Mode I and mixed mode crack-tip fields in strain gradient plasticity

Strain gradients develop near the crack-tip of Mode I or mixed mode cracks. A finite strain version of the phenomenological strain gradient plasticity theory of Fleck–Hutchinson (2001) is used here to quantify the effect of the material length scales on the crack-tip stress field for a sharp stationary crack under Mode I and mixed mode loading. It is found that for material length scales much smaller than the scale of the deformation gradients, the predictions converge to conventional elastic–plastic solutions. For length scales sufficiently large, the predictions converge to elastic solutions. Thus, the range of length scales over which a strain gradient plasticity model is necessary is identified. The role of each of the three material length scales, incorporated in the multiple length scale theory, in altering the near-tip stress field is systematically studied in order to quantify their effect.