Gradient plasticity crack tip characterization by means of the extended finite element method

TL;DR

This paper introduces a novel gradient-enhanced X-FEM framework for crack tip analysis that improves accuracy and efficiency in modeling strain gradient plasticity effects at small scales.

Contribution

A new numerical method combining gradient plasticity and X-FEM is developed, enabling efficient crack tip analysis with enriched displacement fields.

Findings

Outperforms standard finite element methods in crack tip simulations

Enables detailed modeling of microstructurally-motivated plasticity effects

Provides a MATLAB code for practical implementation

Abstract

Strain gradient plasticity theories are being widely used for fracture assessment, as they provide a richer description of crack tip fields by incorporating the influence of geometrically necessary dislocations. Characterizing the behavior at the small scales involved in crack tip deformation requires, however, the use of a very refined mesh within microns to the crack. In this work a novel and efficient gradient-enhanced numerical framework is developed by means of the extended finite element method (X-FEM). A mechanism-based gradient plasticity model is employed and the approximation of the displacement field is enriched with the stress singularity of the gradient-dominated solution. Results reveal that the proposed numerical methodology largely outperforms the standard finite element approach. The present work could have important implications on the use of microstructurally-motivated models in large scale applications. The non-linear X-FEM code developed in MATLAB can be downloaded from www.empaneda.com/codes.