Size Scaling of Plastic Deformation in Simple Shear: Fractional Strain-Gradient Plasticity and Boundary Effects in Conventional Strain-Gradient Plasticity

Abstract

A recently developed model based on fractional derivatives of plastic strain is compared with conventional strain-gradient plasticity (SGP) models. Specifically, the experimental data and observed model discrepancies in the study by Mu et al. (2016, “Dependence of Confined Plastic Flow of Polycrystalline Cu Thin Films on Microstructure,” MRS Com. Res. Let. 20, pp. 1–6) are considered by solving the constrained simple shear problem. Solutions are presented both for a conventional SGP model and a model extension introducing an energetic interface. The interface allows us to relax the Dirichlet boundary condition usually assumed to prevail when solving this problem with the SGP model. We show that the particular form of a relaxed boundary condition does not change the underlying size scaling of the yield stress and consequently does not resolve the scaling issue. Furthermore, we show that the fractional strain-gradient plasticity model predicts a yield stress with a scaling exponent that is equal to the fractional order of differentiation.

Use of effective multiscale cohesive models in the simulation of spall in metal plates

“…This extension introduces additional flexibility in the model that enables a closer match with experimentally-measured scaling and size effect relations. 41,42 Another possible extension concerns ductile fracture under mixed-mode conditions. In the context of optimal scaling, a straightforward extension of the void-sheet construction accounting for both opening and shear is likely to deliver the desired effective law.…”

“…have considered the case in which the nonlocal dissipation is expressed in terms of fractional derivatives. This extension introduces additional flexibility in the model that enables a closer match with experimentally‐measured scaling and size effect relations 41,42 . Another possible extension concerns ductile fracture under mixed‐mode conditions.…”