Asian Pacific Confnc fo Matials and Mchanics 29 at Yokohama, Japan, Novmb 13-16 ANALYI OF HE WELDING DEFORMAION OF REIANCE PO WELDING FOR HEE MEAL WIH UNEQUAL HICKNE Yuanxun Wang a Png Zhang a Zhigang Hou a, b Ying Wu a, * a chool of Civil Engining and Mchanics, Huazhong Univsity of cinc and chnology,wuhan, 4374, China b chool of Mchanical and Elctonic Engining & Automobil Engining, Yantai Univsity, Yantai, 2645, China Body of ummay: wangyuanxun@mail.hust.du.cn hgwuying@163.com Rsistanc spot wlding (RW) pocss is widly usd in sht mtal joining pocss du to its high spd, suitability fo automation and inclusion in high-poduction assmbly lins with oth fabicating opations. It is a complx pocss in which coupld intactions xist btwn lctical, thmal, mchanical, mtallugical phnomna, and vn sufac bhavios. Duing RW pocss, dfomation, stss and stain will b gnatd and changd in th wldmnt du to th lctod foc and Joul hating, and sidual stss and stain will tain in th wldmnt aft wlding. Numous sachs of th mchanical fatus fo such a complx pocss hav bn pfomd. hs sachs undwnt all kinds of wlding conditions and matials, using both thotical and xpimntal mthods [1-3]. It can b concludd fom ths sachs that failu of spot wld is likly latd to many paamts of th RW pocss,.g. sidual stss, wlding paamts, wlding schdul, thicknss, gap, nuggt siz, and matial poptis. hs paamts also affct th fatigu lif of th wldd joint. Rsults of th lativ sachs [4-6] show that th fatigu stngth is mainly contolld by th sidual stss, gap and stss concntation at th notch of nuggt. Rcntly, numical mthod povids a powful tool in studying ths intactions, spcially th finit lmnt analysis (FEA) mthod, which can dal with nonlina bhavios and complx bounday conditions. It has bcom th most impotant mthod fo th analysis of RW pocss [7-8]. sai t al. [9] dvlopd a al-tim contol mthod in RW and obtaind dict colations btwn nuggt fomation and xpansion displacmnt of lctods. Nid [1] dvlopd th fist FEA modl fo th RW pocss, invstigatd th ffct of th gomty of lctod on wokpic and pdictd th dfomation and stsss. Howv, th dvlopd modl was stictd to lastic dfomation, and could not calculat th contact aas at th lctodwokpic and faying sufac. hfo, many sachs dvlopd mo sophisticatd FEA modls that takn th contact status, phas changing, and coupld fild ffcts into th simulation of RW [11-13]. h itativ mthod was mployd to simulat th intactions btwn coupld lctical, thmal, and stuctual filds [14-15]. In this mthod, th stss fild and contact status w initially obtaind fom th thmo-mchanical analysis, and thn th tmpatu fild was obtaind fom th fully coupld lctical-thmal analysis basd on th contact aa at th lctod-wokpic intfac and faying sufac. h calculatd tmpatu fild was thn passd back to th thmo-stuctual analysis to updat th stss fild and contact status. h itativ mthod can povid th
Asian Pacific Confnc fo Matials and Mchanics 29 at Yokohama, Japan, Novmb 13-16 tmpatu fild, th lctic potntial fild, th stss and stain distibutions of th spot wlding in on calculation, but th simulation of tansint pocsss with such a mthodology would pobably qui lag amount of computing tim. h objctiv of this pap is to dvlop a multi-coupld mthod to analyz th wlding dfomation of th RW pocss, in od to duc th computing tim with th minimum loss of computing accuacy. Basd on th analysis of tmpatu fild, thmo-lastic-plastic finit lmnt analysis was attmptd on th RW pocss to analyz th distibution and chang of th wlding stss, stain and dfomation in this pap. Fo th solution of th wlding dfomation of th RW pocss in this sach an axisymmtic modl was dvlopd and solvd using th FEA mthod basd on ANY cod. h two-dimnsional axisymmtic modl is illustatd schmatically in Fig.1 wh x and y psnt th faying sufac and th axisymmtic axis spctivly. Its cosponding dimnsions a OE=HI=2.5mm, OI=EH=15mm, PA=FG=5mm, PB=11mm, AG=18mm, EF=12.5mm, ED=3mm, OP=32mm, α=3. h modl was mshd using th typs of lmnts, as shown in Fig.2. h solid lmnts w mployd to simulat th thmo-lastic-plastic bhavio of th shts and lctods. h contact pai lmnts w mployd to simulat th contact aas. h w th contact aas in th modl. Contact aa 1 and 2 psntd th lctod- wokpic intfac and contact aa 3 psntd th faying sufac. hy w all assumd to b in contacts with two dfomabl sufacs, and ths sufacs w allowd to undgo small sliding. In od to obtain liabl sults, fin mshs w gnatd na ths contact aas, whil th mshs of oth aas w lativly coas. Coupld lctical-thmal and thmolastic-plastic analysis w pfomd to analyz th tansint thmal and mchanical bhavios of sistanc spot wlding (RW) pocss of th mild stl sht mtals with unqual thicknss. Fo th thmo-lastic-plastic analysis, som hypothss a citd. h mchanical poptis, stss and stain latd with th wlding tmpatu a linaly changd in a small tim incmnt. Elastic stss, plastic stss and tmpatu stss a spaabl. tain stiffning is occud in th plastic fild and obys th Rhology s thoy. h Miss Yild Cition is usd fo th matial yild stngth. h wlding thmolastic-plastic analysis is constuctd by stain-displacmnt lationship o compatibility condition; stss-stain lationship o constitutiv lationship; quilibium condition and bounday conditions. h constitutiv quations of th matial in th tmpatu fild can b wittn as quation (16). h dvloping pocss of th wlding sidual stss and dfomation of th RW can b dynamically simulatd though thmo-lastic-plastic analysis basd on th FEA of th tmpatu fild.7-9 h tmpatu filds and its changing of th sht mtal RW hav bn obtaind and wll discussd though th coupld lctical-thmal analysis in Rf. [7] and Rf. [8]. But th sachs w limitd at th RW with th sam thicknss sht mtal. Fig.4 shows th tmpatu distibution of th RW with unqual thicknss mild stl shts at th tim of th nuggt foming. And Fig. 5 shows th tmpatu changing couss at th cnt of th wld nuggt, th cnt of th upp lctod and th low lctod. Diffnt fom th tmpatu fild distibution of RW with th sam thicknss mild stl sht mtals, th sach shows that th cnt of th wld nuggt of RW with unqual thicknss mild stl shts lans to th thick wokpic; fo mo thmal is poducd and lss bing givn out in th thick wokpic. Bcaus th faying sufac of th two mild stl sht wokpics is futh fom th lctod acting on th thick wokpic and thfo th sistanc is bigg. h tmpatu fild analysis
Asian Pacific Confnc fo Matials and Mchanics 29 at Yokohama, Japan, Novmb 13-16 with th coupld lctical-thmal analysis showd that th cnt of th wld nuggt of th RW with unqual thicknss mild stl shts land to th thick wokpic, fo th asymmty of th stuctu, th tmpatu fild distibution was asymmtic too. Loading th tmpatu fild at th cosponding tim as th nod body load, th stuctu analysis showd that th dfomation of th RW with unqual thicknss mild stl shts was also asymmtic. Fig.6 shows th wlding dfomation of th RW of two mild stl shts with th thicknss 1.mm and 1.5mm in which th dashd is th outlin bfo dfomation. imulating analyss showd that th dgs of th two mild stl shts wapd to th thinn on du to th stuctu asymmty. aking th two mild stl shts as an intgatd stuctu aft wlding, th dg s wapag dfomation could b xpssd with th nomal displacmnt of th dg of th mild stl sht. h wapag dfomation of th two mild stl shts with th thicknss 1.mm and 1.5mm was 5 μm aft RW. h asymmtic dfomation is poducd by th asymmtic sidual plastic stain. Fig.7 shows th distibution of th sidual plastic stain of th mild stl sht with unqual thicknss aft RW. It shows that th distibutions of th sidual plastic stain in th two mild stl shts a diffnt. h locations of th maximum sidual plastic stain in th thick sht and th thinn on a diffnt, and th adius of th distibution of th sidual plastic stain in th thick mild stl sht is lss than that in th thinn on. o study th impact of th sidual plastic stain on th wlding dfomation, add th sidual plastic stains of th nods at th sam thicknss as its gnal sidual plastic stain, it is diffnt at th diffnt thicknss. Fig.8 shows th distibutions of th sidual plastic stain of th two mild stl shts with unqual thicknss. h lina appoximation of th sidual plastic stain shows that th distibution of th sidual plastic stain in th thick mild stl sht is appoximatly unifom along with th thicknss of th sht. And th lina appoximation cuv is an appoximat lvl blin (s Fig.8(a)). But th distibution of th sidual plastic stain in th thinn mild stl sht is linaly changd along with th thicknss of th sht, it is small whn na th faying sufac and bigg on th oth sid (s Fig.8(b)). Dtaild studis showd that th wapag dfomation of th asymmtic sht stuctu was poducd du to th changd sidual plastic stain. 4. Equations, abls and Gaphs h distibution and chang of th stain, spcially th plastic stain, is vy impotant to th analysis of sidual stss and dfomation of th RW pocss. h wlding sidual stss is poducd in wldd joint as a sult of plastic dfomation causd by non-unifom thmal xpansion and contaction in th RW pocss. o th analysis of wlding tmpatu fild is vy impotant and ncssay fo th wlding dfomation analysis, but it is a non-lina tansint hat xchang poblm. h govning quation fo axisymmtic tansint thmal analysis is givn by th Foui Law and th Engy Consvation hoy, ρ c = k x + k y + k z + qv (1) t x x y y z z wh ρ is th dnsity of th matial, c is th spcific hat capacity of th matial, is th tmpatu, t is th tim cous, k x k y k z a th thmal conductivity in th dictions, q v is
Asian Pacific Confnc fo Matials and Mchanics 29 at Yokohama, Japan, Novmb 13-16 th at of intnal hat gnation. Fo isotopic matial, k x =k y =k z =k. h thmal bounday conditions of th wlding tmpatu fild can b dcomposd fom th nonlina isotopic Foui thmal flux dnsity and hat xchang. h thmal flux dnsity shows th intnsity of th wlding thmal souc, and th sufac hat xchang psnts th hat convction and hat adiation with th ambinc. On th bounday sufac, it is kn = qs ( x, y, z, t) (fo thmal flux dnsity bounday ) (2a) n k n n = h ( ) a s (fo hat convction bounday c ) (2b) k n n ( ) = κ (fo hat adiation bounday ) (2c) s in which, n is th outwad nomal to th sufac, k n is th thmal conductivity though th bounday nomal, q s is th thmal flux though th bounday sufac, h is th hat convction cofficint, a is th ambinc tmpatu, κ is hat adiation cofficint, is th adiation objct tmpatu, s is th bounday tmpatu. o solv th nonlina patial diffntial Equ.(1), th functional analysis can b stablishd as, 2 2 2 1 1 2 Π= kx + ky + kz d d 2 h a s s x y z c 2 (3) 4 1 5 ε fσ s s d d d 5 q s s qv 2 wh is th inn tmpatu of th objct, s is th sufac bounday tmpatu. Using th vaiation pincipl, function (3) can b obtaind as, δ Π = (4) that is ( ) ( ) K d h δd c a s s κ δd qδd qδd = s s s s v 2 (5) wh, = (6) x y z K k x = k y k z (7)
Asian Pacific Confnc fo Matials and Mchanics 29 at Yokohama, Japan, Novmb 13-16 K is th thmal conductivity matix. Fo th FEA quation, th tmpatu fild is dispsd into n lmnts, thn, th vaiation Equ.(4) can b xpssd as, Π = n δ δπ = (8) 1 wh, δπ is th vaiation quation fo ach lmnt. Lt th lmnt shap function matix b N, th lmnt inn tmpatu can b xpssd as, = N (9) wh, is th lmnt nod tmpatu matix. h divativ of can b xpssd as, = B (1) wh, B = N x N y N z. Fom Equ.(5), on obtains, n δ B KBd + δ N hnd + δ N κnd c 1 1 1 p d a c 1 1 p = δ N h + δ N κd t n δ d δ s 2 1 1 + N q + N q d v (11) Lt K = BKB, d K = d c N hn, K = κ d c N N, C = d N CN, RB = N qshd, R = d c N h a, R = κ d c N, R = N qsd, 2 K wh, is th lmnt thmal conductivity matix; is th lmnt hat convction matix; K is th lmnt hat adiation matix; C is th lmnt spcific hat capacity matix; RB is th nod thmal flux vcto of th inn thmal souc; Rc is th nod thmal flux vcto of th hat convction; R is th nod thmal flux vcto of th hat adiation; R is th nod thmal flux vcto of th thmal conductivity. Lt C b th gnal spcific hat capacity matix, K b th gnal thmal conductivity matix, P b th gnal thmal flux vcto, th FEA quation of th tansint tmpatu fild can b obtaind as, Kc C + K = P (12) s h govning quation of th lctical analysis is, φ C φ φ C + + C = z z (13)
Asian Pacific Confnc fo Matials and Mchanics 29 at Yokohama, Japan, Novmb 13-16 in which, C is th lctical conductivity, φ is th lctical potntial. h coupld lctical-thmal poblm is solvd by th following matix quation: t [ C ] [] { t } [ K ] [] { } { Q} + = (14) [] [] { v } [] [ K ] { } { I} t t v wh, [ C ] is th thmal spcific hat matix; [ K ] is th thmal conductivity matix; [ K ] is th lctic cofficint matix; { } is th tmpatu vcto; { } is th lctic potntial vcto; {Q} is th hat flow vcto; {I} is th cunt vcto. Fo th stuctual analysis, th stss quilibium quation is givn by, σ (, t) + b(, t) = (15) wh,σis th stss, b is th body foc, is th coodinat vcto. h constuctiv quations of th matials basd on thmo-lastic-plastic thoy a givn by, d σ = [ D]d ε C d (16) { } { } { } C} = [ D ] D { } [ ] α + { σ} 1 { (17) wh, { σ } is th stss vcto; { ε} is th stain vcto; { } α is th cofficint of thmal xpansion; p [D] is th lastic-plastic matix: [D]=[ D ] in th lastic aa,whil [D] = [ D ] -[ D ] in th p plastic aa. [ D ] is th lastic matix and [ D ] th plastic matix. h following bounday conditions a spcifid on th sufac of Γ 1, Γ 2 and Γ 3 (s Fig. 1), Γ 1 (AB): σ y = q, wh q is th unifom pssu which can b dtmind accoding to th lctod foc and th sction aa of th lctod. Γ 2 (FEOJ): U x =, wh U x is th displacmnt of x-diction. Γ 3 (KL): U y =, wh U y is th displacmnt of y-diction. y P Cooling wat F Γ 2 E O J G D A Γ 1 B C α H I Upp lctod hts x Low lctod K Γ 3 L Figu 1. chmatic diagam fo th modl of RW
Asian Pacific Confnc fo Matials and Mchanics 29 at Yokohama, Japan, Novmb 13-16 Contact aa 1 Upp lctod Coas msh Contact aa 3 Contact aa 2 Low lctod hts Fin msh Figu 2. Msh gnation of th dvlopd modl Young's Modulus (GPa) 25 2 15 1 5 mild stl copp lctod 2 4 6 8 mpatu ( ) (a) Young s Modulus Cofficint of thmal xpansion (1-6/ ) 2 15 1 5 mild stl copp lctod 2 4 6 8 1 mpatu ( ) (b) cofficint of thmal xpansion
Asian Pacific Confnc fo Matials and Mchanics 29 at Yokohama, Japan, Novmb 13-16 hmal conductivity (W/m ) 45 4 35 3 25 2 15 1 5 mild stl copp lctod 2 4 6 8 1 12 mpatu ( ) (c) thmal conductivity Rsistivity (1-8Ωm) 14 12 1 8 6 4 2 mild stl copp lctod 2 4 6 8 1 12 mpatu ( ) (d) sistivity Figu 3 mchanical, lctical and thmal poptis of th mild stl and copp lctod Figu 4 mpatu distibutions of th RW pocss
Asian Pacific Confnc fo Matials and Mchanics 29 at Yokohama, Japan, Novmb 13-16 Figu 5 mpatu changing histois of th RW pocss Figu 6 h wlding dfomation of th mild stl sht with unqual thicknss aft RW (amplifid by1 tims) Figu 7 h sidual plastic stain of th mild stl sht with unqual thicknss aft RW (amplifid by1 tims)
Asian Pacific Confnc fo Matials and Mchanics 29 at Yokohama, Japan, Novmb 13-16 (a) th thick mild stl sht (b) th thinn mild stl sht Figu 8 h distibution of sidual plastic stain of th mild stl sht Rfncs [1].H. Lin, J. Pan,. yan and P. Pasad, A gnal failu cition fo spot wlds und combind loading conditions, Int. J. olids tuc., vol. 4,5539 5564, 23 [2] Y.J. Chao, Ultimat stngth and failu mchanism of sistanc spot wld subjctd to
Asian Pacific Confnc fo Matials and Mchanics 29 at Yokohama, Japan, Novmb 13-16 tnsil, sha, o combind tnsil/sha loads, J. Eng. Mat. chnol. ans. AME, vol. 125, 125 132. 23 [3] X. Dng, W. Chn and G. hi, h-dimnsional finit lmnt analysis of th mchanical bhavio of spot wlds, Finit Elm. Anal. Ds., vol. 35,17 39, 2 [4] H. Adib, J. Gilgt and G. Pluvinag, Fatigu lif duation pdiction fo wldd spots by volumtic mthod, Int. J. Fatigu, vol. 26 (1), 81 94, 24 [5] N. Pan and. hppad, pot wlds fatigu lif pdiction with cyclic stain ang, Int. J. Fatigu, vol. 24,519 528, 22 [6] H. Kang, M.E. Baky and Y. L, Evaluation of multiaxial spot wld fatigu paamts fo popotional loading, Int. J. Fatigu, vol. 22, 691 72, 2 [7] Hou, Z.G., Wang, Y.X., Li, C.Z. and Chn, C.Y., A multi-coupld finit lmnt analysis of sistanc spot wlding pocss, Acta Mchanica olida inica, vol. 19 (1),86 94, 26 [8] Hou, Z.G., Kim, I.., Wang, Y.X., Li, C.Z. and Chn, C.Y., Finit lmnt analysis fo th mchanical fatus of sistanc spot wlding pocss, Jounal of Matials Pocssing chnology, vol. 185 (1-3), 16 165,27 [9] C.L. sai, W.L. Dai, D.W. Dickinson and J.C. Papitan, Analysis and dvlopmnt of a altim contol mthodology in sistanc spot wlding, Wlding J., vol. 7 (12), 339s 351s, 1991 [1] H. A. Nid. h finit lmnt modling of th sistanc spot wlding pocss. Wlding Jounal, vol. 63 (4), 123s 132s, 1984 [11] H.. Cho, Y. J. Cho. A study of th thmal bhavio in sistanc spot wlds. Wlding Jounal, vol. 68 (6), 236s 244s, 1989 [12] D. J. Bown, H. W. Chandl, J.. Evans, J. Wn. Comput simulation of sistanc spot wlding in aluminum: pat I. Wlding Jounal, vol. 74 (1),339s 344s, 1995 [13] K.. Yung, P. H. honton. ansint thmal analysis of spot wlding lctods. Wlding Jounal, vol. 78(1): 1s 6s, 1999 [14] J. A. Khan, L. Xu, Y. Chao. Pdiction of nuggt dvlopmnt duing sistanc spot wlding using coupld thmal lctical mchanical modl. cinc and chnology of Wlding and Joining, vol. 4 (4), 21 27, 1999 [15] B. H. Chang, M.. Li, Y. Zhou. Compaativ study of small scal and lag scal sistanc spot wlding. cinc and chnology of Wlding and Joining, vol. 6 (5), 273 28, 21 [16] M. ogl,. hppad. Elctical contact sistanc und high loads and lvatd tmpatus. Wlding Jounal, vol. 72 (6), 231s 238s, 1993
Asian Pacific Confnc fo Matials and Mchanics 29 at Yokohama, Japan, Novmb 13-16 [17].. Babu, M. L. antlla, Z. Fng, B. W. Rim, J. W. Cohon. Empiical modl of ffcts of pssu and tmpatu on lctical contact sistanc of mtals. cinc and chnology of Wlding and Joining, vol. 6 (3), 126 132, 21