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Creep and recrystallization of large polycrystalline masses Part II: Constitutive theory for crystalline media with transversely isotropic grains
Sérgio H. Faria, Gilberto M. Kremer and Kolumban Hutter
By combining the theory of mixtures with continuous diversity with the method of Lagrange multipliers for the exploitation of the entropy principle, a thermodynamically consistent constitutive theory is derived for large polycrystalline masses made up of transversely isotropic crystallites. The media are considered incompressible and subjected to strain-induced anisotropy and recrystallization e ects, under the constraint of vanishing grain shifting (i.e., negligible grain boundary sliding). Owing to the fabric (texture) evolution caused by lattice rotation and the bending/twisting of crystallites by polygonization, the polycrystal and its composing grains are modelled as (micro-)polar media. Among other interesting results of the theory, the existence of a dislocation potential is inferred, which represents for polycrystalline media the counterpart to the chemical potential of physical chemistry. Furthermore, it is shown that one of the terms of the dissipation inequality is proportional to the recrystallization rate and gives rise to the notion of a driving pressure for grain boundary migration. The vanishing of the Voigt couple stress and the existence of internal couples responsible for polygonization are also analysed.