Influence of thin Slip Bands on Grain Boundary Stress Fields and Microcrack Initiation: Analytical and Numerical Approaches☆

Abstract Strain localization is often observed in single and poly-crystals, for instance forming clear bands or persistent slip bands respectively during post-irradiation tensile loading or cyclic loading. This concerns FCC, BCC or HCP crystallographic structures. At the intersection of the so-called slip bands (SBs) and grain boundaries (GBs), stress concentration areas emerge contributing to intergranular microcrack initiation. Indeed, GB stress fields show singularities due to the SB plastic shearing of the surrounding elastic matrix. Since Stroh's work [[?]], GB normal stress fields have been computed using pile-up theory assumptions. However, as these approaches assume that slip occurs along only one single atomic plane, they overestimate GB normal stress fields because SBs generally display finite thickness, from a few ten nm to a few μm. Crystalline finite elements (FE) computations are carried out using the Cast3 M software. Meshed microstructure includes an elastoplastic SB within a main elastic grain which which is embedded at free surface of an elastic matrix. Results show in fact that using the pile-up formalism leads to large GB stress field overestimations. Therefore, an analytical formula describing the normal GB stress fields is proposed in the current paper, extend- ing the pile-up solution in the neighbourhood of the SB corner. The relationships between SB length and thickness and stress singularities are established in the light of the theory of matching asymptotic expansions. A double fracture criterion allows the prediction of intergranular microcrack initiation based on the computed stress singularities. Another analytical model based on the solution of the thermoelastic problem allow to propose a more general formula of the grain boundary stress fields accounting for the unloading effects. Using only one stress field computed by FE, the prefactors are computed and both analytical formulae are shown to be validated for all the range of grain size, SB thickness and remote applied stress.