Numerical and Experimental Study on Nugget Formation in Resistance Spot Welding for High Strength Steel Sheets in Automobile Bodies

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1 rasactios of JWRI, ol.38 (9), No. rasactios of JWRI, ol.38 (9), No. Numrical ad Exprimtal Study o Nuggt Formatio i Rsistac Spot Wldig for High Strgth Stl Shts i Automobil Bodis MA Nishu* ad MURAKAWA Hidkazu** Abstract Rsistac spot wldig is th most popular joiig procss i automobil body assmbly productio lis. hr hav b may rsarchs cocrd with spot wldig for two pics of shts. I ordr to rduc th cost ad improv th strgth of th lightwight automobil bodis, rsistac spot wldig for multi-pics of shts has to b ivstigatd bfor productio. I this papr, rsistac spot wldig for thr pics of high strgth stl shts is maily tak as a objct ad th uggt formatio procss is firstly ivstigatd by xprimts. h th spot wldig procss is simulatd by FEM program JWRIAN dvlopd by th authors with th couplig of th lctrical fild, thrmal fild ad mchaical fild. h uggt siz ad its formatio procss prdictd by FEM agr vry wll with xprimtal rsults. Basd o th simulatio rsults, wldabl coditios (currt, cycls ad forc) of spot wldig for both two pics ad thr pics of high strgth stl shts ca stimatd with a good accuracy. KEY WORDS: (Spot wldig), (Wldig coditios), (Nuggt Formatio), (Simulatio), (Exprimt) 1. Backgroud Fiit Elmt Mthod (FEM) has b routily applid i automobil idustris for th aalysis of structural strgth ad compot dsig bcaus of th sprad of computrs with high prformac, low pric ad dvlopmt of FEM softwar. It has also b playig a sigificat rol i prdictig th bhavior of th wld crackig, wld distortio ad rsidual strss i a wldig ara 1). o assmbl various compots of automobil bodis, th rsistac spot wldig procss is widly usd bcaus of its low cost ad high productivity. I ordr to dtrmi spot wldig coditios i productio, may xprimts hav to b prformd. Compard with xprimtal rsarchs, oly a fw simulatio xampls for simpl two pics of shts ar rportd -11). his is bcaus th rsistac spot wldig procss is couplig with thr physical filds which ar th lctrical fild, th thrmal fild ad th mchaical fild. I this papr, spot wldig for thr pics of high strgth stl shts usd i lightwight automobil bodis is maily tak as a objct ad th uggt formatio procss wr firstly ivstigatd by xprimts. FEM program JWRIAN 1-4) dvlopd by th authors ad th visualizatio optio is addd rctly. Rcivd o Dcmbr 18, 9 * Gust Associat Profssor ** Profssor h, th simulatios for lctric currt flow, hat gratio ad uggt formatio i th spot wldig procss ar carrid out. By comparig th simulatio rsults with xprimtal os, th accuracy of FEM program JWRIAN is vrifid. Lastly, th wldabl coditios (currt, cycls ad forc) of rsistac spot wldig for thr pics of high strgth stl shts ar stimatd basd o simulatio rsults.. Exprimtal coditios ad rsults Rsistac spot wldig coditios iclud thr paramtrs which ar forc (axial squzig forc), lctric currt ad currt cycls, rspctivly. h wldig coditios for thr pics of high strgth stl shts ar show i abl 1 which idicats that th tsil strgth ad thickss of shts ar 7MPa ad.7mm, 59MPa ad 1.4mm, 59MPa ad 1.8mm, rspctivly. hr lvls of wldig currt (5.kA, 6.kA, 7.kA) ar slctd i xprimts. h tim of currt flow is xprssd by currt cycls which ar widly usd i idustry whthr th dirct currt or altrativ currt is slctd. O cycl is.sc ad dirct currt is usd i this papr. h maximum cycls of wldig currt ar 17 cycls (tim is.34sc). h axial forc applid to lctrods is 5kgf (45N). rasactios of JWRI is publishd by Joiig ad Wldig Rsarch Istitut, Osaka Uivrsity, Ibaraki, Osaka , Japa 19

2 Numrical ad ad Exprimtal Study Study o Nuggt o Nuggt Formatio Formatio i Rsistac i Spot Rsistac Wldig Spot for High Wldig Strgth for Stl High Shts Strgth i Automobil Stl Shts Bodis i Automobil Bodis +Elctrod 7C/t.7 59Y/t1.4 59Y/t1.8 -Elctrod abl 1 Spot wldig coditios 5.kA, 17cycls 5kgf st pics 7C/t.7 59Y/t1.4 59Y/t1.8 6.kA, 17cycls 5kgf Currt 5.kA 6.kA 7.kA Cycls 17(34ms) 17(34ms) 17(34ms) 7.kA, 17cycls 5kgf Forc 5kgf 5kgf 5kgf D=4.99, h=.53 D=6.7, h=.9 D=7.9, h=.95 Fig. 1 Masurd uggt sizs at diffrt wldig currts Cycl=4(8ms) 7.kA,5kgf Not wldd D:Nuggt diamtr h:nuggt dpth Cycl=5(1ms) 7.kA,5kgf Cycl=7(14ms) 7.kA,5kgf Cycl=1(ms) 7.kA,5kgf Cycl=13(6ms) 7.kA,5kgf Cycl=17(34ms) 7.kA,5kgf D=3.9, h=.55 D=5.8, h=3.8 D=6.1, h=3.5 D=6.5, h=3.5 D=7.9, h=.95 Fig. Nuggt sizs masurd at diffrt wldig cycls Fig. 3 Schmatic showig of rsistac spot wldig procss h uggt diamtr D ad dpth h masurd i xprimts with diffrt wldig currts ar show i Fig. 1. o kow th uggt formatio procsss, th uggt sizs for 7.kA wldig currt ar masurd at th cycls 4, 5, 7, 1, 13, 17, rspctivly. As show i Fig., th uggt is ot gratd bfor th 4-th cycl ad uggt sizs icras slightly with icrasig of wldig tim aftr 5-th cycl. 3. horis ad FEM quatios for rsistac spot wldig procss Figur 3 shows a simpl modl of spot wldig. Currt ad forc applid to th lctrods ar lctrical load ad mchaical load, rspctivly. As simply dscribd i th abov sctios, th spot wldig procss coupls lctrical fild, thrmal fild ad mchaical fild durig cotact. 3.1 hory ad FEM quatios of static lctrical fild If th ffct of magtic fild ad its tim drivativs ar gligibly small, th lctrical fild ca b xprssd by lctrical pottial satisfyig th Laplac quatio Eq. (1) which is a charactristic of th static lctrical fild. 1 ( r ) ( ) r r r z z (1) Whr, is th lctrical coductivity of th matrial. h rlatio btw lctrical coductivity ad lctrical rsistivity R is giv by Eq. (). 1/ R () h lctrical pottial ca b dtrmid by solvig Eq. (1) if th lctrical boudary coditios ar cosidrd. I spot wldig, thr ar two typs of boudary coditios which ar zro pottial boudary coditio (BC1) ad currt boudary coditio (BC) dfid by Eq. (3 ) ad Eq. (4), rspctivly. for BC1 (3) i i[ A/( mm s)] for BC (4a) ids I for BC (4b) Whr, i is currt flux at uit ara of surfac ds of BC. h itgral of currt flux i will b th total wldig currt I. If altratig currt is applid i spot wldig, th currt I should b rplacd by I si(ft) whr f is frqucy of altratig currt. If lctrical pottial ad lctrical coductivity ar kow, th currt dsity i i x, y z dirctios ad th Joul hat gratio pr uit volum q ca b calculatd by Eqs. (5) ad (6), rspctivly. ir, iz (5) r z 3 1 q [ J /( mm s)] ( ir iz ) (6) Wh FEM is usd to solv th lctrical pottial { } at FEM ods, th static lctrical FEM quatio Eq. (7) for spot wldig ca b drivd as follows, [ K]{ } { I} (7a) { BC1} for BC1 (7b) Whr, [K] is th global lctric matrix which is assmbld from lmt lctric matrix [K ] usig shap fuctio [ of lmt for lctrical pottial. h compots of quivalt odal currt vctor I giv by Eq. (7) hav ozro valu oly at th spcifid ods (BC) whr wldig currt is applid ( r, z) Ni( r, z) i (7c) [ [ [ [ [ K ] ( ) r dr dz (7d) r r z z

3 rasactios of JWRI, ol.38 (9), No. rasactios of JWRI, ol.38 (9), No. { I } { I} { I } BC i [ ds {,,,, I BC,,,,} (7) 3. hory ad FEM quatios of thrmal fild h thrmal fild ca b dscribd by Eq. (8) with various boudary coditios. 1 c ( r ) ( ) q (8) t r r r z z whr, q is th Joul hat gratio rat pr uit volum ad c,, ar th hat capacity, dsity ad thrmal coductivity of th matrials. hr ar thr typs of thrmal boudaris, tmpratur boudary (BC1), hat flux boudary (BC) ad hat covctio boudary (BC3) dfid by Eq. (9), Eq. (1) ad Eq. (11), rspctivly. BC1 at BC1 (9) q q [ J /( mm A s)] at BC (1) q ( BC3 ) at BC3 (11) whr 1, q BC A,, BC3, ar th giv tmpratur at BC1, hat flux at BC, hat trasfr cofficit for both covctio ad radiatio boudary, tmpratur at BC3 ad tmpratur of th surroudig air, rspctivly. If FEM is usd to dscrib th thrmal coductio ad hat trasfr boudary dfid by Eqs. (8)-(11), trasit tmpratur { } ad its rat { } at all t ods ca b giv by Eq. (1). C K Q (1) t whr, [K], [C] ad {Q} ar th thrmal coductivity matrix, hat capacity matrix ad quivalt odal hat, rspctivly. h lmt valu of [K], [C] ad {Q} ar giv by Eqs. (13a), (13b) ad (13c), rspctivly. [ [ [ [ )r dr dz r r z z (13a) [ [] ds [ K ] ( BC3 [ C ] c[ N ] [ N ] r dr dz (13b) Q q [ d (13c) q [ ds [ ds BC BC3 h q i Eq. (13c) is th itral Joul hat gratio which is giv by Eq. (6). If th tmpratur rat is dfid by Eq. (14) t basd o th Crak-Nicolso mthod, th tmpratur { } at tim t dt ca b calculatd by Eq. (15). { } t dt { } t { } t dt (14) 1 [ C] 1 K t dt Q t dt Q t t (15) [ C] 1 K t t 3.3 hory ad FEM quatios for mchaical fild h mchaical fild is xprssd by displacmt at FEM ods ad ca b obtaid by solvig lastic plastic FEM quatio Eq. (16) which was dscribd i dtail i rfrc 1, 1). [ K]{ u} { F} { R} (16) Whr, [ K],{ u},{ F}, { R} ar th stiffss matrix, vctor of odal displacmt, vctor of quivalt odal forc ad vctor of rsidual odal forc, rspctivly. h lmt valu of [ K],{ F}, { R} is giv by Eqs. (17a), (17b) ad (17c), rspctivly. p [ K ] [ B] [ D ]{ B]r dr dz (17a) p { F } [ B] [ D ]{ } r dr dz (17b) { R } { F} [ B] { } r dr dz (17c) h strss { } ca b computd by Eq. (18) basd o thrmal lastic plastic thory. { } t dt { } t { } (18a) p { } [ D ]({ } { } { }) (18b) whr, [ D ] : Elastic matrix p [ D ]: Elastic-plastic matrix { } : Strss icrmt { } : otal strai icrmt { } : hrmal strai icrmt cosidrig th chag of Youg s modulus ad yild strss with tmpratur p { } : Plastic strai icrmt 3.4 Elctrical-thrmal-mchaical cotact modl h cotact btw a lctrod ad a sht or btw two shts is modld by a itrfac lmt 1) as show i Fig. 4. If th strai of th itrfac lmt i th ormal dirctio of th cotact itrfac is largr tha -.99, th stat of th itrfac is th o-cotact stat. I th iitial stat ad o-cotact stat, th lctrical coductivity, thrmal coductivity ad Youg s modulus E will b zro. his mas that currt flow Elctrod / Sht Itrfac lmt Sht / Elctrod strai.99 Cotact Elctric coductivity : hrmal coductivity : Youg ' s mod ulus : E Fig. 4 Itrfac lmt for cotact 1

4 Numrical ad ad Exprimtal Exprimtal Study Study o Nuggt o Nuggt Formatio Formatio i Rsistac i Spot Rsistac Wldig Spot for High Wldig Strgth for Stl High Shts Strgth i Automobil Stl Shts Bodis i Automobil Bodis through th itrfac lmt ad hat gratio will b zro at th itrfac lmt.if th strai of th itrfac lmt i th ormal dirctio of th cotact itrfac is qual to or lss tha -.99, th stat of th itrfac is th i-cotact stat. I th cotact stat, th lctrical coductivity, thrmal coductivity ad Youg s modulus E will b a giv valu. his mas that currt flows through th itrfac lmt ad hat is gratd at th itrfac lmt. I th cotact stat, th itrfac lmt has a strog stiffss. 3.5 Simulatio procdur for rsistac spot wldig procss h simulatio procdur for rsistac spot wldig procss is show i Fig. 5. At th first stp, iitial cotact aras btw lctrod ad a sht or btw two shts ar prdictd wh forc is applid to th lctrod usig lastic plastic FEM solvr for mchaical aalysis. h th currt flowig through th cotact aras ca b computd usig lctrical FEM solvr dscribd i sctio 3.1. Wh currt dsity is obtaid ad Joul hat gratio is kow, tmpratur distributio ca b computd by thrmal FEM solvr dscribd i sctio 3.. h dformatio of wldig shts ad lctrods ca b simulatd by thrmal lastic plastic FEM solvr dscribd i sctio 3.3. Lastly, th w cotact stat is prdictd for th xt tim stp as dscribd i sctio 3.4. his simulatio flow is rpatd for vry tim stp. 4. FEM simulatio coditios Spot wldig is assumd to b a symmtric problm i this papr. Figur 6 shows th gomtry ad th msh divisio. h miimum msh siz is about.mm. SAR Iitial Cotact h currt flows from th uppr lctrod ad zro pottial is applid to th boudary of th lowr lctrod show i Fig. 6(a). h lctrical rsistivity R of stl shts 7C ad 59Y is show i Fig. 7. hrmal coductivity, hat capacity c ad hat trasfr cofficit for hat coductio aalysis ar show i Fig. 8. h mchaical proprtis Youg s modulus E, Yild strss Y, Poisso s ratio, liar plastic hardig cofficit H ad thrmal xpasio cofficit of stl shts usd i thrmal lastic plastic aalysis ar show i Fig. 9. h chag of matrial proprtis with tmpratur is cosidrd i th thr fild coupld simulatio. Currt boudary Elctrod Shts I Forc Pottial Boudary Nuggt t1 t t3 (a) Full modl (b) Dtail msh Fig. 6 FEM modl for spot wldig procss Elctrical rsistivity(ωmm) E 59Y 7C/t.7 59Y/t1.4 59Y/t1.8 Elctrical Fild hrmal Fild Mchaical Fild Nw Cotact Currt dsity Joul hat mpratur Displacmt Strai-Strss mpratur ( ) Fig. 7 Elctrical rsistivity ad tmpratur dpdc hrmal coductivity(j/mm s) c ( g / mm ) ( J / mm s) Hat capacity(j/g ) END Fig. 5 Simulatio flow for spot wldig procss mpratur( ) Fig. 8 hrmal proprtis ad tmpratur dpdc

5 rasactios of JWRI, ol.38 (9), No. rasactios of JWRI, ol.38 (9), No. Youg's modulus(kgf/mm) Y E ( 59Y ) (1/ ).3, H' E/ Y ( 7E) mpratur( ) Fig. 9 Mchaical proprtis ad tmpratur dpdc abl Matrial proprtis of lctrods (Cu) ρ(g/mm3) R(Ω ) λ(j/mm* *s).89 1.E c(j/g* ) E(kg/mm) υ α(1/ ) E-5 h dsity ρ, lctrical rsistivity R, thrmal coductivityλ, hat capacity c ad Youg s modulus E, Poisso s ratio υ of lctrod matrial (Cu) usd i lctrical-thrmal-mchaical simulatio ar show i abl.. A costat odal currt (wldig currt I ) is applid to o od at th top positio of th uppr lctrod ad a costat odal forc (axial squzig forc) is applid to th top surfac of th uppr lctrod. h pottial ad displacmt at th lowr lctrod markd by i Fig. 6(a) ar st to zro i th static lctrical fild simulatio ad dformatio simulatio, rspctivly. 5. Rsults computd by FEM h computd currt dsity ad its distributio at th 17-th currt cycl of spot wldig for thr pics of shts ar show by Fig. 1. h currt dsity coctrats at th shap chagig corrs. h uggt shap ad sizs (diamtr D ad dpth h) which ar dfid by mltig tmpratur (153 ) at diffrt wldig currt ar show by Fig. 11. With th icras of wldig currt, uggt sizs icras. Figur 1 shows th uggt formatio procss durig spot wldig. h uggt forms from th 5th cycl wh wldig currt is 7.kA. Diamtr D of uggt icrass with th icras of wldig currt cycls. h umbr of wldig currt cycls has a lss ffct o uggt dpth h. A/mm Yild strss(kgf/mm) 7C/t.7 59Y/t1.4 59Y/t1.8 5.kA, 17cycls 5kgf D=4.9, h=3.1 6.kA, 17cycls 5kgf D=5.8, h=3.6 7.kA, 17cycls 5kgf D=6.4, h=3.75 Fig. 11 Computd Nuggt shap ad sizs at diffrt wldig currt Cycl=4(8ms) 7.kA,5kgf Not wldd D:Nuggt diamtr h:nuggt dpth Cycl=5(1ms) 7.kA,5kgf Cycl=7(14ms) 7.kA,5kgf Cycl=1(ms) 7.kA,5kgf Cycl=13(6ms) 7.kA,5kgf Cycl=17(34ms) 7.kA,5kgf D=4.4, h=3.35 D=4.98, h=3.6 D=5.5, h=3.7 D=5.97, h=3.8 D=6.39, h=3.75 Fig. 1 Computd uggt sizs durig spot wldig procss 6. Compariso btw computd ad masurd rsults Figur 13 shows th chags of uggt sizs with wldig currt cycls computd by FEM (FEM) ad masurd by xprimt (xp) wh th currt is 7.kA ad th forc is 5kgf. Lis i Fig. 13 ar simulatio rsults by FEM ad marks, ar th rsults masurd by xprimts. h uggt is ot gratd bfor th 4th cycl. h uggt forms iitially from th 5 cycl which is calld th uggt formatio cycl i this papr for asy dscriptio. h diamtr of th uggt icrass with wldig cycls aftr th uggt formatio cycl. h dpth of uggt kps almost th sam valu aftr th 5th cycl. h uggt formatio cycl, diamtr ad dpth of uggt computd by FEM agr vry wll with th rsults masurd by xprimts. Figur 14 shows th chags of uggt diamtr with wldig currt cycls wh wldig currt is 7.kA, 6.kA ad 5.kA, rspctivly. h marks,, ar th masurd rsults rspctivly. h uggt formatio cycl for ths thr currt lvls is th 5th cycl, th 7th cycl ad th 1th cycl, rspctivly. h uggt diamtrs prdictd by FEM at ths thr currt lvls hav a good agrmt with thos masurd by xprimts. Usig th simulatio rsults, th possibl wldig zo dfid ca b prdictd accordig to th wldig currt ad currt cycls show i Fig. 15. With th icras of wldig currt, th uggt formatio cycls dcras. Nuggt sizs (mm) D:FEM D:xp D h h:fem h:xp 7kA 5kgf Fig. 1 Computd currt dsity Cycls Fig. 13 Nuggt formatio procss 3

6 Numrical Numrical ad ad Exprimtal Exprimtal Study Study o Nuggt o Nuggt Formatio Formatio i Rsistac i Spot Rsistac Wldig Spot for High Wldig Strgth for Stl High Shts Strgth i Automobil Stl Shts Bodis i Automobil Bodis Nuggt diamtr (mm) Cycls Cycls kA:FEM 6kA:FEM 5kA:FEM 7KA:xp 6kA:xp 5kA:xp D Cycls Fig. 14 Wldig currt vs. uggt formatio 7KA 6KA 5KA wldabl Not wldd Currt (KA) Fig. 15 Wldabl coditios for thr pics of shts KA 5KA Not wldd Currt (KA) Fig. 16 Wldabl coditios for thr pics of shts h possibl wldig coditios of spot wldig for traditioal two pics of shts which prdictd by FEM is also show by Fig. 16. h uggt formatio cycls for two pics of shts ar lss tha th cycls for thr pics of shts. 7. Coclusios 1) h uggt sizs of rsistac spot wldig for thr pics of high strgth stl shts ar masurd by xprimts with diffrt wldig currts ad diffrt wldig currt cycls. ) Nuggt formatio procss is simulatd with a good accuracy for various spot wldig coditios. 3) Miimum wldig currt cycls for uggt formatio ad wldabl coditios ca b accuratly prdictd by FEM simulatio. Rfrc 1) Y.Uda, H.Murakawa ad N.Ma:Computatioal Approach to Wldig Dformatio ad Rsidual Strsss (i Japas), Sapo-pub, Oct. 7, ISBN ) H.Murakawa, H.Kimura ad Y. Uda: Wldability aalysis of spot wldig o Alumium usig FEM, ras of JWRI, ol4 (1995) No.1, Mathmatic modlig of wld phoma 3 (1997), Editd by H. Crjack, p , ISBN X. 3) J. Zhag ad H. Murakawa : FEM Simulatio of th Spot Wldig Procss (Rport-), Effct of Iitial Gap ad Elctrod-typ o Nuggt Formatio ad Expulsio, ras. JWRI. ol.7, No., 1998, p ) H. Murakawa, J. X.Zhag ad H. Miami: FEM Simulatio of th Spot Wldig Procss (Rport-3), Cotrol of WldigCurrt Usig Elctrod Displacmt for Formatio of Larg Eough Nuggt without Expulsio, ras. JWRI. ol.8, No.1, 1999, p ) K.Matsuyama: Simulatio chiqus i Rsistac Spot Wldig, Joural of th Japa Wldig Socity, ol.7 (1) No.5 6) A.Chakalv: Evaluatio for th thrmal stat of th Mtal i Spot wldig with th hlp of th computr, Wldig productio, ol.(1973)no.1 7) U.Dilthy ad P.Ohs: h Frot Li i Modlig of Rsistac Wldig, Joural of th Japa Wldig Socity, ol.76 (7) No. 8) H.A.Nid: h Fiit Elmt Modllig of th Rsistac Spot Wldig Procss, Wldig Rsarch Supplmt, ol.63 (1984) No.4 9) W.Zhag: Rct advacs ad Improvmts i simulatio if rsistac wldig procsss, Eldig i th world, ol.5 (6) 1) J.Kha t al: Numrical Simulatio of rsistac spot wldig procss, Numrical hat trasfr, part A, ol.37 () 11) A.D t al: Numrical modllig of rsistac spot wldig of alumium alloy, ISIJ itratioal, ol.43 (3) No. 1) Y. Uda ad. Yamakawa: Aalysis of hrmal Elastic-Plastic Strss ad Strai durig Wldig by Fiit Elmt Mthod, ras. of Japa Wldig Socity, ol. (1971) No. 4

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