  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.
