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. THE CHARACTERIZATION of the stress and deformation fields in the region near the tip of a crack is essential for the development of sound fracture criteria. HUTCHINSON (1968) and RICE and ROSENGREN (1968) developed the elastoplastic asymptotic solution for the near-tip stresses in a homogeneous material (known as the HRR solution) and showed that the magnitude of the dominant term in the expansion of the solution is determined by the J-integral (RICE, 1968). If the region of dominance of the leading-order term in the expansion of the solution is sufficiently larger than the region over which the fracture micro-mechanisms take place, then the J-integral can be used as the fracture parameter. If the region of J-dominance, however, is smaller than the fracture process zone, then two or more parameters may enter the fracture criterion. LI and WANG 0986) suggested the use of a parameter k2, which is the magnitude of the second term in the near-tip stress plastic solution, as the second parameter to be used together with the J-integral in the fracture criterion. BETEGrN and HANCOCK (1991) used a modified boundary layer formulation of the small-scale yielding problem, in which the boundary conditions are defined in terms of the mode I stress intensity factor Kt and the constant stress term T that enters the near-tip expansion of the elastic solution (LARSSON and CARLSSON, 1973; RICE, 1974), and