Multiple development of new phase inclusions in elastic solids

We consider an initial stage of a stress-induced phase transformation as a process of heterogeneous deformation due to multiple appearance of new phase inclusions. We develop a model describing how multiple development of interacting new phase inclusions depends on external strains and how the new phase development affects the macro-behavior of a deformable material. We assume that the random fields of the inclusions and strains are symmetric in a statistical sense. We use the notion of the symmetry of the effective inclusion and assume that this symmetry is the symmetry of an ellipsoid. Then we accept the idea that the geometry of the two-phase structure, in contrast to usual composite materials, is adapted to strains so that certain correspondences between the symmetries of the inclusions and strain fields are settled. A symmetry consistent approach developed as an alternative to a self-consistent (effective) field method for materials undergoing phase transformations allows us, similar to the effective field method, to construct average free energy as a function of a new phase volume concentration and two tensors which characterize the orientation and the shape of the effective ellipsoid and the set of inclusions. Then the problem of equilibrium two-phase structure reduces to the free energy minimization on the class of self-organizing two-phase structures controlled, given average strains, by the symmetry restrictions. We show that the average energy minimization requirements are equivalent to the thermodynamic condition written for the effective ellipsoid. We obtain the dependencies of the new phase concentration and the effective ellipsoid tensor on average strains or stresses. We discuss the stability and estimate energy changes due to phase transformations. We construct domains of existence of the described two-phase structures in strain space and emphasize that the new phase development by the mechanism considered is not possible at any deformation path. We also derive average stress–average strain relationships which demonstrate strain softening effect on the path of the phase transformation.