Equilibrium two-phase microstructure at phase transformation in a constrained solid

Thermodynamics of a coherent phase transformation in a constrained solid is analyzed. Under mechanical constraint the phase transformations in single component systems result in an equilibrium two-phase mixture. A typical equilibrium two-phase microstructure of the initial-product phase mixture is an alternation of the plane-parallel layers of the phases with a special crystallographic orientation of interfaces between layers. The relative fractions of the phases are determined by the external conditions. The two-phase free energy is a non-convex function of constrained strain. Therefore, the stress-strain relation at displacement controlled deformation of the transforming two-phase mixture is characterized by a negative Youngʹs modulus. If deformation proceeds under stress control, a hysteretic stress-strain curve on loading and unloading should be observed instead of a negative stress-strain slope.