STRAIN RATE RELAXATION EFFECT ON FREEZING FRONT GROWTH INSTABILITY DURING PLANAR SOLIDIFICATION OF PURE METALS, PART 2. COUPLED THEORY

Abstract

In this second pan we modify the mathematical developments of the growth instability problem in Part 1 based upon the assumption that the thermal and mechanical problems are coupled along the mold interface through a pressure-dependent thermal contact resistance. Thermomechanical coupling results from the fact that heat is extracted from the casting across the thermal resistance. The thermal boundary condition, which contains a spatial perturbation in heat flux, is accompanied by a similar perturbation in the contact resistance at the mold interface. Using the plane strain thermoviscoelasticity theory developed in the companion paper, coupled differential equations are derived for the function representing residual stress and the spatial perturbation of the mean casting thickness. The two differential equations are then decoupled, and this leads to a single equation for the casting thickness perturbation. Then the evolution of the contact pressure perturbation can be calculated, and the results used to de...