DETERMINATION OF HIGHER-ORDER TERMS IN ASYMPTOTIC ELASTOPLASTIC CRACK TIP SOLUTIONS

A METHODOLOGY for the calculation of higher-order terms in asymptotic elastoplastic crack tip solutions is developed. The J2-deformation plasticity theory with power law hardening is used to describe the constitutive behavior of the continuum. A two-term expansion of the solution in the near crack tip region is developed. Plane stress and plane strain solutions for a crack in a homogeneous material as well as for a crack lying along the interface between a rigid substrate and an elastoplastic medium are obtained. For the case of a plane strain crack in a homogeneous material, it is shown that, when the hardening capacity of the material is small, the effects of elasticity enter the asymptotic solution to third order or higher; when there is substantial hardening, however, elastic effects enter the solution to second order and the magnitude of the second term in the expansion of the solution is controlled by the J-integral.