On the effects of loading conditions and geometry on time-dependent singular crack tip fields

Abstract

The amplitudes C( t) of non-steady singular crack tip fields in power law creeping solids are investigated under pure mode I loading and combined mode I and II loading conditions. Approximations to both transient and steady state values of the C( t)-integral for three different specimen geometries and for an intersection geometry representative of a typical power plant component configuration are compared with results obtained from detailed finite element analyses. The effect of crack depth, geometry, creep exponent, and primary (mechanical) loading on the accuracy of C( t) estimates is determined. Finite element solutions for the intersection geometry are used to study the extent of mode mixity under creep conditions in the resulting combined mode I and II crack tip fields. These solutions showed that, within the crack tip region where creep strains dominate, the opening stresses appear more singular than the Hutchinson-Rice-Rosengren (HRR)-type fields, r −1/( n+1) , while the in-plane shear stress component and the equivalent stress are slightly less singular. The solutions also revealed that mode I dominance increases primarily during a very short period immediately after the load is applied, while small scale creep conditions prevail, and does not significantly change thereafter. HRR-type plane strain approximations based on known solutions for mixed mode elastic-plastic cracks under a moderate degree of mode mixity accurately predict axisymmetric finite element solutions.