Simulation of the Hall-Petch effect in FCC polycrystals by means of strain gradient crystal plasticity and FFT homogenization

TL;DR

This paper uses FFT-based homogenization combined with strain gradient crystal plasticity to simulate the Hall-Petch effect in FCC polycrystals, accurately capturing grain boundary strengthening and dislocation density effects.

Contribution

It introduces a computational approach integrating FFT and strain gradient plasticity to model grain boundary effects in polycrystals with realistic microstructure representations.

Findings

Simulation results agree with experimental data for grain sizes > 20 microns

Higher grain boundary strengthening in Al and Ni explained physically

Method effectively includes grain boundary effects in mechanical behavior

Abstract

The influence of grain size on the flow stress of various FCC polycrystals (Cu, Al, Ag and Ni) has been analyzed by means of computational homogenization of a representative volume element of the microstructure using a FFT approach in combination with a strain gradient crystal plasticity model. The density of geometrically necessary dislocations resulting from the incompatibility of plastic deformation among different crystals was obtained from the Nye tensor, which was efficiently obtained from the curl operation in the Fourier space. The simulation results were in good agreement with the experimental data for Cu, Al, Ag and Ni polycrystals for grain sizes > 20 microns and strains < 5% and provided a physical explanation for the higher strengthening provided by grain boundaries in Al and Ni, as compared with Cu and Ag. The investigation demonstrates how the combination of FFT with strain gradient crystal plasticity can be used to include effect of grain boundaries in the mechanical behavior of polycrystals using realistic representative volume elements of the microstructure.