Thermo-mechanical models of steel solidification based on two elastic visco-plastic constitutive laws

Seid Koric, Brian G. Thomas

Research output: Contribution to journalArticlepeer-review


Two thermo-mechanical models based on different elastic-visco-plastic constitutive laws are applied to simulate temperature and stress development of a slice through the solidifying shell of 0.27%C steel in a continuous casting mold under typical commercial operating conditions with realistic temperature dependant properties. 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 elastic-visco-plastic constitutive laws of Kozlowski [P.F. Kozlowski, B.G. Thomas, J.A. Azzi, H. Wang, Simple constitutive equations for steel at high temperature, Metall. Trans. 23A (1992) 903-918] for austenite in combination with the Zhu power-law [H. Zhu, Coupled thermal-mechanical finite-element model with application to initial solidification, PhD thesis, University of Illinois, 1993] for delta-ferrite with ABAQUS [ABAQUS Inc., User Manuals v6.6, 2006] using a user-defined subroutine UMAT [S. Koric, B.G. Thomas, Efficient thermo-mechanical model for solidification processes, Int. J. Num. Meth. Eng. 66 (2006) 1955-1989], and the Anand law for steel [L. Anand, Constitutive equations for the rate dependant deformation of metals at elevated temperatures, ASME J. Eng. Mater. Technol. 104 (1982) 12-17; S.B. Brown, K.H. Kim, L. Anand, An internal variable constitutive model for hot working of metals, Int. J. Plasticity 6 (1989) 95-130] using the integration scheme recently implemented in ANSYS [ANSYS Inc., User Manuals v100, 2006]. The results from these two approaches are compared and CPU times are benchmarked. A comparison of one-dimensional constitutive behavior of these laws with experimental tensile test data [P.J. Wray, Plastic deformation of delta-ferritic iron at intermediate strain rates, Metall. Trans. A 7A (1976) 1621-1627; P.J. Wray, Effect of carbon content on the plastic flow of plain carbon steel at elevated temperatures, Metall. Trans. A 13 (1982) 125-134] and previous work [A.E. Huespe, A. Cardona, N. Nigro, V. Fachinotti, Visco-plastic constitutive models of steel at high temperature, J. Mater. Process. Technol. 102 (2000) 143-152] shows reasonable agreement for both models, although the Kozlowski-Zhu approach is much more accurate for low carbon steels. The thermo-mechanical models studied here are useful for efficient and accurate analysis of steel solidification processes using convenient commercial software.

Original languageEnglish (US)
Pages (from-to)408-418
Number of pages11
JournalJournal of Materials Processing Technology
Issue number1-3
StatePublished - Feb 1 2008


  • Constitutive models
  • Elastic-visco-plastic material
  • Finite elements
  • Solidification and melting
  • Steel casting
  • Thermo-mechanical processes

ASJC Scopus subject areas

  • Ceramics and Composites
  • Computer Science Applications
  • Metals and Alloys
  • Industrial and Manufacturing Engineering


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