The role of macroscopic hardening and individual length-scales on crack tip stress elevation from phenomenological strain gradient plasticity

This paper quantifies the effect of strain gradient plasticity (SGP) on crack tip stress elevation for a broad range of applied loading conditions and constitutive model parameters, including both macroscopic hardening parameters and individual material length-scales controlling gradient effects. Finite element Simulations incorporating the Fleck-Hutchinson SGP theory are presented for an asymptotically sharp stationary crack. Results identify fundamental scaling relationships describing (i) the physical length-scales over which strain gradients are prominent, and (ii) the degree of stress elevation over conventional Hutchinson-Rice-Rosengren (HRR) fields. Results illustrate that the three length-scale theory predicts Much larger SGP effects than the single length-scale theory. Critically, the first length-scale parameter dominates SGP stress elevation: this suggests that SGP effects in fracture can be predicted using the length-scales extracted from nanoindentation, which exhibits similar behavior. Transitional loading/material parameters are identified that establish regimes of SGP relevance: this provides the foundation for the rational application of SGP when developing new micromechanical models of crack tip damage mechanisms and associated subcritical crack propagation behavior in structural alloys. (c) 2008 Published by Elsevier Ltd.