Characterization of three-dimensional crack border fields in creeping solids

Creep fracture of solids at high temperature is vital to applications of many advanced materials, but most of the previous works are performed within the frame of two-dimensional theory. By using the out-of-plane stress constraint factor Tz, here we derive out three-dimensional asymptotic fields near the border of mode-I through-thickness cracks in power law creeping solids. It is found that the asymptotic fields near the crack border are dominated by both Tz and C(t) integral. Detailed finite element analyses are carefully performed for single-edge cracked specimens and centre-cracked tension specimens to investigate the dominance of the asymptotic solution for the crack border fields. It is shown that the C(t) − Tz description based on the obtained three-dimensional asymptotic solution can provide efficient prediction for the tensile stress ahead of the crack front under small scale creep condition. Under extensive creep conditions, a third parameter Q∗ should be introduced to take into account of the loss in the in-plane constraint caused by in-plane geometries and loading configuration at extensive creeping, and a three-parameter C(t) − Tz − Q∗ description is proposed and proven to be efficient to predict the tensile stress on the ligament ahead of the crack for both specimens. Therefore, the two-parameter C(t) − Tz and three-parameter C(t) − Tz − Q∗ descriptions can provide advanced theoretical basis for small and extensive creeping fracture assessments, respectively.