  The crack tip mechanics of strain gradient plasticity solids is investigated
analytically and numerically. A first-order mechanism-based strain gradient
(MSG) plasticity theory based on Taylor's dislocation model is adopted and
implemented in the commercial finite element package ANSYS by means of a user
subroutine. Two boundary value problems are considered, a single edge tension
specimen and a biaxially loaded plate. First, crack tip fields are
characterized. Strain gradient effects associated with dislocation hardening
mechanisms elevate crack tip stresses relative to conventional plasticity. A
parametric study is conducted and differences with conventional plasticity
predictions are quantified. Moreover, the asymptotic nature of the crack tip
solution is investigated. The numerical results reveal that the singularity
order predicted by the first-order MSG theory is equal or higher to that of
linear elastic solids. Also, the crack tip field appears not to have a
separable solution. Moreover, contrarily to what has been shown in the higher
order version of MSG plasticity, the singularity order exhibits sensitivity to
the plastic material properties. Secondly, analytical and numerical approaches
are employed to formulate novel amplitude factors for strain gradient
plasticity. A generalized J-integral is derived and used to characterize a
nonlinear amplitude factor. A closed-form equation for the analytical stress
intensity factor is obtained. Amplitude factors are also derived by decomposing
the numerical solution for the crack tip stress field. Nonlinear amplitude
factor solutions are determined across a wide range of values for the material
length scale l and the strain hardening exponent N. The domains of strain
gradient relevance are identified, setting the basis for the application of
first-order MSG plasticity for fracture and damage assessment.
