Multi-scale Analysis of Void Closure for Heavy Ingot Hot Forging

Transcription

1 Modrn Applid Scinc; ol. 6, No. ; ISSN E-ISSN 9-85 Publishd by Canadian Cntr of Scinc and Education Multi-scal Analysis of oid Closur for Havy Ingot Hot Forging Xiaoxun Zhang, Fang Ma, Kai Ma & Xia Li School of Matrials Enginring, Shanghai Univrsity of Enginring Scinc, Shanghai, China Collg of Automotiv Enginring, Shanghai Univrsity of Enginring Scinc, Shanghai, China Corrspondnc: Xiaoxun Zhang, School of Matrials Enginring, Shanghai Univrsity of Enginring Scinc, Longtng Road, Songjiang District, Shanghai 6, China. Tl: xx.zhang.cn@gmail.com Rcivd: August 9, Accptd: August 8, Onlin Publishd: Sptmbr, doi:.559/mas.v6np5 URL: Abstract A multi-scal modl towards simulating th void closur during hot forging was introducd in th prsnt study and th drivd void volution modl was programmd into commrcial cod DEFORM to simulat th void closur bhavior in havy ingot during th upstting and blocking procsss. From th simulation rsults, it can b concludd that: () th cymbal-shapd di is good at closing voids not only nar th di but also around th axis of th ingot whn th rduction is 6% in th upstting procss, () th ffctivnss of -shapd di is th bst for consolidating voids around th axis and nar th di whn th rduction is 4% in a singl blocking procss, howvr, at about % rduction aftr 9 rotat, th void-closd rgions bcom quit larg around th axis both for flat dis and FML dis and th loads ar much lowr than thos of -shapd dis. Upon that, void closur in multi-strok and multi-pass forging was also discussd. Th multi-scal modl and simulation rsults provid valuabl sourcs of rfrnc for dsign and optimization of di shaps and pass schduls for havy ingots during hot working procsss. Kywords: multi-scal, modling and simulation, void closur, havy ingot, hot forging. Introduction Intrnal dfcts such as shrinkag cavitis and porosity ar usually gnratd in havy ingots during solidification in stl casting. Ths tiny voids must b closd up in th subsqunt hot forging procss to nsur high quality of th product (Dudra & Im, 99). Bcaus of its importanc, void closur has bn studid for mor than yars. arious mthods, such as physical simulation and xprimntal study (Chaaban & Alxandr, 976), uppr bound analysis (Ståhlbrg, 986), finit lmnt (FE) mthod (Tanaka t al., 986; Park & Yang, 997; Jiang t al., 5; L t al., ) ar usd to dvlop prdictiv masurs for void closur in havy ingot during hot forging. Howvr, sinc a larg numbr of small voids usually xist in havy ingot and th volum of th void is xtrmly small compard with th havy ingot, modling void closur in havy ingot during hot forging is a multi-scal problm, and it is vry difficult to find prdictiv masurs basd only on macro-mchanics. In this study, a mso-mchanics approach is mployd to dal with th multi-scal problm. A cll modl is adoptd to study th dformation rat of th void and a thortical modl towards simulating th void closur during hot forging is introducd. Th drivd void volution quation is programmd into commrcial softwar DEFORM to simulat th bhavior of void closur in havy ingot during th upstting and blocking procsss. Th rlativ void volum, which is dfind as th ratio of currnt void volum to initial void volum, is calculatd during th dformation of havy ingots in th hot working procsss. Rlativ void volum and its distribution ar usd to valuat th ffctivnss of diffrnt di shaps and th procsss for consolidating intrnal voids. Both upstting and blocking procsss for havy ingots ar studid. Upon that, void closur in multi-strok and multi-pass forging is also discussd.. A Multi-scal Modl for oid Closur. Cll Modl and oid Evolution A cll modl is adoptd to dal with th multi-scal problm of void closur and to analyz th volution of void. Th cll modl which includs matrix and void is shown in Figur with volum c and outr surfac S c, and 5

2 Modrn Applid Scinc ol. 6, No. ; subjctd to rmot (macroscopic) uniform strss. Th matrix matrial is assumd to b isotropic and incomprssibl. Th constitutiv rlation of th matrix during hot forging can b givn as (Cocks, 989; Duva & Hutchinson, 984) n ε σ () whr and ar rfrnc strain-rat and strss rspctivly, n ( n ) is th Norton xponnt, σ is th strss dviator and : / σ σ is th ffctiv strss. An initially sphrical void is containd in th cll. Th volum of th void is and th void surfac is S. Th void volum fraction is assumd small and void intraction is ignord. Th aim is to obtain th vlocity fild in th matrix of th cll, and thn th volution of th void can b dtrmind by this vlocity fild. n oid Matrix (a) (b) Figur. (a) Havy ingot: comprisd of a matrix and a dilut disprsion of traction-fr voids and (b) Cll modl: volum c, outr surfac S c, uniform tractions n ovr S c To obtain an volution quation of th void, a Rayligh-Ritz procdur basd on Hill s minimum principl (Hill, 956) for th vlocitis is dvlopd. Th trial local vlocity and strain-rat within th matrix ar xprssd as v v v, () whr v and E ar th uniform vlocity and strain-rat du to Σ in th absnc of th void. Thn, among all additional vlocity filds v, th actual vlocity fild minimizs th functional (Duva & Hutchinson, 984) F v w w d v n ds () ( ) [ ( ) ( ) : ] m whr m is th volum of th matrix matrial in th cll, S is th surfac of th void, n is th unit normal to th surfac of th void pointing into th matrix, and S ( n)/ n n w() ε (4) n in which / is th local ffctiv strain-rat. Not that ( : ) lim E E, whr / c is th void volum fraction and is th volum of th void. Sinc th cll modl considrd for havy ingots is infinit compard with th void, E E will b usd throughout and 6

3 Modrn Applid Scinc ol. 6, No. ; n E E Σ ' (5) As th matrix matrial is incomprssibl, th stram function can b introducd to charactriz th additional vlocity fild v and th unknown variabls in th stram function can b dtrmind by minimizing F( v ) in Eq.() (Budiansky t al., 98; L & Mar, 994). Onc th vlocity fild v has bn computd from th Rayligh-Ritz procdur, th chang-rat of void volum is givn by ds v n (6) S. Th Multi-scal Modl for oid Closur Basd on th calculations of th Ritz procdur mntiond abov, th numrical solutions wr obtaind in a prvious study by Zhang t al. (9). Ths numrical rsults can b usd to formulat an xplicit xprssion of th multi-scal modl for void closur, which is suggstd as n m ( n )(5n ) m 4 xp sign( m) E q qe qe q 4 for n 5n n t xp sign( m) m for n (7) whr Σ and : / m tr( ) ar th rmot man strss and th rmot ffctiv strss, rspctivly, and E : / E E is th rmot ffctiv strain-rat, m / is th masur of strss triaxiality and q 4 ar four paramtrs and E is th macroscopic ffctiv strain. In th prsnt study, FE computations basd on a cubic cll modl ar carrid out to dtrmin th valus of q and q 4 and th valus of q and q 4 ar suggstd and givn in Tabl. Tabl. Th valus of q and q 4 in Eq. (7) n 5 q q q q Multi-scal Simulation of oid Closur Upstting and blocking ar two typical oprations in th procss of manufacturing havy forgings. Upstting is a procss which incrass th cross-sction of th billt by comprssing its lngth, whil blocking is a procss which rducs th cross-sction of th billt and incrass its lngth by rptitiv sid prssing and altrnat ingot rotations. Both upstting and blocking procsss ar oftn usd to liminat intrnal voids in havy ingots. Nw di gomtris which lowr th prss loads hav also bn invstigatd sinc th prss load capacity of th forging machin is a limitation whn forging havy ingots. In this sction, th drivd void volution quation is programmd into commrcial softwar DEFORM to simulat th bhavior of void closur in havy ingot during th upstting and blocking procsss. Th rlativ void volum R, which is dfind as th ratio of currnt void volum to initial void volum, is calculatd during th dformation of havy ingots in th hot working procsss. Rlativ void volum and its distribution ar usd to valuat th ffctivnss of diffrnt di shaps and th procsss for consolidating 7

4 Modrn Applid Scinc ol. 6, No. ; intrnal voids.. oid Closurs in Upstting Upstting of a cylindrical ingot with concav sphr di, flat di, M-shapd di, convx sphr di and cymbal-shapd di ar simulatd in this subsction to rval th ffct of di shaps on void closur. Th FE modls for upstting with diffrnt di typs ar shown in Figur and th diamtr of th cylindrical ingot is D = mm and th hight is H = mm. Th rsults of R by applying th multi-scal mthod (MSM) in simulation ar shown in Figur at 6% rduction. Not that R mans void closur, whras R indicats void has not closd. From Figur, it is clar that: () Thr is a void-unclosd rgion nar th di during upstting with concav sphr di and flat di (Figur (a) (b)). Th void-unclosd rgion producd by concav sphr di is th biggst and R approachs in that rgion. Th void-unclosd rgion producd by flat di is smallr than that by concav sphr di, but it is still a disadvantag to obtain high quality forgings. It indicats that, from a point of viw of liminating voids in havy ingots, concav sphr di and flat di ar not suitabl for upstting. () Th void-unclosd rgions producd by convx surfac di ar much smallr than thos by concav surfac di and flat di (Figur (c) (d) ()). Comparing M-shapd di, convx sphr di and cymbal-shapd di with ach othr, it can b sn that thr is a rlativly big void-unclosd rgion producd by M-shapd di nar th intrsction of th convx and concav surfac, and R around th axis is also not uniform. Convx sphr di and cymbal-shapd di, howvr, can consolidat th void nar th di during upstting. Morovr, cymbal-shapd di upstting provids an idal rsult for void closur not only nar th di but also around th axis of th ingot (Figur ()). () Sinc th void-unclosd rgion always xists nar th di during upstting with concav sphr di, flat di and M-shapd di (Figur (a) (b) (c)), it is vry difficult to achiv th goal of liminating void in havy ingots vn by multipl upstting along th axis. Howvr, th voids nar th di and thos around th axis of th ingot can b liminatd with convx sphr di and cymbal-shapd di (Figur (d) ()), so that th goal of liminating voids can b achivd by multipl upstting along th axis with convx sphr di and cymbal-shapd di. (4) Sinc th mtallurgy dfcts in havy ingots scattr mainly along th axis, th cavity dfcts would b liminatd compltly only whn all of th voids around th axis ar closd. Sinc cymbal-shapd di is good at closing voids not only nar th di but also around th axis of th ingot, and th loads for cymbal-shapd di ar also rlativly small, th cymbal-shapd di is suggstd to us in upstting. (a) (b) (c) 8

5 Modrn Applid Scinc ol. 6, No. ; (d) () Figur. Finit lmnt modls for upstting with diffrnt di typs: (a) concav sphr di, (b) flat di, (c) M-shapd di, (d) convx sphr di and () cymbal-shapd di (a) (b) (c) (d) () Figur. Rlativ void volum for upstting with diffrnt dis at 6% rduction: (a) concav sphr di, (b) flat di, (c) M-shapd di, (d) convx sphr di, () cymbal-shapd di 9

6 Modrn Applid Scinc ol. 6, No. ;. oid Closurs in Blocking Blocking of a cylindrical ingot with -shapd di, flat di and FML dis ar simulatd in this subsction to valuat th ffctivnss of ths dis for consolidating intrnal porosity. Th FE modls for blocking with diffrnt dis ar shown in Figur 4 and th diamtr of th cylindrical ingot is 4 mm. Th rsults of R at 4% rduction ar shown in Figur 5, Figur 6(a) and Figur 7(a). Prss loads rquird for diffrnt dis ar shown in Figur 8. From Figurs 4~8, it is found that: () Th distribution of void-closd rgion is significantly influncd by di shaps. oid-closd rgion producd by -shapd di is th largst and ffctivnss of -shapd di is th bst for consolidating voids around th axis and nar th di (Figur 5). oid-closd rgion producd by flat di is mainly distributd around th axis (Figur 6(a)) and void-closd rgion producd by FML dis is mainly cntrd on a small ara around th axis (Figur 7(a)). () Th loads for -shapd di incras rapidly from th bginning of loading and kp a high growth rat, whras th loads for flat di and FML dis ar rlativly much smallr (s Figur 8). Th loads for flat di and FML dis ar almost th sam whn th rduction is lss than % (th rduction tim is 6 s). Th loads for flat di ar highr than thos for FML dis whn th rduction is gratr than %. It indicats that, from a point of viw of liminating voids in havy ingots, th ffctivnss of -shapd di is th bst but th loads rquird ar also th highst. Th ffctivnss of flat di taks scond plac with lowr loads. Th FML dis ar lss ffctiv in ach strok than othr dis for consolidating void in havy ingot, but th loads rquird for FML dis ar also th smallst. If th prss load of th forging machin is nough, thn th pair of -shapd dis would b a good choic for blocking. Ths rsults ar in good agrmnt with th xprimntal and thortical rsults in litraturs. () On of th charactristics of blocking is that th billt can b prssd rptitivly with altrnat ingot rotations. Th distributions of R at 4% rduction and thos at % rduction aftr 9 rotat ar displayd in Figur 6 and Figur 7 with flat dis and FML dis, rspctivly. At th first 4% rduction, th void-closd rgions producd by flat di and FML dis ar vry small (s Figur 6(a) and Figur 7(a)). At about % rduction aftr 9 rotat, howvr, th void-closd rgions bcom quit larg around th axis both for flat dis and FML dis (s Figur 6(b) and Figur 7(b)), and th loads ar much lowr than thos of -shapd dis (Figur 8). Th void-closd rgion nar th di during blocking with FML dis is largr than that with flat dis. If prss load of th forging machin is a constraint, thn th FML dis would b a bttr choic. It also implis that th voids in havy ingots would b closd by multi-strok and multi-pass blocking with flat dis and FML dis. (a) (b) (c) Figur 4. Finit lmnt modls for blocking with diffrnt di typs: (a) 5 dis, (b) flat dis, (c) FML dis

7 Modrn Applid Scinc ol. 6, No. ; Figur 5. Rlativ void volum for 5 dis blocking at 4% rduction (a) (b) Figur 6. Rlativ void volum for flat dis blocking: (a) 4% rduction, (b).% rduction aftr 9 rotats (a) (b) Figur 7. Rlativ void volum for FML dis blocking: (a) 4% rduction, (b).6% rduction aftr 9 rotats

8 Modrn Applid Scinc ol. 6, No. ; 5 FML dis Flat dis -dis (5 ) A singl pass Load ( 4 N) 5 5 Th first pass Th scond pass Tim (s) Figur 8. Loads for blocking with diffrnt dis. Multi-strok and Multi-pass Forging Th forging procss of havy ingots usually nds a lot of stroks and many passs, thrfor study on void closur in multi-strok and multi-pass is vry important. Only in this way, th cours of forging can b valuatd in an all-round way and th procss can b optimizd as a whol. oid closur in a squar billt during multi-strok blocking with a pair of flat dis is invstigatd in this subsction. Th FE modl of th squar billt is shown in Figur 9 and its width is W = mm, hight is H = mm and lngth is L = mm. Th rsults of R aftr four stroks in th first pass ar shown in Figur (a) and th rduction for ach strok is 5%. Figur (b) is a slicd plan viw. Aftr th first pass, th ingot is rotatd 9 and fiv stroks ar prformd in th scond pass. Figur (c) displays th rsults of R in th scond pass. From Figur 9 and Figur, it can b sn that: () Looking from sid, thr ar X shapd aras whos intrnal cavitis ar closd fairly wll aftr four stroks in th first pass (s Figur (a)(b)). () Th slicd plan viw indicats that th voids in som local rgions of th ingot has bn closd aftr four stroks, nvrthlss, continuous void-closd rgions along th cntrlin of th ingot still hav not appard aftr on pass forging. () Sinc void-unclosd rgion always xists nar th flat dis during vry strok, and void-unclosd rgion appars btwn stroks, th multi-pass blockings ar ndd to liminat th intrnal voids in th ingot. oid-closd rgions will b continuously producd by altrnat prss and rotat in multi-pass blocking (s Figur (c)). Th goal of liminating void would b achivd whn ths local void-closd rgions ar unitd as a whol in th ingot. (4) Application of th critrion for void closur in th CAE analysis maks it vry convnint to valuat and optimiz various traditional forging procsss, and provids a novl way for nw procss dsign in trms of limination of voids in havy ingots.

9 Modrn Applid Scinc Figur 9. Finit lmnt modls for multi-strok and multi-pass forging (a) (b) ol. 6, No. ;

10 Modrn Applid Scinc ol. 6, No. ; (c) Figur. oid closur in multi-strok and multi-pass forging: (a) aftr four stroks in th first pass, (b) sction plan viw aftr four stroks in th first pass, and (c) aftr fiv stroks in th scond pass 4. Conclusions A multi-scal modl towards simulating th void closur during hot forging is introducd in this study. A cll modl, which includs a void-fr matrix and a void, is adoptd, and Rayligh-Ritz procdur is usd to study th dformation rat of th void. Th drivd void volution modl is programmd into commrcial cod DEFORM to simulat th void closur bhavior in havy ingot during th upstting and blocking procsss. It can b concludd that: () From a point of viw of liminating voids in havy ingots, concav sphr di and flat di ar not suitabl for upstting sinc a larg void-unclosd rgion xists nar th di. Sinc th cymbal-shapd di is good at closing voids not only nar th di but also around th axis of th ingot, and th loads for cymbal-shapd di ar also rlativly small, th cymbal-shapd di is suggstd to us in upstting. () From a point of viw of liminating voids in havy ingots, th ffctivnss of -shapd di is th bst for blocking but th load rquird is also th highst. Th ffctivnss of flat di taks scond plac with lowr loads. Th FML dis ar lss ffctiv in ach strok than othr dis, but th loads rquird for FML dis ar also th smallst. If th prss load of th forging machin is nough, thn th pair of -shapd dis would b a good choic for blocking. If prss load of th machin is a constraint, thn th FML dis would b a bttr choic. () Sinc void-unclosd rgion xists nar th flat di during vry strok, and void-unclosd rgion appars btwn stroks, th multi-pass blockings ar ndd to liminat th intrnal voids in havy ingots. oid-closd rgions will b continuously producd by altrnat prss and rotat in multi-pass blocking. Whn th local void-closd rgions ar unitd as a whol in th ingot, th goal of liminating void will b achivd. (4) By applying th multi-scal modl for void closur in th CAE analysis, th optimal forging procss, in trms of limination of voids in havy ingot, can b carrid out and th schdul for multi-strok and multi-pass can b arrangd conomically, and thn high product quality would b obtaind. Acknowldgmnts This work is supportd by Shanghai Lading Acadmic Disciplin Projct undr grant J54 and supportd by Innovation Program of Shanghai Municipal Education Commission undr grant ZZ8 and supportd by Scinc Foundation for th Excllnt Youth Scholars of Shanghai Municipal Education Commission undr grant gjd8. Rfrncs Budiansky, B., Hutchinson, J. W., & Slutsky, S. (98). oid growth and collaps in viscous solids. In: Hopkins, H.G., Swll, M.J. (Eds.), Mchanics of Solids (pp. -45), Prgamon Prss, Oxford. Chaaban, M. A., & Alxandr, J. M. (976). A Study of th Closur of Cavitis in Swing Forging. In: Tobias, S.A. (Ed.), Procdings of th 7th Intrnational Machin and Tool Dsign Rsarch Confrnc (pp ), Birmingham, UK. 4

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