Virtual Mold Technique in Thermal Stress Analysis during Casting Process

360J. Mater. Sci. Technol, Vol.24 No.3, 2008of friction and gap element has two status, open andclosed & sliding mode. Elasto-plastic-thermal stressanalysis is performed for the casting and the moldModelingparts. The node-to-node contact technique is requiredboth meshes for the casting and the mold, thus theFOM methFEM metmethod supplies a reliable solution. But the largegenerabongeneratonnumber of meshes cause ineffectiveness in the compu-FOMFEtational time and mesh generation work.(2) Rigid mold contactThe contact problem can be classified as the con-TemperatunThemal too。tact element type: node-to-node, surface-to-node,mnalyidsanalyadtsurface-to- surface. In general, the node to-node con-tact element gives good solution but requires dificultFeld data interdacework in FE mesh generation for a complicate shape|Nproduct. The volume of mold is two or three timesHST>Speciledbigger than that of casting, so the mold mesh needslots of computational time and memory.RatumComvege?The mold is more rigid than the casting in diecasting process, s0 it is possible to assumne the mold isrigid. The rigid means that the relative deformationAnlyisreulsis zero in the mold. The rigid mold contact methoddoes not need mesh for mold, so the computationalFig.1 Procedure of FDM/FEM hybrid analysis for cast-time and memory can be saved. However the rigiding processmold induces high stress in casting domain.(3) Virtual mold contactThe rigid mold contact technique is eficient, butInitial gap widththe accuracy is low. Therefore we proposed the vir-tual mold technique. The technique adopts a springt(angential drection)bar element instead of a contact element on the in-terface of the mold and the casting as Fig.3(b). Thewwvn(normal vector)间Fig.2 Configuration of 2-D gap elementto perform non-linear FEM stress analysis.2.2 Contact problem on casting processThe contact of the casting and the mold is commonCastand important phenomena in casting process. ThereContact elementare a couple of algorithms such as penalty method andlagrange method for resolving a contact problem.Mold(1) Cast/mold elasto plastic contactGap element is a 2-node nonlinear element which isused to model node- to-node contact between two bod-ies with or without friction as penalty method. Thegap element configuration of 2-D is shown in Fig.2.We use the gap function as Eq.(1) to determinethe status of a gap element: open or closed.g=(u2 -1)+go1)where (u2 -u1) is the relative displacement in the nor-mal direction of gap and 9o is the initial gap width.The gap condition is represented by the following in-equality equationsSpring elementg> 0 (open status)中国煤化工g≤0 (close status)2)Fig.YHCNM H Gragration for contactGap element has three degrees of freedom (u,U,w) atn the inter-each node and normal compressive force and tangen-face between the casting and the mold, (b) usingtial shear force. In this study, the friction between thespring element on the interface between the cast-casting and the mold was ignored. Frictionless con-ing and the moldtact may be modeled by specifying a zero coefficientJ. Mater. Sci. Technol, Vol.24 No.3, 2008361Table 1 Material, chemical composition and casting condition of the specimenMaterialChemical composition/wt pctCasting conditionCrMo alloy steel 0.22C, 0.42Si, 0.7Mn, 0.93Cr, 0.2Mo_ Pouring termperature: 1600°C permanent moldcomputational efficiency of the technique is high dueto no FEM mold mesh and the accuracy of stress can↑Ybe approved by the elasto-plastic spring element in-stead of a rigid property of mold.Figure 4 is the configuration of the spring bar el-ement arbitrarily oriented, 0, in ry planel6.The relationship between displacement vector andexternal force vector for the spring bar element canbe expressed as(3)→x{詹}=誓[_ 1]{出}Fig.4 Configuration of a spring bar elementThe local stifness matrix, h, is written by(4)4[1]a)where A, E, L are area, elasticity and length of theelement, respectively.And the local stifness matrix, k, in case of arbi-trarily oriented element isC2CS-C2-CS.人k=AE|-CSCS(5)LCs2Mold: elasto-plasticwhere C and S are cos0 and sin0, respectively.3. Results and Discussion3.1 Cast/ mold elasto plastic contact and rigid moldCast olasto-plasticcontactFigure 5(a) is the shape of the specimen which isused for the simulation in this study and the analysisdomain is a quarter part only due to the symmetrygeometry. The chemical composition of the specimenis listed in Table 17,18. Figure 5(b) and (c) show theelasto-plastic contact for the cast/ mold interface andrigid mold contact condition, respectively. Both themeshes of the casting and the mold are required incase of the elasto-plastic cast/ mold interface contactas shown at Fig.5(b). And the rigid mold contact con-dition needs the mesh for the casting only as shownat Fig.5(c).Table 2 shows the efficiency of the analyses withCast elasto-plasticabove contact conditions in casting process. Com-pared with the elasto-plastic contact condition, thecomputational memory and time of the rigid moldconte中国煤化工two times. Fig-ure 6inal (YY) residualstressMH.CNMHGumstressisabout190 Mra under the elasto-plastic contact condition.Fig.5 Cast and mold models used for the simulation inHowever the maximum stress is over 5 GPa under thecontact problem: (a) casting shape for contactrigid mold condition because the rigid contact is theanalysis, (b) meshes for the casting and the mold,very strong constraint.(c) mesh for the casting only362J. Mater. Sci. Technol, Vol.24 No.3, 2008Table 2 Eficiency of analyses with contact conditions in casting processContact conditionNumber of element Computational memory/MB Computational time/s_Elasto-plastic onCast: 4,14239485Cast/Mold interfaceMold: 9,935Rigid Mold1664(434+0Fig.6 YY-stress distributions of the specimen at the final stage: (a) elasto plastic analysis for cast and moldusing contact element, (b) rigid mold condition using the casting mesh only3.2 Virtual mold contactFigure 7 shows the hot tearing prediction of theanalysis without any contact element between thecasting and the mold. The result shows the hot tear-ing defect possibility of the inside column only butthe results of an experiment and the analysis includecontact element show the hot tearing possibility atthe both columns as shown in Fig.8(a). The result ofFig.8(a) shows that the proposed technique is usefulin the prediction of hot tearing.The YY-stress is about 250 MPa in the case ofthe spring contact element on the virtual mold asFig.8(b), the value is much more reasonable, com-Fig.7 Hot tearing prediction of the analysis without anypared with the stress level, over 5 GPa, of the rigidmold contact condition.contact element中国煤化工YHCNMHGFig.8 Analysis results of the specimen using the spring element on the interface between the casting and thevirtual mold: (a) hot tearing prediction, (b) Y Y-stress distribution at the final stageJ. Mater. Sci. Technol, Vol.24 No.3, 20084. Conclusionthe Fifth Int. Conf. on Modeling of Casting, Weldingand Advanced Solidification Processes-V, 1990, 65-70.In the present work, we studied the contact elements[6] G.Fortin, P.Louchez and FHSamuel: AFS Trans,for the interface between the casting and the mold. First,1992, 863.the elasto plastic contact element gives a proper solution[7] R.Song, G.Dhatt and A.B.Cheikh: Int. J. Numer.but the contact element condition needs lots of computa-Meth. Eng, 1990, 30, 579.tional time and memory and mesh generation work. Sec-[8] K.Y.Kim: ISIJ Int, 2003, 43, 647.ond the rigid mold contact condition decreased the com-9 j B.G.Thomas: Int. Conf. on Modeling of Casting &putational time and memory and the condition is not re-Solidification Process-VI, 1993, 519. .quired FEM mesh for the mold. But the technique caused[10] J.W.Kang, B.C.Liu and S.M.Xiong: J. Mater. Scithe high stress level. In conclusion, the proposed virtualTechnol, 1999, 15(3), 267.mold technique using the spring contact element condition[11] z.B.Dong, Y.H.Wei, R.P.Liu and Z.J.Dong: J. Mater.between the casting and the virtual mold gives reasonableSci. Technol, 2005, 21(3), 399.stress results and good indicator for hot tearing defect12] M.Rappaz， J.M.Drezet and M.Gremaud:Metall.prediction.Mater. Trans. A, 1999, 30A, 44[13] C.Monroe and C.Beckermann: Mater. Sci, Technol,REFERENCES2005, 47.[14] H.M.Si, C.Cho and S.Y.Kwak: J. Mater. Process.Technol, 2003, 133, 311[1] R.H.Tien and V.Koump: ASME J. Appl. Mechan,15] S.Y.Kwak, C.HLim, J.H.Hong, J.K.Choi and N.Arai:1969, 36, 763.J. Computational Fluid Dynamics, 2004, 12(4), 638.[2] R.W.Lewis and B.R.Bass: Trans. ASTM, 1976, Au-[16] D.LLogan: A First Course in Finite Element Methodgust, 479.Using Algor, 2nd Edition, 1997.[3] J.R.Williams, R.W.Lewis and K.Morgan: Int. J. Nu-[17] High-Temperature Property Data: Ferrous Alloys,mer. Meth. Eng, 1978, 14, 19.ASM Int, 1988.[4] A.Yosida, S.Nagaki and T.Inoue: J. Soc. Mat. Sci.18] ASM Handbook, Properties and Selection: Irons,Jpn, 1982, 31(348), 897.Steels, and High Performance Alloys, ASM Int,, 1990,[5] H.Huang, J.LHill, V.K.Suri and J.T.Berry: Proc. of628.中国煤化工MYHCNMHG