Mixed mode near-tip fields for cracks in materials with strain-gradient effects

Abstract

Large strain gradients exist near the tip of a crack due to stress singularity. The strain-gradient effect becomes significant when the size of the fracture process zone around a crack tip is comparable to the intrinsic material length, l, typically on the order of microns. Fleck and Hutchinson's [(1993) A phenomenological theory for strain-gradient effects in plasticity. J. Mech. Phys. Solid 41, 1825–1857], strain-gradient plasticity theory is applied to investigate the asymptotic field near a mixed mode crack tip in elastic as well as elastic-plastic materials with strain-gradient effects. It is established that the dominant strain field is irrotational. For an elastic material, stresses and couple stresses have the square-root singularity near the crack tip, and are governed by three variables (two for mode I and II stress fields, and the third, resulting from higher order stresses, for the couple stress field). Stresses ahead of a crack tip in elastic materials with strain-gradient effects could be more than 50% higher than their counterparts in materials without strain-gradient effects. For an elastic-power law hardening strain-gradient material, an analytical solution is obtained. The mixed mode stress field in strain-gradient plasticity is the linear superposition of their counterparts in mode I and II. The angular distribution of stresses and couple stresses for several near-tip mode mixities clearly indicate that the new near-tip field in strain-gradient plasticity differs significantly from the HRR field. Stresses ahead of a crack tip in elastic-plastic solids with strain-gradient effects could be more than 2.5 times their counterparts in the HRR field. The asymptotic analysis compares favorably with available finite element results. The relevance of this solution to materials, in particular the size of the dominant zone, is discussed.