HIGHER-ORDER ASYMPTOTIC CRACK-TIP FIELDS IN A POWER-LAW HARDENING MATERIAL

The asymptotic stress and deformation fields for plane problems are developed for a crack tip embedded in a power-law elastic-plastic material. Using an asymptotic expansion and separation of variables for the stress function, a series solution is obtained for the stress and deformation at a crack tip. The most singular term in the series solution is the HRR solution, after Hutchinson and Rice and Rosengren. The stress exponents and the angular distributions for several higher order terms are obtained for different hardening exponents. Both Mode I and Mode II cases are investigated. Good agreement with the finite element results confirms the analytical findings. It is further demonstrated that in the plane strain, Mode I case the first three terms, controlled by two parameters, can be used to characterize the crack tip stress fields for a variety of specimen geometries and materials with various hardening exponents.