ANNUAL REPORT Meeting date: June 1, Seid Koric * & Brian G. Thomas Engineering Applications Analyst, NCSA & Ph. D.

Transcription

1 ANNUAL REPOR 5 Meeing dae: June 1, 5 Slidificain Sress Mdeling using ABAQUS Seid Kric * & Brian G. hmas Engineering Applicains Analys, NCSA & Ph. D. Candidae Deparmen f Mechanical & Indusrial Engineering Universiy f Illinis a Urbana-Champaign Objecives predic he evluin f emperaure, shape, sress and srain disribuin in he slidifying shell in cninuus casing mld by a nnlinear mulipurpse cmmercial finie elemen package wih an accurae apprach. Validae he mdel wih available analyical sluin and benchmarks wih in-huse cde COND specializing in accurae mdeling f D cninuus casing. enable new mdel be appld he cninuus casing prblems by incrpraing even mre cmplee and realisic phenmena. perfrm a unique realisic 3D hermal sress analysis f slidificain f he shell f a hin slab caser ha can accuraely predic he 3D mechanical sae in sme criical regins impran crack frmain. Apply FE resuls predic he effecs f casing speed n al srain evluin, predic maximum casing speed avid bulging, predic damage srains and ransverse and lngiudinal cracks, find ideal aper and mre. Universiy f Illinis a Urbana-Champaign Meals Prcessing Simulain Lab S. Kric 1

2 Why ABAQUS? I has a gd user inerface, her mdelers in his fld can largely benefi frm his wrk, including ur final cusmers he seel indusry. Abaqus has imbedded pre and ps prcessing ls suppring impr f he majr CAD frmas. All majr general purpse pre-prcessing packages like Paran and I-DEAS suppr Abaqus. Abaqus is using full Newn-Raphsn scheme fr sluin f glbal nnlinear equilibrium equains and has is wn cnac algrihm. Abaqus has a vary f cninuum elemens: Generalized D elemens, linear and quadraic erahedral and brick 3D elemens and mre. Abaqus has parallel implemenain n High Perfrmance Cmpuing Plafrms which can scale wall clck ime significanly fr large D and 3D prblems. Abaqus can link wih exernal user subruines (in Frran and C) linked wih he main cde han can be cded increase he funcinaliy and he efficncy f he main Abaqus cde. Universiy f Illinis a Urbana-Champaign Meals Prcessing Simulain Lab S. Kric 3 Basic Phenmena Basic Phenmena Once in he mld, he mlen seel freezes agains waer-cled walls f a cpper mld frm a slid shell. Iniial slidificain ccurs a he meniscus and is respnsible fr he surface qualiy f he final prduc. lubricae he cnac, il r pwder is added he seel meniscus ha flws in he gap beween he mld and shell. hermal srains arise due vlume changes caused by emp changes and phase ransfrmains. Inelasic Srains develp due bh srain-rae independen plasiciy and ime dependan creep. A inner side f he srand shell he ferrsaic pressure linearly increasing wih he heigh is presen. Mld disrin and mld aper (slan f mld walls cmpensae fr shell shrinkage) affecs mld shape and inerfacial gap size. Many her phenmena are presen due cmplex ineracins beween hermal and mechanical sresses and micr srucural effecs. Sme f hem are sill n fully undersd. Universiy f Illinis a Urbana-Champaign Meals Prcessing Simulain Lab S. Kric 4

3 Gverning Equains Hea Equain: H ( ) k ( ) ρ k ( ) = + x x y y Equilibrium Equain (small srain assumpin): σ ( x) + b = Rae Represenain f al Srain Decmpsiin: ε & = ε& + ε& + ε& el h Cnsiuive Law (Rae Frm, N large rains): &σ = D :( ε& ε& ε& ) h D = µ I+ (k ) I I 3 Inelasic (visc-plasic) Srain Rae (srain rae independen plasiciy + creep): ε & = f ( σ,, ε,%c) 3 1 σ= S: S, S= σ race( σ) I, ε & = ε : 3 3 & ε & hermal Srain: { ε } = ( α( ) ( ) α( )( ))[ 111 ] h ref i i ref Universiy f Illinis a Urbana-Champaign Meals Prcessing Simulain Lab S. Kric 5 Cmpuainal Mehds Used Slve Gverning Equains Glbal Sluin Mehds (slving glbal FE equains) -Full Newn-Raphsn used by Abaqus -Operar-Spliing used by COND Lcal Inegrain Mehds (n every maerial pins inegraing cnsiuive laws) -Abaqus prvided via CREEP subruine, fully implici fllwed by lcal NR -Abaqus prvided via CREEP subruine, explici -Fully Implici fllwed by lcal bunded NR -Fully Implici fllwed by Nema-Nasser -Radial Reurn Mehd fr Rae Independen Plasiciy, fr liquid/mushy zne nly Universiy f Illinis a Urbana-Champaign Meals Prcessing Simulain Lab S. Kric 6 3

4 Big Picure: Maerially Nn-Linear FEM Sluin Sraegy in ABAQUS wih UMA UMA called a all Gauss Pins { σ }, { ε }, { ε } Sress Updae Algriham Implici Inegrain f IVP ReadNdal frmhdaabase { ε } =α( ) {111 } h Elemen Srain Incremen + + { } = [ B]{ } ε i U i Equilibrium Cnfigurain a { U },{ S },{ P } Glbal Exernal Lad Vecr a + { P } = N { b } dv + N { Φ } da V Glbal NR Ierain [ K ] = [ K ]; { S } = { S }; { U } = { U }; i = A Calculain f CO : [ ] J = { σ } { ε } + + { σ }, { ε }, [ J] Elemen Inernal Frce and Elemen angen Marix { } { } el, i S = B σ dv Vel K el, i = B [ J ][ B ] dv Vel Yes = + lerance i = i + 1 [ Ki-1 ]{ Ui-1} = { P }- { Si-1 } { U } = { U } + { U } i i-1 { } { } { } + U i = Ui - U [ K i ] = [ K el, i ], { S el } = { S el,i } N, Sar new NR Ierain i-1 Universiy f Illinis a Urbana-Champaign Meals Prcessing Simulain Lab S. Kric 7 Big Picure : COND Sluin Prcedure Operar Spliing echnique (N glbal ierains, n CO!) Given: ε, σ, ε * + + * + * * Calculae rial Sress: { σ } = [ D ] {} ε { ε } + { ε h } + { ε }, S = σ σhyd LOCAL SEP: Implici Inegrain f cnsiuive law fllwed by level lcal bunded NR. Lcal Sep Oupu: ˆ + ˆ σ, ε + σˆ + * * Radial Reurn Facr: α= * Sress Esimae Expansin: { σ ˆ} + =α σ { S } + { σhyd} { } Inelasic Srain Rae Esimae: ( ) { } + ˆ Ŝ + ˆ + ˆ + ˆ 3 ˆ ε & = f σ, ε, Flw Ru le: ε & = ε& ˆ + σ GLOBAL SEP: Finie Elemen Sluin f equilibrium equain. Using cnsiuive law wih iniial srain. Inelasic srain rae { ˆ } + ε& based n esimae frm Sep1 Slve linear glbal sysem fr nly nce fr every ime incremen: Updae Values : Updae Sress: { } { } { } { } { el} { } { } ( ) { } { } { } d + { + } { ˆ& } { h} Vel Vel Vel Σ [B ][D][B]dV d =Σ [B ][D] ε dv +Σ [B ][D] ε dv + Σ [B ][D] ε dv + Σ [N ] b dv + Σ [N ] φ da Vel Vel Sφ { } { } { } { } { } { } { ˆ } + & { σ } = { σ } + [D]({ ε} { ε} { εh} ) d = d + d, ε = [B] d, ε = ε + Universiy f Illinis a Urbana-Champaign Meals Prcessing Simulain Lab S. Kric 8 4

5 Cnsiuive Mdels fr Slid Seel (<=sl) Kzlwski Mdel fr Ausenie (Kzlwski 1991) Mdifd Pwer Law fr Dela-Ferrie (Parkman ) 5 Srain Rae = 1x1-4 1/sec. Symbls: Experimens [YM WON, Me. rans. B, ] Lines: COND (Kslwski III) 3 Srain Rae = 1.4x1-4 Sress (MPa) C 1 C Sress (MPa) 1 COND, 145 C COND, 155 C Experimen, 145 C Experimen, 155 C 5 13 C Plasic Srain (%) Kzlwski III Law fr Ausenie Plasic Srain (%) Pwer Law fr δ-ferrie Universiy f Illinis a Urbana-Champaign Meals Prcessing Simulain Lab S. Kric 9 Cnsiuive Mdels fr Slid Seel (<=sl) Kzlwski Mdel fr Ausenie (Kzlwski 1991) f3 ( ) ( ) ( ) ( ( )) ( ( K )) f K 1 4 & ε 1/ sec. = f % C σ MPa f1 ( ( K) ) ε ε exp( ( K) ( K )) 3 f1 ( ( K) ) = ( K) 3 f ( ( K) ) = ( K) 3 f3 ( ( K) ) = ( K) f(% C) = % C (% C) Mdifd Pwer Law fr Dela-Ferrie (Parkman ) ( ) ( MPa) f C ( ( K ) ) 4 (% ) = (% ) ( ) ( ) & ε 1/ sec. =.1 σ (% ) 3 (1 + 1 ε) f C C m= K + n= K n m Universiy f Illinis a Urbana-Champaign Meals Prcessing Simulain Lab S. Kric 1 5

6 1D Slidificain Sress Prblem fr Prgram Validain Analyical Sluin exiss (Weiner & Bley 1963). Elasic in slid, Perfecly Plasic in liquid/mushy. N viscplasic law fr slid ye in his mdel. Prvides an exremely useful validain es fr inegrain mehds, since sress updae algrihm in liquid/mushy zne is a majr challenge! Yld sress linearly drps wih emp. frm Slidus emp C A srip f D elemens used as a 1D FE Dmain fr validain Generalized plane srain bh in y and z direcin give 3D sress/srain sae esed bh f ur mehds emulae Elasic-Perfecly Plasic maerial behavir plus bh Abaqus naive CREEP inegrain mehds. Universiy f Illinis a Urbana-Champaign Meals Prcessing Simulain Lab S. Kric 11 Cnsans Used in Abaqus Numerical Sluin f WB Analyical es Prblem Cnduciviy [W/mK] 33. Specific Hea [J/kg/K] 661. Elasic Mdulus in Slid [Gpa] 4. Elasic Mdulus in Liq. [Gpa] 14. hermal Linear Exp. [1/k].E-5 Densiy [kg/m 3 ] 75. Pissn s Rai.3 Liquidus emp [ O C] Slidus emp [ O C] Iniial emp [ O C] Laen Hea [J/kgK] 7. Number f Elemens 3. Unifrm Elemen Lengh [mm].1 Arificial and nn-physical hermal BC frm VB (slab surface quenched 1C), replaced by a cnvecive BC wih h= [W/m K] Simple calculain ge h, frm surface energy balance a iniial insan f ime: ( ) 495 k = h and fr finie values 33 = h x Universiy f Illinis a Urbana-Champaign Meals Prcessing Simulain Lab S. Kric 1 6

7 Analyical, COND, and Abaqus emperaure and Sress Resuls (Weiner-Bley) All differen Sress Updae Inegrain mehds in Abaqus yld he same resul, and are represened by a single Abaqus curve in bellw sress graph emperaure [C] 13 1 Analyical 5 sec Abaqus 5 sec COND 5 sec 11 Analyical 1 sec Abaqus 1 sec COND 1 sec Disance he chilled surface [mm] Sress [MPa] -5-1 Analyical 5 sec Abaqus 5 sec -15 COND 5 sec Analyical 1 sec - Abaqus 1 sec COND 1 sec Disance he chilled surface [mm] Universiy f Illinis a Urbana-Champaign Meals Prcessing Simulain Lab S. Kric 13 Slidifying Slice (.7 %C) wih Realisic Hea Flux and emperaure Dependan Maerial Prpers Cnduciviy [W/mK] Surface Hea Flux [MW/m ] ime Bellw Meniscus [sec] 59.3 W/mK in Liquid Cefficn f hermal Expansin [1/K].4 x emperaure [C] 1.4 x 16 Enhalpy [J/kg] Hf emperaure [C] emperaure [C] Universiy f Illinis a Urbana-Champaign Meals Prcessing Simulain Lab S. Kric 14 7

8 Abaqus and COND emperaure and Sress Resuls fr Realisic Slidifying Slice in CC Mld 16 6 emperaure [C] Abaqus 5 sec COND 5 sec 1 Abaqus 1 sec COND 1 sec Disance he chilled surface [mm] Sress [MPa] Abaqus 5 sec COND 5 sec -1 Abaqus 1 sec COND 1 sec Disance he chilled surface [mm] Universiy f Illinis a Urbana-Champaign Meals Prcessing Simulain Lab S. Kric 15 CPU Benchmarking Resuls CODE Glbal Mehd fr Slving BVP Lcal Inegrain Mehd reamen f Liq./Mushy zne CPU ime (Minues) Abaqus Full NR Implici fllwed by Liquid Funcin 55 lcal Bunded NR Abaqus Full NR Implici fllwed by Liquid Funcin 53 Nema-Nasser Abaqus Full NR Implici fllwed by Radial Reurn 5.6 lcal Bunded NR Abaqus Full NR Implici fllwed by Radial Reurn r Failed lc. full NR (CREEP) Liquid Funcin Abaqus Full NR Explici (CREEP) Liquid Funcin 185 COND Operar Spliing Implici fllwed by Liquid Funcin 6 (Iniial Srain) lcal Bunded NR COND Operar Spliing (Iniial Srain) Implici fllwed by Nema-Nasser Liquid Funcin 5.9 Universiy f Illinis a Urbana-Champaign Meals Prcessing Simulain Lab S. Kric 16 8

9 Cnclusins he emperaure and sress resuls are maching very well beween w cdes. A small discrepancy beween he sress resuls in he cldes zne is under invesigain. I k Abaqus in average -3 ierains wih is glbal full NR mehds achve cnvergence, while COND is using explici perar spliing echnique slve glbal equilibrium equains wihu any ierains per incremen which is CPU cs effecive, bu migh be prne sme minr errrs and scillains. Lcal implici inegrain fllwed by lcal bunded NR mehd urned u be he ms efficn and rbus mehd fr inegraing ur highly nnlinear cnsiuive laws. CPU ime fr Abaqus wih ur UMA using lcal implici rae independen plasiciy algrihm (Radial Reurn) in liquid/mushy zne and fully implici lcal inegrain mehd fllwed by lcal bunded NR in slid is ally cmparable COND, a clear sign ha Abaqus wih ur UMA is nw ready ackle large prblems. Universiy f Illinis a Urbana-Champaign Meals Prcessing Simulain Lab S. Kric 17 Lcal Bunded NR versus Lcal Full NR, a key fas cnvergence Universiy f Illinis a Urbana-Champaign Meals Prcessing Simulain Lab S. Kric 18 9

10 Curren & Fuure Wrk Add mre Phenmena (Physics) he mdel in rder mach real prcess cndiin: Inernal BC wih Ferrsaic Pressure, cnac and fricin beween mld and shell, inpu mld disrin daa. Prgram a cnsisen angen perar wih respec emperaure in ur UMA and perfrm incremenally-cupled D analysis wih Abaqus (L- Shape FE Dmain). Incrprae a realisic gap-size hea ransfer cefficn ha can prduce a reasnable mach wih realisic hea flux frm plan measuremens. Perfrm a realisic 3D hermal sress analysis wih adequae mesh refinemen f slidificain f shell f a hin slab caser ha can accuraely predic he 3D mechanical sae in sme criical znes impran crack frmain. his wuld be he firs f is kind ever perfrmed. Wih enugh dfs (3D), parallel Abaqus feaures will be appld (each ime incremen slved in parallel n NCSA s SMP machines). he UMA presened here has been already cded fr a 3D sress sae. Add cnsiuive mdel fr seels wih dela-ferrie. Universiy f Illinis a Urbana-Champaign Meals Prcessing Simulain Lab S. Kric 19 D Applicain, Shell Behavir wih srand crner Predic he emperaure, sress, and srain evaluain acrss a D secin f he srand Predic he disred shape f he srand Gd fr bille and crner prins f he slab Y(mm) SRESS-Z(MPa) X(mm) V=. m/min V=4.4 m/min Curesy f Chungsheng Li, COND Universiy f Illinis a Urbana-Champaign Meals Prcessing Simulain Lab S. Kric 1

11 3D Applicain, hin Slab Caser Due a funnel ype mld, cmplex gemery in casing direcin is causing an in-plane bending phenmena which was n mdeled in D COND mdels. Only a 3D mdel can give he accurae sress disribuin. Universiy f Illinis a Urbana-Champaign Meals Prcessing Simulain Lab S. Kric 1 Crack defecs in cninuus cas slabs Cracks frm by cmbinain f 1) ensile sress and ) meallurgical embrilemen Surface Cracks (iniiaed in he mld) ransverse crner ransverse surface Lngiudinal midface Lngiudinal crner Sar Inernal cracks (iniiaed a slidificain frn) Midway Sraighening Pinch rll Diagnal riple pin Off crner Radial sreaks Cenerline Universiy f Illinis a Urbana-Champaign Meals Prcessing Simulain Lab S. Kric 11

12 Acknwledgemens Prf. Brian G. hmas Chungsheng Li, PhD, Frmer UIUC suden Hng Zhu, PhD, Frmer UIUC suden Nainal Cener fr Supercmpuing Applicains Universiy f Illinis a Urbana-Champaign Meals Prcessing Simulain Lab S. Kric 3 1