A single grain boundary parameter to characterize normal stress fluctuations in materials with elastic cubic grains

Abstract

A finite element analysis of intergranular normal stresses is performed in order to identify a possible statistical correlation between the intergranular normal stresses and the corresponding grain boundary type within a polycrystalline aggregate. Elastic continuum grains of cubic lattice symmetry are assumed in the analysis. Meaningful results are obtained by analyzing the first two statistical moments of grain boundary normal stresses obtained on several grain boundary types.Among the five macroscopic parameters (5D) describing a grain boundary, the orientation of the grain boundary plane relative to the two adjacent crystal lattices (4D) is found to be the most important property influencing the normal stresses. To account for it, a single new (1D) parameter E12 is introduced, which combines the geometrical aspect of grain boundary with its material properties and measures the average stiffness of grain boundary neighborhood along the grain boundary normal direction. It is demonstrated that E12, in combination with Zener elastic anisotropy index A, is able to accurately predict normal stress fluctuations on any grain boundary type in a material with cubic lattice symmetry. It is argued that largest normal stresses most likely form on grain boundaries whose normals are oriented along the stiffest direction in both adjacent grains (〈111〉 for crystals with A>1 or 〈001〉 for crystals with A<1). Moreover, it is shown that classification of grain boundaries according to their propensity to exhibit large normal stresses can be trivially reduced to the (analytical) calculation of the corresponding effective stiffness parameter E12.A few practical implications are discussed relevant to intergranular stress-corrosion cracking of Coincidence Site Lattice grain boundaries. For example, it is highlighted that in face-centered cubic materials the coherent Σ3 twin grain boundaries, which are known for their very high cracking resistance, nevertheless exhibit largest intergranular normal stresses, indicating that cracking resistance is associated with high grain boundary strength.