FATIGUE LIFE METHODOLOGY FOR TAPERED COMPOSITE FLEXBEAM LAMINATES 1

Transcription

1 FATIGUE LIFE METHODOLOG FOR TAERED COMOSITE FLEBEAM LAMINATES 1 Gretchen B. Murri T. Kevin O'Brien U.S. Army Reserch Lbortory Vehicle Technology Center Hmpton, VA Crl Q. Rousseu Bell Helicopter Textron Ft. Worth, T Americn Helicopter Society 53rd Annul Forum April 29 - My 1, 1997 Virgini Bech, Virgini 1 resented t the Americn Helicopter Society 53rd Annul Forum, Virgini Bech, Virgini, April 29- My 1, Copyright Ó 1997 by the Americn Helicopter Society

2 ABSTRACT The vibility of method for determining the ftigue life of composite rotor hub flexbem lmintes using delmintion ftigue chrcteriztion dt nd geometric non-liner finite element (FE) nlysis ws studied. Combined tension nd bending loding ws pplied to non-liner tpered flexbem lmintes with internl ply drops. These lmintes, consisting of coupon specimens cut from full-size S2/E7T1 glss-epoxy flexbem were tested in hydrulic lod frme under combined xiltension nd trnsverse cyclic bending. The mgnitude of the xil lod remined constnt nd the direction of the lod rotted with the specimen s the cyclic bending lod ws pplied. The first delmintion dmge observed in the specimens occurred t the re round the tip of the outermost ply-drop group. Subsequently, unstble delmintion occurred by complete delmintion long the length of the specimen. Continued cycling resulted in multiple delmintions. A 2D finite element model of the flexbem ws developed nd geometriclly non-liner nlysis ws performed. The globl responses of the model nd test specimens greed very well in terms of the trnsverse displcement. The FE model ws used to clculte strin energy relese rtes (G) for delmintions inititing t the tip of the outer ply-drop re nd growing towrd the thick or thin regions of the flexbem, s ws observed in the specimens. The delmintion growth towrd the thick region ws primrily mode II, wheres delmintion growth towrd the thin region ws lmost completely mode I. Mteril chrcteriztion dt from cyclic double-cntilevered bem tests ws used with the pek clculted G vlues to generte curve predicting ftigue filure by unstble delmintion s function of the number of loding cycles. The clculted ftigue lives compred well with the test dt. NOMENCLATURE c, d, e, f curve fit constnts in eqns. (1), (3), (4) delmintion length long tper bove, mm ' delmintion length long tper below, mm b delmintion length towrd thin region below, mm E 1, E 2 oung's moduli in 1- nd 2- directions, G G totl strin energy relese rte, J/m 2 G 12 sher moduli, G G I mode I strin energy relese rte, J/m 2 G Imx mximum mode I cyclic strin energy relese rte, J/m 2 G II mode II strin energy relese rte, J/m 2 h hõ N t V VÕ mesured ply thickness, mm prescribed ply thickness, mm number of loding cycles xil tension lod, kn ply-group thickness in FE model, mm mesured trnsverse (bending) lod, kn prescribed trnsverse (bending) lod, kn v b q d e e mx n 12 trnsverse displcement t tip of flexbem, mm flexbem tper ngle, degrees wviness ngle, degrees lminte flpping ngle, degrees trnsverse stroke of ATB test mchine, mm flexbem surfce strin mximum cyclic surfce strin oisson's rtio INTRODUCTION Hingeless nd beringless helicopter rotor hubs re being designed using lminted composite mterils to reduce weight, drg, nd the number of prts. During flight, the rotor hub rm experiences centrifugl lods s well s bending in the flpping flexure region. In order to ccommodte this bending, the stiffness of the flpping flexure region is chnged by vrying the thickness of the hub rm. This thickness chnge is ccomplished by dropping, or terminting internl plies in tht region. However, these internl ply-drop loctions crete discontinuities which re sources for delmintion initition [1-5]. In order to design dmge resistnt tpered structures, mny prmeters ffecting delmintion t dropped plies, such s the tper geometry nd loction of the ply-drops through the thickness must be considered [6,7]. Severl studies hve considered delmintion filure in tpered lmintes with internl ply drops under pure tension lods [1-12]. References 1-3, 6, 8, nd 9 used finite element (FE) modeling nd stress-bsed filure criteri to predict the strength of tpered lmintes of vriety of different mterils nd with different internl ply-drop configurtions. In ech study it ws determined tht high interlminr stresses t the ply-drop loctions led to delmintion onset t the ply-drops. Other investigtors [4, 5, 7, 10-12] used strin energy relese rte pproch to study delmintion in tpered lmintes subjected to xil tension loding. A two dimensionl (2D) FE model developed in ref. 11 predicted tht for glss/epoxy lminte with three internl ply-drop steps, delmintion will strt t the junction of the thin nd tpered regions, nd will grow unstbly into both the thin nd tpered regions. Reference 7 showed tht the strin energy relese rte ssocited with delmintion growing from ply-drop tip towrd the thick section increses with incresing thickness of the discontinuous plies. In refs. 4, 5, nd 12, strin energy relese rte clcultions from FE models were used with frcture toughness dt to ccurtely predict delmintion onset in unidirectionl glss/epoxy nd grphite/epoxy specimens. Only few studies so fr hve considered the effect of bending lods on tpered lmintes. Reference 6 used 3D FE model to study the effects of severl ply-drop configurtion prmeters on interlminr stresses in lmintes with pure tension, bending, or torsion lods. Reference 13 investigted the possibility of controlling edge delmintion by terminting ply t criticl

3 interfce, smll distnce from the free edge. Tension, bending nd torsion lods were ech pplied to 3D FE model. Terminting -45 o ply resulted in stress reductions t the free edge for tension nd torsion loding, but not for bending. In ref. 14, the effect of combined tension nd bending loding on tpered lminte ws studied using coupon specimens nd simple FE model composed of bem elements which were ble to ccount for the effect of membrne lods on the flexurl response of the lminte. The predicted surfce strins from the FE nlysis compred resonbly well with mesured strins for lmintes with both liner nd nonliner tpers. In this study, the effect of combined tension-bending loding on glss-epoxy lmintes with nonliner tper nd internl ply-drops ws studied. Coupon specimens cut from full-size flexbems were subjected to constnt xil lod nd cyclic trnsverse bending lod. For comprison with the test dt, 2D finite element model ws developed which replicted the geometry nd loding of the specimens. A geometriclly nonliner nlysis ws performed on the FE model. EERIMENTS Specimen Geometry nd Test Conditions In this study, six coupon specimens were cut from full-size S2/E7T1 glss/epoxy flexbem, s shown in fig. 1. The full-length bem ws cut into two pieces crosswise, nd then ech hlf-bem ws cut lengthwise into three 1-inch wide specimens. The specimens were then trimmed to nominl length of 340 mm (13.4 inch) mm 43.2 mm D3 D2 D mm Note: Drwing not to scle 104 mm 140 mm B1 Figure 2. Schemtic of hlf-lminte with plygroup lbels. B2 B3 F thick tper thin 4.3 mm midplne gives the thicknesses of the continuous belt-ply groups nd equivlent orthotropic properties clculted using lminted plte theory nd ssuming symmetry. The mesured verge ply thickness, h, ws mm (0.008 inch) for the tpe mteril nd mm ( in) for the fbric lyer. Tble 1. Mteril roperties Mteril E11, G E22, G G12, G n12 S2/E7T1 tpe E-glss/E7T (fbric) Steel mm Net resin [20] Figure 1. Full-scle flexbem nd coupon test specimens. The specimens were symmetric bout the midplne, nd hd nonliner tper design. The number of plies vried from 145 t the thick end to 41 t the thin end. The flexbem lyup my be visulized s shown schemticlly in fig. 2, by ssuming tht the lminte consists of 5 continuous belt-ply groups (B), continuous surfce ply of woven 7781 E-glss/E7T1-2 fbric (F), nd 4 droppedply groups (D) on ech side of the mid-plne. Ech dropped-ply group consisted of 13 plies of differing lengths, in nonuniform stggered drop pttern, to produce the nonliner surfce contour. The continuous belt-ply groups re primrily composed of 0-degree lmine, nd the dropped-ply groups re composed of 45- degree nd -45-degree plies only. The mteril properties for S2/E7T1 nd E-glss/E7T1-2 re given in Tble 1. The ply-groups re lbeled in fig. 2 s they re referred to lter in this report. The ly-up for ech ply-group is given in Tble 2, where br over the ply-ngle indictes hlf-ply. Tble 2 lso Axil-Tension Bending Mchine Flexbem specimens were tested in servo-hydrulic lod frme, clled the Axil-Tension Bending (ATB) mchine, which ws designed nd built to produce combined tension-bending loding (fig. 3). Becuse the xil lod cell is locted bove the top grip, but below the pivot connecting the xil nd trnsverse ctutors, the tension lod "rottes" with the specimen s the trnsverse lod is pplied. Hence, under xil lod control, the mgnitude of the tension lod,, remins constnt s the specimen rottes under the trnsverse bending lod, V, s shown in fig. 4. Therefore, with the xil tension lod pplied under lod control nd the bending pplied using stroke control, constnt membrne lod should be mintined throughout the loding cycle. Sttic Tests rior to ftigue testing, the reltionship between pplied lods nd specimen deflection nd surfce strins ws determined by holding the xil lod constnt nd

4 Tble 2. ly-group Lyups nd Smered roperties ly Group Lyup Exx, G Eyy, G Gxy, G nxy t, mm B1 [0 2 /45] B2,, [0 4 ] B3 [±45/0 2 ] F woven ± D1, D2, D3, [±45] n * * t thickest point incrementlly incresing the trnsverse lod. Specimens were first instrumented with strin gges t four loctions long the length on ech side: one ner the junction of the thick nd tpered regions, two in the tpered region, nd one in the thin section. (See fig. 4.) The specimen ws then clmped in the grips with the thick end in the fixed bottom grip. The gge length between the grips ws 165 mm (6.5 inches). The specimen ws plced in the fixture so tht there ws 12.7 mm (0.5 inch) thick region, 127 mm (5 inch) tpered region nd 25.4 mm (1 inch) thin region (fig. 4). Axil lod cell Top grip Crosshed Bottom grip Axil ctutor Double pin pivot Specimen Trnsverse ctutor Trnsverse lod cell () schemtic (b) deformed specimen Figure 3. Axil tension nd bending test stnd nd deformed flexbem. As fig. 4 shows, the specimen is mounted in the grips nd the trnsverse lod is pplied t the pivot point, t distnce bove the top grip, rther thn t the top of the specimen. For sttic excursions, constnt xil tension lod,, of pproximtely 35.6 kn (8000 lbs.) ws pplied, nd then the bending lod ws pplied, in steps, to produce trnsverse stroke, d, in increments of pproximtely 2.54 mm (0.1 inch), up to mximum stroke of 30.5 mm (1.2 inch). At ech trnsverse lod step, the strins were recorded, s well s the flpping ngle, q, which ws mesured with digitl protrctor mounted to the top grip. The trnsverse displcement, v, t the top of the specimen, ws lso mesured using spring-loded DCDT which ws mounted to the side of the Note: Dimensions re in mm. strin gge # Bottom grip tper thin thick in ssembly Top grip Lod cell Figure 4. Test specimen nd loding fixtures with combined loding. lod frme nd detected the displcement of brcket ttched to the centerline of the top grip. In ref. 14, the surfce strins in composite flexbem specimen of S2/E773 mteril with similr non-liner tper nd the sme dimensions were mesured t four loctions long the specimen length, with the flexbem specimen subjected to combined tension nd bending loding. Mximum strins lwys occurred on the tension-bending surfce in the tpered region, t pproximtely =90.6 mm. It ws ssumed tht the strin distribution in the current flexbem specimens ws similr. Therefore, pek surfce strins mesured t gge 3 (where =90.9 mm, 3.59 inch) in fig. 4 were plotted in fig. 5 s function of pplied trnsverse stroke, d. The reltionship is liner when the xil lod is held constnt. Ftigue Tests Becuse the ATB boundry conditions differed from those of the full-scle flexbem in the hub, the ftigue tests were controlled to desired mximum surfce strin level, rther thn prescribed trnsverse deflection or bending ngle. Hence, the results shown in fig. 5 were used to select the mximum cyclic trnsverse stroke to pply corresponding to the desired mximum strin level (mesured t gge 3). rior to ftigue testing, the v q 172 V d

5 specimen edges were pinted with wter soluble typewriter correction fluid which cts s brittle coting e, mm/mm =35.6 kn 90.7 mm gge # d, trnsverse stroke, mm Figure 5. Trnsverse stroke-pek surfce strin response of nonliner tpered flexbem in the Axil Tension nd Bending (ATB) lod frme. nd mkes delmintions esier to see. Then the specimens were clmped in the grips nd tension lod of pproximtely 35.6 kn (8000 lbs.) ws pplied. The mximum cyclic trnsverse lod, V, in the ftigue test, ws pplied by cycling the lod sinusoidlly to the desired mximum trnsverse stroke t frequency of 3 Hz, using fully-reversed loding (R=-1). The mximum strin lwys occurred on the tension-side of the pplied bending lod. Four of the six specimens were tested t surfce strin of e mx =11000 me, nd the other two t e mx =10000 me. The specimens were cycled until they either filed by unstble delmintion completely long the length, on one, or both, sides, or reched 2 million loding cycles without filing (considered ÒrunoutÓ ). FINITE ELEMENT ANALSIS Finite Element Model Geometry A finite element model (FEM) of the tpered lminte ws developed to duplicte s closely s possible, the geometry of the tested flexbems, including the non-liner tper in the specimen, nd the boundry conditions of the ATB test configurtion. A schemtic of the configurtion to be modeled by FEM is shown in fig. 6. The fixed-end of fig. 6 corresponds to the composite flexbem, nd the loded end is continuous rectngulr cross-section member tht represents the upper grip nd steel fixture connecting to the pivot point where the trnsverse lod is pplied, s shown in fig 4. In this wy, by pplying the xil tension nd trnsverse lods to the free end of the model, the loding conditions of the model duplicte the test conditions. The FE model ws 2D model nd ws geometriclly symmetric bout the midplne. However, becuse of the unsymmetric loding, the entire flexbem ws modeled. The continuous curvture of the tpered section of the V flexbem ws pproximted in the model by using ten short liner tper sections, ech with grdully decresing tper ngles, from =9.17 o t =12.7 mm (0.5 inch) in Thick tper ngle,, degrees Tper Composite Flexbem Thin Steel Fixtures Figure 6. Nonliner tpered flexbem model with discreet tper ngles nd combined loding. fig. 6 to =0.0 o t =140 mm (5.5 inch). Continuous belt-ply-groups (B) nd dropped-ply-groups (D) were modeled in the nlysis, rther thn ech individul ply. Smered orthotropic mteril properties clculted from lminted plte theory for ech ply-group, ssuming symmetry, were used to represent the different ply-groups. The oisson rtio mismtch ssocited with this pproch ws ssumed to be negligible becuse none of the plygroups contined 90 o plies. The smered moduli in the globl - coordinte system, nd thickness for ech group re presented in Tble 2. Becuse the bending stiffness of the steel fixtures ws two orders of mgnitude greter thn the flexbem [14], nd to simplify the model, the elements t the thin-end tht represent the steel loding fixtures were modeled with rectngulr cross-section equl to the thin end of the composite flexbem, nd were ssigned moduli to yield bending stiffness, EI, equivlent to the ctul ATB fixtures. F Figure 7. Finite element mesh of nonliner tpered flexbem lminte. Finite Element Mesh nd Boundry Conditions The FE model hd 4960 nodes nd 4144 four-noded isoprmetric qudrilterl plne strin elements (see fig. 7). A 3-noded tringulr element ws used to represent resin pocket t the tip of ech of the eight dropped-ply groups. The net resin properties ssigned to the resin elements re given in Tble 1. Ech distinct ply-group ws modeled using one element through the ply-group thickness. The ply thickness in the model ws hõ=0.216 mm ( inch) for the tpe plies nd mm ( inch) for the fbric. To fcilitte ccurte strin V

6 energy relese rte nlysis using the virtul crck closure technique (VCCT) [15], squre elements were used in belt ply-groups B2, B3,, nd, in the tpered region ner the thick end of the model. Becuse the glss fibers were continuous in the belt-plies nd followed the bem contour, locl coordinte system ws defined for ech element in the model, with the 1-direction prllel to the element side from node 1 to node 2 in the longitudinl direction. The locl coordinte system ws then used to define the mteril properties of ech element. Becuse delmintion ws most often observed to occur first in the test specimens t the interfces beneth ply-groups nd (fig. 2), multi-point constrints (MC) were imposed t those interfces to llow simple modeling of delmintions by relesing the MCs. The nodes t the thick end of the model t =0 were fixed in the - nd -directions to simulte clmped end conditions. An xil tension lod of 35.6 kn (8000 lbs.) ws pplied t the thin end s concentrted lod. To produce bending, point lod of 4.45 kn (1000 lbs.) ws pplied in the negtive - direction t the thin end of the model, corresponding to the pivot point in the ATB lod frme, s shown in figs. 4 nd 6. Computtion Methods The ABAQUS finite element code ws used in the nlysis. Becuse the flexbem undergoes lrge deflections, the geometric non-liner solution option ws exercised. Also, s with the ATB lod frme, the xil lod in the model ws ble to "rotte" with the flexbem s it deformed under the trnsverse lod. The output from ABAQUS included nodl displcements, internl rection forces t the nodes, nd internl strins. Nodl displcements nd rection forces were used long with the Virtul Crck Closure Technique (VCCT) to clculte strin energy relese rtes for the simulted 10 bottom grip v flexbem tip q d lod ppliction point delmintions. This technique clcultes the mode I nd mode II components of strin energy relese rte (G I nd G II, respectively), using the forces t the delmintion tip, nd the reltive displcements behind the delmintion tip, both mesured in the locl coordinte system; i.e., the norml-tngentil (n-t) coordinte system for the deformed elements. Detils of these clcultions re given in refs. 15 nd 16. The totl strin energy relese rte, G, is obtined by summing the individul mode components. Hence, G = G I + G II since G III =0 for plne strin conditions. RESULTS AND DISCUSSION Globl Response Comprison Trnsverse displcements nd surfce strins in the FE model were compred to the test results to determine how ccurtely the model reproduced the globl behvior of the test specimens under similr loding. Figure 8 shows comprison of the flexbem-tip deflection, v, s the pplied trnsverse stroke, d, incresed from zero to the mximum vlue. A constnt xil lod of =35.6 kn (8000 lbs.) ws mintined in the model nd test. As the figure shows, there is very good greement between mesured nd predicted tip-displcement for the sme pplied stroke. In fig. 9, the mesured xil surfce strins from the four strin gge loctions re compred to the ABAQUS clculted strins long the flexbem length. The results shown re t the mximum trnsverse stroke condition (d=30.5 mm (1.2 inch)) nd with =35.6 kn (8000 lbs.) =35.6 kn clculted xil strins t d mx =29.2 mm mesured xil strins t d mx =30.5 mm 8 e mm V v, mm 4 2 =35.6 kn DCDT mesured results ABAQUS FE results mm 90.7 mm 157 mm d, mm Figure 8. Flexbem lminte-tip displcement vs. pplied trnsverse stroke in S2/E7T1 nonliner tpered flexbem , mm Figure 9. Surfce strins in nonliner tpered flexbem with combined tension nd bending loding.

7 Although the mesured strins re somewht higher thn predicted t the loction nerest the bottom grip, t the other three loctions there is very good greement between the test nd nlysis results. Mximum surfce strins mesured t gge 3 were lso compred to the ABAQUS results s the pplied stroke, d, ws incresed incrementlly from zero to mximum of 30.5 mm (1.2 inches) nd then in the opposite direction, from zero to d=-30.5 mm (-1.2 inch). The comprison is shown in fig. 10. The greement is very good throughout the rnge of trnsverse stroke, on both the tension-side nd compression-side of the flexbem. Bsed on these results, the FE model ppers to duplicte the globl response of the specimen under loding in the ATB very well. midplne F initil tension crck resin pocket b ' Note: Drwing not to scle. Figure Delmintion strting t tip of ply group mm gge #3 V filures. One specimen did not rech unstble delmintion nd ws considered runout t 2 million cycles (indicted by right-pointing rrow on the dt point in fig. 12) e x mx =35.6 kn Tension surfce Experimentl results ABAQUS FE results delmintion initition t ply-drop unstble delmintion Compression surfce e mx kn R=-1.0 f=3.0 Hz d, mm Figure 10. Clculted nd mesured surfce strins in nonliner tpered lminte. Experimentl Results Throughout the ftigue loding cycle, the specimens were periodiclly monitored for visible delmintion growth. The initil delmintions strted by tension crck t the interfce between the ply-group nd the djcent resin pocket, s shown schemticlly in fig. 11. Delmintions then grew towrd the thick region, either t the interfce under, indicted by delmintion length '; the interfce bove, indicted by delmintion length ; or t both interfces simultneously, (see fig. 11). These delmintions grew in stble mnner until they pproched the juncture of the tpered nd thick regions. As the ftigue loding ws continued, finl unstble filure occurred by delmintions forming nd growing rpidly from the tip of into the thin region of the flexbem, indicted by delmintion length b in fig. 11, long the entire length of the specimen, on one or both edges. Figure 12 shows the number of cycles, N, to the initil visible dmge nd finl unstble delmintion N, cycles Figure 12. Ftigue delmintion response in composite flexbem specimens under combined tension nd bending loding. Figure 13() shows photo of typicl finl filure. There re severl delmintions long the length, including the longest one t the interfce under. Figure 13(b) shows close-up of the re round the tip of, where delmintions were first observed. The delmintion strted s tension crck between the resin pocket nd dropped plies, nd grew towrd the thick region on both sides of the dropped section before ny delmintion ws seen growing towrd the thin region. In ddition to visible delmintion growth on the edges, three of the specimens sustined dmge in the woven fbric surfce ply (F). Splitting of the fbric strted t the specimen edge, ner the initil delmintion site. Crcks grew cross the specimen surfce s the loding continued nd delmintions grew from them in both directions, creting visible delmintion cross the width of the specimens surfce, s shown in fig. 13(c).

8 (b) initil dmge t ply-drop nd ssocited delmintion initil unstble delmintion subsequent unstble delmintion () finl filure with multiple delmintion ply-drop tip Figure 13. Flexbem test specimen with delmintion dmge. (c) dmge in surfce fbric lyer Strin Energy Relese Rte Clcultions The observed dmge ws creted in the FE model by first modeling the tension crck between the tip of the dropped-ply group nd the djcent resin pocket (see fig.11). Then delmintions were simulted in the model by relesing pirs of multi-point constrints t the interfces between nd, between nd, nd between nd (see insert in fig. 7). Strin energy relese rtes were clculted using VCCT for delmintion strting t the tip of nd growing distnce towrd the thick region t the interfce bove ; distnce Õ towrd the thick region t the interfce below ; or distnce b towrd the thin region t the interfce below, (see figs. 2 nd 11). The interfces bove nd below the resin pocket element t (see fig. 11) remined intct in the delminted models. The first G-vlues were clculted for delmintion of length, with no other delmintions in the model ('=0, b=0). The bottom curve on the left side of fig. 14 shows the results for this cse. Initilly, G is very smll nd increses very slowly until =15.1 mm (0.593 inch), where the tper ngle increses from 7.96 o to 9.17 o. At tht point, s the delmintion grows further in the thick direction, G increses more rpidly, nd ttins mximum vlue when the delmintion hs grown ll the wy to the thick section t =29.8 mm (1.17 inch). The higher curve on the left of fig. 14 shows the G results ssuming delmintion of length ' (under ), with no other delmintions in the model (=0, b=0). Agin, G strts out with low vlues nd increses slowly until '=15 mm (0.59 inches). Then G increses very rpidly s the delmintion is llowed to grow, reching pek t '=29.5 mm (1.16 inch), just before the thick region. Figure 14 lso shows tht G is lwys higher for delmintion growing under, rther thn over, mking delmintion more likely to grow t tht interfce. On the right side of fig. 14 re clculted G vlues for two cses of delmintion growing towrd the thin region from the tip of. Becuse test results lwys showed delmintions existed t the interfces bove nd below before they strted growing towrd the thin region, the model ws modified to contin delmintions of =16.1 mm (0.635 inch) nd '=16 mm (0.631 inch) bove nd below. Then G ws clculted for incresing vlues of b. The results re the bottom curve on the right in fig. 14. As the figure shows, G increses to pek t b=30.9mm (1.22 inch), drops quickly, nd then increses to second (lower) pek t b=59.9 mm (2.36 inch). These clcultions were repeted ssuming tht the delmintions bove nd below extended ll the wy to the junction of the tpered nd thick regions, i.e., =30.8 mm (1.21 inch) nd '=30.6 mm (1.2 inch), nd gin letting delmintion grow distnce b towrd the thin end. The results re the higher curve on the right of fig. 14. The initil G vlues re much higher for this cse. This curve lso increses rpidly to pek t b=30.9 mm (1.22 inch) nd drops, nd reches second pek t b=51.2 mm (2.02 inch), similr to the lower curve. G, J/m F ', with ' =0, b =0 Õ, with =0, b =0 b =35.58 kn V=4.45 kn b with =16.1 mm, ' =16 mm b with =30.8 mm, ' =30.6 mm , ' b Delmintion length, mm Figure 14. Strin energy relese rtes for delmintion growth in nonliner tpered lmintes under combined tension nd bending loding. The test results nd clculted G results in fig. 14 suggest tht delmintion will grow first towrd the thick region round, ll the wy to the junction of the tpered nd thick regions. Once the interfces bove nd below re delminted, delmintion will grow unstbly long surfce b. The opening nd sher components of G, (G I nd G II, respectively), were clculted for ll four modeled delmintion configurtions. Figure 15 shows G II /G for the delmintion growing towrd the thick region. The figure shows tht the delmintion growth is lwys t lest 70% mode II for both cses. For delmintion long, G II /G drops from lmost 100% t =5.08 mm (0.2 inch), down to 70% t =11.4 mm (0.45 inch), then

9 increses to pek t =15.1 mm (0.593 inches) where the tper ngle chnges, drops gin to 75%, nd increses stedily bck to 100%. For delmintion long ', G II /G is firly constnt t bout 95% until '=15 mm (0.59 inches). Then there is sudden drop. As the delmintion grows further, G II /G increses bck to ner 100%. The behvior of both curves t the discreet chnge in tper ngle (=15.1 mm nd '=15 mm (0.593 nd 0.59 inches)) is similr to results shown in ref. 17. In tht study, the effect of fiber wviness on strin energy relese 1.0 -b +b F ' =28.2 mm 9.17 o 1.87 o b 7.96 o Õ 5.26 o delmintion long with ' =0 nd b =0 delmintion long ' with =0 nd b=0 F ' Delmintion length, or ', mm Figure 15. G II /G rtio for delmintion round ply-group. b G II /G rte ws studied by modeling delmintion growing long n interfce which chnged from horizontl to n upwrd inclined (-b) or downwrd inclined (+b) ngle. Results of [17] showed tht G II /G incresed s the wviness ngle chnged from the lrgest +b vlues to the lrgest -b vlues. These results cn help explin the sudden locl chnges in mode rtios observed t the chnge in tper ngle in the current model. Figure 16 shows n enlrged view of the FE mesh round. As the figure shows, t the interfce bove, t =15.1 mm (0.593 inches), the tper ngle increses from 7.96 o to 9.17 o (- b). However, on the interfce below, t '=15 mm (0.59 inches), there is lso smll chnge in ngle, but in the opposite direction, (+b). Referring to fig. 15, the -b ngle chnge long surfce resulted in sudden increse in G II /G t tht loction, wheres the +b ngle chnge long surfce ', cused sudden decrese in G II /G. Figure 17 shows the percentge of opening mode strin energy relese rte (G I /G) for the delmintion growing towrd the thin region. As the figure shows, for these delmintions, G ws lmost entirely mode I for both cses nlyzed. However, the G I /G rtio for the first cse (with =16.1 mm nd '=16 mm (0.635 nd 0.631\ =28.2 mm Figure 16. Mesh round =28.19 mm showing tper ngle chnges. inch)) shows smll drops t b=11.7, 25.9, nd 44.2 mm (0.46, 1.02, nd 1.74 inch). There re tper ngle chnges t ech of these loctions, ll in the -b direction, resulting in temporry decrese in the percentge of G I /G t ech chnge. For the second cse, where =30.8 mm (1.21 inch) nd '=30.6 mm (1.2 inch), the effect of these chnges is less pronounced, with smll drop t b=25.9 mm (1.02 inch), nd slightly lrger drop t b=44.2 mm (1.74 inch), the loction of the lrgest tper ngle chnge. Anlyses of the reltive percentges of G I nd G II show tht delmintion growth long surfces or ' is predominntly mode II, but growth in the opposite direction long surfce b is lmost entirely mode I. In both cses, chnging the tper ngle, even by smll mount, in either positive or negtive direction, chnges the rtios of G I nd G II in the re ner the ngle chnge. G I /G F ' Delmintion length, b, mm Figure 17. G I /G rtio for delmintion growth towrd thin region of flexbem. b =16.1 mm, ' =16 mm =30.8 mm, ' =30.6 mm

10 Filure redictions In refs. 4, 12 nd 17, pek vlues of clculted strin energy relese rtes were used with mteril chrcteriztion dt to predict delmintion onset s function of the number of loding cycles. Figure 18 presents G Imx vs. N dt from ref. 18, for S2/E7T1 mteril. Ech dt point represents one double cntilevered bem (DCB) test specimen tht ws cycled until delmintion onset ws detected. A 5% chnge in DCB specimen complince ws used s the criteri for indicting delmintion onset. Although delmintion growth long surfces nd ' ws shown to be primrily mode II, previous studies hve indicted tht there my be little difference in mode I nd mode II G vs. N dt, especilly t long lives [19]. For this reson, nd operting t chosen e mx level, it is more useful to clculte predicted curve of e mx vs. N, for comprison with the test results. The sttic excursion tests showed tht liner reltionship existed between the trnsverse lod, V, nd the surfce strin, e, s shown in fig. 19. e mx =35.4 kn G Imx, J/m DCB ftigue dt [18] curve fit to dt curve fit ± one stndrd devition N, cycles to delmintion onset Figure 18. Ftigue delmintion onset in S2/E7T1 DCB specimen. becuse G IImx dt ws not vilble, the G Imx vlues were used for ll clcultions. For the purpose of this study, curve ws fit through the dt in fig. 18, nd hd the form G Imx = c (N d ) (1) where c=463 J/m 2 nd d= Then, s in [4], [12], nd [17], it ws ssumed tht delmintion onset would occur in the flexbems when the pek G from the FE nlysis equled the cyclic G Imx t which delmintion initited in the DCB tests. Tht is, when é ù GhÕ ê ë VÕ 2 ú = G Imx h (2) û FE V 2 where the terms on the left side of the eqution refer to the FE model nd on the right side, h is the mesured verge ply thickness of the specimens nd V is the clculted bending lod. However, since the tests were conducted by V, kn Figure 19. Mximum mesured surfce strin vs. pplied trnsverse bending lod in tpered flexbem with constnt xil tension lod. The reltionship between V nd e cn be expressed s e = e + f*v (3) where e=3.36e-3 nd f=1.335e-3 kn -1. Eqution (1) cn be substituted into eq. (2) nd rerrnged to solve for the pplied trnsverse lod, V. Substituting the expression for V into eq. (3) gives c N d h e mx (N) = e + f (4) é GhÕù ë ê VÕ 2 û ú FE relting the number of loding cycles to the pplied mximum surfce strin. The number of loding cycles to finl unstble delmintion, N filure, cn be considered s the number of cycles to the onset of stble delmintion long or Õ (N 1 ), plus the number of cycles for delmintion growth long those interfces (N 2 ), plus the number of dditionl cycles to the onset of unstble delmintion long b (N 3 ), once nd Õ hve grown to the juncture with the thick region. If N 2 is considered negligible, then N filure cn be pproximted by N 1 + N 3. Eqution (4) ws used to clculte curves relting mximum cyclic strin nd the number of loding cycles to the onset of delmintion

11 long Õ (N 1), nd to the onset of finl unstble delmintion (N 3 ). Eqution (4) ws first computed for the cse of delmintion growing from the tip of towrd the thick section (incresing '), with no other delmintions (=0, b=0) in the flexbem, using the pek vlue of G FE =98 J/m 2 (0.56 in-lb/in 2 ) from fig. 14. A curve relting the mximum cyclic strin to the number of loding cycles t delmintion onset long Õ (N 1 ) ws clculted nd is shown in fig. 20(). A second curve ws clculted, for flexbem with both interfces round completely delminted (=30.8 mm nd Õ=30.6 mm (1.21 nd 1.2 inch)) nd delmintion of length b growing towrd the thin region. For this cse the pek vlue of G FE =126 J/m 2 (0.72 in-lb/in 2 ), from the right side of fig. 14, ws used. The resulting curve, shown in fig. 20(b) reltes the e (N) mx N = N +N +N filure onset of delmintion long Õ N, cycles to delmintion neglected stble delmintion growth long Õ N 1= delmintion onset t ply-drop Figure 20. Delmintion onset curves for modeled delmintions. onset of delmintion long b with =30.8 mm, Õ =30.6 mm N, cycles to delmintion () delmintion onset curve long Õ (b) delmintion onset curve long b e mx (N) N = unstble delmintion onset 3 cyclic strin to the number of loding cycles t the onset of finl unstble delmintion (N 3 ). Adding the two curves in fig. 20 then results in n e mx vs. N curve for predicted finl delmintion filure, which is shown in fig. 21, long with the test results t unstble delmintion. e mx flexbem test dt predicted ftigue life prediction ± one stndrd devition N, cycles to delmintion filure Figure 21. Flexbem delmintion filure dt nd predicted ftigue life curve. The shded re in fig. 21 represents the prediction, plus nd minus one stndrd devition. All the test dt fll within one stndrd devition of the prediction, lthough the tendency is to slightly under-predict the number of cycles to filure t the higher strin level, nd slightly over-predict t the lower strin level. CONCLUSIONS Nonliner tpered flexbem lmintes cut from fullsize composite rotor hub flexbem were tested under combined xil tension nd cyclic bending lods. The tension lod remined constnt while the cyclic trnsverse bending lod ws pplied. The specimens filed by delmintions first strting round the tip of the outermost ply-drop group nd growing towrd the thick region of the flexbem. Once the interfces both bove nd below this dropped-ply group were delminted, finl filure occurred by unstble delmintion growth into the thin region long the full length of the tper. A 2D finite element model ws developed which closely pproximted the flexbem geometry, boundry conditions, nd loding. The model ws nlyzed using geometriclly nonliner FE code. The FE model ws ble to ccurtely replicte the globl response of the coupon specimens under the combined loding. Delmintions of vrious lengths were simulted in the model by relesing multipoint constrints (MC) t the interfces where delmintions were observed in the test specimens. Strin energy relese rtes (G) clculted using the virtul crck closure technique (VCCT) showed tht: (1) Delmintions originting t the tip of the outermost ply-drop group were more likely to grow t the interfce under the dropped-plies thn t the interfce bove the dropped ply group; (2) Delmintions t either interfce will grow until they extend ll the wy to the junction of the tpered nd thin regions; nd (3) Once the interfces round the dropped-ply group re delminted, delmintion will grow unstbly from the tip of the dropped-ply region towrd the thin re of the flexbem. A comprison of the mode rtios for the different delmintions modeled showed tht delmintion growth towrd the thick region ws mostly Mode II, wheres delmintion growth in the opposite direction ws predominntly Mode I. The mode rtios were very sensitive to the discrete ngle chnges in the model. At loctions where the tper chnged in one direction, G I /G decresed loclly, nd where the ngle chnged in the opposite direction, G I /G incresed loclly. Clculted pek G vlues were used with G Imx vs. N dt generted using DCB specimens to predict filure

12 of the flexbem specimens. The clculted ftigue life grees well with the test dt. The results indicte tht using the clculted G vlues from FE model, with delmintion ftigue chrcteriztion dt, is vible method for determining the ftigue life of composite rotor hub flexbem lmintes. REFERENCES 1. Fish, J. C. nd Lee, S. W., "Tensile Strength of Tpered Composite Structures." AIAA per No , roceedings of the 30th AIAA/ASME/ASCE/AHS Structures, Structurl Dynmics nd Mterils (SDM) Conference, Willimsburg, VA, April 1988, pp Ho, S. V., Doust, J., nd Du, B. L., "Interlminr Stresses in Tpered Lmintes," olymer Composites, Vol. 9, No. 5, October 1988, pp Llnos, A. S., Lee, S. W., nd Vizzini, A. J., "Delmintion revention in Tpered Composite Structures under Unixil Tensile Lods," AIAA per No , roceedings of the 31st AIAA/ASME/ASCE/AHS Structures, Structurl Dynmics nd Mterils (SDM) Conference, Long Bech, CA, April 1990, pp Murri, G. B., Slpekr, S. A., nd O'Brien, T. K., "Ftigue Delmintion Onset rediction in Unidirectionl Tpered Lmintes," Composite Mterils: Ftigue nd Frcture (Third Volume), ASTM ST 1110, T. K. O'Brien, Ed., Americn Society for Testing nd Mterils, hildelphi, 1991, pp Wisnom, M. R., "Delmintion in Tpered Unidirectionl Glss Fibre-Epoxy Under Sttic Tension Loding," AIAA per No , roceedings of the 32nd AIAA/ASME/ASCE/AHS Structures, Structurl Dynmics nd Mterils (SDM) Conference (rt 2), Bltimore, MD, April 1991, pp Doust, J. nd Ho, S. V., "rmeters Affecting Interlminr Stresses in Tpered Lmintes Under Sttic Loding Conditions," olymer Composites, Vol. 10, No. 5, October 1989, pp Trethewey, B. R., Jr; Gillespie, J. W., Jr; nd Wilkins, D. J., "Interlminr erformnce of Tpered Composite Lmintes," roceedings of the Americn Society for Composites, 5th Technicl Conference, Est Lnsing, MI, June 1990, pp Kemp, B. L. nd Johnson, E. R., "Response nd Filure Anlysis of Grphite-Epoxy Lminte Contining Terminting Internl lies," AIAA per No , roceedings of the 26th AIAA/ASME/ASCE/AHS Structures, Structurl Dynmics nd Mterils (SDM) Conference, Orlndo, FL, April 1985, pp Curry, J. M., Johnson, E. R., nd Strnes, J. H., "Effect of Dropped lies on the Strength of Grphite- Epoxy Lmintes," roceedings of the 29th AIAA/ASME/ASCE/AHS Structures, Structurl Dynmics nd Mterils (SDM) Conference, Monterey, CA, April 1987, pp Armnios, E. A. nd rns, L., "Delmintion Anlysis of Tpered Lminted Composites Under Tensile Loding," Composite Mterils: Ftigue nd Frcture (Third Volume), ASTM ST 1110, T. K. O'Brien, Ed., Americn Society for Testing nd Mterils, hildelphi, 1991, pp Slpekr, S. A., Rju, I. S., nd O'Brien, T. K., "Strin Energy Relese Rte Anlysis of Delmintion in Tpered Lminte Subjected to Tension Lod," roceedings of the Americn Society for Composites, Third Technicl Conference, Settle, WA, Sept. 1988, pp Murri, G. B., O'Brien, T. K., nd Slpekr, S. A., "Tension Ftigue of Glss/Epoxy nd Grphite/Epoxy Tpered Lmintes," Journl of the Americn Helicopter Society, Vol. 38, No. 1, Jn. 1993, pp Ocho, O. O. nd Chn, W. S., "Tpered Lmintes: A Study on Delmintion Chrcteriztion," roceedings of the Americn Society for Composites, 3rd Technicl Conference, Settle, WA, September 1988, pp O'Brien, T. K., Murri, G. B., Hgemeier, R., nd Rogers, C., "Combined Tension nd Bending Testing of Tpered Composite Lmintes," Applied Composite Mterils, Vol. 1, No. 6, 1995, pp Rybicki, E. F., nd Knninen, M. F., "A Finite Element Clcultion of Stress-Intensity Fctors by Modified Crck-Closure Integrl," Engineering Frcture Mechnics, Vol. 9, 1977, pp Rju, I. S., ÒSimple Formuls for Strin-Energy Relese Rtes with Higher Order nd Singulr Finite Elements,Ó NASA Contrctor Report , December Li, J., nd O'Brien, T. K., "ly Wviness Effects on the ull-off Lods in Composite Ht Stringer Specimens," roceedings of the 14th U.S. Army Symposium on Solid Mechnics, Myrtle Bech, SC, October 16-18, Mrtin, R. H., "Accelerted Methods for the Determintion of Long Term Ftigue roperties of Glss Reinforced lstics for Rotorcrft Applictions," Mterils Engineering Reserch Lbortory (MERL), Report No. N C-9061, London, August Mrtin, R. H., nd Murri, G. B., ÒChrcteriztion of Mode I nd Mode II Delmintion Growth nd Thresholds in AS4/EEK Composites,Ó Composite Mterils: Testing nd Design (Ninth Volume),

13 ASTM ST 1059, S.. Grbo, Ed., Americn Society for Testing nd Mterils, hildelphi, 1990, pp Shivkumr, K. N. nd Crews, J. H., Jr., "Bolt Clmpup Relxtion in Grphite/Epoxy Lminte," Long Term Behvior of Composites, ASTM ST 813, T. K. O'Brien, Ed., Americn Society for Testing nd Mterils, hildelphi, 1983, pp

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