Stationary and propagating cracks in a strain gradient visco-plastic solid

A first order visco-plastic strain gradient constitutive model and a cohesive zone formulation are embedded within a modified boundary layer (MBL) model for the analysis of crack tip fields and crack growth. The MBL model is loaded using a mode I asymptotic crack tip solution, with the boundary displacement calculated from the stress intensity factor. The influence of the rate-dependent constitutive parameters and the intrinsic material length on fracture relevant quantities are investigated in parametric study. Two scenarios are considered: (1) a stationary crack under constant loading and (2) a crack advance under monotonic loading. Finite element model analyzes are performed. For stationary cracks it was found that the effects of the intrinsic lengthscale of the strain gradient plasticity model are more prominent for large visco-plastic power exponents, and increase with hold time. The results of computations of crack advances under monotonic loading suggest that plastic strain gradients reduce crack growth resistance and crack initiation toughness, especially for a large visco-plastic power exponent. For small values of intrinsic material length the dependence of the initiation toughness and tearing modulus on the intrinsic length is strong, but then saturates for large values of intrinsic material length. Loading rate effects are found to be more pronounced for cases with a small value of the intrinsic lengthscale.