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

In this second part we modify the mathematical developments of the gro wth instability problem in Part 1 based upon the assumption that the t hermal and mechanical problems are coupled along the mold interface th rough a pressure-dependent thermal contact resistance. Thermomechanica l coupling results from the fact that heat is extracted from the casti ng across the thermal resistance. The thermal boundary condition, whic h contains a spatial perturbation in heat flux, is accompanied by a si milar perturbation in the contact resistance at the mold interface. Us ing the plane strain thermoviscoelasticity theory developed in the com panion paper coupled differential equations are derived for the functi on representing residual stress and the spatial perturbation of the me an casting thickness. The two differential equations are then decouple d, and this leads to a single equation for the casting thickness pertu rbation. Then the evolution of the contact pressure perturbation can b e calculated and the results used to determine the growth stability of the freezing front.