Steady-state crack growth and work of fracture for solids characterized by strain gradient plasticity

Mode I steady-state crack growth is analysed under plane strain conditions in small scale yielding. The elastic-plastic solid is characterized by a generalization of J2 flow theory which accounts for the influence of the gradients of plastic strains on hardening. The constitutive model involves one new parameter, a material length l, specifying the scale of nonuniform deformation at which hardening elevation owing to strain gradients becomes important. Gradients of plastic strain at a sharp crack tip result in a substantial increase in tractions ahead of the tip. This has important consequences for crack growth in materials that fail by decohesion or cleavage at the atomic scale. The new constitutive law is used in conjunction with a model which represents the fracture process by an embedded traction-separation relation applied on the plane ahead of the crack tip. The ratio of the macroscopic work of fracture to the work of the fracture process is calculated as a function of the parameters characterizing the fracture process and the solid, with particular emphasis on the role of l.