Solid-liquid equilibrium for non-hydrostatic stress

We examine Gibbs' conditions for equilibrium of a non-hydrostatically stressed single component solid in equilibrium across one of its faces with a pure liquid at pressure p(F). We show that the equilibrium melting temperature T-N for the non-hydrostatically stressed solid in contact with a melt at pressure p(F), is below the equilibrium melting temperature T-H of the hydrostatically stressed solid at p(F). Furthermore, for small strain and linear isotropic elasticity, the deviation, T-H-T-N, is shown to be quadratic in the differences between the principal values of the stress tensor and -p(F). The result depends on both the bulk modulus and the shear modulus of the solid. Even for stresses as large as a typical yield stress, T-H-T-N is equal to I K or less. Nevertheless, the liquid in equilibrium with this non-hydrostatically stressed solid is always unstable with respect to the formation of hydrostatic solid. (C) 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.