Numerical predictions of intralaminar and interlaminar damage in thin composite shells subjected to impact loads

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 Thin- Walled S uc u es, Vol. 192, on No embe 2023, a ailable a : h ps://doi.o g/10.1016/j. ws.2023.111148 Copy igh 2023 Else ie . En idUS Licencia C ea i e Commons CC BY-NC-ND Highligh s Nume ical p edic ions o in alamina and in e lamina damage in hin composi e shells subjec ed o impac loads L.M. Fe ei a, C.A.C.P. Coelho, P.N.B. Reis •In es iga ion o he impac dynamics on composi e shells using he explici ini e elemen me hod. •Nume ical p edic ions o in alamina damage using a con inuum damage mechanics model. •Nume ical p edic ions o in e lamina damage using a su ace-based cohe- si e model. •P edic ion o ene gy dissipa ion o ms o di↵e en hicknesses. Nume ical p edic ions o in alamina and in e lamina damage in hin composi e shells subjec ed o impac loads L.M. Fe ei aa,b,⇤ , C.A.C.P. Coelhoc, P.N.B. Reisd aG upo de Elas icidad y Resis encia de Ma e iales. Escuela T´ecnica Supe io de Ingenie ´ıa. Uni e sidad de Se illa. Camino Descub imien os, S/N 41092 Se illa. Espa˜na bEscuela Poli ´ecnica Supe io . Uni e sidad de Se illa. C/ Vi gen de ´ A ica, 7, Se illa, 41011. Espa˜na cUnidade Depa amen al de Engenha ias. Escola Supe io de Tecnologia de Ab an es. Ins i u o Poli ´ecnico de Toma . Rua 17 de Agos o de 1808 S/N 2200-370 Ab an es. Po ugal dUni e si y o Coimb a, CEMMPRE, ARISE, Depa men o Mechanical Enginee ing, 3030-194 Coimb a, Po ugal Abs ac This pape in es iga es he impac dynamics o hin semicylind ical wo en composi e lamina e shells, wi h a pa icula ocus on unde s anding he in lu- ence o hickness. U ilising he ini e elemen (FE) me hod, he s udy e al- ua es bo h in alamina and in e lamina damage associa ed wi h he impac esponse. The indings show ha he implemen a ion o he explici FE me hod, along wi h a con inuum damage mechanics model, o he in alamina damage, and a su ace-based cohesi e model, o he in e lamina damage, may be used o co ec ly p edic he load his o ies, as well as he maximum impac o ce, maximum displacemen , con ac ime and impac bending s i↵ness (IBS). The nume ical p edic ions ep oduce well he linea esponse o he maximum im- pac o ce and maximum displacemen o he hickness a ia ion, as well as he 2nd o de polynomial cu e o he IBS, wi h e o s anging om 2.7% o 15.9%. Mo eo e , he damage a eas and he e↵ec o hickness on he damage se e i y we e accu a ely eplica ed. These esul s’ alida ion enables he p edic ion o he ene gy his o ies and he ensuing ene gy dissipa ion o ms. Acco ding o he indings, he in alamina damage is a ound 5 imes mo e signi ican han he o he ene gy dissipa ion o ms. The accu acy o he simula ion c ea es he possibili y o mo e impac in es iga ions using a simila nume ical app oach, educing he expendi u es o expe imen al es ing. Keywo ds: Fini e elemen me hod (FEM), Con inuum damage mechanics (CDM), Cohesi e beha iou , Low- eloci y impac , Wo en- ab ic composi es, Composi e shells P ep in submi ed o Thin-Walled S uc u es Feb ua y 1, 2024 1. In oduc ion Composi e ma e ials ha e become inc easingly popula due o hei unique combina ion o high s eng h, low weigh , and excellen a igue esis ance. How- e e , hey a e suscep ible o damage om low- eloci y impac s ha can occu du ing handling, anspo a ion, main enance, and se ice. These impac s can5 cause localised damage o he s uc u e, which can esul in educed s eng h, s i↵ness, and du abili y o he composi e ma e ial [1–5]. The e o e, unde s and- ing he damage mechanisms and beha iou o composi e ma e ials unde low- eloci y impac s is o u mos impo ance o ensu e he eliabili y and sa e y o composi e s uc u es. In his con ex , i is no su p ising ha li e a u e p esen s10 se e al s a egies o inc ease impac s eng h, such as he use o nanopa icles [6], mul iaxial mesh ab ics [7], hyb id lamina es [8], sandwich composi es [9, 10] o simply changing he s acking sequence o he lamina es [11]. Since he ea ly 1990s, impac analysis on composi e s uc u es has been a subjec o s udy. The ea e , se e al nume ical esea ch s udies ha e been done15 using di↵e en abs ac ion scales and applied me hods. The ini e elemen (FE) me hod has been used ex ensi ely o de elop models o unidi ec ional composi e pla es and e alua e a ious pa ame e s such as ma e ial cha ac e is ics, impac ene gy, and geome y. Ye , he e a e ela i ely ew s udies ha analyse he impac dynamics on cylind ical shells, pa icula ly when i comes o composi es20 made o wo en ab ics. The mos ele an s udies ound in li e a u e ega ding low- eloci y impac on cylind ical shells, a e dedica ed o analyse he e↵ec o cu a u e o he shell on he impac o ce, displacemen (de lec ion) and con- ac ime [12–15]. The indings o hese s udies a e consis en and e eal ha he impac o ce inc eases wi h he inc ease in cu a u e, while de lec ion and25 con ac ime dec ease. In es iga ions ha e also been conduc ed o de e mine how hickness a↵ec s he impac esponse o composi e lamina e pla es and shells [16–21]. These s udies ha e shown ha inc easing he hickness o he lamina es leads o no able e↵ec s on se e al impac - ela ed pa ame e s. I was ound ha inc easing he hickness o he composi e lamina es esul s in in-30 c eased s i↵ness. This highe s i↵ness impa s he lamina es wi h he abili y o wi hs and highe impac loads. As a esul , he lamina es exhibi smalle de lec ions and educed con ac imes du ing impac e en s. Fu he mo e, he damage onse and damage e olu ion we e s udied in [22], and i was ound ha o unidi ec ional composi e pla es and shells, damage p og esses di↵e en ly.35 Al hough he nume ical app oach u ilizing FE models allows he simula ion o complica ed s uc u es unde os ensibly complex ex e nal loads and bounda y condi ions, om he nume ical pe spec i e, simula ing impac is s ill a complex ask. Mo eo e , achie ing a sui able le el o accu acy in a ai amoun o ime con inues o be a challenge [23, 24].40 Composi e ma e ials expe ience se e al di↵e en damage modes unde im- ⇤Co esponding au ho Email add ess: [email p o ec ed] (L.M. Fe ei a) 2 pac loads such as ma ix c acking, delamina ion, ib e ailu e and pe o a ion, which can conside ably lessen he ma e ial’s s eng h and s i↵ness [25]. I is hen c ucial o de elop c edible FE models capable o o ecas ing hese dam- age modes. Focus is he e on ab ic- ein o ced composi e lamina e shells wi h45 a semicylind ical c oss-sec ion. These composi es ha e p ac ical in e es o impac - esis an cons uc ions like wind u bine blades o ai c a s uc u es. The buil -in con inuum damage mechanics model (CDM) o ab ic ein o ced composi es a ailable in ABAQUS [26] and de eloped by Johnson [27], is em- ployed o model he in alamina damage, while he in e lamina damage, know50 as delamina ion, is modelled using he su ace-based cohesi e damage model (S-BCM). The wo-s ep homogeniza ion me hod p oposed by Liu e al. [28] is used o p edic he laminas’ p ope ies om he cons i uen s p ope ies. This s udy ollows he expe imen al and nume ical wo k p e iously de eloped by he au ho s [29–31]. Fi s ly, he e↵ec o hickness on he mul i-impac esponse55 o semicylind ical composi e lamina ed shells wi h 6-, 9-, and 12-laye s was ex- pe imen ally analysed in [29]. Subsequen ly, based on he expe imen al esul s ob ained, a FE model o a single hickness was gene a ed, and in which he physical in alamina and in e lamina p og essi e damage models we e in o- duced [30]. This wo k ocused on e↵ec o he FE mesh disc e iza ion and60 mass-scaling on he load his o y p edic ions and in e alua ing he e iciency and eliabili y o he nume ical model. A e wa ds, he in luence o in e lamina p ope ies on delamina ion p edic ions o a single hickness was s udied in [31]. Finally, he p esen pape ep esen s an expansion o he analysis and alida- ion p ocess o encompass di↵e en hicknesses, while s i ing o comp ehend65 he unde lying damage mechanisms a bo h he in alamina and in e lamina le els. The e o e, o summa ize, he cu en wo k se es as a con inua ion o he p e ious nume ical in es iga ion and complemen s he expe imen al indings. I in oduces no el con ibu ions, including he de elopmen and alida ion o FE70 models capable o in es iga ing he impac dynamics o semicylind ical wo en composi e lamina e shells wi h di↵e en hicknesses. Mo eo e , he s udy o- cuses on p edic ing and e alua ing he in alamina and in e lamina damage modes, as well as iden i ying he ene gy dissipa ion mechanisms ha occu du - ing low- eloci y impac e en s. As a as he au ho s a e awa e, hese opics75 in he domain o hin semicylind ical composi e shells, a e s ill lacking comp e- hensi e unde s anding and esea ch. 2. Damage models Low- eloci y impac s on composi e lamina es can cause ib e ailu e and ma- ix c acking (in alamina damage), as well sepa a ion o he in e ace egions,80 known as delamina ion (in e lamina damage) [32, 33]. To model hese damage mechanisms in semicylind ical wo en composi e lamina e shells, a CDM a he lamina le el o add ess he in alamina damage, and a S-BCM a he lamina’s in e ace o accoun o he in e lamina damage, we e implemen ed. These 3 damage models a e ully desc ibed in [26, 34, 35], hus only he main aspec s o 85 he CDM and S-BCM will be b ie ly desc ibed in he ollowing subsec ions. 2.1. In alamina damage model To e alua e he complex damage e olu ion a he in alamina le el, he buil -in cons i u i e model o ab ic ein o ced composi es a ailable in ABAQUS/Explici [36], de eloped by Johnson [27] and based on Lade eze and Ledan ec wo k90 [37], was employed. This damage model is applied as a buil -in VUMAT use sub ou ine and accessed by naming he use -de ined ma e ial wi h he s ing “ABQ PLY FABRIC” [26]. This VUMAT sub ou ine is compa ible only wi h plane-s ess elemen s and conside s each ab ic ein o ced lamina as a homo- geneous o ho opic elas ic ma e ial ha wi hs ands s i↵ness educ ion due o95 ib e ailu e and/o ma ix c acking and plas ic de o ma ion unde shea load- ing. I uses he maximum s ess ailu e c i e ion o de e mine he damage onse o he ib es, and a damage e olu ion model based on he ac u e ene gies o con ol he s i↵ness educ ion. The Hooke’s law o a deg aded o ho opic ma e ial is exp essed as,100 "=2 6 4 S1 (1d1)S12 0 S21 S2 (1d2)0 00S6 (1d12) 3 7 5(1) whe e Sij a e he componen s o he compliance ma ix o he undamaged o - ho opic ma e ial, is he nominal Cauchy s ess enso , "is he elas ic s ain enso , and d1,d2and d12 a e he damage coe icien s. No ice ha he damage coe icien s d1and d2a e associa ed wi h ib e ac u e along di ec ions 1 and 2, espec i ely, and d12 is associa ed wi h he ma ix mic o-c acking due o shea 105 de o ma ion. As men ioned be o e, he CDM uses he maximum s ess c i e ion o de- e mine he damage onse o he ib es, and o simula e he wo ailu e modes ( ib e ension and ib e comp ession). The e o e, he elas ic domain, a any gi en ime, is calcula ed in e ms o he damage ac i a ion unc ions, F↵, as110 F↵=˜↵ X↵  ↵0wi h↵=1±,2±,12 (2) whe e ˜↵and X↵a e he ensile/comp essi e/shea e↵ec i e s esses and s eng hs, espec i ely, and ↵a e he damage h esholds, which a e ini ially de ined wi h a alue o 1. A e eaching he damage onse , ha is, when ˜↵ X↵= 1, he e olu ion he damage coe icien s, d1and d2, associa ed wi h he ensile and comp essi e loading, a e ob ained using equa ions 3 and 4, while he damage115 coe icien d12 associa ed wi h shea loading, is ob ained by equa ion 5, d1,2=11 1,2 eA1,2( 1,21) (3) A1,2=2g1,2 0Lch G1,2 g1,2 0Lch wi h g1,2 0=X2 1,2 2E1,2 (4) 4 d12 =min [↵12 ln ( 12),d max 12 ] (5) whe e 1,2and 12 co espond o he damage h esholds o he ensile/comp essi e and shea loading, espec i ely, G1,2 o he ac u e ene gies pe uni a ea, g1,2 0 o he elas ic ene gy densi y a he damage onse , and Lch o he cha ac e is ic leng h o he elemen . The shea damage pa ame e ↵12 is ob ained h ough a120 calib a ion p ocedu e de ailed in [26]. A he in alamina le el, he shea damage esponse is d i en by he ma ix’s nonlinea beha io caused by he ma ix mic oc acking, and i in ol es bo h s i↵ness loss and plas ici y. The yield and ha dening unc ions ep esen ed in equa ions 6 and 7, espec i ely, a e used by he VUMAT sub ou ine o de ine125 he plas ici y esponse o he ma ix, Fpl =|˜12|˜0(¯"pl)0 (6) ˜0(¯"pl)=˜y0+C(¯"pl)p(7) whe e ˜12 is he e↵ec i e shea s ess, ˜y0is he ini ial e↵ec i e shea s ess, and ¯"pl is plas ic s ain due shea de o ma ion. The ha dening unc ion’s coe icien and powe e m a e deno ed by Cand he supe sc ip p, espec i ely. To be able o alida e he nume ical models based on he expe imen al e -130 idence p esen ed in [29], he s i↵ness p ope ies o he wo en ab ic composi e laminas we e es ima ed om he cons i uen s’ p ope ies o he es ed speci- mens, using he wo-s ep homogeniza ion me hodology p esen ed by Liu e al. [28]. The ob ained elas ic p ope ies a e consis en wi h hose epo ed in li e - a u e o plain wea e E-glass wo en ab ic composi es [38–40]. This mul iscale135 app oach in ol es i s es ima ing he e↵ec i e p ope ies o he ows om he ib e and ma ix p ope ies and hen p edic ing he lamina p ope ies om he p ope ies o he ows and he ma ix. This me hodology was implemen ed us- ing he so wa e TexGen4SC [41, 42]. Each lamina is composed o a polyes e esin ma ix (AROPOL FS 1963 wi h MEKP-50 ha dene ) ein o ced wi h a140 bi-axial E-glass plain wea e ab ic (EC9 68×2). The lamina’s s i↵ness p op- e ies we e es ima ed om he elas ic cons an s ex ac ed om [43–46]. The emaining p ope ies and coe icien s equi ed o implemen he VUMAT sub- ou ine, such as he s eng h p ope ies, ac u e oughness and shea plas ici y, we e aken om li e a u e [38, 47–51]. The lamina’s in alamina p ope ies145 a e shown in Table 1. No ice ha a good ag eemen be ween he expe imen al esul s and he nume ical p edic ions was a ained in p e ious wo k de eloped by he au ho s, and in which he same p ope ies and coe icien s we e employed [30, 31]. The ans e se shea s i↵ness o he laminas mus be de ined o he VUMAT150 sub ou ine [26] because i canno be calcula ed by ABAQUS/Explici [36] o composi e shell elemen s. Conside ing ha each lamina can be hough o as a homogeneous shell wi h o ho opic elas ic p ope ies, equa ions 8 we e used o calcula e he ans e se shea s i↵ness, 5 Table 1: In alamina p ope ies de ined o each lamina [30]. P ope y Symbol Uni s Value Densi y ⇢kg/m31900 S i↵ness p ope ies E+, 1=E+, 2GPa 21.9 E3GPa 8.6 G12 GPa 3.4 G13 GPa 2.4 ⌫12 - 0.14 S eng h p ope ies X+ 1=X+ 2MPa 250 X 1=X 2MPa 200 X12 MPa 40 F ac u e oughness G1,2 J/m24500 Shea plas ici y dmax 12 -1 ˜y0MPa 25 C- 800 p- 0.552 k s 1=5 6G13 , k s 2=5 6G23 , k s 12 = 0 (8) whe e G13 and G23 a e he ou -o -plane shea moduli o he lamina, is he155 hickness o he lamina, and 5/6 is a shea co ec ion coe icien ha is ob- ained by compa ing he ans e se shea ene gy o ha o an 3D s uc u e in pu e bending, as sugges ed in [36]. Conside ing he ou -o -plane shea mod- uli calcula ed by he homogeniza ion p ocess, he ollowing alues we e used in he de ini ion o he in alamina p ope ies: k s 1=k s 2=3.5⇥105N/m and160 k s 12 = 0. 2.2. In e lamina damage model To accoun o he in e lamina damage, i.e. delamina ion, he bond be ween he laminas o he composi e lamina e was modelled using a S-BCM. This model is p ima ily in ended o negligible small in e ace hicknesses and o↵e s e y165 simila capabili ies o cohesi e elemen s. The cohesi e beha iou is de ined as a su ace in e ac ion p ope y, and iden ically o he cohesi e elemen s i is go e ned by a ac ion-sepa a ion cons i u i e model. Hence, he in e lamina ac u e beha iou (delamina ion) is de ined as a cons i u i e ela ion be ween he ac ion ⌧and he sepa a ion , see Fig. 1.170 The ini ial linea esponse un il he damage onse i eached is con olled by he alue de ined o he no mal knand angen ial ks,k cohesi e s i↵nesses. These pa ame e s in luence he pe o mance o he FE model and o which he e a e di↵e en app oaches a ailable in li e a u e o ob ain i s alue [52–55]. Fo ins ance, Daude ille e al. [52] de e mined he cohesi e s i↵ness as a unc ion175 6 Figu e 1: Bilinea ac ion-sepa a ion esponse o he cohesi e su ace. o he in e ace’s hickness and he elas ic modulus o he esin- ich laye , while Zou e al. [53] sugges ed he use o in e ace s i↵ness alues be ween 105and 107 imes he in e ace s eng h di ided by leng h uni . Ano he app oach was p esen ed by Tu on e al. [55], in which he in e ace s i↵ness is calcula ed as unc ion o he elas ic p ope ies o he lamina e. The cohesi e s i↵ness in his180 s udy is se a 106N/mm3, as sugges ed by Camanho e al. [54]. Also, i is conside ed ha i s alue is he same o all di ec ions, ha is, kn=ks=k , as used in [30, 31, 55–57] wi h sa is ac o y esul s. I is no ewo hy ha conside ing high alues o he cohesi e s i↵ness po en ially leads o con e gence p oblems, on he o he hand, he use o low alues may a↵ec he global s i↵ness and hus185 comp omise he alida ion o he FE model [56]. The ollowing s ess-based quad a ic ailu e c i e ion was employed o p edic he damage ini ia ion, ✓h⌧ni ⌧0 n◆2 +✓⌧s ⌧0 s◆2 +✓⌧ ⌧0 ◆2 = 1 (9) whe e ⌧n,⌧ sand ⌧ ep esen he in e ace no mal and shea con ac s esses, and ⌧0 n,⌧0 sand ⌧0 ep esen he co esponding in e ace s eng hs. The Macaulay190 b acke s hiindica e ha he comp essi e s ess doesn’ con ibu e o damage. The ollowing in e lamina s eng hs we e used in he S-BCM: ⌧0 n= 15 MPa and ⌧0 s=⌧0 = 30 MPa [30]. Once he onse o damage is eached, ha is, when he quad a ic in e ac ion unc ion o he s ess a ios eaches 1, he cohe- 7 Figu e 7: E↵ec o hickness on he nume ical and expe imen al [29] maximum displacemen esul s. 4.2. De o ma ion his o ies The de o ma ion his o ies o he 6-, 9- and 12-laye composi e lamina es a di↵e en s ep imes a e shown in Fig. 8. The selec ed ime s eps o analysis a e ep esen ed in Fig. 4, deno ed as Ai,B iand Ci, which co espond o he ollowing con ac imes: Ai o hal o he peak o ce ime; Bi o he peak o ce340 ime; Ci o hal o he ime be ween he peak o ce and he o al con ac ime. He e, he subsc ip i=6,9,12, iden i ies he con igu a ion o he lamina e. A no able end can be obse ed whe ein an inc ease in hickness esul s in a co esponding inc ease in he s i↵ness o he composi e lamina e. Among he lamina es s udied, he 6-laye lamina e exhibi s he highes deg ee o de-345 o ma ion, ollowed by he 9-laye and 12-laye lamina es. As an icipa ed, he de o ma ion s eadily in ensi ies un il i eaches he peak o ce, a which poin he impac o ebounds and he specimen commences i s elas ic eco e y. 4.3. Impac bending s i↵ness The s udies de eloped by Liu [64] and Da id-Wes e al. [65] sugges ha 350 he impac bending s i↵ness is an impo an pa ame e o e alua e he damage esis ance o a composi e, in pa icula delamina ions. Acco ding o hese au- ho s, he slope o he ascending b anch o he load-displacemen cu e de ines he IBS, because he pla e is unde bending a he beginning o he impac 14 Figu e 8: De o ma ion his o ies o he 6-, 9- and 12-laye composi e lamina es. 15 Figu e 9: E↵ec o hickness on he nume ical and expe imen al [29] IBS esul s. egime [65]. In his s udy, he IBS is calcula ed om he expe imen al and nu-355 me ical cu es depic ed in Fig. 5, and Table 2 p esen s and compa es he alues ob ained. I should be no ed ha he IBS p edic ions o he 6-laye FE model had he la ges pe cen age o e o . This is mos likely because damage begins o appea a sligh ly di↵e en loads han simula ed. Ac ually, un il eaching he peak o ce, he expe imen s shown a smoo he damage g ow h han he360 simula ions. This di↵e ence in he ini ial beha iou can be a ibu ed o he use o he semi-au oma ic mass scaling echnique in he nume ical models [30]. Ne e heless, all he p edic ed IBS alues a e wi hin he limi s o he expe i- men al e idence. The e olu ion o he IBS wi h hickness is shown in Fig. 9. The igu e ou lines he FE models capabili y o accu a ely ep oduce he 2nd 365 o de polynomial cu e ollowed by he expe imen s, and which a e ep esen ed by he plo ed end lines. 4.4. Damage The nume ical p edic ions o he in alamina damage (ou pu a iables SDV1 o SDV5) and he in e lamina damage (ou pu a iable CSDMG>0.6)370 we e o e lapped o allow a comple e ep esen a ion o he damage se e i y o he di↵e en lamina e hicknesses, see Figs. 10, 11 and 12. No ice ha he ou pu iden i ie CSDMG, ep esen s he scala s i↵ness deg ada ion o cohesi e su aces, and measu es delamina ion a e damage ini ia ion. When i eaches 16 Figu e 10: Nume ically p edic ed ensile and comp essi e damage along he ib e di ec ions and delamina ed a ea o he 6-laye lamina e. he alue o 1, he in e ace is conside ed o be ully delamina ed. Mo eo e , he375 CDM o ab ic ein o ced composi es used in his s udy does no di↵e en ia e be ween ib e and ma ix damage a he in alamina le el, i includes only he ou pu s a iables o ensile/comp essi e damage along he ib e di ec ions and he shea damage. The e o e, i limi s a mo e de ailed iden i ica ion o he damage modes a he in alamina le el.380 The simula ions show ha lamina e’s hickness a↵ec s how se e e he dam- age is. The 6-laye FE model sus ained damage commencing a he poin o impac and ex ending he ull leng h o he shell. The 9-laye FE model p e- dic ed a less se e e damage bu qui e simila o he one ob ained wi h he hinne lamina e. On he o he hand, damage is es ic ed o he impac loca ion o 385 he 12-laye FE model. This esponse can be explained by he ac ha mo e in e aces a e a ailable o dissipa e he impac ene gy as hickness inc eases and consequen ly, he e is less ene gy a ailable o inc ease damage. These esul s a e consis en wi h he expe imen al indings, which showed ha he damaged se e i y inc eases wi h dec easing hickness [29]. Mo eo e , i co ela es wi h390 he la ge displacemen s obse ed in hinne lamina es, see Fig. 5. Mo eo e , i is also possible o app ecia e in Figs. 10 o 12, ha ega dless o he hickness, he damaged incu ed in he bo om laye s o he shell is mo e se e e in compa ison o he op laye s. I is known ha du ing a low- eloci y impac e en , he bo om laye s o he shell, loca ed opposi e o he395 impac side, expe ience ensile s esses esul ing in ma e ial ( ib e and ma ix) elonga ion. Con e sely, he op laye o he shell, which comes in o di ec con ac 17 Figu e 11: Nume ically p edic ed ensile and comp essi e damage along he ib e di ec ions and delamina ed a ea o he 9-laye lamina e. Figu e 12: Nume ically p edic ed ensile and comp essi e damage along he ib e di ec ions and delamina ed a ea o he 12-laye lamina e. 18 Figu e 13: Delamina ion p edic ions along he di↵e en in e aces o he 6-, 9-, and 12-laye composi e lamina es. wi h he impac o , expe iences comp ession o ces. These comp ession o ces induce localized de o ma ion in he impac ed egion which unde goes plas ic de o ma ion and comp ession. Al hough he CDM does no p o ide speci ic400 iden i ica ion o he a ious damage modes, he nume ical p edic ions sugges ha a he in alamina le el, he mos p ominen damage mechanisms a e ib e b eakage and/o ma ix c acking. These damage modes a e closely associa ed wi h he ensile s esses de eloped in he bo om laye s du ing he impac e en . The delamina ion a eas p edic ed o each in e ace o he lamina es a e il-405 lus a ed in Fig. 13. Once again, i is e iden ha delamina ion p ima ily occu s wi hin he impac egion. Howe e , as p e iously obse ed, he delamina ion in he 6- and 9-laye lamina es p opaga es along he leng h o he shell. Rega ding he in e aces, i is no ewo hy ha o he same lamina e hickness, hey gen- e ally exhibi simila delamina ion a eas in e ms o size and se e i y. Howe e ,410 he e is an excep ion obse ed o in e ace 7 o he 12-laye lamina e. This pa icula in e ace is loca ed app oxima ely in he middle o he lamina e’s hickness, be ween laye 7 and laye 8. The p edic ed delamina ion egion o his in e ace is sligh ly la ge and mo e se e e compa ed o he o he in e aces. Ne e heless, he o e all esul s ha e a good co ela ion wi h he expe imen al415 e idence p esen ed in Fig. 14. The p edic ed impac oo p in s, esul ing om he o e lapping o he in- alamina and in e lamina damage modes a e compa ed wi h he ac ual impac oo p in s ob ained expe imen ally, in Fig. 14. No ice ha he damage on he es ed specimens was cap u ed h ough pho og aphy using in ense backligh ,420 19 Figu e 14: Nume ical and expe imen al [29] impac oo p in s o he 6-, 9- and 12-laye composi e lamina es. aking ad an age o he anslucen cha ac e is ic o he lamina es. Despi e he limi a ions on he accu acy o he non-des uc i e es ing echnique employed o assess he damage ex ension, he p ojec ed damage a eas a e gene ally well p edic ed by he FE models. The uni o m FE mesh size used, con ibu ed o he co ec p edic ions o he damaged a eas ha can be seen along he leng h425 o he lamina es. Howe e , i should be no ed ha hey end o be sligh ly o e es ima ed a ound he impac loca ion. The sca e ed poin s ha can be app ecia ed in he simula ions o he 6- and 9-laye lamina es ou side he con- cen a ed damaged a eas, co espond o isola ed nodes which ha e expe ienced delamina ion.430 4.5. Ene gy his o ies In he loading s age o a low- eloci y impac es , a sizeable po ion o he kine ic ene gy ha is ans e ed om he impac o o he lamina e is con e ed in o elas ic ene gy. The emaining ene gy is dissipa ed owing o ic ion and o he di↵e en ailu e modes ha occu a he in alamina and in e lamina le -435 els. The elas ic ene gy ha he specimen s o es is eleased du ing he unloading s age, causing he impac o o ebound. As he impac o loses con ac wi h he specimen, he ene gy s abilizes [66, 67]. Since in he expe imen al se up he im- pac o ’s mass and he d op heigh emained consis en ac oss di↵e en hickness a ia ions, he peak alues obse ed on he ene gy- ime cu es emained iden i-440 cal. This beha iou can be app ecia ed in he ene gy his o ies o he 6-, 9- and 12-laye lamina es shown in Fig. 15. O e all, a good nume ical-expe imen al co ela ion can be app ecia ed. No ice ha he nume ical p edic ed impac en- e gy cu es o he 6- and 9-laye lamina es p esen a ugged beha iou du ing 20 Figu e 15: E↵ec o hickness on he nume ical and expe imen al [29] ene gy- ime esul s. he unloading s age, which is due o he ib a ions o he FE model. On he445 o he hand, gi en i s highe s i↵ness, he 12-laye lamina e p esen s a smoo he beha iou . The alida ion o simula ions o he ene gy and load his o ies, along wi h he well p edic ed damage a eas, opens he possibili y o iden i ying he amoun o ene gy ha is dissipa ed h ough in alamina damage, delamina ion and ic-450 ion. The expe imen ally measu ed impac ene gy con e ed om he impac o , and he nume ical p edic ions o he impac ene gy and he subsequen dissi- pa ed ene gy o ms ob ained wi h 6-, 9- and 12-laye s FE models, a e shown in Figs. 16, 17 and 18, espec i ely. Rega dless o he hickness unde conside a ion, he in alamina damage455 ou weighs he o he ene gy dissipa ion o ms by abou 5 imes, con i ming ha i is he p ima y damage mode. The ene gy dissipa ion due o delamina ion and ic ion is negligible, howe e , a sligh inc ease as hickness inc eases can be obse ed. The la ge numbe o in e aces may explain his beha iou . Mo e- o e , he high in e lamina ac u e oughness and low in-plane s eng h o he460 wo en ab ic composi es may jus i y he p opensi y o in alamina damage p opaga ion a he han delamina ion. The o al ans e ed ene gy cu e’s peak, which co esponds o he ins ance o maximum displacemen , is co ec ly p edic ed, and he ene gy balance is accu a ely ep oduced. I is no ewo hy o men ion ha he o al ene gy (ou pu 465 ETOTAL), emains s able, which indica es a co ec de ini ion o he s ep ime 21 Figu e 16: Nume ical and expe imen al [29] ene gy his o y o he 6-laye lamina e. Figu e 17: Nume ical and expe imen al [29] ene gy his o y o he 9-laye lamina e. 22 Figu e 18: Nume ical and expe imen al [29] ene gy his o y o he 12-laye lamina e. inc emen s. Also, he ex e nal ene gy (ALLAE ou pu ), is a small ac ion o he in e nal ene gy (ALLIE ou pu ), meaning he hou glass con ol me hod is adequa e. 5. Conclusions470 The in alamina and in e lamina damage and he impac esponse o hin semicylind ical wo en composi e lamina e shells unde low- eloci y impac loads was simula ed using he ini e elemen me hod, wi h pa icula ocus on e al- ua ing he e↵ec o hickness. The nume ical p edic ions we e compa ed wi h he indings o he p e ious expe imen al wo k conduc ed by he au ho s.475 The esul s ob ained in his s udy, demons a e ha he low- eloci y impac esponse o hin semicylind ical wo en composi e lamina e shells can be eli- ably simula ed using he explici FE me hod oge he wi h a CDM, o accoun o in alamina damage, and a S-BCM, o accoun o in e lamina damage. The nume ical models we e able o sa is ac o y p edic he load his o ies, as480 well as he maximum impac o ce, maximum displacemen , con ac ime, and IBS. Fo example, he simula ions we e able o ep oduce he expe imen al lin- ea esponse o he maximum impac o ce and maximum displacemen o he hickness a ia ion, as well as he 2nd o de polynomial cu e o he IBS ollowed by he expe imen s.485 23 plain-wo en ab ics wi h an epoxy ma ix: Mac o-homogeneous and Meso-715 he e ogeneous app oaches, Composi es Pa B: Enginee ing 88 (2016) 114– 130. doi:10.1016/j.composi esb.2015.10.039. [64] D. Liu, Impac -Induced Delamina ion—A View o Bending S i↵ness Mis- ma ching, Jou nal o Composi e Ma e ials 22 (7) (1988) 674–692. doi: 10.1177/002199838802200706.720 [65] O. Da id-Wes , D. Nash, W. Banks, An expe imen al s udy o damage accumula ion in balanced CFRP lamina es due o epea ed impac , Com- posi e s uc u es 83 (3) (2008) 247–258. [66] T. G´omez-del Rıo, R. Zae a, E. Ba be o, C. Na a o, Damage in CFRPs due o low eloci y impac a low empe a u e, Composi es Pa B: Engi-725 nee ing 36 (1). doi:10.1016/j.composi esb.2004.04.003. [67] A. Ama o, P. Reis, M. de Mou a, M. Ne o, In luence o open holes on composi es delamina ion induced by low eloci y impac loads, Composi e S uc u es 97 (2013) 239–244. doi:10.1016/j.comps uc .2012.09.041. 30