Multiscale model of deformed polycrystals. Hall-Petch problem

Abstract

The paper puts forward a multiscale model of deformed polycrystals according to which the basis for self-consistent deformation of grains is rotational wave flows of planar structural transformations at their boundaries. Computer-aided engineering of grain boundaries reveals two types of rotational wave flows defined by the misorientation angle of adjacent grains. Grain boundary flows of the first type develop at low-angle boundaries and feature low curvature. These flows generate dislocations in the grain bulk and the Hall-Petch equation for them has the form σ=σ0+kd−1/2. Grain boundary flows of the second type develop at high-angle boundaries and feature high curvature. These flows generate curvature bands in near-boundary zones and inject them into the grain bulk, resulting in fragmentation of grains and breakdown of translation invariance. For such self-consistency of grains in a polycrystal, the Hall-Petch equation has the form σ=σ0+kd−1. Experimental data in support of the proposed multiscale model are presented.