Mode I and Mode II stress intensity factors and dislocation density behaviour in strain gradient plasticity

In this study, we use the mechanism-based strain gradient plasticity theory to evaluate both crack tip dislocation density behaviour and the coupled effect of the material plastic properties and the intrinsic material length on non-linear amplitude factors. The two planar classical stress-strain states are examined, namely, plane strain and plane stress, both under pure mode I and pure mode II loading conditions. The constitutive relations are based on Taylor's dislocation model, which enables gaining insights into the role of the increased dislocation density associated with large gradients in plastic strain near cracks. The material model is implemented in a commercial finite element (FE) software package using a user subroutine, and the nonlinear stress intensity factors (SIF) are evaluated as a function of the intrinsic material length, characterising the scale at which gradient effects become significant. As a result of the FE calculations of dislocation density distributions, the effects of both the fracture mode and the stress-strain state are determined. In pure mode I, the geometrically necessary dislocation (GND) density is located symmetrically with respect to the blunted crack tip. On the contrary, under pure mode II, the GND density becomes concentrated in the blunted and sharp parts of the crack tip. In this case, fracture initiation is shown to be likely to occur near the blunted region of the crack tip, where both the stress triaxiality and the GND density are at their maximum. The relation between the equilibrium state of dislocation densities and the intrinsic material length as well as the plastic SIF as a function of the work hardening exponent is discussed.