1 0.038 0.57 1.50 810 0.58 

C-2-6 0.038 0.82 1. 80 681 0.71 

C-2-20 0.038 0.82 1.53 752 0.73 

C-2-24 0.038 0.87 1.66 729 0.78 

75 
r"\ 

a [m] : 

L [m] : 

W[m] : 

Mode II: End Notched Flexure 

APC-2* 

BT 9a2pc

2C 

GIIC 2w (2L 3+3a 3) 

Nomencluture 

Crack length 

Half Span 

Width** 

Pc[N]: Maxium Load 

C[m/N]: Initial Compliance 

t[m]: Thickness** 

Summary *** 

Number of Half Span BT GIIC Precrack Plies em] 

[kj/m2] 

No Precrack 26 0.051 2.73±0.33 

l-lode I 

Mode I 

Mode II 

Hode I 

Mode I 

* 

** 

*** 

26 0.051 

40 0.051 

26 0.051 

26 0.038 

40 0.038 

Non-linear load deflection response 

-2 Average width: 2.54±0.01xlO m 

1. 78±0 .11 

1. 87±0 .11 

1. 93±0. 28 

1.89±0.16 

1. 84±0. 07 

Average Thickness: 3.37±0.02xlO- 3m (26 ply); 

5.26±0.05xlO- 3m (40 ply) 

Instron Rate: 21xlO- 6m/s [0.05 in/min] 

76 
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-I-II 

A-1-3 

A-1-21 

A-1-15 

Mode II: End Notched Flexure 

APC-2 

No Pre crack (26 E1ies) 

L a C Pc 

[m] L [10-6m/N] [N] 

0.051 0.49 3.21 1546 

0.051 0.50 3.47 1368 

0.051 0.49 2.91 1724 

Mode I Precrack (26 plies) 

0.051 0.53 3.89 1079 

0.051 0.52 3.56 1112 

0.051 0.52 2.81 1257 

0.051 0.51 3.02 1212 

0.051 0.50 2.78 1301 

0.051 0.52 2.64 1303 

0.051 0.53 3.02 1268 

0.051 0.53 2.57 1535 

0.051 0.51 2.57 1303 

0.051 0.53 2.92 1201 

0.051 0.51 2.62 1414 

77 

BT GIIC 

[kj/m2 ] 

2.72 

2.39 

3.07 

1. 80 

1. 70 

1. 74 

1.66 

1. 72 

1. 76 

1.93 

2.01 

1. 68 

1.67 

1.99 
Mode II: End Notched Flexure 

APC-2 

Mode I Precrack (40 plies) 

Sample L C Pc BT 

a GIIC [m] L [10- 6m/N] [N] Ikj/m2 ] 

A-3-1 0.051 0.50 0.73 2630 1.86 

A-3-2 0.051 0.52 0.67 2624 1.82 

A-3-3 0.051 0.54 0.69 2489 1. 84 

A-3-4 0.051 0.53 0.71 2530 1. 80 

A-3-5 0.051 0.52 0.67 2677 1. 86 

A-3-6 0.051 0.53 0.77 2694 2.26 

A-3-7 0.051 0.52 0.83 2483 2.01 

A-3-8 0.051 0.50 0.74 2618 1. 86 

A-3-9 0.051 0.50 0.73 2778 2.08 

A-3-10 0.051 0.50 0.76 2542 1. 87 

A-3-11 0.051 0.51 0.76 2483 1. 77 

r.1ode II Precrack (26 plies) 

A-2-5 0.051 0.51 4.78 1012 1. 81 

A-2-9 0.051 0.49 2.77 1546 2.35 

A-2-18 0.051 0.52 3.07 1268 1.95 

78 
r-. 

Mode II: End Notched Flexure 

APC-2 

l-1ode I Pre crack (26 E1ies) 

Sample C Pc BT L a G11C L [10- 6m/N] [N] [kj/m2 ] 

A-1-6 0.038 0.68 1. 36 1312 1. 69 

A-1-8 0.038 0.66 1. 35 1410 1.88 

A-1-7 0.038 0.68 1. 30 1423 1.94 

A-1-12 0.038 0.65 1. 35 1414 1. 86 

A-1-24 0.038 0.53 1.09 1801 1.96 

A-1-19 0.038 0.52 1. 03 1890 1. 88 

A-1-20 0.038 0.51 1.16 1922 2.15 

A-1-22 0.038 0.48 1.12 1926 1.90 

A-1-23 0.038 0.52 1.26 1766 2.05 

'" A-1-2 0.038 0.32 0.95 2847 1. 83 

A-1-9 0.038 0.34 1.00 3069 2.08 

A-1-1 0.038 0.35 0.96 2433 1.56 

Mode I Precrack (40 E1ies) 

A-3-12 0.038 0.54 0.32 3203 1. 79 

A-3-13 0.038 0.51 0.32 3410 1.86 

A-3-14 0.038 0.58 0.34 3114 1.98 

A-3-15 0.038 0.51 0.31 3380 1. 79 

A-3-16 0.038 0.56 0.33 3084 1. 77 

79 
~ 1 

a [m] : 

L [m] : 

w[m]: 

t [m] : 

Mode II: End Notched Flexure 

APC-2 Rate Dependence* 

9a 2pc2C 

= 

2w (2L 3+3a3) 

Nomenclature 

Crack Length 

Half Span (O.OSlm) 

Width (2.S4±0.OlO-2) 

Thickness -3 

(3.37 0.02xlO m) 

Pc[N]: Maximum Load 

PNL[N]: Load at the onset 

nonlinear response 

C[m/N]: Init~al compliance 

Averaged Results 

Mode II Rate Dependence: APC2* 

on 

Instron Cross Head 

Rate, (/ 

Averaged Results 

Crack Tip Shear 

• CT Rate, <5 II 

BT GIISC 

[in/min] [lO-6m/ s1 [lO-10m/s1 

0.01 4 26 

O.OS 21 1S0 

0.10 42 260 

1.00 423 2S00 

10.00 4233 2S000 

Overall Average 

* Mode I Precrack unless noted otherwise 

so 

0.9S±0.lS 

1.02±0.20 

1.01±0.09 

0.98±0.16 

1. 40± 0 .13 

1. 31 

1.84±0.27 

1.78±0.20 

1.82±0.20 

1. 87± 0.24 

1.40±0.13 

1. 73 
Instron 

Sample 

EP-.Ol-l 

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 

Mode 

Cross 

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 

II Rate Dependence: 

-

Head Rate: 4xl0-6m/s 

C PnL 

[10-6m/N] [N] 

2.63 956 

2.72 801 

2.84 1001 

2.02 1045 

3.45 1001 

Head Rate: -6 42xl0 m/s 

2.54 1134 

2.85 890 

2.43 1001 

2.86 956 

2.75 979 

2.87 1112 

3.15 956 

3.02 1023 

3.85 945 

Mode II Precrack 

3.64 

3.07 

2.88 

2.97 

81 

1212 

1268 

1290 

1245 

APC-2 

[0.01 

PC 

[N] 

1303 

1130 

1334 

1619 

1312 

[0.10 

1512 

1210 

1326 

1228 

1370 

1312 

1257 

1257 

1101 

1323 

1401 

1446 

1368 

in/min] 

BT GIISC 

[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 GIIC 

[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 
~ 

~ 

Mode II Rate Dependence: APC-2 

Instron Cross Head Rate: -6 423x10 m/s [1. 00 in/min] 

Sample C PnL Pc BT BT a GIISC GIIC L [10-6m/N] [N] [N] [kj/m2 ] [kj/m2] 

EP-1-1 0.53 2.92 1023 1379 1.24 2.25 

EP-1-2 0.53 2.55 912 1379 0.85 1.94 

EP-1-3 0.52 3.06 890 1157 0.96 1.62 

EP-1-4 0.53 2.99 845 1214 0.86 1. 77 

EP-1-5 0.51 2.58 1001 1334 Q.99 1.75 

Instron Cross Head Rate: -6 4233x10 m/s [10.0 in/ml.n] 

EP-10-1 0.51 2.59 1210 1210 1. 43 1.43 

EP-10-2 0.52 3.11 1103 1103 1. 46 1. 46 

EP-10-3 0.52 2.82 1192 1192 1.57 1.57 

EP-10-4 0.53 3.42 939 939 1.21 1.21 

EP-10-5 0.53 3.16 1023 1023 1.32 1. 32 

82 
End of Document