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

Previous models of thermomechanically induced freezing front growth in stability have assumed hat the casting accumulates elastic strains as it solidifies. While this assumption is useful in providing insight in to solidification thermomechanics, it fails to account for inelastic s trains that normally accompany elevated temperature deformations. In h is 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 b e developed for a solidifying metal The viscous component leads to str ain 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 t he extent to which the casting deforms due to viscous creep. Both shor t-time and long-time solutions for the contact pressure are developed and subsequently examined for selected values of the strain rate relax ation parameter. The thermal and mechanical fields are assumed to be u ncoupled along the metal/mold interface in the present paper while the y are coupled along this interface in the companion paper.