SIMULATION OF STRUCTURAL BEHAVIOUR OF FIBRE METAL LAMINATE JOINTS

Transcription

1 5 TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES SIMULATION OF STRUCTURAL BEHAVIOUR OF FIBRE METAL LAMINATE JOINTS Peer Linde 1, Henk de Boer, Jürgen Pleiner 1 1 Airbus, Kreeslag 10, DE-119 Hamburg ALE, Advaned Lighweigh Engineering, Roerdamseweg 145, NL-68 Delf Fibre Meal Laminaes, Fasener Model, Join, Numerial Modelling Absra In reen years Fibre Meal Laminaes (FML) have been developed as an alernaive o monolihial aluminium for use in airraf sruures. FML onsiss of a buil-up maerial, omprising hin layers of aluminium alernaed by layers of glass fibre reinfored epoxy [1]. The buil-up maerial displays advanageous properies in erms of faigue, orrosion and fire resisane. This paper deals wih he developmen of numerial models for simulaing he damage behaviour of joins in fibre meal laminaes. The fous is plaed on joins fasened by rives, being numerially hallenging, and sill highly relevan in several insanes for maerials suh as FML and CFRP. A deailed model for FML skin based on he finie elemen mehod has been developed and validaed exensively [, 3]. In his model eah layer is disreized by solid elemens and damage mehanisms, suh as marix raking, fibre failure and inerlaminar delaminaion, are reaed separaely. A model for damage behaviour of rives omprising plasiiy and ensile failure has been addiionally developed. In ombinaion wih he model for he skin simulaions of he sruural behaviour of riveed lap joins were arried ou. al ess have been performed o validae he model. In his paper he failure models of he skin maerial and rives are presened, followed by an inroduion o experimenal ess of lap joins. Numerial models of he join ess are reaed and simulaion of he sai behaviour of he joins is inrodued. Thereby boh unloading and reloading behaviour is sudied, and omparison wih he experimenal daa is performed. Finally a summary and onlusions are provided and reommendaions for fuure researh are given. 1. Inroduion o Modelling of Fasener Conneions Numerial modelling of faseners for simulaion of sruural behaviour may be arried ou a differen levels of deail. From he lieraure hree ommon levels of deail may be idenified as follows: Mirosopi fasener models: hese models are ypially buil up by solid elemens ou of whih a onsiderable number are used o model one single fasener. The surrounding maerial will ypially as well be modelled by solid elemens. This kind of fasener model is used for he sudy of he deailed damage behaviour. All physial effes ourring in realiy an be inorporaed in hese models. A seond level is represened by meso models, whih may onsis of e.g. beam elemens wih several degrees of freedom a eah node. Some of he physial effes may be inluded, suh as pre sress, fasener olerane, e. Marosopi models, ommonly offered as faseners by ommerial finie elemen programs, represen he las level. They ypially onsis of a bar elemen e., and do ommonly no display failure rieria oher han simplified ones. The fous of his paper is plaed on mirosopi modelling of faseners. Wih inreasingly omplex skin maerials, suh as hybrid omposies 1

2 Peer Linde, Henk de Boer, Jürgen Pleiner like Fibre Meal Laminaes, and arbon fibre omposies, failure modes may be manifold. This ogeher wih he fa ha faseners oninue o play an imporan role in joining hese new maerials alongside alernaive joining ehnologies, onsiues a reason for developing a fasener model apable of providing deailed informaion of is sai damage behaviour unil final failure. This paper is organized as follows. A firs he model of he fasener iself, based on solid elemens, is presened, followed by desripion of damage and he modelling of he squeezing. The modelling of he surrounding skin is hen briefly summarized followed by numerial examples omprising validaion of he model. Finally a summary and onlusions are presened.. Modelling of Faseners The fasener model reaed here has been developed wihin he framework of a researh program FIMELAS (Fiber Meal Laminae Simulaion) arried ou during 003 hrough 005 in ooperaion beween Airbus, ALE - Advaned Lighweigh Engineering, Delf, and he Tehnial Universiy of Delf, [4]. The purpose of he fasener model is o inlude he behaviour of splied areas involving he fibre meal laminaes and o sudy he omplex Fig. 1: Cross seion of an aluminium rive in fibre meal laminae damage mehanism ha may our in he skin, around he fasener and in he fasener iself. Amongs faseners onsidered are: aluminium rives, lok bols, ianium bols, e. This paper will fous on aluminium rives, whih are squeezed ino heir final posiion by a squeezing ool. A ypial ross seion of suh a fasener is shown in figure 1. The fasener is modelled by solid elemens. The developmen has been based on he finie elemen program ABAQUS, jus like for he developmen of he skin models inrodued laer. Damage is onsidered o our wihin he fasener and is desribed in he following seion. 3. Damage Modelling for Fasener The model allows for fasener damage mainly represened by prinipal sress ensile failure of he aluminium (ension or shear load on he fasener), or plasi damage in ompression. Two models for fasener damage were developed during he ourse of he researh program menioned above. The firs model reas ensile failure by ensile raking, implemened in a user subrouine in ABAQUS, based on he smeared rak onep. This omprises a ensile rak in he maerial perpendiular o he prinipal sress direion. Upon rak opening, he rak may develop in is deph and is widh. Over he inegraion poin ha is raked, he rak opening is working in a smeared manner, hus he designaion he smeared rak model. The mos ommon ype of he smeared rak models is he so-alled fixed smeared rak model, whih indiaes ha he rak angle says as i was a he rak opening. The rak an poenially arry some shear aross i due o eeh aion, and his is numerially represened by a shear reenion faor, usually aken as some peren of he former full shear siffness in he maerial siffness marix. The seond damage model employed is a plasiiy model as provided in ABAQUS.

3 SIMULATION OF STRUCTURAL BEHAVIOUR OF FIBRE METAL LAMINATE JOINTS 4. Simulaion of Squeezing al ess have shown ha he sruural behaviour of a squeezed aluminium rive is highly dependen on is squeezing fore. Is inernal behaviour mus inlude he sress fields aually presen afer he squeezing has been arried ou. Thus wihou simulaing his effe realisially, here exiss no large hope of obaining a useful model. In lieraure, aemps have been made o simulae he squeezing by applying a virual emperaure. However, i is needless o menion ha hese models will no funion properly when aual ondiions inluding differen emperaures mus be simulaed. The high deformabiliy of he model using ABAQUS/Explii proved useful here and i was used simulaing he squeezing sequene of he rive. In he modelling, he unsqueezed rive is a firs modelled wih is size and is geomery as is. The shees o be riveed ogeher are equally modelled wih he iniial rive hole and hikness as is. Cona surfaes are defined on boh he rive and in he hole of he shees. The load sep of he squeezing of he rive ino is final plae using ABAQUS/Explii is shown wih deformed shapes in figure a hrough. By his, a realisi shape of he squeezed rive was obained, and he subsequen sruural behaviour also for he firs ime beame realisi. The pre-sress effe as well as he radial pressure were examined for differen rives applied o differen shees, and were found o be realisi [3]. Reen versions of ABAQUS provide he Cona Fi opion, leing surfaes ener ino lose ona wih eah oher. This opion was used, in ombinaion wih Bol Load o obain desired pre-sress level, as an alernaive o he explii simulaion in obaining he squeezing effe of he fasener. Figure 3 shows a sequene using he ona fi opion. The ona fi model proved o deliver a) undeformed shape of rive b) iniial deformaion ) final deformed shape Figure. Squeezing sequene by explii numerial model realisi soluions wih a low ompuaional effor ompared o he explii ompuaion. A omparison beween he final saes obained from he explii ompuaion and he ona fi 3

4 Peer Linde, Henk de Boer, Jürgen Pleiner a) Underformed ona fi model a) Residual sresses afer explii ompuaion b) lose-up of undeformed ona fi model b) Residual sresses afer ona fi Figure 4. Comparison of residual sresses in rive a final rive sae ) final deformed shape Figure 3. Squeezing sequene by ona fi numerial model a) Radial sresses afer explii ompuaion model is shown in Figure 4, displaying residual sresses. A visible differene is he deformed mesh in he head, however of hardly any signifiane o he resuls here, sine i lies ouside he major sress pahs. The sresses obained a he beginning of he onial par and in he ener of he rive are of omparable magniudes. b) Radial sresses afer ona fi Figure 5. Comparison of radial sresses a final rive sae 4

5 SIMULATION OF STRUCTURAL BEHAVIOUR OF FIBRE METAL LAMINATE JOINTS The radial sresses are shown in figure 5 for boh mehods of simulaing he squeezing, displaying omparable magniudes. 5. Skin Modelling The skin model used ogeher wih he deailed rive model desribed here will be summarized only. For a deailed desripion, see [4]. For laminaed maerials, eah layer is modelled by separae solid elemens. The inerfae beween he elemens is modelled by a user inerfae, a developmen equally performed based on an ABAQUS user subrouine [5]. This allows for inerlaminar delaminaion beween he layers. The maerial in prepreg layers inludes fibre failure and marix raking. For hybrid omposies suh as FML, he meal layers would inlude plasiiy. The failure modes are summarized in figure 6. The delaminaion behaviour is desribed hrough a failure rierion based on relaive displaemens [6]. Failure in his model is a) delaminaion b) fibre failure ) marix failure Figure 6. Failure modes of he skin model relaed o he equivalen relaive displaemen, κ, defined by κ = where u u u f f 1 + u + u 3 u fs u fs u f leading o failure and is he gap opening displaemen u fs denoes he maximum shear displaemen. Failure will our when κ > u f. Noie ha he failure funion is based on relaive displaemens. The siffness of he inerfae is aken equal o he siffness of he marix maerial. The srengh of he inerfae is aken from experimenal resuls. This leads o u f σ = E /,max τ max u fs = G / Here denoes he hikness of he resin rih layer, E, G and maximum sresses relae o he marix maerial. This relaive displaemen is inrodued in damage expressions also involving he fraure energies in mode I (ension) and mode II (shear), as disussed in [4]. The failure rierion for fibre failure is given by f f ( ( 11) = 11) Here 11 and 11 are he failure srains in fibre direion in ension and ompression, respeively. Failure ours when f exeeds is hreshold value 11. This is also inrodued ino a damage expression []. Finally for marix failure he following failure rierion is used ( ) ( ( 1) = f m ) + + s 1 where and are he failure srains perpendiular o he fibre direion in ension and ompression, respeively. The failure srain s for shear is. Failure ours when he f m 1 quaniy exeeds is hreshold value, and f 5

6 Peer Linde, Henk de Boer, Jürgen Pleiner whih is employed in he reduion by damage of he finie elemen maerial modulus marix of he prepreg, onsising of onribuions from boh he fibres and he marix, as disussed in [4]. 6. Validaion of Model The model desribed above was validaed using several ess arried ou wihin he same researh program. They omprised aluminium rives as well as lok bols. The firs example shown here will be a lap join es wih aluminium rives joining wo glare shees. a) model of riveed lap join b) Radial sresses afer ona fi Figure 8. Two rive row lap join The ess of lap joins wih aluminium rives resuled in eiher rive shear or ension failure alernaively rive pull hrough, depending on relaive skin and rive dimensions. These failure modes ould be reprodued by simulaion. Figure 7. Tes seup of wo rive row lap join Figure 7 shows he es seup of one suh lap join es. The orresponding numerial model employing he models for fasener and skin presened above is seen in figure 8. A omparison of he fore-deformaion behaviour is shown in figure 9. The loading omprised iniial loading, unloading and reloading in he same direion repeaedly. Fore [N] Join displaemen [mm] Tes 1 Glare-Glare Tes Glare-Glare Tes 3 Glare-Glare Tes 4 Glare-Glare Tes 5 Glare-Glare Tes 6 Glare-Glare Tes 7 Glare-Glare Abaqus Glare-Glare Figure 9. Load-displaemen diagram of riveed lap join es simulaion 6

7 SIMULATION OF STRUCTURAL BEHAVIOUR OF FIBRE METAL LAMINATE JOINTS Figure 10. Sress onour plos of simulaion of lap join es Figure 1. Deformed shape of lok bol lap join es; omparison beween es and simulaion In figure 10 sress onour plos are shown for he lap join simulaion. A seond example omprises a similar lap join wih lok bols. Figure 11 shows omparison fore and deformaion beween es and simulaion. Figure 1 shows deformed shape of simulaion ompared wih es. The general deformaion paern ould be reprodued well. This also holds rue for he damage ypes ourring during he es, inluding bearing damage omprising plasiiy of he aluminium and delaminaion in he viiniy of he fasener. The pull hrough failure mode ourring in he ess wih he lok bols ould be reprodued in he simulaion [3]. Fore [N] Abaqus 7. Summary, Conlusions and Reommendaions An overview of differen models for he simulaions of he sai srengh behaviour of faseners has been given. The developmen of a deailed fasener model, based on solid finie elemens, was inrodued. The model of surrounding maerials, in pariular fibre meal laminaes was also inrodued. The modelling of damage wihin he fasener as well as in he surrounding maerials was desribed. Fous was plaed on aluminium rive. The squeezing sequene for suh a rive was simulaed numerially and wo mehods for his were presened. Numerial simulaion of lap joins using he above model was hen presened inroduing a physial es arried ou in he same researh program. The numerial resuls allowed for he following onlusions: Join displaemen [mm] Figure 11. Load-displaemen diagram of lok bol lap join es simulaion he mos imporan physial aspes of a rive onneion an be readily aouned for in he model in pariular he squeezing of an aluminium rive an be realisially arried ou 7

8 Peer Linde, Henk de Boer, Jürgen Pleiner by he model using wo mehods boh 8. Referenes giving realisi resuls [1] Vlo, A., Gunnink, J. W., Fibre Meal Laminaes - An inroduion, Kluwer Aademi he sai ess ould be simulaed Publishers, 001. realisially inluding he behaviour displayed a unloading and reloading [] P. Linde, FIMELAS, ouline proposal for Researh & Tehnology proje, inernal repor, Airbus Deushland GmbH, 00. he desribed models were apable of reproduing he differen ype of fasener failure ourring during ess he es ondiions applied here are more severe han real airraf ondiions Reommendaions for furher researh an be made as follows. The deailed models here should be supplemened wih ompuaionally more effiien models, inorporaing he mos imporan haraerisis of fasener behaviour, o be applied in engineering ompuaions. The deailed models presened here should be furher developed and be adaped o furher laminaed maerials. [3] Linde, P., FIMELAS WP 3 Modelling of Joins and Sruural Deails, Tehnial Repor RP041481, Airbus, 005. [4] Linde, P., FIMELAS WP 1 FML Skin Maerial Models: Numerial Models, Tehnial Repor RP041473, Airbus, 005. [5] Wriing User Subrouines wih ABAQUS, Hibbi, Karlsson and Sorensen In., Pawuke, RI, 001. [6] Shipperen, J. H. A., Compuaional Modelling of Failure in Fibre Rinfored Plasi, Disseraion, Delf Universiy of Tehnology, Delf, 001. [7] Linde, P., de Boer, H., Modelling of Iner Rive Bukling of Hybrid Composies, Comp. Sru. 73, pp. 1-8, 006. Aknowledgemens The sudies presened here were par of he R&T proje FIMELAS sponsored by Airbus 003 hrough 005 under a gran in he Advaned Numerial Mehods luser. The auhors are graeful o Koen Vervenne and Aila Nagy of ALE for proofreading he manusrip. 8