Crack tip fields in strain gradient plasticity

Solutions are presented for mode I and mode II crack tip fields for plane strain deformations of an elastic-plastic solid whose constitutive behavior depends on both strains and strain gradients. The constitutive law is the simplest generalization of the J 2 deformation theory of plasticity to include strain gradient effects. Only one new constitutive parameter enters, a length parameter characterizing the scale over which gradient effects become important. The formulation is cast within the framework of coupled stress theory. Crack tip solutions are obtained which display the transition from the HRR fields, governing behavior in an intermediate region with the plastic zone, to the dominant fields at the tip. The dominant fields are obtained in closed form, and finite element methods have been used to produce the solution over the entire field. Some of the difficulties encountered in arriving at an accurate numerical scheme are detailed. Implications of the solutions for fracture are discussed, as are avenues for further research.