Crack-tip-opening-displacement-based description of creep crack border fields in specimens with different geometries and thicknesses

Creep crack growth is accompanied by strong nonlinear deformation and stress relaxation. Finding an appropriate parameter to characterize the crack tip fields, as well as the fracture resistance, has long been a challenge. Most previous studies were performed within the framework of the C(t)-integral, which is limited to the assumptions of small deformation and simple proportional loading. By using the crack tip opening displacement (CTOD), we propose a new creep stress intensity factor K_{δ ( t ) -Tz} consisting of the time-dependent CTOD, δ(t) and the out-of-plane stress constraint factor T_z to characterize the three-dimensional creep crack tip fields. Four typical specimens, single-edge cracked tension specimens, compact specimens, centre-cracked tension specimens and single-edge-notched bending specimens under three-point bending are comprehensively analysed using the power-law creeping model and three-dimensional finite element analyses. It is found that under both small-scale and large-scale creep conditions, the change in K_{δ ( t ) -Tz} along the thickness direction for different specimens is within 8.6%, whereas the change in C(t) can exceed 400%, showing that K_{δ ( t ) -Tz} is a stable parameter that governs the creep crack tip fields. With the exception of the centre-cracked tension specimens under large-scale creep conditions, good agreements are obtained between the two-parameter description δ(t)-T_z of crack border stress fields with the three-dimensional finite element results under small-scale and large-scale creep conditions. These results indicate that the CTOD-based two-parameter description δ(t)-T_z can be taken as the basis of creep fracture criteria.