On the interface modelling of crystal growth processes. Part II. Uncoupled thermoelastic theory

Abstract

Solidification of an elastic sphere from melt in a quasi-static formulation has been investigated in "singular surface approach" and in "finite slab approach". Thermal stresses in the solid phase are derived for both approaches due to the uncoupled thermoelastic quasi-static theory. In the interfacial layer, which has been regarded as a boundary layer between the liquid and the solid phase, special constitutive relations for the purely mechanical problem are posed in order to have a continuous change from the liquid to solid phase. It has been found that the solutions corresponding to the "singular surface approach" are the zero order terms of the asymptotic expansions in the small parameter of the "finite slab approach" solutions.