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

Abstract

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.