A coupled thermomechanical model for the solidification of cast metals

A coupled thermomechanical model to simulate solidification problems in casting is presented. The model is formulated from a phenomenological point of view using a general isotropic thermoelasto-plasticity theory. Generalized phase-change effects accounting for the different thermomechanical behaviour of the solidifying material during its evolution from liquid to solid have been considered. For this purpose, a phase-change function, plastic evolution equations and a temperature-dependent constitutive law have been defined. Full thermomechanical effects as well as variable thermal and mechanical boundary conditions are also taken into account. Particular details concerning the numerical implementation of the model are given, where special emphasis is devoted to the resulting highly non-linear fully coupled finite element equations. The behaviour of this formulation is studied first in a simple quenching problem. Finally, a cylindrical casting test problem including phase-change phenomena, temperature-dependent constitutive properties and contact effects is analysed. Numerical results are compared with laboratory measurements.