Dr. Samir El Shawish and dr. Timon Mede from the Reactor Engineering Division at Jožef Stefan Institute, in collaboration with dr. Jeremy Hure from Université Paris-Saclay, CEA (France) published the article “A single grain boundary parameter to characterize normal stress fluctuations in materials with elastic cubic grains” in the European Journal of Mechanics / A Solids.

The paper identifies a statistical correlation between the intergranular normal stresses in a polycrystalline aggregate and the corresponding grain boundary type. The latter has been shown to be well described by a single cleverly chosen macroscopic parameter, namely the local effective Young’s modulus, which represents the average stiffness of crystal boundary neighbourhood along the grain boundary normal direction and combines its geometrical aspect with material properties. It has been demonstrated that the newly introduced parameter of effective stiffness of the pair of grains enclosing the selected boundary, together with Zener elastic anisotropy index, enables an accurate prediction of normal stress fluctuations on any grain boundary type in a material with cubic crystal structure and thus the corresponding probability for occurrence of large stresses under external loading.

The analysis is based on numerical simulations of intergranular normal stresses performed with finite element method and assuming elastic continuum grains of cubic lattice symmetry. The distributions of normal stresses at individual grain boundary types are characterized by their first two statistical moments – the mean value and the standard deviation. The largest normal stresses most likely form on grain boundaries whose normals are oriented along the stiffest direction in both adjacent grains. They increase the likelihood for crack initiation, which can lead to material degradation and fatigue processes.

Figure: (a) Standard deviation of normalized INS distributions 𝑠(𝜎𝑛𝑛∕𝛴) as a function of grain boundary type characterized by its effective Young’s modulus 𝐸12 in 𝛾-Fe. (b) Probability density functions (PDF) of 𝜎𝑛𝑛∕𝛴 belonging to different grain boundary types – from the softest corresponding to (001)-(001) grain boundaries and 𝐸12 = 0.35 to the stiffest (111)-(111) grain boundaries and 𝐸12 = 1.