Irreversible thermodynamics of creep in crystalline solids

TL;DR

This paper develops a thermodynamic framework for modeling creep in crystalline solids, incorporating microstructure evolution, vacancy diffusion, and non-conserved lattice sites, providing new insights into creep mechanisms.

Contribution

It introduces a comprehensive irreversible thermodynamics approach for creep, including gradient thermodynamics and phase fields, to describe microstructure and vacancy dynamics.

Findings

Derived a general entropy production expression for creep.

Analyzed a 1D bicrystal model showing vacancy-driven grain boundary migration.

Demonstrated the role of vacancy concentration gradients in creep deformation.

Abstract

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-hydrostatically stressed multi-component solid medium with non-conserved lattice sites and inhomogeneities handled by employing gradient thermodynamics. Phase fields describe microstructure evolution which gives rise to 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 phenomenological 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.