Analytic and numerical studies on mode I and mode II fracture in elastic-plastic materials with strain gradient effects

Abstract

This paper presents a study on fracture of materials at microscale (∼1 µm) by the strain gradient theory (Fleck and Hutchinson, 1993; Fleck et al., 1994). For remotely imposed classical K fields, the full-field solutions are obtained analytically or numerically for elastic and elastic-plastic materials with strain gradient effects. The analytical elastic full-field solution shows that stresses ahead of a crack tip are significantly higher than their counterparts in the classical K fields. The sizes of dominance zones for mode I and mode II near-tip asymptotic fields are 0.3l and 0.5l,while strain gradient effects are observed within land 2l to the crack tip, respectively, where l is the intrinsic material length in strain gradient theory and is on the order of microns in strain gradient plasticity (Fleck et al., 1994; Nix and Gao, 1998; Stolken and Evans, 1997). The Dugdale–Barenblatt type plasticity model is obtained to provide an estimation of plastic zone size for mode II fracture in materials with strain grain effects. The finite element method is used to investigate the small-scale-yielding solution for an elastic-power law hardening solid. It is found that the size of the dominance zone for the near-tip asymptotic field is the intrinsic material lengthl. For mode II fracture under the small-scale-yielding condition, transition from the remote classical K IIfield to the near-tip asymptotic field in strain gradient plasticity goes through the HRR field only when K IIis relatively large such that the plastic zone size is much larger than the intrinsic material length l. For mode I fracture under small-scale-yielding condition, however, transition from the remote classical K I field to the near-tip asymptotic field in strain gradient plasticity does not go through the HRR field, but via a plastic zone.