STRAIN RATE RELAXATION EFFECT ON FREEZING FRONT GROWTH INSTABILITY DURING PLANAR SOLIDIFICATION OF PURE METALS,PART 1. UNCOUPLED THEORY

Previous models of thermomechanically induced freezing front growth instability have assumed that the casting accumulates elastic strains as it solidifies. While this assumption is useful in providing insight into solidification thermomechanics, it fails to account for inelastic strains that normally accompany elevated temperature deformations. In this paper, growth instability during solidification of a pure metal is reexamined, assuming that the strain rate within the solidifying shell is the sum of elastic, thermal, and viscous components. This requires that a theoretical framework for plane strain thermoviscoelasticity be developed for a solidifying metal. The viscous component leads to strain rate relaxation within the casting and subsequently influences the evolution of the contact pressure and macromorphology of the freezing front. We define a strain rate relaxation parameter that determines the extent to which the casting deforms due to viscous creep. Both short-time and long-time solutions for the contact pressure are developed and subsequently examined for selected values of the strain rate relaxation parameter. The thermal and mechanical fields are assumed to be uncoupled along the metal /mold interface in the present paper while they are coupled along this interface in the companion paper.