Slip localization is widely observed in metallic polycrystals after tensile deformation, cyclic deformation or pre-irradiation followed by tensile deformation. Such strong deformation localized in thin slip bands induces local stress concentrations in the quasi-elastic matrix around, at the intersections between slip bands (SBs) and grain boundaries (GBs) where microcrack initiation is often observed. Since the work of Stroh, such stress fields have been mostly modeled using the dislocation pile-up theory which leads to stress singularities similar to the LEFM ones. The Griffith criterion has then been widely applied, leading usually to strong underestimations of the macroscopic stress to GB crack initiation.
In fact, slip band thickness is finite: 20nm-1000nm depending on material, temperature and loading conditions. Then, many slip planes are plastically activated through the thickness, and not only one single atomic plane. To evaluate more realistic stress fields, numerous crystalline finite element (FE) computations have been carried out using microstructure inputs (slip band aspect ratio, crystal and GB orientation...).
A strong influence of slip band thickness close to the slip band corner has been highlighted, which is not accounted for by the pile-up theory. But far away, the thickness has a negligible effect and the predicted stress fields are close to the one predicted by the pile-up theory. Closed-form expressions are deduced from the numerous FE computation results allowing a straightforward prediction of GB stress fields. Slip band plasticity parameters, such as length and thickness, as well as crystal orientation, GB plane and remote stress are taken into account. The dependence with respect to the various parameters can be understood in the framework of matching expansions usually applied to cracks with V notches of finite thickness.
As the exponent of the GB stress close-field is only about one-half of the pile-up or LEFM crack one, the Griffith criterion may not be used for GB microcrack prediction in case of finite thickness. That is why finite crack fracture mechanics is used together with both energy and stress criteria. Taking into account SB finite thickness, t>0, leads to predicted remote stresses to GB microcrack initiation three to six times lower than the ones predicted using the to pile-up theory, in agreement with experimental data.
From non-local Eringen’s model to fractional elasticity
