Modeling damage and fracture within strain-gradient plasticity

TL;DR

This paper numerically analyzes how strain-gradient plasticity affects crack tip stress fields in metals, revealing significant size effects and implications for damage modeling under large strains.

Contribution

It develops a large deformation numerical framework for strain-gradient plasticity and quantifies its impact on crack tip stress fields compared to conventional plasticity.

Findings

Strain-gradient effects increase stress magnitudes near crack tips.

Large strains extend the influence zone of strain gradients.

Plastic size effects are significant for damage mechanism modeling.

Abstract

In this work, the influence of the plastic size effect on the fracture process of metallic materials is numerically analyzed using the strain-gradient plasticity (SGP) theory established from the Taylor dislocation model. Since large deformations generally occur in the vicinity of a crack, the numerical framework of the chosen SGP theory is developed for allowing large strains and rotations. The material model is implemented in a commercial finite element (FE) code by a user subroutine, and crack-tip fields are evaluated thoroughly for both infinitesimal and finite deformation theories by a boundary-layer formulation. An extensive parametric study is conducted and differences in the stress distributions ahead of the crack tip, as compared with conventional plasticity, are quantified. As a consequence of the strain-gradient contribution to the work hardening of the material, FE results show a significant increase in the magnitude and the extent of the differences between the stress fields of SGP and conventional plasticity theories when finite strains are considered. Since the distance from the crack tip at which the strain gradient significantly alters the stress field could be one order of magnitude higher when large strains are considered, results reveal that the plastic size effect could have important implications in the modelization of several damage mechanisms where its influence has not yet been considered in the literature.