On the constitutive modeling of coupled thermomechanical phase-change problems

Published in International Journal of Plasticity Vol. 17 (12), pp. 1565-1622, 2001
doi: 10.1016/S0749-6419(00)00094-2

Abstract

This paper deals with a thermodynamically consistent numerical formulation for coupled thermoplastic problems including phase-change phenomena and frictional contact. The final goal is to get an accurate, efficient and robust numerical model, able for the numerical simulation of industrial solidification processes. Some of the current issues addressed in the paper are the following. A fractional step method arising from an operator split of the governing differential equations has been used to solve the nonlinear coupled system of equations, leading to a staggered product formula solution algorithm. Nonlinear stability issues are discussed and isentropic and isothermal operator splits are formulated. Within the isentropic split, a strong operator split design constraint is introduced, by requiring that the elastic and plastic entropy, as well as the phase-change induced elastic entropy due to the latent heat, remain fixed in the mechanical problem. The formulation of the model has been consistently derived within a thermodynamic framework. All the material properties have been considered to be temperature dependent. The constitutive behavior has been defined by a thermoviscous/elastoplastic free energy function, including a thermal multiphase change contribution. Plastic response has been modeled by a J2 temperature dependent model, including plastic hardening and thermal softening. The constitutive model proposed accounts for a continuous transition between the initial liquid state, the intermediate mushy state and the final solid state taking place in a solidification process. In particular, a pure viscous deviatoric model has been used at the initial fluid-like state. A thermomecanical contact model, including a frictional hardening and temperature dependent coupled potential, is derived within a fully consistent thermodinamical theory. The numerical model has been implemented into the computational finite element code COMET developed by the authors. Numerical simulations of solidification processes show the good performance of the computational model developed.