MODELING THE INFLUENCE OF STITCHING ON DELAMINATION GROWTH IN STITCHED WARP-KNIT COMPOSITE LAP JOINTS

Transcription

1 MODELING THE INFLUENCE OF STITCHING ON DELAMINATION GROWTH IN STITCHED WARP-KNIT COMPOSITE LAP JOINTS E.H. Glessgen, I.S. Rju 2 nd C.C. Poe, Jr. 2 Ntionl Reserch Council 2 Mechnics of Mterils Brnch NASA Lngley Reserch Center, Hmpton, VA, 2368 SUMMARY: The effect of stitches on the filure of single lp joint configurtion ws determined in combined experimentl nd nlyticl study. The experimentl study ws conducted to determine debond growth under sttic monotonic loding. The stitches were shown to dely the initition of the debond nd provide lod trnsfer beyond the lod necessry to completely debond the stitched lp joint. The strin energy relese rtes t the debond front were clculted using finite element-bsed technique. Models of the unstitched configurtion showed significnt vlues of modes I nd II cross the width of the joint nd showed tht mode III is zero t the centerline but increses ner the free edge. Models of the stitched configurtion showed tht the stitches effectively reduced mode I to zero, but hd less of n effect on modes II nd III. KEYWORDS: virtul crck closure technique, plte finite elements, textile composites, stitching, debonding, lp joints INTRODUCTION Structures mnufctured from stitched wrp-knit textile composite mterils offer dvntges in mnufcturbility nd dmge tolernce over conventionl composite nd metllic structures. However, it is often impossible to mnufcture complete component s n integrl unit, nd hence seprte sections of the component need to be joined together. Rther thn bolting or bonding sections, stitching is used in the textile composites discussed here. Improvements in dmge tolernce re observed becuse the Kevlr stitches tend to prevent propgtion of debonds nd delmintions tht my be cused by in-plne nd out-of-plne lodings. 2

2 The objective of this pper is to quntify the effect of stitches on the response of lp joints in wrp knit crbon epoxy textile composites under monotonic tensile loding. Filure mechnisms nd filure lods of unstitched nd stitched lp joints re determined using combined nlyticl nd experimentl technique. Comprisons re mde between the experimentlly determined filure lods of the stitched nd similr unstitched lp joint pnels to ssess the contribution of the stitches to preventing delmintion growth. Strin energy relese rtes nd stitch forces re evluted using finite element nlyses. LAP JOINT CONFIGURATION A stitched lp joint subjected to remote tensile loding is shown in Figure. The configurtionl prmeters of the joint considered in this study re the length of the composite, L, the length of the overlp, L 2, the width of the coupon, b, nd the thickness of the mteril, t nd re shown in Figure 2. Mteril nd skin thicknesses tht re representtive of the hybrid IM7/35-6 nd AS4/35-6 wrp-knit fbric stitched composite upper wing skin re considered. The mteril consists of IM7 yrns in the xil direction nd AS4 yrns in the off-xis directions. Ech stck of mteril is ssumed to be oriented with its primry xis in the x-direction nd hving thickness of.4 cm. The equivlent lminte stcking sequence of ech stck of mteril is (45/-45//9//-45/45) ns where n=2 for both of the joined lmintes. p L L 2 S x x= b x S y z t Loction A y Stitch row Loction A' Loction B' Incresing stitch column number Loction B Stitch row 4 x=l 2 x=l /2 2 p Figure. Stitched lp joint configurtion. Figure 2. Stitched joint configurtion ( S x = S y =.38 cm., t=.279 cm., b=2.54 cm., L =68.6 cm., L 2=9.37 cm.). Unstitched nd stitched lp joint specimens were fbricted with dimensions presented in Figure 2. The specimens were loded in monotonic tension t rte of.27 cm./min. Debonds initited nd grew t the ends of the lp joints. Increse in debond length with incresing lod ws determined using x-ry rdiogrphs. FINITE ELEMENT ANALYSIS Three-dimensionl modeling nd nlysis of the complex lp joint configurtion shown in Figure my require lrge finite element model with severl thousnd degrees of freedom.

3 However, considerble insight into the behvior of such complicted configurtion cn be obtined by studying much simpler configurtion such s the strip lp joint configurtion shown in Figure 2 while reducing modeling complexity. The method of nlysis uses plte elements to model the configurtion, nonliner fstener elements to model the stitches, nd multipoint constrints to model the contct problem. The specimen configurtionl prmeters re shown in Figure 2. Debond lengths,, in the rnge.635 cm. to 3.8 cm. re considered. A finite element model of the test specimens ws developed. Two cses of trnsverse (ydirection) boundry conditions were considered nd simulte both the finite width lp joint tht ws tested in the experimentl progrm nd n infinite width lp joint similr to the structure shown in Figure. The finite width lp joint configurtion is modeled to provide insight into the experimentl results while the infinite width lp joint configurtion is modeled to eliminte the effect of free edge boundry conditions on strin energy relese rtes nd stitch forces in the lp joint configurtion of Figure. Thus, results from the finite width nd infinite width configurtions should bound the response of ctul stitched lp joint configurtions. Anlyses for both the finite nd infinite width configurtions use experimentlly determined lod vs. crck length curves tht were developed from n experimentl study of unstitched nd stitched lp joints in the configurtion shown in Figure 2. 3 The nlyses were performed in increments of debond length,, of.38 cm. Mteril Properties In these nlyses, the lmintes re ssumed to be homogeneous with xil properties determined experimentlly nd ll others estimted using the equivlent stcking sequence nd clssicl lmintion theory s E =8.7 GP m 2 =7.2 GP u 2 =.4 E 22 =35.4 GP m 3 =2.2 GP u 3 =.3 E 33 =2.3 GP m 23 =6.7 GP u 23 =.3 where E ii, m ij, u ij (i,j=,2,3) re the YoungÕs moduli, sher moduli, nd PoissonÕs rtio, respectively, nd the subscripts,2,3 represent the fiber, trnsverse nd out-of-plne directions, respectively. Strin Energy Relese Rtes The lp joint configurtion ws modeled with the STAGS (Structurl Anlysis of Generl Shells) finite element code using 9-node qudrtic sher deformble plte/shell element. 4 The virtul crck closure technique (VCCT) 5,6 ws used to clculte strin energy relese rtes, G, with plte elements using the techniques discussed in references 7-9. A comprison of strin energy relese rtes computed with the plte element-bsed models nd similr plne strin element-bsed models for skin-stiffener configurtions without stitching is discussed in

4 reference 9. Additionl considertions tht rise from debond modeling with plte elements re discussed in reference 8. Modeling Stitches The configurtions were nlyzed with geometriclly nonliner finite element nlysis within the STAGS finite element code. The plte element-bsed modeling technique does not llow through-the-thickness modeling of detils such s the stitches; nor does it llow nodl connections other thn t the plte element reference surfce. Thus, the stitches re modeled s STAGS fstener elements. The fstener elements re imposed s nonliner springs offset by rigid links within the plte element model. 4 Fstener elements representing the stitches hve both xil nd sher stiffnesses, K xil nd K sher s determined in reference. Filure of the stitches occurs t lod of 258 N per stitch in tension nd 69 N per stitch in sher. Only the stitches behind the debond front re considered since the upper nd lower plte elements hed of the debond front re coupled using constrint equtions to hve identicl trnsltionl displcements. The fstener element loction spcing presented in Figure 2 coincides with plte element nodl loctions. Modeling the Contct Problem In the finite element nlysis, contct of the debonded fces is llowed, while interpenetrtion is not. The contct problem ws modeled using multipoint constrints rther thn gp elements becuse the no-penetrtion condition could be imposed exctly with the multipoint constrints wheres the STAGS gp elements enforce no-penetrtion to smll but finite tolernce tht is significnt in this nlysis. EXPERIMENTAL RESULTS Since limited mount of the mteril ws vilble, only two replictes of ech specimen configurtion were tested. The filure lods of these specimens re presented in Tble. The unstitched lp joint specimens ctstrophiclly filed t the interfce. The stitched lp joint specimens completely debonded t the interfce while mintining their lod crrying cpbility. Finl filure of these specimens ws due to combined tensile nd bending lods t the ends of the lp joint. Thus, the filure lods listed for the stitched specimen represent lower bounds. Rdiogrphic imges were tken t periodic intervls during loding to determine the length of the debond t ech pplied lod level. Figures 3() nd 3(b) present the dmge within representtive lp joints of the unstitched nd stitched configurtions, respectively. For convenience in presenttion, the line corresponding to x=l 2 in Figure 2 is denoted s the top of the lp joint, while the line corresponding to x= is denoted s the bottom of the lp joint.

5 Tble : Test Specimen Filure Lods Specimen Unstitched (U) or Filure Lod, kn Stitched (S) Slp - U 2.65 Slp -2 U 9.6 Slp -S S 52.6 Slp -2S S 5.73 Figures 3() nd 3(b) present the dmge t lods ner the filure lods within representtive lp joints of the unstitched nd stitched configurtions, respectively. Figure 3() shows the unstitched lp joint of length L 2 =9.37 cm. with debond of length,, growing from the top of the lp t lod of 9. kn. No debonds were observed growing ner the bottom of the lp. This could be the result of smll symmetry in the specimen or lod frme nd is likely due to the debond t the top of the lp inititing first nd relieving the driving force t the bottom of the lp. The primry debond shown in Figure 3() grew t the interfce of ±45 yrns. A split initited in the 45 yrns nd llowed secondry debond to initite nd grow between the 45 nd yrns s shown in Figure 3(). Ctstrophic filure due to unstble debond growth ws observed t 2.7 kn. L 2 Secondry debond Split within 45 yrns Primry debond L 2 Dmge t end of lp joint Strin gge Aluminum tpe 2 Debond throughout lp joint All lod trnsfer through stitches Dmge within stck () Unstitched specimen t P=9.4 kn (=.98 cm.). (b) Stitched specimen t P=49.2 kn( =4.68 cm., 2 =4.68 cm.). Figure 3. Rdiogrphs showing debond in lp joint. Figure 3(b) shows completely debonded stitched lp joint tht mintined lod of 49. kn. Debonds initited nd grew from both ends of the joint completely debonding the lp joint. Finl filure occurred t 52.6 kn nd ws not due to stitch filure but ws due to tensile nd bending stress filure t the ends of the lp. The vlue of 52.6 kn my then be treted s lower bound of lod crrying cpbility for this specimen. The verge filure lod of the stitched lp joints ws 2.6 times the filure lod of the unstitched lp joints.

6 ANALYTICAL RESULTS Experimentlly determined verge debond length vs. lod curves for the unstitched nd stitched single lp joints re given in reference 3 nd re used s input prmeters in the nlysis. In generl, the lp joint configurtions my exhibit mode I, mode II nd mode III strin energy relese rtes. Also, lthough stright debond front is employed to simplify the nlyses, vrition in both strin energy relese rte nd stitch force my exist long the length (x-) nd cross the width (y-) of the finite width lp joint. In the results tht follow, quntities for the finite width configurtions re given t y-direction loctions corresponding to: n interior row of stitches ner the centerline of the stitched configurtion (stitch row ); n exterior row of stitches ner the edge of the stitched configurtion (stitch row 4); nd intermedite loctions between stitch rows nd 2 nd stitch rows 3 nd 4. These lter loctions re considered only for the stitched configurtion. The y loctions denoted s loctions A, B, AÕ nd BÕ re locted t y=.59 cm., y=. cm., y=.38 cm. nd y=.953 cm., respectively, from the configurtion centerline. Quntities for both the unstitched nd stitched infinite width configurtions re lso provided. When cylindricl bending repeting unit boundry conditions (v=, q x = on y=, b/2 in Figure 2) re pplied to the models, the clculted G-vlues re constnt in the y-direction for the unstitched configurtion nd periodic in the y-direction for the stitched configurtion. Figures 4 through 6 show the individul modes of the strin energy relese rtes, the y- direction distribution of strin energy relese rtes, nd the stitch forces, respectively, s functions of debond length. The vlues of strin energy relese rte for lods corresponding to the debond lengths in Figure 4 re significntly greter thn the G Ic nd c vlues determined for typicl crbon / brittle epoxy mteril systems. In reference, G Ic nd c for AS4/35-6 composites re given s.8 kj/m 2 nd.55 kj/m 2, respectively. Both the unstitched nd stitched lp joint configurtions re ble to sustin these high G-vlues due to severl energy bsorbing phenomen. In the unstitched mteril, splitting of the 45 yrns nd the formtion nd growth of secondry debond between the 45 nd yrns seen in Figure 3() contribute to the pprent high vlue of frcture toughness. In the stitched mteril, there is lso some dmge within the stcks of mteril s shown in Figure 3(b). This occurs over only smll portion of the debonded length of the stitched lp joint. A full three-dimensionl nlysis my be required to ccount for the individul contributions of ech of the dmge mechnisms. However, using the debond length nd pplied lod from the experiment, the plte element-bsed nlyses cn predict the effective vlues of G s seen in Figures 4 nd 5. These G-vlues cn then be used s rnking prmeters. Note tht the lods considered for the stitched configurtion re much greter thn the lods considered for the unstitched configurtion s shown in Tble, so Figures 4() nd 4(b) cnnot be compred directly. Figure 4() shows G-vlues plotted ginst debond length for the unstitched configurtion with debond t only one end of the single lp joint corresponding to the rdiogrph shown in Figure 3(). Figure 4() shows two nonzero components of G ner the centerline of the finite width lp joint (Loction A) nd three nonzero components of G ner the free edge of the finite width lp joint (Loction B). Mode I increses t both loctions s the debond

7 grows. Mode II is the lrgest component of energy relese rte nd lso increses with incresing debond length. Mode III hs vlue ner zero (thus, not shown) in the interior t loction A but increses ner the free edge (Loction B). Vlues of 2/L 2 greter thn.5 correspond to ctstrophic debond growth in the unstitched configurtion shown in Figure 3(). The energy relese rtes computed t loctions A nd B in the finite width configurtion bound the energy relese rtes computed for the infinite width configurtion (shown s G I nd in Figure 4(). This is result of the cylindricl bending boundry conditions in the infinite width models preventing nticlstic deformtion while the stress free boundry conditions in the finite width models do not. Additionlly, the cylindricl bending boundry conditions in the infinite width models require mode III to be identiclly zero. 2 Strin Energy Relese Rte, G, kj/m G A II G B II G I G A I G B I I B Debond Length, 2/L 2 Figure 4(). Strin energy relese rte in unstitched lp joint. Figures 4(b) nd 5 show the G-vlues plotted s functions of debond length nd lp joint width, respectively, for the stitched configurtion with debond t ech end of the single lp joint corresponding to the rdiogrph shown in Figure 3(b). The computed vlues of G in Figure 4(b) re t discrete loctions between the stitch columns nd smooth curve is drwn between the points. Figure 4(b) shows one nonzero component of G t loctions A nd AÕ nd two nonzero components of G t loctions B nd BÕ. For ll debond lengths t ll loctions, the mode I component is ner zero. As with the unstitched configurtion, mode II is the dominnt component nd is seen to increse with debond length. Although increses with incresing debond length, the stitches prevent the debond growth from becoming unstble. As seen in Figure 5, mode II is significntly lrger t the loctions between the stitches (Loctions AÕ nd BÕ) thn t the stitch loctions (Loctions A nd B) indicting some locliztion of the effectiveness of the stitches. As in the unstitched configurtion, mode III hs vlue ner zero in the interior (Loctions A nd AÕ) but increses ner the edge (Loctions B nd BÕ). Cylindricl bending boundry conditions lso prevent nticlstic deformtion in the infinitely wide stitched lp joint. The resulting is periodic cross the width of the joint s shown

8 in Figure 5. For long debonds (2/L 2 )=.83, the lrgest vlues of mode II re found t (2y/b)= for the infinite width configurtion nd (2y/b)=.969 for the finite width configurtion. Becuse of the cylindricl bending boundry conditions mode III is identiclly zero t y=, b/2 nd nerly zero for other vlues of y in this rnge. 2 Strin Energy Relese Rte, G, kj/m Stitch Column Stitch Column 2 A B I B I B' A'B' AB L 2 B' A' B' B Row 4 C L Stitch Column5 Col. 3 x Col. y z A' A Row 2 Debond Length, 2/L 2 Figure 4(b). Strin energy relese rte in stitched lp joint. Strin Energy Relese Rte, G, kj/m Stitch Row 4 Loction B 36, 36.8 Loction B' G 83 III G 36 III Stitch Row 3.6 B B' Row 4 G 83, II G 83 II b/2 Stitch Row Loction A 2y/b Figure 5. Strin energy relese rte distribution for 2/L 2 =.36 nd.83. CL x y A' z A Row.4 Stitch Row 2 Loction A'.2 The dominnt component of stitch force is longitudinl sher nd is presented in Figure 6. The figure shows how ech of the stitches begins to crry lod s the debond of length,, psses its loction in the model. Since the results were evluted from the finite element model with increments of debond length of.38 cm. (2/L 2 )=.678, the force in the stitches for debond lengths corresponding to the intervl between the stitch loction nd the next whole increment of debond length is not known nd is represented by the thin lines.

9 Figures 6() nd 6(b) show the longitudinl sher forces (F xz ) in stitch rows nd 4, respectively. In both rows, ll stitches re loded nd show incresing vlues of sher force s the debond grows. The vlues shown in Figures 6() nd 6(b) for stitch rows nd 4 re lmost identicl. This is not unexpected s vlues t loctions A nd B re similr. The lod shring mong ll of the stitches is result of the stitch nonlinerity nd contributes to the increse in strength of the stitched lp joints tht were tested in the experimentl study. The longitudinl sher stitch forces for stitches in the infinitely wide lp joint do not vry with y loction nd re represented by the dshed lines in Figure 6. Stitch Force, F xz /F sher filure Stitch Column Stitch Column 2 Stitch Column5 Stitch Force, F xz /F sher filure Stitch Column Stitch Column 2 Stitch Column Debond Length, 2/L Debond Length, 2/L2 () Longitudinl sher forces in stitch row. Figure 6. Stitch forces. (b) Longitudinl sher forces in stitch row 4. CONCLUDING REMARKS The effect of stitches on the filure of finite width nd infinite width single lp joint configurtions ws studied. An experimentl progrm ws conducted to determine the lods necessry to grow the debond through complete debonding of the specimens. Modeling ws performed using method tht uses the virtul crck closure technique to clculte the strin energy relese rtes, plte elements to model the configurtion, nonliner fstener elements to model the stitches nd multipoint constrints to model the contct problem. The stitches were shown to dely the initition of the debond nd provide lod trnsfer beyond the lod necessry to completely debond the lp joint. For the configurtions considered, the filure lod of the stitched lp joints ws bout two nd hlf times the filure lod of the unstitched lp joints. Models of the finite width unstitched configurtion showed tht the nonzero components of strin energy relese rte vry nerly linerly with debond length. All three modes increse with incresing debond length t loctions ner the configurtion centerline nd ner the configurtion free edge. Mode II is the lrgest of the three components, while mode III is the smllest. An infinite width lp joint ws modeled by pplying cylindricl bending repeting unit boundry conditions to the edges of the model. Vlues of modes I nd II were bounded

10 by the vlues of the corresponding modes of the finite width lp joint nd mode III ws identiclly zero. Models of the finite width stitched configurtion showed tht one nonzero component of G exists ner the centerline while two nonzero components exist ner the free edge. The stitches reduce G I to ner zero vlues for ll debond lengths. However, the stitches re much less effective in reducing s it is the dominnt component nd is seen to increse over the entire rnge of debond lengths considered. The effectiveness of the stitches in reducing mode II is further reduced t loctions between the rows of stitching. Mode III is significnt only ner the free edge. Vlues of mode II for n infinitely wide lp joint re periodic nd of bout the sme mgnitude s those for finite width lp joint. Mode III is nerly zero. Longitudinl sher force is trnsferred by ll rows of stitches in the debonded region nd increses with incresing debond length. REFERENCES. Dow, M.B. nd Dexter, H.B., ÒDevelopment of Stitched, Brided nd Woven Composite Structures in the ACT Progrm nd t Lngley Reserch Center,Ó NASA TP , November Wng, J.T., Jegley, D.C., Bush, H.G. nd Hinrichs, S.C., ÒCorreltion of Structurl Anlysis nd Test Results for the McDonnell Dougls Stitched/RFI All-Composite Wing Stub Box,Ó NASA TM-267, Glessgen, E.H., Rju, I.S. nd Poe, C.C., ÒDelmintion nd Stitch Filure in Stitched Composite Joints,Ó 4th AIAA/ASME/ASCE/AHS Structures, Structurl Dynmics nd Mterils Conference, AIAA Pper , Brogn, F.A., Rnkin, C.C., Cbiness, H.D. nd Loden, W.A., STAGS User Mnul, Lockheed Mrtin Missiles nd Spce Co., July Rybicki, E.F. nd Knninen, M.F., ÒA Finite Element Clcultion of Stress Intensity Fctors by Modified Crck Closure Integrl,Ó Engineering Frcture Mechnics, Vol. 9, 977, pp Rju, I.S., ÒClcultion of Strin-Energy Relese Rtes with Higher Order nd Singulr Finite Elements,Ó Engineering Frcture Mechnics, Vol. 28, No. 3, 987, pp Wng, J.T. nd Rju, I.S., ÒStrin Energy Relese Rte Formule for Skin-Stiffener Debond Modeled with Plte Elements,Ó Engineering Frcture Mechnics, Vol. 54, No. 2, 996, pp Glessgen, E.H., Riddell, W.T. nd Rju, I.S., ÒEffect of Sher Deformtion nd Continuity on Delmintion Strin Energy Relese Rte,Ó 39th AIAA/ASME/ASCE/AHS Structures, Structurl Dynmics nd Mterils Conference, AIAA Pper CP, Glessgen, E.H., Rju, I.S. nd Poe, Jr., C.C., ÒPlte Element-Bsed Models for Mixed- Mode Debonding of Stitched Stiffened Pnels,Ó STP 36, Ftigue nd Frcture Mechnics: 3th Volume, ASTM, 998, in press.. Adms, D.O., ÒStitch Complince in Delminted Composites,Ó 29th SAMPE Technicl Conference, Orlndo, FL, October 28-3, Reeder, J.R., ÒA Biliner Filure Criterion for Mixed-Mode Delmintion,Ó ASTM STP 26, E.T. Cmponeschi, Jr., Ed., ASTM, Phildelphi, PA, 993, pp