Geometry independent C*-T_z dominance of three-dimensional quasistatic growing crack-tip fields in creeping solids

In creeping solids, plane stress and plane strain solutions for asymptotic singular crack-tip fields have been first put forward by Riedel and Rice with C* as the dominating parameter and developed by Xiang and Guo into three-dimensional solution (3D) for stationary cracks under the domination of C* with the constraint factor T_z. However, how to characterize the 3D crack-tip fields under creep damage-induced quasistatic growing conditions remains challenging. In this study, we reveal that, for 3D quasistatic growing cracks, the leading singular solution can effectively characterize the crack-tip stress distributions with relative errors less than 10.8% for relative creep time up to 0.8 in various specimens with finite thickness. For a given relative time, T_z distributions can be unified by the equivalent thickness concept, B_eq. The results show that C*-T_z can effectively quantify both the load and constraint effects on the crack-tip fields. Such geometry independent dominance can considerably simplify the treatments of load and constraint effects, thereby promoting the application of fracture mechanics in high-temperature damage tolerance designs.