Higher order asymptotic elastic-plastic crack-tip fields under antiplane shear

The asymptotic stress and strain fields near the crack tip under antiplane shear are developed in an elastic power-law hardening material. Using an asymptotic expansion and separation of variables for the stress function, a series solution for all of the hardening exponents can be obtained. The stress exponents for the higher order terms are analytically determined; the angular distributions which are governed solely by plastic strains are also analytically obtained. Good agreement with the finite element solutions confirms the proposed approach. It is further demonstrated that the first three terms, controlled by two parameters, can be used to characterize the crack tip stress and strain fields with various hardening exponents.