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In this study, we use the mechanism-based strain gradient plasticity theoryto evaluate both crack tip dislocation density behaviour and the coupled effectof the material plastic properties and the intrinsic material length onnon-linear amplitude factors. The two planar classical stress-strain states areexamined, namely, plane strain and plane stress, both under pure mode I andpure mode II loading conditions. The constitutive relations are based onTaylor's dislocation model, which enables gaining insights into the role of theincreased dislocation density associated with large gradients in plastic strainnear cracks. The material model is implemented in a commercial finite element(FE) software package using a user subroutine, and the nonlinear stressintensity factors (SIF) are evaluated as a function of the intrinsic materiallength, characterising the scale at which gradient effects become significant.As a result of the FE calculations of dislocation density distributions, theeffects of both the fracture mode and the stress-strain state are determined.In pure mode I, the geometrically necessary dislocation (GND) density islocated symmetrically with respect to the blunted crack tip. On the contrary,under pure mode II, the GND density becomes concentrated in the blunted andsharp parts of the crack tip. In this case, fracture initiation is shown to belikely to occur near the blunted region of the crack tip, where both the stresstriaxiality and the GND density are at their maximum. The relation between theequilibrium state of dislocation densities and the intrinsic material length aswell as the plastic SIF as a function of the work hardening exponent isdiscussed.

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