Efficient thermo-mechanical model for solidification processes.

*(English)*Zbl 1110.74822Summary: A new, computationally efficient algorithm has been implemented to solve for thermal stresses, strains, and displacements in realistic solidification processes which involve highly nonlinear constitutive relations. A general form of the transient heat equation including latent-heat from phase transformations such as solidification and other temperature-dependent properties is solved numerically for the temperature field history. The resulting thermal stresses are solved by integrating the highly nonlinear thermo-elastic-viscoplastic constitutive equations using a two-level method. First, an estimate of the stress and inelastic strain is obtained at each local integration point by implicit integration followed by a bounded Newton-Raphson (NR) iteration of the constitutive law. Then, the global finite element equations describing the boundary value problem are solved using full NR iteration. The procedure has been implemented into the commercial package Abaqus (Abaqus Standard Users Manuals, v6.4, Abaqus Inc., 2004) using a user-defined subroutine (UMAT) to integrate the constitutive equations at the local level. Two special treatments for treating the liquid/mushy zone with a fixed grid approach are presented and compared. The model is validated both with a semi-analytical solution from J. Weiner and B. Boley [“Elasto-plastic thermal stresses in a solidifying body”, J. Mech. Phys. Solids 11, 145–154 (1963; Zbl 0111.21703)] as well as with an in-house finite element code CON2D [Metal. Mater. Trans. B 35B, No. 6, 1151–1172 (2004); Continuous Casting Consortium Website. http://ccc.me.uiuc.edu [30 October 2005]; Ph.D. Thesis, University of Illinois, 1993; Proceedings of the 76th Steelmaking Conference, ISS, vol. 76, 1993] specialized in thermo-mechanical modelling of continuous casting. Both finite element codes are then applied to simulate temperature and stress development of a slice through the solidifying steel shell in a continuous casting mold under realistic operating conditions including a stress state of generalized plane strain and with actual temperature-dependent properties. Other local integration methods as well as the explicit initial strain method used in CON2D for solving this problem are also briefly reviewed and compared.

##### MSC:

74F05 | Thermal effects in solid mechanics |

74S05 | Finite element methods applied to problems in solid mechanics |

80A20 | Heat and mass transfer, heat flow (MSC2010) |

PDF
BibTeX
XML
Cite

\textit{S. Koric} and \textit{B. G. Thomas}, Int. J. Numer. Methods Eng. 66, No. 12, 1955--1989 (2006; Zbl 1110.74822)

Full Text:
DOI

**OpenURL**

##### References:

[1] | Weiner, Journal of the Mechanics and Physics of Solids 11 pp 145– (1963) |

[2] | Li, Metallurgical and Materials Transactions B 35B pp 1151– (2004) |

[3] | Coupled thermal-mechanical finite-element model with application to initial solidification. Ph.D. Thesis, University of Illinois, 1993. |

[4] | , . Application of thermo-mechanical model for steel behaviour in continuous slab casting. Proceedings of the 76th Steelmaking Conference, ISS, vol. 76, 1993. |

[5] | Kristiansson, Journal of Thermal Stresses 5 pp 315– (1982) |

[6] | Risso, International Journal for Numerical Methods in Engineering |

[7] | Grill, Ironmaking and Steelmaking 3 pp 38– (1976) |

[8] | , . Thermomechanically-coupled analysis of the steel solidification process in continuous casting mold. Abaqus Users Conference, 1996; 749–769. |

[9] | , , . Temperature fields, solidification progress and stress development in the strand during a continuous casting process of steel. Numerical Methods in Thermal Problems. Pineridge: Swansea, 1979; 712–722. |

[10] | Kristiansson, Journal of Thermal Stresses 7 pp 209– (1984) |

[11] | , , . The Finite Element Method in Heat Transfer Analysis. Wiley: New York, 1996. |

[12] | , . Thermal stress analysis of a novel continuous casting process. In The Mathematics of Finite Elements and its Applications, (ed.) (V3 edn). Academic Press: New York, 1978. |

[13] | Boehmer, Advances in Engineering Software 29 pp 679– (1998) |

[14] | . A Fixed-mesh Eularian–Lagrangian Approach for Stress Analysis in Continuous Casting. Instituto Argentina de Siderurgia: Argentina, 2002. |

[15] | Farup, Metallurgical and Materials Transactions 31 pp 1461– (2000) |

[16] | Stangeland, Metallurgical and Material Transactions 30 pp 2903– (1999) |

[17] | Tan, Materials Science and Engineering |

[18] | Samanta, Materials Science and Engineering |

[19] | Abaqus Theory Manual v6.4. Abaqus Inc., 2004. |

[20] | Multidimensional integral phase change approximations for finite element conduction codes. In Numerical Methods in Heat Transfer, (ed.). Wiley: New York, NY, 1981; 201–213. |

[21] | Dupont, SIAM Journal on Numerical Analysis 11 pp 392– (1974) |

[22] | Thomas, Transactions of the Iron and Steel Society 7 pp 7– (1986) |

[23] | . Continuum Mechanics for Engineers (2nd edn). CRC Press: Boca Raton, FL, 1999. · Zbl 0991.74500 |

[24] | Anand, ASME Journal of Engineering Materials Technology 104 pp 12– (1982) |

[25] | Lush, International Journal of Plasticity 5 pp 521– (1989) |

[26] | Plasticity: Theory and Applications. Krieger: New York, 1983. |

[27] | . Mechanics of Solid Materials. Cambridge University Press: Cambridge, 2001. |

[28] | Abaqus Standard User Manuals v6.4. Abaqus Inc., 2004. |

[29] | . Finite Element Method: Solid and Fluid Mechanics Dynamics and Non-linearity. McGraw-Hill: New York, 1991. |

[30] | . Inelastic Deformation of Metals: Models, Mechanical Properties, Metallurgy. Wiley: New York, 1995. |

[31] | Simo, Computer Methods in Applied Mechanics and Engineering 48 pp 101– (1985) |

[32] | Nonlinear FEA of Solids and Structures. Wiley: New York, 1991. |

[33] | . Augmented Lagrangian and Operator-splitting Methods in Non-linear Mechanics. SIAM: Philadelphia, PA, 1989. |

[34] | Zienkiewicz, International Journal for Numerical Methods in Engineering 8 pp 821– (1974) |

[35] | Guidelines for writing user subroutine CREEP. Attachment to answer #805 from abaqus online support system. http://www.abaqus.com (May 2005 ). |

[36] | Zabaras, International Journal for Numerical Methods in Engineering 33 pp 59– (1992) |

[37] | Continuous Casting Consortium Website. http://ccc.me.uiuc.edu (30 October 2005). |

[38] | Nemat-Nasser, Computers and Structures 44 pp 937– (1992) |

[39] | Nemat-Nasser, Computer Methods in Applied Mechanics and Engineering 95 pp 205– (1992) |

[40] | ANSYS 5.3. Swanson Analysis Systems, Inc.: Houston, PA, 2005. |

[41] | , . Nonlinear FE for Continua and Structures. Wiley: New York, 2000. |

[42] | Rappaz, Metallurgical and Materials Transactions A 30A pp 449– (1999) |

[43] | Kozlowski, Metallurgical Transactions 23A pp 903– (1992) |

[44] | Wray, Metallurgical and Materials Transactions 7A pp 1621– (1976) |

[45] | Suzuki, Ironmaking and Steelmaking 15 pp 90– (1988) |

[46] | , . Summary of thermal properties for casting alloys and mould materials. Report No. NSF/MEA-82028, Department of Materials and Metallurgical Engineering, University of Michigan, 1982, PB83 211003 |

[47] | Investigation of the shrinkage and the origin of mechanical tension during the solidification and successive colling of cylindrical bars of Fe-C alloys. Ph.D. Thesis, Technical University of Clausthal, 1989. |

[48] | Huang, Metallurgical Transactions B 23B pp 339– (1992) |

[49] | , . Shrinkage and formation of mechanical stresses during solidification of round steel strands. 4th International Conference Continuous Casting, Brussels, Belgium, vol. 2. Verlag Stahleisen, P.O. Box 8229, D-4000, Dusseldorf 1, FRG, 2, 1988; 633–644 (preprints). |

[50] | Jimbo, Metallurgical Transactions B 24B pp 5– (1993) |

[51] | Mizukami, Journal of the Iron and Steel Institute of Japan 63 pp s-652– (1977) |

[52] | . Maximum casting speed for continuous cast steel billets based on sub-mold bulging computation. Steelmaking Conference Proceedings 2002, ISS, Warrendale, PA, Nashville, TN, 10–13 March 2002; 109–130. |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.