Higher order J-Tz-AT solution for three-dimensional crack border fields in power-law hardening solids

Higher order J-A2 solution has been developed to improve the HRR singular solution under ideal plane strain conditions in power-law hardening solids with the the second A2 being considered to take into account of the in-plane constraint effect, and the J-Tz singular solution has been obtained for three-dimensional (3D) cracked body by introducing the out-of-plane stress constraint factor Tz. Here a higher order J-Tz-AT solution is developed on the basis of the J-Tz and J-A2 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-Tz-AT 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-Tz leading singular solution itself shows sufficient accuracy. This universal characterization of crack border stress fields confirms that the developed J-Tz-AT solution combines the advantages of the J-Tz and J-A2 solutions, which can service as a solid foundation of elastic-plastic fracture mechanics.

Fig. 11. Comparisons of the tensile stress σθθ and out-of-plane stress σzz obtained by the 3D FE results and the J-Tz, J-A2, J-Q, J-Tz-QT and developed higher order J-Tz-AT solutions. (a) z/B = 0, σθθ; (b) z/B = 0.45, σzz; (c) z/B = 0, σθθ; (d) z/B = 0.45, σzz.