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

The asymptotic stress and deformation fields for plane problems are de veloped for a crack tip embedded in a power-law elastic-plastic materi al. Using an asymptotic expansion and separation of variables for the stress function, a series solution is obtained for the stress and defo rmation at a crack tip. The most singular term in the series solution is the HRR solution, after Hutchinson and Rice and Rosengren. The stre ss exponents and the angular distributions for several higher order te rms are obtained for different hardening exponents. Both Mode I and Mo de II cases are investigated. Good agreement with the finite element r esults confirms the analytical findings. It is further demonstrated th at in the plane strain, Mode I case the first three terms, controlled by two parameters, can be used to characterize the crack tip stress fi elds for a variety of specimen geometries and materials with various h ardening exponents.