Springback Simulation with Complex Hardening Material Models

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1 7. LS-DYNA Anwendefoum, Bambeg 8 Metallumfomung I Singback Simulation with Comlex Hadening Mateial Models L. Kessle, J. Gelach and M.-S. Aydin ThyssenKu Steel AG, Duisbug, Gemany Summay: The ise in the light weight automotive design necessitates the usage of the high stength steels, which incease the singback tendency in the sheet metal foming. Contay to the conventional steels, the high stength steels showing lage Bauschinge effect equie comlex hadening mateial models to edict the singback accuately. Nowadays lots of FEM mateial models egading isotoic-kinematic hadening exist as well as a vaiety of comlex measuements to detemine the mateial aametes of these models. In this study, Yoshida-Uemoi mateial model [, ] imlemented into LS-DYNA via the use mateial inteface is used to efom channel daw tests with vaious die adii fo some steel gades. In ode to detect the singback accuacy of this use model, the standad LS-DYNA mateial models Mat36 and Mat3 have been evaluated. Diffeent test stategies to identify the mateial aametes by LS-OPT have been investigated to claify that the test used to calibate the mateial model is as imotant as the mateial model. Keywods: Bauschinge effect, isotoic-kinematic hadening, model calibation, channel daw test, singback 8 Coyight by DYNAmoe GmbH C - I -

2 Metallumfomung I 7. LS-DYNA Anwendefoum, Bambeg 8 Intoduction One of the most imotant challenges of the sheet metal foming simulation is the ecise singback estimation of the high stength steels. The Bauschinge effect the main eason fo the singback and athe dominant in case of the high stength steels can be obseved when evesing the diection of staining, fo instance, comession followed by tension, o sheaing (as in a tosion test on a thinwalled tube) followed by sheaing in the oosite diection. Simly, the Bauschinge effect is the eduction of the yield stess uon eloading that follows unloading [3]. Fo the FEM modelling of the Bauschinge effect, the combined isotoic-kinematic hadening concet has been used fo a long time. Although lots of mateial models have been oosed to deal with the Bauschinge effect, the choice of the most oe one is still a conflict fo the use. Some cucial questions that the use can confont while efoming singback simulations may be aanged as below: Is it economical to use the combined hadening mateial models instead of the isotoic ones fo all of the stuctual ats? Ae the combined hadening mateial models always the coect choices fo all of the steel gades? Does the most comlex combined hadening mateial model yield always the moe ecise esults in comaison to the simle combined one? Pootional to the comlexity of the mateial model, the numbe of the mateial aametes inceases. Recently, by means of the useful otimization softwae like LS-OPT, the use can easily detemine the mateial aametes. Bending-evese bending and tension-comession tests ae some otions fo the combined hadening mateial model calibation. At that oint the use should be awae of the fact that diffeent exeiments as well as the same exeiment efomed with vaying conditions can esult in diffeent aamete sets which may affect the singback ediction. In the context of this study, the singback edictability of a conventional micoalloyed steel gade (HSLA) MHZ 34, a dual hase steel DP-K 34/6, a tansfomation induced lasticity steel (TRIP) RA- K 4/7 and a comlex hase steel CP-K 6/8 is investigated via caying out channel daw simulations. As a mateial model, the use imlemented Yoshida-Uemoi mateial model as well as the standad LS-DYNA mateial models Mat3 and Mat36 have been utilized. Mat3 is a elatively simle combined isotoic-kinematic hadening mateial model with esect to the use imlemented Yoshida-Uemoi, wheeas Mat36 eesents a basic isotoic one. A yield and cyclic stess-stain cuve obtained eithe fom the in-lane tension-comession and comession-tension test, o fom the out-of-lane bending and evese bending exeiment ae the basis fo the LS-OPT based mateial model validation. Besides, the continuous and inteuted test stategies ae discussed to distinguish these fom each othe fom the view of the Bauschinge effect [4]. Use Imlemented Yoshida-Uemoi Mateial Model An elasto-lastic combined isotoic-kinematic hadening mateial model oiginally oosed by Yoshida and Uemoi [, ] has been imlemented as a use model fo the shell elements. The time integation of the evolution equations is achieved by using the backwad Eule integation scheme. The global solution fo the model is obtained eithe exlicitly o imlicitly via a consistent mateial tangent fomulation by means of the Newton Rahson method. A Hill48 yield citeion with lane stess and lane isotoy ( 45 9 ) is emloyed fo the yield and the bounday function. φ T TA () C - I - 8 Coyight by DYNAmoe GmbH

3 7. LS-DYNA Anwendefoum, Bambeg 8 8 Coyight by DYNAmoe GmbH A T ε ε ε ε ( ) ( ) ( ) R B F Y f S ef φ φ () In equation (), f and F ae denoting the yield and the bounday functions esectively, whee Y and B ae the mateial aametes while, and R ae the histoy vaiables. ef A T ef ef A S T S S T f D λ ε λ (3) ( ) : 3 φ Y R B a D D a S Y a C ef (4) ( ) X R R k R sat λ (5) P P bd k (6) C, R sat, k and b ae the othe mateial aametes of this imlementation. In the identity (6), denotes the deviatoic comonent of.totally, thee ae six mateial aametes (Y, B, C, R sat, k, b) to be detemined by the otimization. The oiginal Yoshida-Uemoi mateial model ostulated [, ] diffes fom this imlementation via its wok hadening stagnation equations. That is, the use model does not egad the identities mentioned. 3 Testing Stategies and Model Calibation Isotoic hadening mateial models like Mat36 necessitate simle uniaxial tests without equiing any invese identification. Howeve, the develoment of the new comlex hadening mateial models has aised the need fo the sohisticated exeiments to validate these models by some otimization softwae. Recently, the availability of the otimization tools woking aallel to the FEM ogams has extended the ossible model calibation test stategies of the sheet metal fom an in lane tensioncomession o comession-tension test o shea tests to a lage vaiety of exeiments. The in lane tension-comession o comession-tension test stategy can be fulfilled eithe by an inteuted o by a continuous test ocedue. In the continuous test ocedue, with the aid of secial secimen geomety and state of the at testing devices, a diect load evesal without buckling unde comession stesses is achievable. On the othe hand, the inteuted test ocedue allows a load evesal of the seconday secimen manufactued fom an initial e stained one [4]. Metallumfomung I C - I - 3

4 Metallumfomung I 7. LS-DYNA Anwendefoum, Bambeg 8 Bake hadening and ageing ae two imotant mateial oeties inceasing the yield stength of the steel sheet. Both of them deend stongly on the amount of the solute cabon content. The diffusion of cabon to dislocations and the inning of dislocations imaiing a subsequent defomation is the mechanism leading to the bake hadening and the ageing. Whilst the ageing effect usually takes lace at oom temeatue in a eiod of seveal weeks o months, the bake hadening effect aises at elatively high temeatues within a few minutes (e.g. min, 7 C). The ageing henomenon occus befoe foming and ainting duing stoage and tansotation of the mateial [5]. The multihase and the TRIP steels have a tendency to show the ageing effect because of thei high cabon content and comlex micostuctue. Accoding to the evious eseaches, a e defomed dual hase secimen shows aound /3 of the bake hadening effect if it is stoed long enough at oom temeatue. To check the effect of the ageing on the Bauschinge, the inteuted tests of two % e stained secimens have been caied out. The fist secimen was baked at 7 C / min befoe alying the comession foce wheeas the othe one was diectly tested unde comession. In Fig., the left diagam summaizes both of the mentioned inteuted tests as a stess-stain cuve of DP-K 34/6. Besides, the ight diagam deicts the Bauschinge coefficients fo a oof stain of.%. Accoding to Fig., egading the coelation done between the bake hadening and the ageing effect, the Bauschinge coefficient, denoted by, vaies between.5 and.8 deending on the time inteval used fo the seconday secimen eaation and the test set-u. Consequently, as the singback takes lace diectly afte the foming, the coect mateial model identification makes it necessay to use eithe the continuous test ocedue o the inteuted test with the immediate testing of the seconday secimen [4]. Fig. : Bake hadening effect in tension-comession tests [4] In this study, mateial aametes wee detemined eithe by using the continuous (DP-K 34/6, RA-K 4/7, PM-K 6/8) o the inteuted exeiments (MHZ 34) fo the invese identification. The weight factos fo the extaolated tensile cuve and the tension-comession test wee.4 and.6 in case of the imlemented use model. Fo Mat3, the aamete imlying the distibution of the kinematic o isotoic hadening and sigy, efeing to the yield value, wee the only aametes to be identified fom the cyclic test. The otimization was accomlished via LS-OPT unning aallel to LS-DYNA. Additionally, to analyse whethe the in-lane cyclic tension-comession and out-of-lane bending and evese bending tests yield the same aamete set and the same singback, the behaviou of DP-K 34/6 was evaluated by emloying Mat3. The best fits of the mateial models in inteest fo the in-lane cyclic tension-comession and the tensile test ae exhibited by figues (DP-K 34/6), 3 (RA-K 4/7), 4 (CP-K 6/8) and 5 (MHZ 34). Accoding to Fig. and Fig. 3, we can easily conclude that Mat3 is unable to esult in a smooth behaviou as Yoshida-Uemoi does. In othe wods, it is not flexible enough fo the best aoximation. Contay to Fig. and Fig. 3, Fig. 4 shows that Mat3 is almost as good as Yoshida- Uemoi mateial model to meet the exeimental cuve. Hence, deending on the steel gade, simle combined hadening models like Mat3 may also be the coect choice fo the singback ediction. Consideing Fig. 5, the deviation between the extaolated yield cuve and Yoshida-Uemoi tensile otimization inceases afte 5% lastic stain. The yield cuves wee extaolated by TEM method based on the idea to geneate one additional stess oint at a stain level of aoximately two to fou times the unifom elongation fom the tensile test [6]. As the calibation u to 5% lastic stain is satisfactoy enough, the otimization is accetable to neglect the deviation occuing in an inteval C - I Coyight by DYNAmoe GmbH

5 7. LS-DYNA Anwendefoum, Bambeg 8 Metallumfomung I whee the exeimental measuement of the stesses is not ossible. Besides the left diagam of Fig. 5 indicates that the comession at of the cyclic test can be descibed by an isotoic hadening mateial model like Mat36 (m) with a little eo aising fom the at of lastification. Fig. : Mateial model calibation of Yoshida-Uemoi and Mat3 fo DP-K 34/6 Fig. 3: Mateial model calibation of Yoshida-Uemoi and Mat3 fo RA-K 4/7 Fig. 4: Mateial model calibation of Yoshida-Uemoi and Mat3 fo CP-K 6/8 8 Coyight by DYNAmoe GmbH C - I - 5

6 Metallumfomung I 7. LS-DYNA Anwendefoum, Bambeg 8 Fig. 5: Mateial model calibation of Yoshida-Uemoi fo MHZ 34 The diagam below comaes the calibation of Mat3 (out-of-lane) obtained fom the bending and evese bending test [7] with Mat3 (in-lane) validated by means of the cyclic tension-comession test (denoted as Exeiment in Fig. 6) fo DP-K 34/6. The aamete efeing to the atio of kinematic to isotoic hadening is.47 fo Mat3 (in-lane), wheeas it has the value of.68 fo Mat3 (out-of-lane). The lage Bauschinge diffeence of these otimizations makes it essential to eseach the exeiments used fo the identification of the combined isotoic-kinematic hadening models futhe. In the next toic, by keeing this deviation in mind, we can analyze the singback edictions of these two calibations. Fig. 6: Hadening chaacteization of DP-K 34/6 via two diffeent kinds of tests 4 Numeical Alications fo Singback Pediction To investigate the imact of the mateial model and its calibation on the singback, channel daw tests wee efomed. The thickness of the steel gades used was.5 mm excet fo DP-K 34/6 having a thickness of.4 mm. The exeimental set-u is given in Fig. 7. Since the exeimental setu ossesses symmety, only one quate of the whole geomety was modelled fo the FEM simulations. A fully integated shell element (Element tye 6) fomulation with 5 integation oints though the thickness was utilized fo the mm x mm in size blank elements. The steel secific fiction coefficients wee calibated so that the exeimental unch foces wee met. C - I Coyight by DYNAmoe GmbH

7 7. LS-DYNA Anwendefoum, Bambeg 8 Metallumfomung I Fig. 7: Exeimental set-u fo the channel daw test The quantitative inteetation of the singback foced us to intoduce a mean deviation of the simulation geomety fom the exeimental one. As it is exhibited in Fig. 8, the mean deviation of the simulation was comuted via dividing the aea between the exeiment and the simulation by the ofile length. Positive deviations imly lowe singback, whilst negative ones efe to moe singback in comaison to the exeiment. As long as the deviation is below.5 / mm, we assume a good coelation of the exeiment and the simulation [4]. Fig. 8: Evaluation aamete fo deviations comaed with exeimental esults [4] In Fig. 9, the singback ediction eos of the mateial models discussed in the evious toics ae shown fo DP-K 34/6. Mat36 (m) eesenting the isotoic hadening mateial model yields accetable esults as the die adius inceases fom to mm. The quality of the ediction is geneally imoved when Mat3 (in-lane) o Mat3 (out-of-lane) wee emloyed instead of the isotoic hadening model fo the small die adii. Having Fig. 6 in mind, the most astonishing oint to be undelined is the little effect of two diffeent Mat3 model calibations on the singback. Focusing on the diagam, the ediction eos of both Mat3 calibations ae vey close to each othe fo and 3 mm die adii. Regading all the esults togethe, the best ediction was obtained by means of the use imlemented Yoshida-Uemoi mateial model. Howeve, because of the long comutation time of the use imlemented Yoshida-Uemoi model, it would be economical to use the isotoic hadening model fo the lage die adii in case of DP-K 34/6. Similaly, in figues and (RA-K 4/7, CP-K 6/8), Mat36 (m) is the wost alication to foecast the singback fo mm die adius. Paying focus on Fig. 4 and Fig., Mat3 may be a substitution fo Yoshida-Uemoi mateial model when assessing the singback behaviou of CP-K 6/8. In geneal, Yoshida-Uemoi model is the most eliable to evaluate the singback of thee high stength steels in attention. In contast to the evious statement, Yoshida-Uemoi model edicts the singback in the wong diection (cul-out) fo the MHZ 34 ofile having a die adius of mm (Fig. ). As Mat36 (m) satisfies the equied singback accuacy fo the conventional micoalloyed steel MHZ 34, the emloyment of Yoshida-Uemoi model fo this steel gade would be a waste of time and money necessay to cay out the exensive cyclic tests. 8 Coyight by DYNAmoe GmbH C - I - 7

8 Metallumfomung I 7. LS-DYNA Anwendefoum, Bambeg 8 Fig. 9: FEM singback ediction eos fo DP-K 34/6 Fig. : FEM singback ediction eos fo RA-K 4/7 Fig. : FEM singback ediction eos fo CP-K 6/8 C - I Coyight by DYNAmoe GmbH

9 7. LS-DYNA Anwendefoum, Bambeg 8 Metallumfomung I Fig. : FEM singback ediction eos fo MHZ 34 5 Conclusion The singback ediction of the high stength steels equies not only sohisticated FEM mateial models but also state-of-the-at exeiments allowing the best fit of them. Desite the existence of seveal tests to chaacteize the Bauschinge effect, the aamete validation via these ones does not yield one unique identical aamete set. In othe wods, these tests, such as cyclic tensioncomession and bending-evese bending tests could not be obtained fom each othe by FEM. Moeove, to eliminate the aging o the bake hadening effect, the continuous test ocedue o the inteuted test with the immediate testing of the seconday secimen should be efeed when efoming the cyclic tension-comession test. As two diffeent calibations of Mat3 estimate almost the same singback fo the small die adii (DP-K 34/6), we have to think about whethe channel daw exeiments esented hee ae comlex enough to distinguish between the hadening models. Accoding to ou esults, Yoshida-Uemoi model is the most eliable and also the most exensive one to detect the singback of the high stength steels. To save some comutation time, an isotoic model like Mat36 (m) may be emloyed when simulating a die adius / sheet thickness atio of >3.. Additionally, deending on the steel gade, fo examle fo CP-K 6/8, Mat3 can be a substitution fo Yoshida-Uemoi model. Hee we have to emhasize that Mat3 could be calibated via the simle Bauschinge coefficient. Contay to the multihase steels, the singback simulation with the isotoic mateial model Mat36 (m) maintains good esults fo all the die adii of the conventional micoalloyed steel gade investigated. 6 Liteatue [] Yoshida, F., Uemoi, T., A model of lage-stain cyclic lasticity and its alication to singback simulation, Intenational Jounal of Mechanical Sciences 45, 3, [] Yoshida, F., Uemoi, T., A model of lage-stain cyclic lasticity descibing the Bauschinge effect and wokhadening stagnation, Intenational Jounal of Plasticity 8,, [3] Lubline, J., Plasticity theoy, Macmillan Publishing Comany, 99 [4] Kessle, L., Gelach, J., Aydin, M.-S., Does the measuement of moe mateial data necessaily esult in highe foming simulation accuacy?, IDDRG Intenational Confeence, 8 [5] Esche, C., Bandenbug, V., Heckelmann, I., Bake hadening and ageing oeties of hot-di galvanized ULC steel gades, Intenational Symosium on Niobium Micoalloyed Sheet Steel fo Automotive Alication, 6 [6] Kessle, L., Gelach, J., The imact of mateial testing stategies on the detemination and calibation of diffeent FEM mateial models, IDDRG Intenational Confeence, 6, 3- [7] Ino: Biegevesuche und Mateialabgleich, Diektauftag ThyssenKu Steel, 7 8 Coyight by DYNAmoe GmbH C - I - 9

10 Metallumfomung I 7. LS-DYNA Anwendefoum, Bambeg 8 C - I - 8 Coyight by DYNAmoe GmbH

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