Higher order C(t)-T_z-A_T solution for three-dimensional creep crack border fields

A higher order C(t)-T_z-A_T solution is developed for power-law creeping solids on the basis of the C(t)-A₂(t) and C(t)-T_z solutions. Validations against comprehensive 3D FE analysis results in specimens with through-thickness, corner, surface and embedded cracks show that the developed C(t)-T_z-A_T solution can provide an accurate description of the 3D crack border stress fields in all the simulated conditions. At small-scale and large-scale creep stages, the absolute value of in-plane constraint coefficient A_T is within 0.05 in the SECT, CT and SENB specimens, which indicates that the higher order C(t)-T_z-A_T solution could degenerate into the C(t)-T_z solution in such high constraint specimens. However, in CCT and part-through cracked specimens, the absolute value of A_T may increase remarkably with creep time, and the C(t)-T_z-A_T solution is necessary. Based on the numerical results, a set of explicit empirical formulae of T_z are obtained for all the specimens, and the detailed values of A_T are listed in Appendix.