Microscopical observations of inter-fibre failure under tension

Depósi o de In es igación de la Uni e sidad de Se illa h ps://idus.us.es/ This is an Accep ed Manusc ip o an a icle published by Else ie in Composi es Science and Technology, Vol. 158, on Feb ua y 2018, a ailable a : h ps://doi.o g/10.1016/j.compsci ech.2017.12.009 © 2017 Else ie . En idUS Licencia C ea i e Commons CC BY-NC-ND Mic oscopical obse a ions o in e - ib e ailu e unde ension Elena Co ea, Ma ía Inmaculada Val e de, Ma ía Luisa Velasco, Fede ico Pa ís Depa amen o de Mecánica de Medios Con inuos y Teo ía de Es uc u as, G upo de Elas icidad y Resis encia de Ma e iales, Escuela Técnica Supe io de Ingenie ía, Uni e sidad de Se illa, Camino de los Descub imien os s/n, 41092, Se illa, España Abs ac The nume ical s udy o he in e - ib e ailu e a mic omechanical le el p edic s he appea ance o di e en s ages in he de elopmen o his damage mechanism; hese s udies ha e also allowed he main ea u es o each s age (such as he in e acial debond leng h and he kinking angle) o be iden i ied. The de elopmen o expe imen al s udies aiming o check he ele ance o he a o emen ioned nume ical esul s is c ucial. Based on his, his esea ch ocused on he ensile es unde di e en loading le els o specimens manu ac u ed om ca bon-epoxy c oss-ply symme ical lamina es. The mic oscopic obse a ion o he 90º laye s leads o he analysis o he appea ance o he ans e se c acks as a unc ion o he load, he iden i ica ion o he p e iously nume ically p edic ed s ages o he mechanism o damage, he measu emen o key pa ame e s and he e alua ion o he in luence o nea by ib es. A clea connec ion be ween he nume ical and expe imen al esul s has been ound. Keywo ds: debonding; ans e se c acking; op ical mic oscopy; c oss-ply. A.1. In oduc ion Ma ix/In e - ib e ailu e a ises in plies subjec ed o ans e se loads, being cha ac e is ic, among o he s, o 90° plies belonging o c oss-ply lamina es subjec ed o loads pa allel o hei 0° plies. P e ious nume ical s udies allowed he iden i ica ion o h ee main s ages in he mechanism o damage a mic omechanical le el, Figu e A.1. In pa icula , in he case o ensile loads (Pa ís e al [1]), damage ini ia es wi h he appea ance o small debonds a he ib e-ma ix in e aces aligned wi h he applied load (S age I); hese debonds g ow uns ably in Mixed Mode along he in e aces un il eaching an ex ension (semi-debonding angle,  d) o 60°-70° (S age II); a his posi ion, a change o s able g ow h in pu e Mode II akes place (caused by he appea ance o a physically ele an con ac zone a he c ack ip), a ou ing he kinking o he c ack owa ds he ma ix (S age III). The c ack inally p opaga es along he ma ix (uns ably and in Mode I) ollowing he di ec ion pe pendicula o he load applied. The coalescence o his ype o c acks coming om di e en ib es gi es ise o ans e se mac o-c acks in he ply, e en ually leading o i s ca as ophic ailu e. Figu e A.1. S ages o he mechanism o damage. Pa ís e al [1]. The e ec ha he p esence o a seconda y load (Pa ís e al [2], Co ea e al [3]) has on he e olu ion o hese s ages, he conside a ion o he mal esidual cu ing s esses (Co ea e al [4]), and he case o cyclic loading (Co ea e al [5]), ha e also been s udied nume ically. The impo an ole ha mic omechanical s udies can play in helping i s in he unde s anding o he mechanism o ailu e and second in e i ying and p oposing ailu e c i e ia was poin ou in hese wo ks. In pa icula , his ou s anding ques ion was deeply analysed in Pa ís [6]. A common pa e n o hese s udies is he usage o a single ib e (assumed isola ed) Bounda y Elemen model. Mo e ecen wo ks, ocusing on S age II o he mechanism o damage, also include a la ge numbe o ib es, see o ins ance Sandino e al [7] ( wo- ib es models), Tá a a e al [8] ( en- ib es models) and Tá a a e al [9] (one hund ed- ib es models). FEA has also been used o s udy his p oblem; see o ins ance Hojo e al [10], Kushch e al [11] y Sai o e al [12]. A his poin , i u ns ou c ucial o check, by means o expe imen al s udies, he alidi y o he esul s de i ed om he nume ical models, speci ically, by means o mic oscopic obse a ion o es ed samples. P e ious wo ks om di e en au ho s ocusing on he expe imen al mic omechanical obse a ion o he ma ix ailu e can be ound in he li e a u e; among hem i can be s ood ou he al eady classical wo ks by Zhang e al [13] (single ib e es s unde ension) and Gams ed and Sjög en [14] (based on Zhang bu s udying he e ec o cyclic load), and also hose om Sai o e al [15] (analysing he e ec o he 90º ply hickness in c oss ply lamina es), Ba al e al [16] (s udying he e ec o he ib e ype), Hobbieb unken e al [17] (compa ing he beha iou be ween high and low cu ing empe a u e esins in h ee poin s bending es s) o STAGE I a ≈10º  d=60-70º STAGE II STAGE III Genz e al [18] (e alua ing he p esence o he mal esidual s esses). In he p esen wo k, an op ical mic oscope is used o obse e he 90 plies o c oss-ply specimens es ed unde longi udinal ensile load (which will be hus ans e se o he 90 plies), in o de o check i he nume ically p edic ed mic omechanical s ages o he ma ix/in e - ib e ailu e a e in ac p esen and can be dis inguished. The iden i ica ion o he di e ences ha hese s ages show in eal lamina es wi h a high ib e olume con en e sus he nume ical single (and isola ed) ib e models, is also pu sued. In addi ion, he measu emen o he inal ex ension o he c ack a he in e ace ha gi es ise o he kinking owa ds he ma ix (  d= 60-70, om he nume ical models), as well as he s udy o he di e en damage ypologies, he analysis o he in luence o he applied loading le el and he e ec o he p esence o neighbou ing ib es, a e also objec i es o he s udy. A.2. Coupons manu ac u ing and es ing [03,903]s ensile coupons we e manu ac u ed om ca bon-epoxy (AS4-8552) p e-p eg, ein o cing hei ends wi h glass-epoxy abs. Thei dimensions a e de ailed in Figu e B.2. Figu e A.2. Coupons dimensions. A i s se o 5 coupons was selec ed o es ing unde ension. The esul s p o ided by he ensile s eng h (X) show a mean alue o 942.47 MPa, a s anda d de ia ion o 41.25 MPa and a a ia ion coe icien o 4.38%, he e o e implying an excellen esul in e ms o dispe sion. Subsequen es ing campaigns we e pe o med unde maximum loads lowe han he p e iously measu ed X, in o de o gene a e damage in he 90 plies wi hou eaching he ca as ophic ailu e o he whole lamina e. In pa icula , he loads applied can be g ouped in 5 le els: 80%X, 60%X, 40%X, 30%X and 20%X. The numbe and denomina ion o he coupons es ed as well as he exac loading le el applied a e included in Table A.1. Table A.1. Denomina ion o he coupons and co esponding es ing load. Coupons denomina ion Tes ing load (%X) 80-1 84.2 80-2 82 60-1 62.4 60-2 59.5 60-3 60.5 40-1 42.6 40-2 40.3 40-3 39.2 30-1 31.5 30-2 29 30-3 27.6 20-1 21 A.3. P epa a ion o samples The cen al pa o he specimens was cu in wo hal es o app oxima ely 28 mm leng h; each pai was encapsula ed in esin (using he Ve soCi -2 ki ). A e ha , he samples we e polished using Saphi 20 polishe (au oma ic head and p og ammable) om NEURTEK Ins umen s, LaboDose liquide dispense and LaboPol-5 as pe iphe al polishe om S ue s. The esul o he polishing p ocess mus allow he ib es co esponding o he 90 plies o be clea ly obse ed in an op ical mic oscope a 1000x magni ica ion. A sui able polishing p ocess should also a oid he appea ance o ma ks ha could in e e e in he la e mic oscopical inspec ion. To his pa icula end, a speci ic polishing p ocess was designed and es ed, consis ing o ou s eps. 40N p essu e and 50 pm speed a e selec ed o all s eps, he disc ype, e ige a o liquid and ime used a e de ailed nex : S ep 1: Disc: SiC #320. Liquide: Wa e . Time: 5’. S ep 2: Disc: MD-La go. Liquide: DiaP o Alleg o/La go 9 μm (2). Time: 6’. S ep 3: Disc: MD-Dac. Liquide: DiaP o Dac 3 μm (1). Time: 5’. S ep 4: Disc: MD-Dac. Liquide: DiaP o Nap B1 1 μm (3). Time: 4’. A.4. Mic oscopic obse a ion Once he samples ha e been polished he mic oscopic inspec ion is unde aken. The e is a double objec i e he e: i s , using low magni ica ion (25x), he analysis o he appea ance o ans e se c acks in he 90 plies as a unc ion o he load applied. Second, he s ages o he mechanism o damage p e iously iden i ied by he nume ical models wan o be de ec ed, along wi h he expe imen al alues o hei main pa ame e s; o his end, obse a ion a high magni ica ion (500x and 1000x) is equi ed. A.4.1. Inspec ion a low magni ica ion A i s inspec ion is made a 25x in o de o coun he numbe o ans e se mac o-c acks ha appea s in each specimen, and hus i s loading le el dependence. In Table A.2 he numbe o c acks obse ed pe cm in each coupon is de ailed. The mos ele an conclusion is ha o loads lowe han 30%X no ans e se mac o-c acks a e obse ed in he samples. A la e inspec ion a g ea e magni ica ion will also show, Sec ion A.4.2, ha no damage o any ype is de ec ed below his loading le el. I is also obse ed ha he numbe o c acks encoun e ed inc eases as he loading le el does. No ice in any case he educed numbe o samples chosen o he lowes loading le els. Table A.2. Numbe o mac o-c acks as a unc ion o he loading le el. %X Numbe o mac o-c acks/cm 84.2 9 82 9.2 62.4 6.4 59.5 4 60.5 3.6 42.6 3.5 40.3 1.2 39.2 0.8 31.5 2.3 29 0 27.6 0 21 0 Al hough no being di ec ly he objec i e o his pape , making use o he Classical Lamina e Theo y (CLT) and selec ing a sui able ailu e c i e ion i is possible o p edic he s ess associa ed wi h i s -ply ailu e (XFPF). Then, i is in e es ing a his poin o check i he lowes s ess alue o which damage has been de ec ed in he ma e ial (31.5%X in his case, see Table A.2) is accu a ely p edic ed by he Lamina e Theo y in combina ion wi h ailu e c i e ia. To his end, a selec ion o ailu e c i e ia (Maximum S ess, Tsai-Hill (Azzi and Tsai [19]), Tsai- Wu [20], Maximum S ain, Hashin [21], Hashin and Ro em [22] and Puck [23]) has been pe o med, and hei XFPF p edic ions calcula ed, see Table A.3. Table 3. Fi s -ply and ul ima e ailu e p edic ions o a selec ion o ailu e c i e ia. Failu e C i e ion XFPF (MPa) XUF (MPa) XFPF/XUF (%) Maximum S ess 374.4 1112.9 33.6 Tsai-Hill 374.1 1109.5 33.7 Tsai-Wu 368.1 1149.1 32.0 Maximum S ain 367.2 1124.6 32.7 Hashin 374.4 1112.9 33.6 Hashin-Ro em 374.4 1112.9 33.6 Puck 374.4 1113.8 33.6 Fi s o all, i can be obse ed ha all ailu e c i e ia show simila p edic ions wi h a mean alue o 372 MPa. This alue can be compa ed wi h he lowes expe imen al load o which ans e se c acks a e obse ed, 31.5%X in his case, which co esponds o a s ess alue o 297 MPa. Taking in o accoun ha he numbe o coupons included in he 30%-40%X g oup is small (see Table A.2) and also ha all o hem show a e y educed numbe o ans e se c acks, a good ag eemen be ween he analy ical p edic ion and he expe imen al esul is ound. The appea ance o he i s c ack a a alue lowe han ha p edic ed by he c i e ia o he ailu e o he ply is, on he o he hand, a e y cohe en ac , as he appea ance o one ans e se c ack does no mean he o al ailu e o he ply. The appea ance o ans e se c acks in a 90 ply is a con inuous (no sudden) phenomenon, and i can be checked ha (as men ioned abo e), o he i s ply ailu e p edic ed by he c i e ia, only a e y educed numbe o c acks appea in he specimen, his ac no implying a signi ican educ ion in he con ibu ion o he 90 ply o he p ope ies and pe o mance o he lamina e. Ano he in e es ing ea u e a ises when using he CLT o also p edic he s ess associa ed wi h he ul ima e ailu e (XUF) and hen o calcula e he a io be ween XFPF and XUF (Table A.3), i.e. using only he analy ical ool o e alua e a which pe cen age o he analy ical ul ima e s ess he heo y p edic s he ini ia ion o damage. This calcula ion o XUF has been pe o med by means o a p og essi e damage model, using a deg ada ion coe icien D equal o 0.1 ha ac s on all ma e ial p ope ies bu jus sligh ly in his pa icula case due o i s small alue. The esul s show again simila p edic ions o all c i e ia and an app oxima e alue o 33%XUF is ob ained o XFPF. An excellen ag eemen is ound now be ween his p edic ion and he expe imen al esul , as he i s ans e se c acks we e de ec ed a 31.5%X. The obse a ion o he 25x mic og aphs shows some ele an di e ences be ween he di e en loading le els, in pa icula : 1) Specimens es ed a 20%X (see Figu e A.3a as an example): No damage is de ec ed. 2) Specimens es ed a 30%X (see Figu eA.3b as an example): Jus a ew and e y hin ans e se c acks a e ound in one specimen. A educed numbe o delamina ions be ween 90º and 0º plies a e p esen . 3) Specimens es ed a 40%X (see Figu e A.3c as an example): Some ans e se c acks a e ound al hough hey appea like hin lines in he mic oscope. Delamina ions be ween 90º and 0º plies a e p esen . 4) Specimens es ed a 60%X (see Figu e A.3d as an example): Many and well de ined ans e se c acks a e ound. Some c acks show a pa h de ia ed om he ans e se di ec ion. Delamina ions be ween 90 and 0 plies a e de ec ed. 5) Specimens es ed a 80%X (see Figu e A.3e as an example): Many and well de ined ans e se c acks a e ound (mo e han in he p e ious case). Mos o hem appea like hick lines a he mic oscope, which is associa ed wi h a clea ly de eloped damage and p obably wi h a signi ican opening o he c ack lips. Mo e de ia ed c acks a e obse ed. Delamina ions be ween 90 and 0 plies a e also de ec ed. I should be ema ked ha he h ough hickness c ack loca ion does no show a p e e en ial pa e n, which seems o be in acco dance wi h CLT p edic ions (assuming he 90 ply as homogeneous) and also wi h he ou comes o a ecen nume ical s udy by he au ho s (modeling he 90º ply as he e ogeneous and dis inguishing be ween ib es and ma ix), Pa ís e al [24]. (a) (b) (c) (d) (e) Figu e A.3. 25x mic og aphy om (a) 20-1 specimen, (b) 30-1 specimen, (c) 40-1 specimen, (d) 60-1 specimen, (e) 80-2 specimen. A.4.2. Inspec ion a high magni ica ion The inspec ion o he samples using a g ea e magni ica ion is nex pe o med in o de o y o expe imen ally iden i y he di e en phases o he mechanism o damage nume ically p edic ed in [1] (Figu e A.1); in pa icula , he occu ence o S ages I, II and III, hei connec ion wi h he loading le el as well as he measu emen o speci ic pa ame e s ele an o he de elopmen o he mechanism o damage, a e pu sued. Indeed, he obse a ion o samples a high magni ica ion exposes he appea ance o all s ages o he ailu e mechanism (I, II and III, Figu e A.1) o loading le els highe han 30%X. Speci ically, damage appea s in clea ly less quan i y in he 30%X g oup, maximizing i s appea ance in he 60%X g oup (p obably associa ed wi h he ac ha in he 80%X g oup isola ed s ages disappea o ming a g ea e numbe o mac o-c acks). Figu e A.4 shows 1000x images o S ages I and II (a), and S age III (b). No ice ha he nominal ib e adius is 3.56 m, use ul as scale e e ence o Figu e A.4 and he o hcoming Figu es A.5, A.7, A.8 and A.9. (a) (b) (c) Figu e A.4. 1000x mic og aphies o : (a) S ages I and II (30%X), (b) S age III (40%X), (c) Aligned debonds (40%X). I is necessa y o ema k ha i is no possible o dis inguish be ween S ages I and II wi h he a ailable ools because, among o he hings, i is no nume ically clea i a eal sepa a ion be ween bo h s ages exis s. The uns able cha ac e o he mechanism o ailu e and he dependence o he ini ia ion o ailu e on he p ope ies o he in e ace (in pa icula on he ac u e oughness) a e some o he ea u es ha poin i as an open ques ion. The mo e ecen publica ions on Fini e F ac u e Mechanics (Man ič [25], Man ič and Ga cía [26]) s udy in dep h his p oblem. Wi h e e ence o S age II, i is common o ind he debonds a his s age e y close o a eas whe e mac o-c acks al eady exis , al hough a low loading le els hey a e also de ec ed as isola ed, a om hese a eas. The S age II debonds o en appea aligned in high ib e densi y zones, so ha he pa h ollowed by he u u e mac o-c ack can be en isaged, Figu e A.4c. No e y equen ly, ib es wi h bi-la e al debonds a e obse ed (Figu e A.5a) al hough cu en ly bo h debonds do no p esen he same ex ension and hus, no simul aneous g ow h is deduced. The exis ence o hese bi-la e al debonds can be also obse ed in mac o-c acks, Figu e A.5b; in hese cases he bi-la e al debond seems o appea when he ib e is placed in he middle o he pa h o he mac o-c ack. (a) (b) Figu e A.5. 1000x mic og aphies o bi-la e al debonds (a) a S age II (60%X), (b) in mac o-c acks (60%X). Re e ing o S age III, se e al kinking pa hs addi ional o he nume ical heo e ical one ha e been iden i ied using he mic oscope. Figu e A.6 shows all ypologies ound, ha ing been named as de ailed: A. Theo e ical, B.1. De ia ed +, B.2. De ia ed –, C. Bila e ally angen ial, D. G adual ansi ion and E. Spli ing. STAGE I STAGE II STAGE III [20] S.W. Tsai, E.M. 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