On the micromechanical modelling of the effective diffusion coefficient of a polycrystalline material

Abstract

This study focuses on calculation of the effective diffusion coefficient of a polycrystalline material accounting for the grain size and shapes. Polycrystal is modelled as a composite consisting of a matrix with high diffusivity (grain boundaries and triple junctions) and inhomogeneities with low diffusivity (bulk grains including crystal defects like dislocations). The segregation at the grain boundaries is accounted for. Typical micromechanical models are re-written for diffusivity assuming that the grains have the shape of ellipsoids of revolution (spheroids). The results are compared with (1) numerical results for hydrogen diffusion in an imaginary polycrystalline material and (2) experimental results for diffusion of hydrogen in nickel polycrystal available in the literature. The approach can be used for extraction of information on diffusivity along the grain boundaries.

Keywords:

• diffusion
• polycrystal
• grain boundaries
• homogenization
• micromechanical modelling

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the Russian Foundation for Fundamental Research [grant #13-01-0044413] and European Union FP7 IRSES project TAMER IRSES-GA-2013-610547.