A Practical Meso-Scale Polycrystal Model to Predict Dislocation Densities and the Hall–Petch Effect

Abstract

A practical SuperDislocation Model (SDM) has been developed and implemented to predict dislocation density distributions in a plastically deforming polycrystal and thereby the Hall­Petch effect. The model is composed of two stepwise simulation scales; the first scale is a finite element model of a polycrystal using a novel single-crystal constitutive equation and the second scale redistributes the mobile part of the dislocation density within grains consistent with the plastic strain distribution, and enforces slip transmission criteria at grain boundaries that depend on local grain and boundary properties. In this work, deformation of Fe­3% Si tensile specimen is simulated using SDM to compare dislocation densities obtained from the highresolution electron backscatter diffraction (HR-EBSD). The model accurately predicts the measured dislocation density at 10% deformation. In addition, size-dependent simulations show that the model qualitatively predicts Hall­Petch slope as well as the grain boundary strength of Fe­ 3% Si. [doi:10.2320/matertrans.MA201305]