Creep and recrystallization of large polycrystalline masses. II. Constitutive theory for crystalline media with transversely isotropic grains

By combining the theory of mixtures with continuous diversity with Liu's method of Lagrange multipliers, a thermodynamically consistent constitutive theory is derived for large polycrystalline masses made up of transversely isotropic crystallites. The media under study are supposed to be incompressible and subjected to strain-induced anisotropy and recrystallization effects. Owing to the fabric (texture) changes caused by lattice rotation and polygonization, the polycrystal and its composing grains are modelled as polar media. Among other results of the theory, the existence of a dislocation potential is inferred, which represents for polycrystals the counterpart to the chemical potential of physical chemistry. Furthermore, exploitation of the dissipation inequality gives rise to the notion of a driving pressure for grain boundary migration . Besides, the vanishing of the Voigt couple stress is analysed together with the existence of internal stresses and couples responsible for the bending/twisting of crystallites by polygonization and heterogeneous strain.