Modelling, simulation and identification of the solid state sintering after ceramic injection moulding

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1 Mollig imlatio a itificatio of th oli tat itrig aftr cramic ijctio molig Jipg Sog * ** Ghaa Aya * hirry Barrir * Ja-Cla Gli* Baohg Li ** Davi Ralt *** * Fmto-S titt LMA ESMM/CRS 4 Chmi l épitaph 5 Baço Frac [email protected] {thirry.barrir ja-cla.gli}@iv-fcomt.fr ** Dpartmt of Appli Mchaic Sothwt Jiaotog Uivrity 611 Chg Sicha P. R. Chia *** O. D. Sim C Chmi palt 5 Baco Frac RÉSUMÉ. U moél coti baé r l voltio loi comportmt vico-platiq t tilié por écrir l procéé ificatio par iffio pha oli por compoat fabriqé par l procéé molag par ijctio por céramiq CM. L moèl a été implémté a co élmt fii vloppé r la platform Matlab. U métho opimiatio t propoé afi itifir l paramétr moél la loi comportmt. La imlatio prothé hach t ralié par c procéé CM t pri comm xmpl poit v mériq t xpérimtal. L réltat mériq ot valié par ai xprimtax. ABSRAC. o crib th itrig proc of oli tat iffio for th compot of cramic powr obtai by th powr ijctio molig a biig a cotim mol ba o th cotittiv law i vicoplatic typ i itroc. hi phyical mol ha b implmt i a Fiit Elmt Softwar vlop o th platform Matlab. h a optimizatio mtho ha b vlop for th itificatio of paramtr i th propo itrig mol. h itificatio by optimizatio oftwar ha b appli o a powr mol compot of th hip implat coit of th almia cramic powr. Ba o th compario btw xprimt a mollig by FE imlatio th itificatio procr giv accrat rlt. MOS-CLÉS : ificatio molag par ijctio por céramiq imlatio mériq itificatio. KEYWORDS: itrig cramic ijctio molig almia cramic mrical imlatio itificatio.

2 1. troctio Cramic ijctio molig CM i a combiatio of tchologi i particlat matrial ijctio molig a itrig proc. t i crrtly i cramic itri to mafactr i larg qatiti th mall complx a ar-t-hap compot with high prformac. CM th itrig tag i o of th mot importat tp i which th bi gr compot ar trat at th tmpratr blow th mltig poit of th mai cotitt to obtai th ir fial proprti by boig th powr particl togthr. h hrikag btw th gr compot a th itr o i grally i th rag 1-% a th ity of th fial compot i i th rag 9-1% Grma Bca of th larg hrikag i itrig proc trmiatio of th imioal chag a itortio i cary i itrial proctio to proc th compot i ar-t-hap a high qality. Bi th covtioal trial a rror mtho mrical imlatio of th itrig tag may b a fat a cotffctiv altrativ to olv thi problm. Svral cotittiv mol ba o th cotim mchaic hav b vlop to crib th itrig proc. A prly phomological mol to Olvky m ay to b implmt i mrical imlatio bt i rtrict for th poibiliti to gt accrat rlt Olvky th xprimtal mol to Bovar Bovar 1996 ata ar irctly obtai from ral matrial bt th ivtigatio o loaig coitio i limit at high tmpratr a th othr tr coitio ar calclat by xtrapolatio. h micromchaical mol to Ril a Kraft Ril t al m comprhiv for oli itrig bca it coir majority of th mchaim a factor i th tir itrig proc bt it i cary to ajt th mol paramtr for vario matrial. thi papr a vicoplatic cotittiv mol a th aociat fiit lmt mtho FEM ar to imlat th itrig proc. h mrical itificatio mtho icorporat with ilatomtr xprimt ar to trmi th paramtr i cotittiv mol. Mor accrat imlatio ca b carri ot ba o thi mol bca th cotittiv paramtr ar trmi with th am oftwar that will b for imlatio. h imlatio ar appli o th compot of almia cramic powr obtai by CM a biig. Compar with th xprimtal ata th imlatio rlt ar raoabl.. Sitrig mol.1. Cotittiv itrig mol o t p th rlatiohip btw th macrocopic trai rat tor a th tr tor i itrig a liar vicoplatic crp law i Ril t al Sch a cotittiv law i xpr: σ σ ε vp tr σ [1] G 9K

3 whr σ i th viatoric tr tor trσ i th trac of tr tor i th itity tor of co orr G i th har vicoity mol K i th blk vicoity mol a σ i th itrig tr. o itify th paramtr i th cotittiv law for itrig proc iffrt mol hav b vlop. th prt ty followig xprio ar McMkig t al. 199: r G 1 [] 9Diff r K 1 [] 54Diff 1 8 σ γ [4] r whr r i th iitial rai of phrical powr particl th iitial rlativ ity i rlativ ityγ i th rfac rgy of th particl. D iff i a iffio trm grally writt i th followig form: Qb R Ωδ D Diff b [5] k whr k i th Boltzma cotat Ω th atomic volm δd b i a iffio cofficit at grai itrfac R th pcific ga cotat a Q b i a activatio rgy. h mai limitatio of rlatiohip i [] [] a [4] ar rlat to thir valiity from th iitial ity of th poro mia to th fial tat.. Govrig qatio h momtm corvatio qatio a ma covratio qatio crib th mchaical bhavior of th powr aggrgatio rig th itrig tag Ralt t al. h momt covratio qatio i writt a : σ f ρ [6] t whr σ i th Cachy tr tor f i xtral appli forc i th iplacmt fil a t i th crrt procig tim. Bca th itrig proc i vry low th irtia forc i th right ha of th qatio [6] ar oft glct. h calclatio of rlativ ity i rlat to th ma corvatio qatio xpr a:

4 4.tr vp ε [7].. FEM oltio procr h copl qatio [1 6 7] ar olv by FEM i th followig form. h vlocity a rlativ ity ar cho a th mai oal variabl: B ε [8] whr ar th matrix of itrpolatio fctio B i trai rat itrpolatio matrix. Galrki mtho i appli to bil th rltig FE qatio xpr a: F K C M [9] h matrix M C K a F ar xpr by th followig rlatiohip: V f V V V Ω Ω Ω Ω tr B F B A B K B C M σ [1] whr ta for th ambly oprator ovr th lmt. A i a tor cribig th vicoplatic cotittiv bhavior: A ε A σ : 4 vp G K G σ [11] whr i th torial proct oprator. For fr itrig f icl oly gravity ffct xpr a:

5 5 f ρ g th [ 1] [1] whr ρ th i th thortical ity a g i gravity acclratio. Galrki mtho i to bil th FEM procr for oltio of th govrig qatio a cotittiv qatio. A xplicit high orr Rg-Ktta chm i mploy for th tim itgratio vlop o th platform of Matlab.. mrical itificatio.1. tificatio algorithm for itrig phyical paramtr h itificatio algorithm i ig for propr trmiatio of th matrial paramtr i th cotittiv mol which i to b i bqt mrical imlatio. h ilatomtr xprimt ar to ty th ificatio bhavior of th pcifi matrial i which th hrikag crv i obtai for 1D ca. O th othr ha th mrical imlatio ba o th abov itrig mol ar carri ot for 1D part with th giv iitial val for th matrial paramtr. A mrical rpo crv i obtai by ma of th FE imlatio. h optimizatio tratgy i propo to miimiz th iffrc btw both th hrikag crv obtai by ilatomtr xprimt a mrical imlatio rpctivly. h matrial paramtr ar th variabl to b optimiz. So th optimizatio i formlat a a miimizatio problm xpr a mi F x F x f i 1 x [ δdb Q b x i γ r ] f x i [1] whr f x i th hrikag crv rltig from th ilatomtr xprimt f x i th hrikag crv of mrical imlatio Fx i th ma rial qar btw both th two crv whr i1 ar itrig tmpratr x i th t of matrial paramtr... tificatio for almia cramic powr h itificatio mtho i appli to gt th matrial paramtr of ijctio mol almia cramic powr. h ata giv i Opfrma t al ar a rfrc for ilatomtr xprimt. h hrikag crv obtai by ig th iitial matrial paramtr i optimiz i orr to approach th crv obtai from ilatomtr xprimt a how i Fig. 1. h iitial val ar cho from th rfrc.

6 6 Shrikag im mi Fig. 1. Compario btw hrikag crv obtai by xprimt a optimizatio h iitial matrial paramtr of almia cramic powr obtai from th rfrc a th o obtai by itificatio ar lit i abl 1. abl1. tifi matrial paramtr Paramtr itial Rfrc tifi Q b KJ/mol 84 H t al δd b m / Cao t al γ J/m.71 Rh S.K r m H t al Ω m Chvalir t al Valiatio xampl h ijctio mol hip implat part of almia cramic powr ar cho a a xampl to valiat th itrig mol a propo itificatio procr. Fig.. Mh of th hip implat compot

7 7 h mh of th part i giv i Fig.. h tmpratr cycl for FE imlatio i hatig to 14 C with th rat 5 C/mi. h itifi matrial paramtr giv i abl.1 ar for FE imlatio. With th itifi paramtr th fial rlativ ity obtai by imlatio i th part i giv i Fig.. Fig.. h fial rlativ ity i hip implat compot h avrag hrikag ratio i 11.85%. h fial rlativ ity i abot 84.5%. Sch a rlt i i goo agrmt with th ilatomtr xprimt. Fig. 4 h photo of th itr hip implat For itrig xprimt th gr part of hip implat aftr biig i itr i a frac. h tmpratr cycl i th am a prcrib i imlatio. h

8 8 photograph o th part of hip implat aftr molig a itrig rpctivly ar how i Figr. xprimt th hrikag i abot 1% a th fial rlativ ity i abot 95%. gral th imlatio rlt agr with th xprimt. Bt th fial rlativ ity obtai by imlatio i l tha th xprimtal o. hi i to th fact that th itrig mol xpr by qatio [-5] i ot totally itabl for th fial itrig tag. 4. Coclio A phomological mol for th itrig by oli tat iffio ha b propo ba o th phyical coiratio a th trmiatio of mai rivig paramtr. h xprimt ig ilatomtr hav b carri ot o almia cramic powr with iffrt tmpratr cycl. h xprimt provi th cary ata for itificatio of th paramtr i th cotittiv mol mploy i imlatio. hi itificatio i rly combi with th of imlatio oftwar a vlop optimizatio tool. hi mtho i jtifi by th compario of xprimtal rlt a th o i by imlatio o a xampl of th itrig of a hip implat compot. Sch a compot i obtai by th ijctio molig a biig of th almia cramic powr. h rlt ar i goo agrmt which valiat th mollig imlatio a th itificatio procr. Ackowlgmt h athor prt thir thak to th pport of Frch Embay i Chia for th altrat octorial catio projct a th Ecatio Miitry of Chia for th octoral catio f 615. Rfrc Grma R. M. Bo A. jctio molig of mtal a cramic USA MPF Olvky E. A. hory of itrig : from icrt to cotim Matrial Scic a Egirig R 1998 p Bovar D. mrical imlatio of itrig a imioal chag of complx part Sitrig Cor ot EPMA 1999 p Ril H. Kozak V. Svoboa J. Eqilibrim por rfac itrig tr a cotittiv qatio for itrmiat a lat tag of itrig Part : Difioal ificatio a crp Acta Mtall. vol p Kraft. Ril H. mbrical imlatio of oli tat itrig mol a applicatio Joral of Erop Cramic Socity vol. 4 4 p

9 9 McMkig R. M. Kh L.. A iffioal crp law for powr compact Acta Mtall. vol p Ralt D. Barrir. a Gli J.C. Exprimt a mrical imlatio ba o a micro-macro cal mol for oli tat itrig h 7th itratioal cofrc o mrical mtho i itrial formig proc UMFORM' 1 oyohahi 18-1 J 1 Eitio Mori K. Japa p. 7-. Opfrma J. Blmm. J Emmrich W. D. Simlatio of itrig bhavior of a cramic gr boy ig avac thrmo-kitic aalyi hrmochimica Acta vol p.1-. H Z. Ma. J Cotittiv mollig of almia itrig: grai-iz ffct o omiat ificatio mchaim Comptatioal Matrial Scic vol i Fbrary 5 p Cao R.M. Rho W.H. Hr A.H. Platic formatio of fi-grai almia AlO: trfac cotroll iffioal crp Joral. of Amrica. Cramic. Socity. vol p Rh S.K. Critical rfac rgi of AlO a graphit Joral of Amrica. Cramic. Sociyt. vol p. -. Chvalir.J. Olago C. Fatozzi G. Gro H. Crp bhavior of almia zircoia a zircoia-togh almia Joral of th Eropa Cramic Socity Vol p