A finite element analysis of the end notch flexure specimen for mode II interlaminar fracture toughness measurement was conducted. The effect of friction between the crack faces and large deflection on the evaluation of G sub IIc from this specimen were investigated. Results of this study are presented in this paper

Kochhar, N. K.

Mall, S.

English

NASA Technical Reports Server

.. 
NASA Contractor Report 178113 
NASA-CR-178113 
19860017957 
FINITE ELEMENT ANALYSIS OF END NOTCH FLEXURE SPECIMEN 
S. Mall and N. K. Kochhar 
UNIVERSITY OF MISSOURI-ROLLA 
ROLLA) MISSOURI 
GRANT NAGl-425 
May 1986 
NI\S/\ 
National Aeronautics and 
Space Administration 
LIBRARV COpy 
JUL 8 1980 
LANGLEY RESEARCH CENTElt 
USRARY, NASA 
HAMPTON, VIRGINIA 
Langley Research Center 
Hampton, Virginia 23665 
1111111111111 1111 11111 11111//11/1//11 11111111 
NF00156 
https://ntrs.nasa.gov/search.jsp?R=19860017957 2020-03-20T14:10:38+00:00Z
1.. 
ABSTRACT 
A finite element analysis of the end notch flexure specimen for mode II 
interlaminar fracture toughness measurement was conducted. The effect of 
friction between the crack faces and large deflection on the evaluation of 
GIIC from this specimen were investigated. This -analysis showed that the 
friction effect is negligible when crack length is greater than one-fourth 
of length of the specimen. Further,. geometric nonlinear analysis is required 
to evaluate G1IC when deflection is greater than the thickness of specimen. 
1 
INTRODUCTION 
The delamination of laminated fiber reinforced composites is of 
. current interest, particularly with regard to their durability and 
damage tolerance. It is the most commonly observed failure mode 
in composites. Fracture mechanics has been found to be a useful 
tool for understanding delamination [1]. Most of the work reported 
in this area has been concerned with the delamination in the opening 
mode, i.e. mode I. Delamination under shear sliding mode i.e. mode II 
and combined mode I-II situations are also the possible fracture modes 
of potentially greater significance in composite structures. Several 
studies un mixed--mode interlaminar fracture are also reported [1-4]. 
Recently attention has been given -to mode II shear delamination 
[5-9]. Several investigators have used end notch flexure (ENF) 
specimen to measure shear mode strain energy release rate, GIIC ' for 
delamination growth [6-9]. This specimen is a beam with a crack 
(delamination) located on the neutral plane at one end and is 
subjected to the three-point bending. This specimen was initially 
utilized by Barrett and Foschi to measure Mode II critical-stress-
intensity factor, K IIC' for a strongly anisotropic fibrous material, 
wood [10]. Currently an ASTM task group is conducting a round 
robin test program using an end notch flexure specimen as a prelude 
to developing an ASTM standard for measurement of mode II interlaminar 
fracture toughness of composites. In this study, the end notch flexure 
specimen was analyzed using the finite element method for understanding 
its behavior and performance. 
2 
FINITE ELEMENT ANALYSIS 
The end notch flexure specimen geometry is shown in Fig. 1. 
Two geometries of the specimen were analyzed; (1) total length, 
2L = 7.62 cm and (2) 2L = 10.16 cm. For both geometries, the 
thickness (2h) of the specimen was taken equal to 0.30 cm which 
is nominal thickness of a 24 ply composite panel. These dimensions 
of Land h were selected since they were employed in experimental 
works [6,9]. The width of specimen was 2.54 cm. Only one material 
system was analyzed; unidirectional graphite/epoxy. The material 
properties used in finite element analysis are presented in Table 1. 
A two-dimensional finite element program called GAMNAS [11] 
was used. A typical finite element mesh, shown in Fig. 2 consisted 
of about 1000 isoparametric four-node elements and had about 2400 
degrees of freedom. The element size in the vicinity of the crack 
was 0.02 x 0.02 mm in order to evaluate accurately the strain energy 
release rate Gil. This size was selected by previous experience [121 
as well as by conducting the convergence test on Gil calculation with 
mesh refinement. The error in Gil obtained in the present study is 
estimated to be less than ±2%. The strain energy release rate, Gil' 
in the analysis was computed using a virtual crack closure technique 
[13] . Plane-strain condition was assumed in the finite element analysis. 
The analysis indicated that mode II deformation is achieved at 
the crack tip and that the accompanying mode I deformation causes 
closure and overlapping of the opposite faces of the crack. This is 
not possible physically. To prevent the overlapping of crack faces, 
the nodal coupling technique, available with GAMNAS program [11]. 
was used. For this purpose, the multipoint constraint was applied 
at corresponding nodes to have the same displacements normal to the 
3 
crack faces. This resulted in pure mode II condition, i.e. GI = O. 
When the crack faces are pressed together as in this specimen, 
friction effects will occur. The friction effects on ell calculation 
will be rather difficult to assess in the practical situation, however 
a reasonable estimate of its role can be investigated with the finite 
element analysis. The friction effect was modeled in. the following 
manner. The analysis was conducted intially with the frictionless 
. crack faces where displacements normal to the crack faces were 
matched at corresponding nodes. The normal reactions at the crack 
faces were obtained from this first step of calculation. The friction 
forces at the nodes on the crack faces were calculated for the assumed 
coefficient of friction. The finite element analysis of the specimen 
was conducted with these computed friction forces applied at the crack 
faces. This second step of analysis provided the new normal forces 
at the crack faces and corresponding friction forces. The analysis 
was repeated till the applied friction forces matched with the computed 
normal reactions. This required about two or three iterations. 
4 
, 
' .... 
RESULTS AND DISCUSSIONS 
Comparison Between Theoretical and FEM Gil Values 
The measured compliance, c, versus crack length, a, relationship 
of a test specimen, in general, provides the most accurate evaluation 
of fracture toughness. However, it requires several measurements. On 
the other hand, fracture toughness can be measured from a single 
measurement of critical load if the necessary expression for G calculation 
is available. The experimental dc/da values were found to be subject to 
large errors due to small variation in compliance with crack length for 
small crack length values in the ENF specimen [7]. Therefore, the 
fOI/owing expression for mode II strain energy rt!lease rat.::'!, Gil for 
this specimen was developed by Russeli [7]: 
{O 
where P, a, b, h are defined in Fig. 1 and Ell is the Young's modulus 
in longitudinal direction. The G", as expressed above, is based on a 
linear beam theory where shear deformation is neglected and the curvature 
1 = d 2y/dx2 
R [1 + (dy/dx)2]3/2 
is approximated with l/R ~ d 2y Idx2 • The Gil values obtained from FEM 
analysis and from Eq. (1) for both geometries of the specimens; (1) 
2l = 7.62 cm and (2) 2l = 10.16 cm, are compared for the normalized 
crack length, all, ranging from 0.125 to 0.9. The normalized crack 
length commonly used for measurement of GIIC with this specimen was 
0.5 [6,7,9]. Figure 3 shows that G"C from a linear beam theory, 
5 
i.e. from Eq. (1), is within 8% and 6% of its counterpart from FEM 
analysis for all = 0.5 for specimens with 2l = 7.62 cm and 2l = 10.16 cm, 
respectively. Further, Fig. 3 shows that deviation between Gil from 
Eq. (1) and FEM analysis decreases with longer crack lengths and 
increases with shorter crack lengths. This comparison shows that the 
GIIC should be evaluated from the end notch flexure specimen for 
all ~ 0.5 if Eq. (1) is used. 
Effect of Overhang length 
The effect of overhang length beyond the sllpport was also 
investigated with finite element analysis. Specimens with overhang 
lengths of 6.35, 12.7 and 25.4 mm on each side were analyzed. The 
Gil values obtained for these cases were within ±1% of each other. 
Thus, the overhang portion of this specimen has no effect in the 
evaluation of GIIC . 
Friction Effect 
As mentioned previously, the friction was also modeled in FEM 
analysis. The most difficult task is to evaluate the actual coefficient 
of friction, ~, between two pressed crack faces of ENF specimen. 
This was beyond the scope of the present study. However, a simple 
experiment was performed to estimate the coefficient of friction between 
two unidirectional graphite/epoxy laminates. This experiment involved 
the measurement of the force to initiate sliding between the two 
laminates with a known compressive load. The coefficient of friction, 11, 
was found to be about 0.35. Therefore, the finite element analysis 
was conducted with the three values of ~ = 0.1, 0.3 and 0.5 to under-
stand the role of friction in a qualitative manner. Results of this 
analysis are ~hown in Fig. 4. Several observations can be made from 
6 
•. 
.' 
• .J. 
this analysis. For crack length commonly used in experimental 
investigation, i.e. all = 0.5, the effect of friction is negligible 
for all practical purposes if p is about 0.3. And, this effect is 
less in the ENF specimen with 2l = 10.16 cm in comparison to 
specimen with 2l = 7.62 cm. The friction effect shows a pronounced 
effect for shorter crack lengths and is negligible for longer crack 
lengths. This leads to an apparent conclusion that longer crack 
length should be employed for G"C evaluation, but this may cause 
the large deflection of specimen during testing and henceforth it 
may require the geometric nonlinear analysis as discussed later on. 
The friction forces between the crack faces were prilnarily 
in the region above the support pin. Since it is always desirable 
to have the friction force as small as possible, it might, therefore, 
be preferable to use the shims or rollers between the crack face 
just above the support pin to reduce the coefficient of friction. 
Barrett and Foschi [10] suggested the use of roller between crack 
faces for measurement of K'IC of wood from this type of specimen. 
However, it may not be convenient in composite specimens due to 
their small thicknesses. 
Geometric Nonlinear Analysis 
To investigate the effect of finite rota'tion due to large 
deflection, the geometric nonlinear analysis of the ENF specimen 
was conducted with the GAMNAS finite element program [11]. This 
analysis was conducted without friction. Figure 5 shows the comparison 
of GIl obtained from linear and geometric nonlinear analysis for both geo-
metries of specimens for crack length a = 0.5L. Linear and nonlinear solution 
7 
are in agreement with each other up to deflection, l:!., equal to the 
thickness of specimen, 2h. For larger deflection, i.e. l:!. ~ 2h, the 
Gil would be overestimated from a linear analysis or Eq. (1). This 
overestimation depends on the deflection as shown in Fig. S. 
8 
CONCLUDING REMARKS 
A finite .element analysis of the end notch flexure specimen 
for mode II interlaminar fracture toughness measurement was 
conducted. The effect of friction between the crack faces and 
large deflection on the evaluation of GIIC from this specimen were 
investigated. Two geometries of the specimen, and one material 
system was studied. This study showed that this specimen should 
be preferably used for GIIC measurement with crack length, 
a ~ O.5L and deflection,/!. ~ 2h. 
ACKNOWLEDGEMENT 
The work reported here was supported by NASA Langley 
Research Center, Hampton, VA and Weldon Spring Foundation, 
University of Missouri. The authors wish to acknowledge the 
support and encouragement of Dr. W. S. Johnson, NASA Langley 
Research center during the course of this investigation. 
9 
REFERENCES 
1. O'Brien, T.K., "Interlaminar Fracture of Composites", NASA TM 85768, 
June 1984. 
2. Wilkins, D.J., Eisenmann, J.R., Camin, R.A., Margolis, W.S. and Benson, 
R.A., "Characterizing Delamination Growth in Graphite-Epoxy", Damage in 
Composite Materials: Basic Mechanisms, Accumulation, Tolerance, Charac-
terization, ASTM STP 775, American Soc. for Testing and Materials, 1982, 
pp. 168-183. . 
3. Ramkumar, R.L. and Whitcomb, J.D., "Characterization of Mode I and Mixed-
Mode Delamination Growth", Delamination and Debonding of Materials, ASTM, 
STP 876, American Society for Testing and Materials, Philadelphia, 1985, 
pp. 315-335. 
4. Armanios, E.A., Rehfield, L.W., and Reddy, A.D., "Design Analysis and 
Testing for Mixed-Mode and Mode II Interlaminar Fracture of Composites" 
Composite Materials: Testing and Design (Seventh Conference), ASTM STP 
893, Ameti';an So:iety for Test.i1g and Materials, Philadelphia, 1986, 
pp. 232-255. 
5. Chatterjee, S.N., Pipes, R.B. and Blake, R.A., Jr., "Criticality of 
Disbonds in Laminated Composites", Effects of Defects in Composite Materials, 
ASTM, STP 836, American Society for Testing and Materials, Philadelphia, 
1984, pp. 161-174. 
6. Russell, A.J. and Street, K.N., "Moisture and Temperature Effects on the 
Mixed-Mode Delamination Fracture of Unidirectional Graphite Epoxy", 
Delamination and Debonding of Materials, ASTM, STP 876, American Society 
for Testing and Materials, Philadelphia, 1985, pp. 349-370. 
7. Russell, A.J., "Factors Affecting the Interlaminar Fracture f'ne.rgy of 
llraphite/E:.poxy Laminates", Progress in Science and Engineering of 
Composites; Proceedings of ICCM-IV, Tokyo, 1982, pp. 279-286. 
8. Giare, G.S., "Fracture Toughness of Unidirectional Fibre Reinforced 
Composites in Mode II", Engineering Fracture Mechanics, Vol. 20, No.1, 
pp. 11-21, 1984. . 
9. 
10. 
Murri, G.B. and O'Brien, T.K., "Interlaminar GIIC Evaluation of Toughened-Resin Matrix Composite Using the End-Notched Flexure Test", AIAA 
Paper No. 85-0647, Proceedings of the 26th AlAA/ASME/ASCE/AHS Structures, 
Structural Dynamics and Materials Conference, April 15-17, 1985, Orlando, 
Barrett, J.D. and Foschi, R.O., "Mode II Stress-Intensity Factors for 
Cracked Wood Beams", Engineering Fracture Mechanics, Vol. 9, pp. 371-378, 
1977 • 
10 
FL. 
" 
11. Whitcomb, J.D. and Dattaguru, B., "User's Manual for GAMNAS--
Geometric and Material Nonlinear Analysis of Structures", 
NASA TM 85734, Jan. 1984. 
12. Mall,S., Johnson, W.S., and Everett, R.A., Jr., "Cyclic Debonding 
of Adhesively Bonded Composites", Adhesive Joints: Their Formation, 
Characteristics, and Testing, K. L. Mittal, Ed; Plenum Press, 
New York, 1984, pp. 639-658. 
13. Rybicki, E.F. and Kanninen, M.F., "A Finite Element Calculation of 
Stress Intensity Factors by a Modified Crack Closure Integral ll , 
Engineering Fracture Mechanics, Vol. 9, NO.4, 1977, pp. 931-938. 
11 
131.0 
TABLE 1 - GRAPHITE/EPOXY MATERIAL PROPERTIESa 
b Modulus , GPa 
13.0 6.4 
Poisson's Ratiob 
0.34 0.35 
b: The subscripts 1, 2 and 3 correspond to the longitudinal, transverse, 
and thickness directions, respectively, of a unidirectional ply. 
12 
CL-~--
J. 
13 
c 
OJ 
E 
....... 
u 
OJ 
0. 
CI) 
OJ 
L 
::l 
X 
OJ 
...--. 
u.. 
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___ --11-- -"·r--r-r~r--r~HI~~~!-JL~ __ ~__ J-
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14 
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....... 
LL 
..... 
U1 
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f.30r-1 ---.,..-----,---..---or----...,.-------. 
::E ~(!) 1=11 ~ (!) I=l 
LID .L=38.fmm 
1.05 
1.000 ,0.2 0.4 0.6' 0.8 1.0 
NORMALIZED CRACK LENGTH, aiL 
Fig. 3. Ratio of GIl from FEM ~nalysis to GIl from Eq. (1) 
as a function of normalized crJck length. 
. . 
" 
--0'\ 
1.05- i 
1.04 
fL =0.1 
1.03 
o a 
~ II :2E II 
lLJ :L w :L 
ll.. J::I u.. 1=1 1.02 
<.!) (!) 
L=38.1mm 
1.01 
1.000 0.2 0.4 0.6 0.8 1.0 
NORtv1ALIZED CRACK lENGTH, all 
Fig. 4 {a}. Ratio o.f GIl with II = 0.0 to G1Iwith .p = 0,1 from FEM analysis 
as a function of normal1zed crack length. 
" 
-' 
'" 
'.-
ro, 
o d 
:E II ~ II 
IJJ :t. lJJ :t. 
LL 1=1 LL ~ (!) (!) 
'~ 
1.16 r' --,-----r--,.-----.r-----
~=0.3 
1.12 
1.08 ". 
' .. 1.04 L=38.1mm 
• 
1.000 0.2' 0.4 0.6 0.8 1.0 
NORMALIZED CRACK lENGTH~ all 
- -
Fig. 4 (b). Ratio of GIl with u = 0.0 to GIl with u = 0.3 from FEM analysis 
as a function of normalIzed crock length. 
--00 
1.25.-. -----.----r----r---,----, 
fL = 0.5 
1.20 
1.15 
LO 
o d 
II II 
:.E :t..:E ::t. 1 10 lJJ lJJ I-f • u. 1=1 u. t-I (!) (.!) L=38.I·mm 
1.05 
1.00_ -- - A -- -- '0 
NORMALIZED CRACK lENGTH, all 
Fig. 4 (c), Ratio of GIl with lJ = 0.0 to GIl 'with lJ = 0.5 from FEM analysIs 
as a function of normalized crack length. 
.., 
--' 
1.0 
,. 
1.00 
~ 0.95 
w 0:: 
z « 
:i W Z~Z ~ zO lJJ :J 0.90 
l1J LL. ~ 
LLt::I (!) (!) 
0.85 
. a = 0.5 L 
L=50.8mm 
'. 
0.800 2· 3 4 
NORf\1ALIZED DEFLECTION, f::l/2h 
Fig, 5, Ratio of Gil from nonlinear analysis ~o GIl from linear analysis 
as a fu~ction of normalIzed d~flection, 
~ 
Standard Bibliographic Page 
1. Report No. J 2. Government Accession No. 3. Recipient's Catalog No. 
NASA CR-178113 
4. Title and Subtitle 5. Report Date 
FINITE ELEMENT ANALYSIS OF END NOTCH FLEXURE SPECIMEN May 1986 
6. Performing Organization Code 
7. Author{s) 8. Performing Organization Report No. 
S. Mall and N. K. Kochhar 
9. Performing Organization Name and Address 10. Work Unit No. 
University of Missouri-Rolla 
Department of Engineering Mechanics 11. Contract or Grant No. 
Roll a, MO 05401 NAGl-425 
12. Sponsoring Agency Name and Address 13. Type of Report and Period Covered Contractor Report 
National Aeronautics and Space Administration 14. Sponsoring Agency Code Washington, DC 20546 534-06-23-03 
15. Supplementary Notes 
Langley Technical Monitor: Dr. W. S. Johnson 
Final Report 
16. Abstract 
A finite element analysis of the end notch flexure specimen for mode II inter-
laminar fracture toughness measurement was conducted. The effect of friction 
between the crack faces and large deflection on the evaluation of GIl from this 
specimen were investigated. Results of this study are presented in c this paper. 
18. Distribution Statement 17. Key Words (Suggested by Authors{s)) 
Interlaminar fracture toughness 
Mode-II delamination 
End notch flexure specimen Unclassified-Unlimited 
Subject Category 24 
19. Security Classif.(of this report) 
Unclasslfied 
J 20. Security Classif.(of this page) 
Unclassifled 
21. No. of Pages 122. Price 
20 A02 
For sale by the National Technical Information Service, Springfield, Virginia 22161 
NASA Langley Form 63 (June 1985) 
End of Document 


Finite element analysis of end notch flexure specimen

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