Lg. Hector et al., STRAIN-RATE RELAXATION EFFECT ON FREEZING FRONT GROWTH INSTABILITY DURING PLANAR SOLIDIFICATION OF PURE METALS .1. UNCOUPLED THEORY, Journal of thermal stresses, 17(4), 1994, pp. 619-646
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.