ion characteristics of dcb and enf composite specimens

8/8/2019 ion Characteristics of Dcb and Enf Composite Specimens

1/9

ELSEVIER

Composites Science and Technology 56 (1996) 451-4590 1996 Elsevier Science Limited

SO266.3538(96)00001-ZPrinted in Northern Ireland. All rights reserved

0266-3538/96/$15.00

DELAMINATION CHARACTER ISTICS OF DOUBLE -CANTILE VER BEAM AND END-NOTCH ED F LEXUR E

COM P OS I T E S P E CI M E NSC. T. Sun & S. Zheng

School of Aeronautics and Ast ronautics, Purdue University , W est Lafayett e, Indiana 47907-1282, USA(Received 14 March 1995; revised version received 1.5November 1995; accepted 14 December 1995)

AbstractThe dist ributions of st rain energy release rate, G, at thecrack fronts of double-cantilever beam (DCB) andend-no tched flexure (ENF) specim ens have beenanalysed by means of the plate finite element. Aboundary layer phenomenon in the distribution of G atthe crack front is found. The applicability of beamtheories as dat a reduction too ls for DCB test ing isexamined. The effect of a curved crack front on the useof beam theories in the calculation of strain energyrelease rat e for a DCB specimen is also discussed.Except for unidirectional and cross-ply l amin ates, thedist ribution of strain energy release rat e at the crackfront is found to be sk ewed, and a parameter isintroduced to measure this skew ness. R ecomm enda-tio ns on DCB specimen design are mad e for t hefracture toughness test to minimiz e the non-uniformand sk ewness effect. Finally, it is found that theboundary lay er effect in the ENF specimen is not assevere as that in the DCB specimen.

0 1996 Elsevier Science Limit edKeywords: double-cantilever beam specimen, end-notched flexure specimen, strain energy release rate,delamination1 INTRODUCTIONFracture mechanics has found extensive applicationsin damage analysis of composite laminates, especiallyin delamination analysis. One of the most importantparameters in the application of fracture mechanics incomposite structures is the strain energy release rate.In order to determine the critical strain energy releaserate, fracture experiments must be performed. Thedouble-cantilever beam (DCB) and the end-notchedIlexure (ENF) specimens are the most popularspecimen configurations in the experimental deter-mination of mode I and mode II interlaminar fracturetoughnesses.1-7 A common procedure for datareduction of DCB tests is to use a compliancecalibration technique known as Berrys method.3%8 Asan alternative, it would be desirable to have an

analytical solution to simplify the data reductionprocedure. Since simple beam theory cannot adequ-ately simulate the deformation near the crack tip, agreat deal of effort- has been devoted to a searchfor a better model (such as advanced beam models)for calculating the strain energy release rate at a DCBcrack front. As for the ENF specimen test, owing tothe sensitivity of compliance with respect to cracklength, beam theories with appropriate correctionfactors are used as data reduction too1s.l However,it has been pointed out that strain energy release ratedistribution along the straight crack fronts of a DCBspecimen is not uniform,14-17 thus casting doubt on thesuitability of beam theories as data reduction tools.It has been noted that delamination in a compositelaminate usually occurs at the interface of different plyorientations. DCB and ENF experiments are also usedto determine the critical strain energy release rate atthe interface of different ply orientations.5* Experim-ental results from these tests often revealed thatcritical strain energy release rates thus obtaineddepend on the lay-up sequence of the testspecimen.336 Such a lay-up sequence dependentinterlaminar fracture toughness should not beregarded as a true material property before theinfluence of other factors is determined. One of thevariables that require more careful study is the effectof stacking sequence on the strain energy release ratedistribution at the crack fronts of DCB and ENFspecimens. In fact, this subject is more complicatedthan it appears. In a general laminated DCB or ENFspecimen, the strain energy release rate at the crackfront varies (and is skewed) across the specimenwidth. Consequently, the crack front is also curvedand skewed. Thus, before beam theories are used toreduce experimental data, we must evaluate thevalidity of the beam-based solutions and provideproper interpretations of these solutions.The behavior of strain energy release rate at thecrack front of DCB and ENF specimens has beeninvestigated by a number of researchers. Amongthem, Crews et ~1.~ used a three-dimensional analysis

451


2/9

452 C. T. Sun, S. Zhengto calculate the strain energy release rate in a DCBspecimen. By attributing the variation of strain energyrelease rate, G, to anticlastic curvature, theyemployed Poissons ratio, -v>,~,o determine qualita-tively the anticlastic effect. Davidson, Davidson andShapery,16 and Nilssoni7 analysed the growth of theDCB crack front and found it to be curved andthumb-nail shaped. Davidson and Shapery16 analysedthe strain energy release rate distribution for alaminated DCB specimen. By examining the transitionfrom plane strain to plane stress, they proposed aparameter D, = D&/D11D22 to describe the variationof strain energy release rate at the crack front, whereD12, D1, and Dz 2 are bending stiffness components inthe laminate D matrix. When dealing with laminatedcomposite specimens, all of the above analyses haveassumed symmetry in the width direction with respectto the X axis. Consequently, their results showed thatthe distribution of G along the crack front wassymmetric with respect to the X axis (see Fig. 1) evenfor angle-ply laminated composite specimens.i4yt5

In the present paper, a double-plate model hasbeen used to perform the delamination crack analysis.Both isotropic and composite DCB specimens wereinvestigated. The boundary layer in the distribution ofG was identified. The applicability of beam theories asdata reduction tools has also been addressed and theeffect of a curved crack front on the use of beamtheories for calculating strain energy release rate at aDCB crack front has been examined. A parameter isproposed to account for the stacking sequence effecton the distribution of the strain energy release rate. Adesign recommendation is made to minimize thevariation and skewness of the strain energy releaserate distribution for a composite specimen. Finally,the ENF specimen is analysed and conclusions drawn.2 PROBLEM DESCRIPTIONThe dimensions of the DCB specimen are shown inFig. 1. At the split ends of the DCB specimen,uniform displacements in the 2 direction are applied

1 Pt-l LFi g. 1. DC B specimen configuration.

Fig. 2. E NF specimen configuration.

symmetrically for specimens with symmetric. _ arms. Forspecimens with unsymmetric arms, symmetric forcesare applied while the displacement components in the2 direction for nodes at the end of each DCB arm arekept uniform. This kind of loading is typical of theusual DCB test loading condition. Unless otherwisespecified, the end load used in the analyses of bothDCB and ENF specimens (see Fig. 2) is 32 N/m.

For the numerical analysis, the double-plate modelproposed by Zheng and Sun* was employed tocalculate the strain energy release rate. In thedouble-plate model, a delaminated composite plate ismodeled by two separate Mindlin plates. In the intactregion, the two plates are tied together to ensuredisplacement continuity; in the delaminated region,the two plates are not constrained except for thecontact conditions. A crack closure method was usedto calculate the strain energy release rate at the crackfront. By comparing with the three-dimensional finiteelement solutions for a DCB specimen, thisdouble-plate model was shown to be computationallyefficient and accurate.Two different finite element meshes were usedthroughout this study: one with 12 elements along thewidth and the other with 24 elements. The elementsize at the crack tip is 1% of the crack length. Linearanalyses were performed except for laminatedspecimens with asymmetric lay-up sequences, forwhich geometric non-linearity was considered. Forasymmetric laminates, the geometrically non-lineareffect is magnified by the extension-bending coupling,and large deflection theory must be employed. Forisotropic and cross-ply composite specimens, only halfof the specimen was modeled in the numericalsimulation on account of the symmetry. For specimenscontaining angle plies, the whole specimen wasmodeled. The eight-node isoparametric element(element type S8R) in the commercial finite elementcode ABAQUS2 was used to perform delaminationcrack analysis. The non-penetration condition withinthe crack region was imposed through the use of gapelements (element type GAPUNI).Table 1 lists the properties of the materialsconsidered in this paper.


3/9

DCB and ENF composit e specimens 453

Table 1. Material properties Table 2. Average strain energy release rate G,, ( X lo-J /m*) for aluminum DCB with various widthsMaterial

AluminumResinGraphite/epoxy

Material constantsE = 1 GPa, Y = 0.3E = 4 GPa, Y = 0.3E, 134 GPa, E, 13 GPa,G,, = 6.4 GPa, vi2 = 0.34

b (mm) 12.5 25 50 100 200 300 600G, 9.61 9.47 9.23 9.05 8.95 8.92 8.91

3 BOUNDARY LAYERFigure 3 shows the strain energy release ratedistributions across the width in aluminum DCBs withvarious beam widths, b. All of these specimens havethe same thickness h = 1.65 mm. In these plots, thestrain energy release rate is normalized with respect tothe average value, G,,, listed in Table 2. A distinctfeature of these distribution curves is the identicalboundary layer near the edge of the beam. Within thisboundary layer, the strain energy release rate exhibitssignificant variation. Away from the boundary layer,the value of G approaches a constant value of8.91 X 10-2J/m2. For this example, we estimate thethickness of the boundary layer to be about 20h. ForDCBs of smaller widths, the two boundary layersalong the two beam edges may merge, and a constantG may not exist as shown in Fig. 4.

that for the aluminum specimen. To obtain a uniformstrain energy release rate along the crack front, theboundary layer effect must be eliminated. Forisotropic materials, this can be achieved by imposingthe boundary conditions for cylindrical bending, i.e.suppressing the rotation at the edge of the DCBspecimen (+1 = 0 at y = *b/2). Alternatively, we canchoose a material with a vanishing Poisson ratio.However, for composite DCB specimens, theboundary layer effect cannot be eliminated by theabove methods. For illustration, Fig. 6 shows the Gdistribution along the crack front for a compositeDCB specimen with zero Poisson ratio (lay-upsequence [8.3672/58.367,], for each arm). Thedistribution of G is not uniform (denoted by normalin Fig. 6). Even with the edge rotation suppressed(denoted by no edge rot in Fig. 6), the G distributionstill varies across the beam width.

This boundary layer is caused by the anticlasticcurvature associated with bending-bending couplingin the X and Y directions.14 It exists in both isotropicand composite specimens. Figure 5 shows theboundary layer effect for a laminated DCB specimenwith the lay-up sequence [03/906/03] for both arms.The average strain energy release rates are 6.126 x10e2, 6.121 X 10mm2nd 6.120 X o-* J/m* for b = 100,200 and 300mm, respectively. Apparently, theboundary layer thickness in this case is smaller than

4 APPLICABILITY OF BEAM THEORIES4.1 Straight crack frontAs analytical tools, beam theories12,i3 are usuallyemployed to calculate the strain energy release ratefor DCB specimens. However, from the discussionabove it is noted that the strain energy release rate atthe crack front is not a constant. This prompts us toinvestigate what the results of beam models represent.

4 0.6

+b=30Omm+b=20OOmlU_--1+b=10omm0 20 40 60 80 100Y/h

Fig. 3. Strain energy release rate in aluminum DCB withlarge width.

1.41.2

0.8$Q 0.6c3

0.4

2 4 6 8 10 12 14 5Y/bFig. 4. Strain energy release rate in aluminum DCB withsmall width.


4/9

454 C. T. Sun, S. Zheng1.2

0.8

isCO.6a

0.4

0.2

0

Fig. 5.

I

-+ b=300mm+ b=200mm+ b=l OOmm

0 20 40 60 80 100Y/h

Strain energy release rate for [0,/90,/O,] laminatedDCB.

A possible way to correlate the results of beammodels and the present plate model is to compare thevalues of the strain energy release rate from beammodels with the average strain energy release ratefrom the plate model. Note that two different valuesof strain energy release rate can be obtained by usingbeam theories, corresponding to the cases of planestrain and plane stress, respectively.

The expression of strain energy release rate for asimple beam model is expressed as:

Table 3 presents a comparison of the results ofstrain energy release rate from the simple beam modeland from some advanced beam models12,13 with the

--c no edge rot-15 -10 -5 y &n) 5 10 15

Fig. 6. Strain energy release rate distribution of a compositeDCB of [8.367,/58-367,], lay-up.

Table 3. Comparison of G ( X lo- J/m2) for aluminumDCB with b = 25 mm

Method

Simple beamSun andPandey OlssonPresent

Plane stress

G e,9.40 0.7%9.80 3.5%9.66 2.0%

Plane strain

G eb8.56 9.6%8.92 5.8%8.79 6.8%

Other(Gay)

9.47

average strain energy release rate from the presentanalysis for an aluminum DCB with b = 25 mm. Fromthe results in Table 3, one may conclude that thesimple beam model with the plane stress assumptionprovides a result that is closest to the present analysis;however, this is not always the case. In fact, the resultfrom the simple beam model just happens to be closeto the present result for the case b = 25 mm. If wecalculate the average strain energy release rate fordifferent beam widths, we would find that G actuallyvaries with beam width. Figure 7 shows the variationof average strain energy release rate with beam width.Several observations are noted in Fig. 7. First, theaverage strain energy release rate for aluminum DCBdecreases as the beam width, b, increases. Second, thelimits are estimated as

lim Gay = G& = 9.72 X lop2 J/m2h+O (2)lim G,, = GrV = 8.91 X 1O-2 J/m2h-m (3)

Since the case b -+O corresponds to plane stress andb + ~0 corresponds to plane strain, we can now

0.9

0.6

0.5 40 100 200 300 400b/h

Fig. 7. Average energy release rate versus beam width foraluminum DCB.


5/9


compare the results from the beam theories with thoseof the present analysis (Table 4). It is evident fromTable 4 that the advanced beam models of Sun andPandey and Olsson13 provide far closer results ascompared with the present results than the simplebeam model. The present results lie between theresults obtained from the Sun-Pandey model andthose obtained from the Olsson model.It is interesting to note that Gz, corresponds to theconstant value of G in DCB specimens with zeroPoisson ratio and GY&corresponds to the constantvalue of G in DCB specimens with edge rotationsuppressed.For practical purposes, when using a beam model tocalculate the strain energy release rate for DCBspecimens, the advanced beam models (such as thoseof Sun and Pandey and Olsson) are not necessarilybetter than the simple beam model as compared withthe plate model. As can be seen in Tables 3 and 4, forthe commonly used testing specimen with b = 25 mm,the simple beam model with plane stress assumptionmay yield better agreement with the plate model.However, in order to reduce the boundary layereffect, specimens with large beam widths arerecommended if beam theories are to be used as datareduction tools. In this situation, a plane strainassumption is selected and the advanced beam modelsshould be used.4.2 Curved cr ack frontSince strain energy release rate varies across beamwidth, the actual DCB crack front after crack growthcould be curved rather than straight.15,7,21 Bycalculating the total strain energy release rate (TG)which is obtained by integrating G along the crackfront, Nilsson17 concluded that TG could be 24%higher at the instant when the curved crack front isfully developed and is propagating than at the instantwhen a straight crack front starts to grow initially atthe center of the DCB. In this section, we shallexamine the effect of curved crack front on the use ofbeam theories in calculating strain energy release rate.

Consider an aluminum DCB specimen, as shown inFig. 1, with L = 100 mm, b = 25 mm, h = 1.65 mm. Inorder to find the actual curved crack front, an effortwas made to search for the crack front where strainTable 4. G ( X 10-zJ /mZ) for DCB in plane stress andplane strain

Method

Simple beamSun and Pandey12OlssonPresent (G,,)

Plane stressG, e,

9.40 3.3%9.80 0.8%9.66 0.6%9.72 0.0%

Plane strainGE eh

8.56 3.9%8.92 0.1%8.79 1.3%8.91 0.0%

k ae 4Fig. 8. Curved crack front in aluminum DCB.

energy release rate equals its critical value, G,,corresponding to the critical loading. Note that G, waschosen to be 1600 J/m* for the present simulation. Figure8 shows a schematic representation of a curved crackfront, which yields the critical loading P = 3940 N/mand the tip displacement 6 = 7.1 mm. At the edge ofthe DCB specimen the crack length is ae = 50.9 mm,and at the center the crack length is a = 52.7 mm.In fracture toughness tests on DCB specimens, thecrack length is usually measured at the edge of thespecimen (ae). If we adopt the straight crack frontassumption as commonly practiced, we can calculatethe average strain energy release rate by using thedouble-plate model for critical load P = 3940 N/m andcrack length ae = 50.9 as GiV = 1479 J/m*. This valueis 6% lower than G, at the curved crack front. Forcomparison, the simple beam model predicts GP =1513 J/m*, which is 5% lower than this G,. However,if we use the critical tip displacement S = 7-l mm tocalculate the strain energy release rate at the straightcrack front, we find Gi, = 1751 J/m2, which is 9%higher than the critical strain energy release rate atthe curved crack front. Again, for comparison, it isnoted that the simple beam model predicts G =1803 J/m*, which is 13% higher than G,.

Thus, if a straight crack front is assumed, anequivalent crack length, aeq, should be used. Theabove discrepancies between the experimentallydetermined critical strain energy release rate, GfV,(determined by using the critical load) and G!&(determined by using the critical tip displacement) isdue to the fact that the measured crack length, ae,underestimates the equivalent crack length, seq. Thisdiscrepancy between GrV and G& can best beexplained by using the simple beam theory.From simple beam theory, the strain energy releaserate at the DCB crack front can be expressed in termsof load, P, and tip displacement, 6, (with crack length,a) as:

3S2Eh3GS =_4a4 (5)


6/9

456 C. T. Sun, S. Zhengrespectively. By using the equivalent crack length, wehave:

G = 12P2(aeq)* 3cS2Eh3=-c Eb2h3 4(aq)4 (6)Since, ae I aeq, from eqns (4)-(6) we have thefollowing bounds:

Gap I G, 5 Gas (7)Thus, by using critical load to calculate the strain

energy release rate, the result would be lower than thecorresponding critical strain energy release rate, G,, atthe curved crack front, and using the critical tipdisplacement would lead to a higher value.

It is worth noting that the current ASTM standardfor DCB test data reduction procedure does not usean analytical solution based on beam theories.Instead, it uses a compliance calibration techniqueknown as Berrys method? Specifically, the formulafor the experimentally determined critical strainenergy release rate is:

G= _h!!!=__=__2 dC P*dCb da 2bC2 da 2b da (8)where U is the strain energy and C is the compliancecalibrated by an empirical formula. Since thecompliance, C, is calibrated experimentally, it includesthe effect of the curved crack front. However, in eqn(8), the quantity b should be replaced with the lengthof the curved crack front. Without such a correction,eqn (8) would overestimate the strain energy releaserate.5 SKEWED G DISTRIBUTIONFor cross-ply and unidirectional laminated compositeDCB specimens, the distribution of strain energyrelease rate at the crack front is similar to that in anisotropic specimen, i.e. it exhibits the boundary layereffect and its distribution is symmetric with respect tothe X axis. Thus, the conclusions drawn above forisotropic DCB specimens are still applicable. Forother types of laminates, even if they are symmetricand balanced, the strain energy release ratedistribution across the width may be quite different.The main reason is, in general, that bending-twistingcoupling is present in the laminates. For unidirectionaland cross-ply laminates, owing to the absence ofbending-twisting coupling, the analysis can beperformed by using half of the specimen. However,caution must be exercised when such a procedure isemployed in the analysis of other types of laminates.

For illustration, consider the following symmetricand balanced lay-up sequences: Ll, [ f 45,],; and L2,[ f @i2/ f 451,. These two specimens are almostidentical except for lay-up sequence. However, theyhave quite different bending-twisting coupling. The

-+- L2, s=O.32

-15 -10 -5 0 5 10 15y hm)

Fig. 9. Variation in G along crack front of angle-plycomposite DCB (large s).

composite material properties are listed in Table 1;the ply-thickness is 0.127 mm. For these laminates, thedistributions of G are shown in Fig. 9. It is clear thatG is not symmetrically distributed with respect to thecenter line. In fact, the G distribution is highlyskewed. This skewness can be qualitatively charac-terized by the parameter:

where D16 and Dll are bending stiffness components inthe D matrix of the laminate. It was found that thelarger the s value, the more severe the skewness.Figure 10 shows additional examples of the G distri-bution at 45/45 and O/O interfaces in laminates L3 toL6 as given in Table 5. The skewed behavior of the G

Fig. 10. Variation in G along crack front of angle-plycomposite DCB (small s).


7/9

DCB and ENF com posit e specimens 457

Table 5. Lay-up sequences for the upper arms of DCBspecimen and value of sNotation Lay-up sequence s

Ll I* 4533, O-5019L2 [ f 45*/ f 451s 0.3153L3 Pl1* 0L4 0.10L.5 0.167L6 0.250

distribution is caused by bending-twisting coupling.The validity of the parameter s as an indicator ofthe skewness of the G distribution is verified by theexamples in Figs 9 and 10 for s values ranging from0 to 0.5.

In fact, careful selection of laminate lay-upsequences can ensure that s = 0 for the specimen, thuseliminating the skewness of the G distribution. Forexample, as long as the lay-up sequence for both armsof the DCB specimen is anti-symmetric (e.g. [ - O/O]or [OJ -@JO,/ -@,I, etc.), then we always haves = 0 (because D16 = 0) for the specimen. Figure 11shows the G distribution for a DCB consisting of a[ - 301301 upper arm and a [4.5/ -451 lower arm.Apparently G achieves a symmetric distribution.6 DESIGN RECOMMENDATIONTo use the DCB specimen to measure fracturetoughness, ideally the strain energy release rate shouldbe uniform along the crack front in order to utilize thebeam model to reduce the experimental data.However, as discussed above, in a composite laminate

-15 -10 -5 Y(k) 5 lo l5Fig. 11. G distribution at crack front for [ T 30/ f 451 (withs =O).

DCB specimen, the G distribution is not uniform andmay be highly skewed. As a result, the crack front ofthe DCB specimen may be curved and skewed, whichmakes the interpretation of test data ambiguous. Sincethe crack length at the two edges of the DCBspecimen may be different, and neither of these twocrack lengths is an appropriate representation of theequivalent crack length, the resulting experimentaldata may not produce accurate fracture toughnessvalues. Meanwhile, since the crack front curvature andskewness depend on the lay-up sequence of thespecimen, these may contribute to the dependency ofthe experimental fracture toughness on the lay-upsequence. Consequently, a good DCB specimenshould both minimize the variation and skewness of itsG distribution.

In order to minimize the variation of G, Davidsonssuggested minimizing the parameter D, = D:2/D11 Dz2.From lamination theory, we have:

D, = i k$, Q~(z: - ~2~)) (9)where n is the number of laminae and the definition of@ can be found in the Appendix.Consider the following:

Note that & = u, - u, cos 4@/, 2 u, - u,. Thus, D12is a minimum at cos 401, = 1, i.e. Ok = 0 or 90.Further numerical examination reveals that D,achieves its minimum when Ok = 0. Thus, the 0unidirectional laminate DCB specimen should havethe smallest G variation across the crack front.To minimize the skewness of the G distribution, we

016should minimize the parameter s = _ . Obviously,I IIIthe best lay-ups are those yielding D16 = 0. Theseinclude O, 90, cross-ply and antisymmetric laminates.

Our task is to find the laminates that minimize theskew behavior of the strain energy release rate alongthe DCB crack front and at the same time keep itsvariations across the width as small as possible. On thebasis of this design guide, the following lay-upsequence is recommended for testing 0(1)/O(2)interfacial fracture toughness: [ - O~~/O,/O~//O~*~/OJ - @*I (s = 0), where /I indicates the location ofthe crack and n is a large integer that makes thebehavior of this specimen approach that in[0,/O//O/O,]. Figure 12 shows the behavior of the Gdistribution for the lay-up [ - 30/0,,/30//45/02,/ - 451,which is designed for testing the 30/45 interfacialtoughness. For the purpose of comparison, the Gdistribution in the [O20/O//O/O,,] specimen is alsoshown. It is evident that the design objective isachieved.


8/9

458 C. T. Sun, S. Zheng

0.2 - -+- o/o+ design#-,I /-15 -10 -5 5 10 15

Fig. 12. Design recommendation.

7 ENF SPECIMENThe ENF specimen in Fig. 2 has also been analysed bythe double-plate model. In order to avoid interpenet-ration within the delamination region, a smoothcontact condition was assumed. That is, nodes at topand bottom plates within the delamination regionwere assumed to have the same displacement in the 2direction. The variation of the G distribution at thecrack front of the ENF specimen behaves more or lesslike that in the DCB specimen. Figure 13 shows the Gdistribution at the crack front for three ENFspecimens: La, [016//016]; Lb, [ f 4&/ F 45,// f 453/ r45,]; and Lc, [ - 30/0,,/30//45/0,,/ - 451. It is notedthat the boundary layer effect in the ENF specimen isnot as pronounced as that in the DCB specimen.However, the G distribution is still skewed for theangle-ply laminate (see Lb in Fig. 13). By adopting thesame design procedure as for the DCB specimen, wecan virtually eliminate the skewness and make the G

d3

1,+-La+-Lb n6 --tLc ,5 --

-15 -10 -5 5 10 15Fig. 13. ENF G distribution at crack front.

distribution similar to that for the 0 laminate asindicated by specimen Lc in Fig. 13. Thus, the samedesign lay-up for DCB specimen is also recommendedhere.8 CONCLUSIONSThe strain energy release rate distributions for DCBand ENF specimens have been analysed. Thefollowing conclusions have been obtained:

. A boundary layer effect causes the strain energyrelease rate to vary along the straight crackfront. The thickness of this boundary layer iswithin 10 times the thickness of the DCBspecimen away from the edge for the aluminumspecimen. While assuming that the crack front isstraight, the beam theories (advanced models)are adequate for calculating the strain energyrelease rate for DCB specimen as long as thebeam width is large enough to represent planestrain. However, for commonly used specimens,the beam theories may cause errors in thedetermination of critical strain energy releaserate. Because of the curved crack front in theactual test specimen, the use of critical loadingin conjunction with beam theory will under-estimate critical strain energy release rate, G,,while the use of critical displacement willoverestimate G,.

l For laminated specimens containing angle plies,the distribution of strain energy release rate isskewed along the crack front. The degree ofskewness depends on the lay-up sequence. Aparameter has been proposed for the qualitativemeasurement of the skewness of G. The lay-upsequence [ - 0~1 ~/0,/0~ ~//0~2 ~/0~ / - O@] is re-commended for testing O()/O@) interfacialfracture toughness.

l The boundary layer in the ENF specimen issmaller than that in the DCB specimen. Thedistribution of G at the crack front isqualitatively similar to that in the DCBspecimen, which is varied and skewed, and thesame design lay-up is recommended for ENFtesting involving angle-ply interface.

ACKNOWLEDGEMENTThis work is supported by NASA Langley ResearchCenter under grant no. NAG-l-1323 to PurdueUniversity. Drs Jerry Housner and John Wang aretechnical monitors.REFERENCES

1. Russell, A. J. & Street, K. N., Factors affecting theinterlaminar fracture energy of graphite/epoxy lamin-ates. ICCM-IV, Tokyo, 1982, pp. 279-86.


9/9


2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.14.

15.

16.

Wilkins, D. J., Eisenmann, J. R., Camin, R. A.,Margulis, W. S. & Benson, R. A., Characterizingdelamination growth in graphite/epoxy. ASTM STP775,1982, pp. 168-83.Berry, J. P., Determination of fracture surface energiesby the cleavage technique. .I. Appl. Phy s., 34 (1963)62-8.Robinson, P. & Song, D. Q., A modified DCB specimenfor Mode I testing of multidirectional laminates. J.Comp. M at er., 26 (1992) 1554-77.Polaha, J. J., Effect of interfacial ply orientation on thefracture toughness of a laminated graphite/epoxycomposite. AIAA-94-1537-CP, 1994, pp. 1707-16.Ishikawa, H., Koimai, T. & Natsumura, T., Interlaminarfracture toughness of Mode I and Mode II in CFRPlaminates. Proc. 2nd Int. Symp. on Composite Materialsand Structures, ed. C. T. Sun & T. T. Loo. Beijing, 1992,pp. 340-5.Whitney, J. M., Browning, D. E. & Hoogsteden, W., Adouble cantilever beam test for characterizing Mode Idelamination of composite materials. J. Reinf: Plast.Comp., 1 (1982) 297-313.ASTM standard test method for Mode I interlaminarfracture toughness of unidirectional continuous fiberreinforced composite materials. ASTM StandardD5528-94A, ASTM, Philadelphia, PA, 1994.Kageyama, K., Kobayashi, T. & Chou, T.-W., Ananalytical compliance method for Mode I interlaminarfracture toughness testing of composites. Composites, 18(1987) 393-9.Hashemi, S., Kinloch, A. J. & Williams, J. G.,Corrections needed in double-cantilever beam tests forassessing the interlaminar failure of fiber composites. J.Mater. Sci. Lett ., 8 (1989) 125-9.Chatterjee, S. N., Analysis of test specimens forinterlaminar Mode II fracture toughness: part I. Elasticlaminates. J. Comp. Ma ter., 25 (1991) 470-93.Sun, C. T. & Pandey, R. K., Improved method forcalculating strain energy release rate based on beamtheory. AI AA .I., 32 (1994) 184-9.Olsson, R., A simplified improved beam analysis of theDCB specimen. Com p. Sci. Technol ., 43 (1992) 329-38.Crews, J. H., Shivakumar, K. N. & Raju, I. S., Strainenergy release rate distribution for double cantileverbeam specimen. AZAA J. (1991) 1686-91.Davidson, B. D., An analytical investigation ofdelamination front curvature in double cantilever beamspecimens. J. Comp. Mater., 24 (1990) 1124-37.Davidson, B. D. & Schapery, R. A., Effect of finite

17.18.

19.

20.21.

width on deflection and energy release rate of anorthotropic double cantilever specimen. J. Comp.Mater., 22 (1988) 641-56.Nilsson, K. F., On growth of crack fronts in the DCBtest. Com p. Engng, 3 (1993) 527-46.Zheng, S. & Sun, C. T., A double plate finite elementmodel for impact induced delamination problems.Comp. Sci. Technol., 53 (1995) 111-18.Sun, C. T. & Chin, H., On large deflection effects inunsymmetric cross-ply composite laminates. J. Comp.Mater., 22 (1988) 1045-59.Hibbitt, Karlsson and Sorenson Inc., ABAQUS,Version 5.3.De Kalbermatten, T., Jaggi, R., Flueler, P., Kausch, H.H. & Davies, P., Microfocus radiography studies duringMode I interlaminar fracture test on composites. J.Mater. Sci. Lett., 11 (1992) 543-6.

APPENDIXThe definitions of 05 in eqn (9) are given below.

Q:, = u, + u, cos 20,, + u , cos 40/(@, = u , - u , cos 20/, + u , cos 4OkQ;2 = u , - u , cos 40/,

1Q:, = - sin 203, + U, sin 401,2U, = 8 (3Qu + 3822 + 2Q12 + 4QwJ

U, =; (QII - Q,,)

U3 = ;

ion characteristics of dcb and enf composite specimens

Documents