Mode I and Mode II Plane-Stress Near-Tip Fields for Cracks in Materials with Strain-Gradient Effects

Large strain gradients exist near the tip of a crack due to the strain singularity. The strain gradient effect becomes significant when the size of fracture process zone around a crack tip is comparable to the intrinsic material length, l, typically on the order of microns. The plane-stress asymptotic field near a crack tip is investigated in the present study for materials with strain gradient effects. It is established that, for a fixed distance to the crack tip, the maximum shear stress in the mode II near-tip field in strain gradient plasticity is more than 3 times its counterpart in the HRR field. In mode I, the maximum shear stress near a crack tip in strain gradient plasticity is twice that in the corresponding HRR field. However, the increase in normal stresses is not observed in strain gradient plasticity because the present theory is based on the rotation gradient of the deformation only. The implication of this significant increase in shear stresses is discussed.