Deformation Of Adaptive Heterophase Crystal

Abstract

A crystal which can be in two possible phase states is considered. During tensile extension the crystal is deformed elastically. After a certain amount of elastic strain a phase transformation begins. For each fixed level of strain an equilibrium mesostructure is established, which corresponds to a minimum in the free energy of the crystal. The equilibrium mesostructure consists of plane, parallel layers of a product phase separated by layers of an initial phase. The product phase itself consists of two or more different domains (twins) forming plane, parallel alternations. The volume fractions of the phases and of different twin components in the product phase are functions of strain and temperature. Above a critical temperature the product phase is a single domain (untwinned). The stress-strain curve which reflects the evolution of the equilibrium mesostructure is calculated. For deformation under a strain control the calculated equilibrium stress-strain curve has a section with negative slope that corresponds to a negative Young’s modulus. If deformation proceeds under stress control, hysteretic stress-strain curves on loading and unloading will result from a section with negative slope.