On the stress field ahead of a stationary crack tip during the transition from primary to secondary creep

Abstract

Despite the rich body of work on crack-tip asymptotics to date, the characterization of cracks in creeping solids remains an open problem. The purpose of this paper is to quantify the influence of primary creep on the near crack-tip stress field. We do this by simulating a classical compact tension test using a unified creep-plasticity model due to Robinson, Pugh, and Corum. This model accounts for the transition between primary and secondary creep organically through a kinematic hardening variable called the “internal flow stress” (which is related to the dislocation density of the material), and reduces to classical, power-law creep when the flow stress is negligible compared to the Cauchy stress. Stamm and Walz have shown that, in the limit of high stresses, the near crack-tip stress field predicted by the Robinson-Pugh-Corum model is well approximated by the so-called RR solution of Riedel and Rice, which was derived for power-law creeping solids. For low stresses, we find that the RR solution only applies when the primary creep response of the specimen is negligible. Indeed, the main contribution of this work is the identification of a dimensionless number Ξ, which characterizes the primary creep response of a compact tension specimen. When Ξ<<1, the specimen exhibits very little primary creep, and consequently, the RR solution is still accurate within a finite region ahead of the crack tip under both small-scale creep and extensive creep conditions. When Ξ>>1, the specimen exhibits significant primary creep, and consequently, the RR solution is not accurate under small-scale creep conditions (although remarkably there does appear to be a region in which the RR solution is still accurate under extensive creep conditions). Our results suggest that the relevant loading parameter is still the familiar stress intensity factor KI under small-scale creep conditions, and the well-known C*-integral under extensive creep conditions, regardless of the primary creep response of the specimen, in agreement with previous work.