Power-law Defect Energy in a Single-Crystal Gradient Plasticity Framework - A Computational Study

TL;DR

This study introduces a single-crystal gradient plasticity model with a power-law defect energy, exploring how the exponent affects size effects and gradient distribution through numerical simulations and analytical solutions.

Contribution

It presents a novel gradient plasticity model incorporating a power-law defect energy and compares different exponents using finite element simulations and analytical analysis.

Findings

The power-law exponent significantly influences size effects.

Numerical results align with analytical solutions for single slip cases.

Gradient distribution varies with the defect energy exponent.

Abstract

A single-crystal gradient plasticity model is presented that includes a power-law type defect energy depending on the gradient of an equivalent plastic strain. Numerical regularization for the case of vanishing gradients is employed in the finite element discretization of the theory. Three exemplary choices of the defect energy exponent are compared in finite element simulations of elastic-plastic tricrystals under tensile loading. The influence of the power-law exponent is discussed related to the distribution of gradients and in regard to size effects. In addition, an analytical solution is presented for the single slip case supporting the numerical results. The influence of the power-law exponent is contrasted to the influence of the normalization constant.