Effect of coating material on the growth instability in solidification of pure metals on a coated planar mold of finite thickness

Abstract

In this study, a theoretical basis of thermomechanical instability during the solidification of pure metals on a coated planar mold is presented. This study extends the previous works by taking into account the presence of a deformable coating layer on the inner mold surface. The thermal and mechanical problems are assumed to be coupled through the pressure dependent thermal contact resistances at the shell/coating and coating/mold interfaces. On the other hands, the thermal capacitance of solidified shell, coating layer and mold materials are neglected for the sake of simplicity. A linear perturbation method is used to reduce the spatial dimension of the problem. The model leads to two coupled differential equations for the shell thickness perturbation and residual stress which are solved numerically. The results document the variation of the perturbed solidification front as a function of ratio between the thermal conductivities of the shell and coating materials for combinations of other process parameters such as the combination of shell and mold materials, the values of coating thickness and coupling rates. In case of weak coupling, the maximum magnitude of this perturbation decreases regardless of the value of coating thickness and shell-mold material combinations when the thermal conductivity of the coating material is decreased. In case of strong couplings however, a critical thermal conductivity ratio between shell and coating materials which leads to a formation of greatest or lowest perturbation in the solidification front depending on the values of other process parameter has been found.