Fracture Analysis in the Continuum Theory of Stress Gradient Plasticity

Abstract

Plastic deformation around a stationary mode I crack in an isotropic material is studied within the continuum theory of stress gradient plasticity ([Formula: see text]GP). This model, as a lower-order plasticity theory, has been quite successful in predicting the size-dependent plastic behavior in micro-torsion as well as micro-bending. However, its application to a problem involving a complex stress state reveals here that it has to be modified with a proper measure of stress gradient in the continuum context. To this end, a new measure of stress gradient is proposed and assessed appropriately. It is then employed to investigate crack tip stress fields within the [Formula: see text]GP theory. Analyses show that a higher stress level is predicted near the crack tip using the [Formula: see text]GP theory when compared with the classical plasticity predictions. The increase of stress level due to stress gradient effects is predicted around 35% which is enough for cleavage cracking. However, relatively higher stress levels were expected due to large stress gradients near the crack tip. Therefore, either a higher-order formulation or involving higher-order spatial gradients of stress is required to study fracture with the [Formula: see text] GP theory.