Higher order J-T-z-A(T) solution for three-dimensional crack border fields in power-law hardening solids

摘要

Higher order J-A(2) solution has been developed to improve the HRR singular solution under ideal plane strain conditions in power-law hardening solids with the the second A(2) being considered to take into account of the in-plane constraint effect, and the J-T-z singular solution has been obtained for three-dimensional (3D) cracked body by introducing the out-of-plane stress constraint factor T-z. Here a higher order J-T-z-A(T) solution is developed on the basis of the J-T-z and J-A(2) solutions and validated against comprehensive 3D finite element (FE) analyses for specimens with through-thickness, surface, embedded and corner cracks. It is shown that better agreements are obtained between the higher order J-T-z-A(T) solution and 3D FE results in all simulated conditions than previously available two- or three-parameter solutions. For specimens of high in-plane constraint, such as the single-edge cracked tension specimen, compact specimen and single-edge-notched bending specimen under three-point bending, the J-T-z leading singular solution itself shows sufficient accuracy. This universal characterization of crack border stress fields confirms that the developed J-T-z-A(T) solution combines the advantages of the J-T-z and J-A(2) solutions, which can service as a solid foundation of elastic-plastic fracture mechanics.