# Mode I crack tip fields: strain gradient plasticity theory versus J2 flow theory

## TL;DR

This paper compares strain gradient plasticity and J2 flow theory in describing the crack tip fields, revealing elastic dominance near the tip and the influence of material length scale on plasticity suppression.

## Contribution

It provides a detailed analysis of the crack tip asymptotic response using strain gradient plasticity and introduces a generalized J-integral for this theory.

## Key findings

- Elastic strains dominate near the crack tip
- A crack tip elastic zone exists within an elasto-plastic zone
- Material length scale influences plasticity suppression

## Abstract

The mode I crack tip asymptotic response of a solid characterised by strain gradient plasticity is investigated. It is found that elastic strains dominate plastic strains near the crack tip, and thus the Cauchy stress and the strain state are given asymptotically by the elastic K-field. This crack tip elastic zone is embedded within an annular elasto-plastic zone. This feature is predicted by both a crack tip asymptotic analysis and a finite element computation. When small scale yielding applies, three distinct regimes exist: an outer elastic K field, an intermediate elasto-plastic field, and an inner elastic K field. The inner elastic core significantly influences the crack opening profile. Crack tip plasticity is suppressed when the material length scale $\ell$ of the gradient theory is on the order of the plastic zone size estimation, as dictated by the remote stress intensity factor. A generalized J-integral for strain gradient plasticity is stated and used to characterise the asymptotic response ahead of a short crack. Finite element analysis of a cracked three point bend specimen reveals that the crack tip elastic zone persists in the presence of bulk plasticity and an outer J-field.