The boundary-layer effect on the crack tip field in mechanism-based strain gradient plasticity

The theory of mechanism-based strain gradient (MSG) plasticity involves two material length parameters, namely the intrinsic material length l and the mesoscale cell size lε, which are on the order of a few microns and 0.1 μm, respectively. Prior studies suggest that lε has essentially no effect on the macroscopic quantities, but it may affect the local stress distribution. We demonstrate in this paper that there is a boundary layer effect associated with lε in MSG plasticity, and the thickness of the boundary layer is on the order of l2 ε / l. By neglecting this boundary layer effect, a stress-dominated asymptotic field around a crack tip in MSG plasticity is obtained. This asymptotic field is valid at a distance to the crack tip between lε and l (i.e., from 0.1 μm to a few microns). The stress in this asymptotic field has an approximate singularity of r−2/3, which is more singular than not only the HRR field in classical plasticity but also the classical elastic K field (r−1/2). The stress level in this asymptotic field is two to three times higher than the HRR field, which provides an alternative mechanism for cleavage fracture in ductile materials observed in experiments.