Influence of cooling rate on deformation due to effective stress in a solidifying alloy

Abstract

The relative volume rate at a local volume element, div V S′, that is used to evaluate the deformation in the two-phase zone of a solidifying alloy, is dependent on history of the effective stress. In a model of unidirectional solidification, the variation of the effective stress with x-direction or time at the fast cooling rate is larger than the one at the slow cooling rate. The different relative volume rates due to the inhomogeneous cooling rates produce deformation mismatch among the various volume elements in an ingot. It is suggested that accumulation of the deformation mismatch gives rise to thermal residual stain and stress, and hot-tearing tendency in the ingot. The effective stress may be residual in the solidified alloy if it is less than the strength of the alloy itself at the fast cooling rate, and may be relaxed by the deformation of the two-phase zone and play a role in forming the channel space filled with the unstable flow at the slow cooling rate.