Plane strain deformation near a crack tip in a power-law hardening material

Crack-tip strain singularities are investigated with the aid of an energy line integral exhibiting path independence for all contours surrounding a crack tip in a two-dimensional deformation field of an elastic material (or elastic/plastic material treated by a deformation theory). It is argued that the product of stress and strain exhibits a singularity varying inversely with distance from the tip in all materials. Corresponding near crack tip stress and strain fields are obtained for the plane straining of an incompressible elastic/plastic material hardening according to a power law. A noteworthy feature of the solution is the rapid rise of triaxial stress concentration above the flow stress with increasing values of the hardening exponent. Results are presented graphically for a range of hardening exponents, and the interpretation of the solution is aided by a discussion of analogous results in the better understood anti-plane strain case.