On the Strain Saturation Conditions for Polycrystalline Ferroelastic Materials

A phenomenological constitutive law is developed for the deformation of polycrystalline ferroelastic materials. The model is framed within a thermodynamic setting common to internal variable plasticity The two significant inputs to this model are a switching (yield) surface, and a hardening potential. To maintain simplicity, the shape of the switching surface is assumed to be spherical in a modified deviatoric stress space. In order to ascertain the functional form of the hardening potential, micromechanical self-consistent simulations of multiple single crystals, with tetragonal crystal structure, embedded in an effective polycrystalline matrix, are performed for differing loading paths in remanent (plastic) strain space. As a result of the asymmetry in the tension versus compression behavior of these materials, it is shown that pure shear loading does not result in pure shear straining. This feature of the material behavior is demonstrated with the self-consistent simulations and predicted by the phenomenological constitutive law. Ultimately the phenomenological theory is able to capture the complex constitutive behavior of ferroelastic materials predicted by the micromechanical model.