Micromechanical Simulation of the Hall‐Petch Effect with a Crystal Gradient Theory including a Grain Boundary Yield Criterion

A viscoplastic strain gradient crystal plasticity theory based on the gradient of the equivalent plastic strain ∇γ eq is proposed. A grain boundary yield condition is introduced. The microstructural explanation of the Hall‐Petch effect, accounting for notch‐like stress concentrations at the grain boundary as a result of discrete slip bands, is reviewed. Periodic tensile test FEM simulation results illustrate the prediction of the numerical model. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)