Sharp interface model of creep deformation in crystalline solids
Yuri Mishin, Geoffrey B. McFadden, Robert F. Sekerka, William J. Boettinger
We present a rigorous irreversible thermodynamics treatment of creep deformation of solid mate- rials with interfaces described as geometric surfaces capable of vacancy generation and absorption and moving under the influence of local thermodynamic forces. The free energy dissipation rate derived in this work permits clear identification of thermodynamic driving forces for all steps of the creep process and formulation of kinetic equations of creep deformation and microstructure evolution. The theory incorporates capillary effects and reveals the different roles played by the interface free energy and interface stress. To describe the interaction of grain boundaries with stresses, we classify grain boundaries into coherent, incoherent and semi-coherent, depending on their mechanical response to the stress. To prepare future applications, we specialize the general equations to a particular case of a linear-elastic solid with a small concentration of vacancies. The proposed theory creates a thermodynamic framework for addressing more complex cases in the future, such as creep in multi-component alloys and cross-effects between vacancy generation/absorption and grain boundary motion and sliding.
Irreversible thermodynamics, creep deformation, diffusion, vacancies, surfaces and interfaces