Irreversible thermodynamics of creep in crystalline solids
Yuri Mishin, James A. Warren, Robert F. Sekerka, William J. Boettinger
We develop an irreversible thermodynamics framework for the description of creep deformation in crystalline solids by mechanisms that involve vacancy diffusion and lattice site generation and annihilation. The material undergoing the creep deformation is treated as a non-classical, non- hydrostatically stressed multi-component solid medium with non-conserved lattice sites. Phase fields describe microstructure evolution and the associated redistribution of vacancy sinks and sources in the material during the creep process. We derive a general expression for the entropy production rate and use it to identify of the relevant fluxes and driving forces and to formulate phenomenoligical relations among them taking into account symmetry properties of the material. As a simple application, we analyze a one-dimensional model of a bicrystal in which the grain boundary acts as a sink and source of vacancies. The kinetic equations of the model describe a creep deformation process accompanied by grain boundary migration and relative rigid translations of the grains. They also demonstrate the effect of grain boundary migration induced by a vacancy concentration gradient across the boundary.
Physical Review B
Irreversible thermodynamics, creep deformation, diffusion, lattice sites, phase field