ID-1193 STUDY ON IMPACT BEHAVIOR OF COMPOSITES USING THE FINITE ELEMENT METHOD INTRODUCTION

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1 ID-1193 STUDY ON IMPACT BEHAVIOR OF COMPOSITES USING THE FINITE ELEMENT METHOD Volne Ta and Jonas de Carvalho Deparmen of Mechancal Engneerng, S. Carlos Engneerng School, Unversy of S. Paulo, Brazl SUMMARY: Durng he las wo decades, research on he developmen of srucural componens wh hgh crashworhness has been carred ou by he auomoble ndusres, aeronaucs, naval, rans and elevaors. The use of compose maerals n hese componens has grown up hgher and hgher and many mehodologes have been creaed o predc he absorpon energy capacy of composes srucures loaded wh mpac forces usng he Fne Elemen Mehod (FEM). Thus, becomes necessary o model he non-lnear problems nvolved, such as he conac beween bodes ha collde, he plasc deformaons of maeral and large dsplacemens on he srucure. In order o address all hese problems, hs work proposes a mehodology o evaluae crashworhness n compose srucures, and gves a frs conrbuon on he modelng of he non-lnear conac problem. A case sudy where a compose plae s mpaced by one seel sphere s suded and he resuls are descrbed and compared wh hose from he leraure. KEYWORDS: composes, mpac, fne elemen mehod INTRODUCTION Among all he numercal mehods avalable, he Fne Elemen Mehod (FEM) has been ncreasngly used o predc he absorpon energy capacy of composes srucures loaded wh mpac forces (Kndervaer and Georg) [1] (Haug and De Rouvray) [2]. More recenly, some works have carred ou numercal analyses and proposed mehodologes o predc compose srucure behavor under mpac loads. Pérez Galán, Clmen and Le Page [3] performed numercal smulaons for meallc and compose fuselage srucures usng a commercal explc fne elemen code (PAM-CRASH). These numercal smulaons were valdaed by a full-scale drop es. Vcene, Bélran, and Marínez [4] made smulaons o reproduce accuraely he non-lnear dynamc response and complex collapse mechansms of compose frames usng a commercal explc fne elemen code (ABAQUS). Thus, several modelng sraeges were esed, evenually leadng o he developmen of equvalen soropc maeral models for represenng he mechancal behavor under he condons of neres. The sraegy adoped by auhors was o capure macroscopcally he falure of he maeral nsead of represenng compose dvded n ples. Therefore, was necessary o develop an equvalen maeral characerzed by a few parameers. Afer several aemps, was decded o defne an elasc-plasc consuve model wh a falure creron governed by he maxmum equvalen plasc sran of he maeral. In such approxmaon, he nvolved parameers of he models had o be calbraed. Such calbraon was performed dfferenly, dependng on he expeced mporance of he par. Kndervaer e al [5] realzed numercal crash and hgh velocy mpac smulaon of meallc and compose arcraf sub-componens usng a commercal explc fne elemen code (PAM-CRASH). The major asks were focused on maeral sudes, falure mechansms and crera, generaon of new compose fabrc models, new desgn conceps, numercal smulaons and correlaon wh expermenal daa. Thus, a mehodology was developed for smulang he response of compose arcraf srucures o hgh velocy mpacs (HVI), such as brd srke or foregn objec damage on wng leadng edges, engne fan blades ec.. Procedures o measure he mechancal properes of compose maerals under large sran and hgh sran rae loadng were developed. New 1

2 maerals consuve laws and falure models for composes under HVI loadng were developed and mplemened no explc dynamc codes. Ths work proposes a mehodology o predc absorpon energy capacy of composes componens loaded wh mpac forces usng numercal smulaons and expermenal ess. In a prelmnary mplemenaon, he numercal smulaons use a commercal explc fne elemen code (ANSYS/LS-DYNA) and he expermenal ess are formed by quas-sac ess as well as dynamc ess (Charpy mpac es and drop-es). Quas-sac ess are used o esmae maeral properes of lamnae n ensle, compresson and flexure. The Charpy mpac es s used o calbrae he maeral model mplemened no fne elemen code consderng he nfluence of sran rae. Laer on, he drop-es s used o valdae he model of componen bul n fne elemen. However, he conac problem beween bodes mus be evaluaed before predcng he maeral behavor. Thus, he focus of hs work s o nvesgae he capacy of conac algorhm from ANSYS/LS-DYNA n modelng mpac on compose srucures. IMPACT PROBLEM Consderng N bodes n conac n me. S C s he oal area of conac for each body L, L = 1,..., N. The prncple of vrual works for N bodes n me gves (Bahe) [6]: C C τ δu f d S (1) S C N N N jδ ej d V = { R } + L = 1 V L = 1 L= 1 C where: f corresponds o conac forces componens by un of area n me and S C corresponds o he surface where hese forces ac. The effec of he conac forces s ncluded as a conrbuon o he enson forces appled. τ j are he caresan componens of he Cauchy s sress ensor and he sran ensor s denoed by δ ej. Assume ha δ u are he vrual dsplacemens appled o he curren me. The forces acng on he body are gven by Equaon 2: B S S R f δud V + f δu d S ρ Hδu & η Hδ& u (2) = V S f where: f are body forces by un of volume; f are surface forces by un of area and B S S f corresponds o he surface where he enson forces are appled. H corresponds o he shape funcon of he fne elemen used o mesh he body; ρ s he mass relaed propery and η s he dampng relaed propery. The erms ρ Hδu & and η Hδu & are more relevan when mpac loads are presen. I should be noed ha he lef sde of equaon (1), whch represens he nernal forces on he loaded body, are drecly relaed o he maeral sran. Ths maeral sran s drecly dependen on he plascy and falure crera adoped, whch for compose maerals are far more complex. In general, he mpac problem can be dvded n wo mporan problems. The frs problem s nvolved by conac beween a body called conacor (slave surface) and anoher body called arge (maser surface). The ANSYS/LS-DYNA program uses Penaly Mehod o solve conac problem [8]. Thus, each slave node s checked for peneraon hrough he maser surface. If he slave node does no penerae nohng s done. If does penerae an nerface 2

3 force s appled beween he slave node and s conac pon. The magnude of hs force s proporonal o he amoun of peneraon. The second problem nvolved s characerzed by he non-lnear maeral behavor durng he analyss. The leraure descrbes many dfferen maeral models, bu he engneer should be careful o choose he more approprae o hs applcaon. Fnally, here are several numercal sraeges o solve mpac problems. Some are explc (Cenral Dfferences Mehod) and ohers are mplc (Houbol, Wlson and Newmark Mehods). Each one has s advanages and dffcules (Bahe)[6](Owen and Hnon)[7]. In hs work, was used explc negraon (Cenral Dfferences Mehod) mplemened n he commercal package ANSYS /LS-DYNA [8]. PROPOSED METHODOLOGY The proposed mehodology aemps o evaluae he mpac behavor of componens made from compose maerals. Ths mehodology s bascally a numerc -expermenal procedure, where fne elemen models are calbraed by expermenal ess. Fg. 1 Proposed Mehodology Quas-sac expermens are used o esmae maeral properes of undreconal lamnae n ensle, compresson and hree-pons flexure ess. Laer on, a fne elemen model of hreepon flexure s creaed and maeral properes are se usng daa from ensle and compresson ess. Then he smulaon resuls are compared o he flexure ess. A new model s bul o smulae Charpy mpac es, consderng he nfluence of sran rae. Ths model s calbraed by resuls from nsrumened Charpy mpac es. Fnally, he fne elemen model of he componen s bul usng he maeral model prevously calbraed. A drop-es s used o valdae hs model. However, n order o apply hs mehodology becomes necessary o evaluae he conac problem and maeral non-lneares wh accuracy. A prelmnary smulaon of he conac problem s done by usng a commercal fne elemen package and he resuls are compared o hose from leraure. 3

4 CASE STUDY The conac algorhm (Cenral Dfferences Mehod), mplemened n he commercal package ANSYS /LS-DYNA [8], s esed usng he problem of a lamnaed plae mpaced by one seel sphere. The resuls obaned are compared wh hose from he leraure (Sun and Chen)[9] (Chrsoforou Swanson)[10] (Yg and Chrsoforou)[11]. The case sudy s based on a seel sphere wh dameer equal o 12.7 mm and mass equal o 8.40 g whch mpacs a compose square plae a 3.00ms -1. The plae has an edge equal o 200mm and s smply-suppored. The sackng sequence s symmerc [0/90/0/90/0] s wh he followng elasc properes: E 11 = 141.2GPa; E 22 = 9.72GPa; G 12 = 5.53GPa; G 23 = 3.74GPa; ν 12 = 0.30; ρ = 1536 Kgm -3. There were used 2048 she ll elemens wh Hughes-Lu formulaon [8] o model he plae and 1024 sold elemens o model sphere (Fg.2), yeldng o a full model wh 3148 nodes. I was adoped elasc behavor of he compose plae wh orhoropc maeral properes and rgd behavor of he seel sphere. The analyss was performed consderng 300 µs as oal mpac me and was dvded n 150 seps of 2 µs each. Compose Plae Fg. 2 Fne elemen models Seel Sphere I was consdered non-lnear conac where he plae was aken as conacor (slave surface) and sphere he arge (maser surface). Fg. 3 Conac Model Fgure 4 shows resuls obaned from smulaons where only he non-lneary of conac s consdered, usng he explc approach. As comparson, some oher resuls from leraure are ncluded [9,10]. The comparson ndcaes ha he presen resul gves a reasonable mach wh he fne elemen calculaon of Sun and Chen [9], and also wh he resuls gven by Wu [15], who also used he fne elemen mehod. However, he presen resuls do no gve a reasonable mach wh he analycal calculaon of Chrsoforou and Swanson [11], who used 4

5 Fourer seres expanson combned wh Laplace ransformaon echnques. However, should be consdered ha analyses hey performed were no exacly he same as here smulaed snce dfferen maeral properes were used. The dsplacemen resuls of he plae s shown n Fg.5. 0,25 0,20 Dsplacemen [mm] 0,15 0,10 Wu (1986) Sun and Chen (1985) Chrsoforou and Swanson (1991) Presen work 0,05 0, me [µs] Fg. 4 Deflecon of plae cener Fg. 5 Calculaed dsplacemen response for compose plae Fgures 4 and 6 ndcae ha he mpac response s dynamc,.e., s a combnaon of local and srucural effecs. The zero poron a Fg. 6 ndcaes loss-of-conac of he sphere wh he plae. Sphere loses conac no because bounces back upon mpac as usually hough, bu because he plae moves away faser han he sphere can follow. The sphere bounces back only a he end of he mpac cycle when he sphere regans velocy n he oppose drecon, provded he plae s no fracured or permanenly deformed (Marur and Nar)[13]. 5

6 0,40 0,35 0,30 Wu (1986) Sun and Chen (1985) Chrsoforou and Swanson (1991) Presen work 0,25 Force [KN] 0,20 0,15 0,10 0,05 0, me [µs] Fg. 6 Conac Force The oal energy n he sysem s dvded beween he knec and sran energes of he plae and sphere n a me-varyng manner. The sphere s modeled as rgd body so s sran energy s zero (Fg. 7). Dampng effecs are no consdered, hus he oal sysem energy s consan and equal o he nal knec energy of he sphere. The knec energy of he sphere decreases rapdly as he sphere slows durng conac wh he plae. The oher sde, he sran and knec energy n he plae ncrease rapdly durng he conac and reman consan afer conac has ended (Trowbrdge, Grady and Aello) [12]. 0,05 0,04 Toal energy Sphere sran energy Plae sran energy Sphere knec energy Plae knec energy 0,03 Energy [J] 0,02 0,01 0, me [µs] Fg. 7 Energes Boh sran and knec energes of he plae show close values unl he compressve sress wave generaed by he mpac reaches he far end of he plae. A ensle sress wave s generaed when he compressve pulse reflecs from he sress free boundary (Trowbrdge, Grady and Aello) [12]. For example, he superposon of he ncden and refleced pulses 6

7 momenarly leaves he plae sress-free. As example, Fg. 8 shows ha close o 230 µs he generalzed normal sress n drecon x decreases o zero Sress (N x ) [N.m/m] sress-free empo [µs] Fg. 8 Generalzed sress n plae cener CONCLUSION The conac algorhm (Cenral Dfferences Mehod), mplemened n he commercal package ANSYS /LS-DYNA [8], was used o defne he force-ndenaon relaonshp for mpac problem beween compose plae and seel sphere. The resuls show good agreemen wh hose from leraure. Thus, hs conac algorhm can be used when mplemenng he proposed mehodology. Fuure work wll address he non-lnear maeral effecs such as plascy and damage n quas-sac and dynamc analyses. ACKNOWLEDGEMENTS Ths work s par of a projec o evaluae he absorpon energy capacy of composes srucures loaded wh mpac forces and s suppored by FAPESP (Research Foundaon of S. Paulo Sae Brazl). The auhors would also lke o hank he CAD/CAE Laboraory (Unversy of S. Paulo) for he suppor n he use of he package ANSYS/LS-DYNA. REFERENCE 1. Kndervaer, C.M. and Georg, H., Compose srengh and energy absorpon as an aspec of srucural crash ressence, Proc. of Srucural Crashworhness and Falure, Aprl, 1993, Lverpool, UK. 2. Haug, E. and De Rouvray, A., Crash response of compose srucures, Proc. of Srucural Crashworhness and Falure, Aprl, 1993, Lverpool, UK. 3. Pérez Galán, J.L., Clmen, H. and Le Page, F., Non-lnear response of meallc and compose eronaucal fuselage srucures under crash loads and comparson wh full scale es, Proc. of ECCOMAS, Sepember, 2000, Barcelona, Span. 4. Vcene, J.L.S., Bélran, F. and Marínez, F., Smulaon of mpac on compose fuselage srucures, Proc. of ECCOMAS, Sepember, 2000, Barcelona, Span. 7

8 5. Kndervaer, C.M., Johnson, A.F., Kohlgrüber, D., Lüzenburger, M. and Penecôe, N. Crash and mpac smulaon of arcraf srucures-hybrd and FE based approaches, Proc. of ECCOMAS, Sepember, 2000, Barcelona, Span. 6. Bahe, K-J. Fne Elemen Procedures. Prence-Hall: London, Owen, D.R.J. and Hnon, E. Fne Elemens n Plascy: Theory and Pracce. Pnerdge Press Lmed: Swansea, Ansys/Ls-Dyna Theorecal Manual Ansys, Inc., Sun, C.T. and Chen, J.K. On he mpac of nally sressed composes lamnaes, J. of Compose Maerals, 1985, Vol Chrsoforou, A.P. and Swanson, S.R. Analyss of mpac response n compose plaes, In. J. of Solds Srucures, 1991, Vol. 27, No Yg, A.S. and Chrsoforou, A.P. Impac dynamcs of composes beams, Compose Srucures, 1995, Vol Trowbrdge, D.A., Grady, J.E. and Aello, R.A Low velocy mpac analyss wh NASTRAN, Compuers & Srucures, 1991, Vol. 40, No Marur, P.R. and Nar, P.S. Two degrees of freedom modelng of precracked beams under mpac, Engneerng Fracure Mechancs,1996, Vol. 53, No Chun, L. and Lam, K.Y. Behavor of unform ansoropc beams of recangular secon under ransverse mpac of a mass, Shock and Vbraon, 1997, Vol 4, No Wu, H.T. Impac damage of composes, Ph.D. Dsseraon, Deparmen of Aeronaucs and Asronaucs, Sanford Unversy,