Effects of Creep Recovery and Hardening on the Stress and Strain-Rate Fields Near a Crack Tip in Creeping Materials

Abstract

It is thought that creep recovery may be one of the main causes of acceleration of crack growth rates under variable loads. To explore this possibility, the effects of creep recovery and hardening on the near-tip fields are examined in this paper. Robinson's constitutive relation, which is based on the Bailey-Orowan model, is used to take these effects into account. In this model, the strain rate is proportional to the nth power of an effective stress, which is the difference between applied stress and internal stress. The rate of the internal stress is given by the difference between a hardening term and a recovery term, which are proportional to the strain rate divided by the βth power of the internal stress and the (n − β)th power of the internal stress, respectively. It is found that the Hutchinson-Rice-Rosengren-type singular fields prevail near a creep crack tip irrespective of the combination of the material parameters n and β. When β < n − 1, the “steady-state creep conditions” prevail near the crack tip; when β > n − 1, the “initial-state creep conditions” prevail, under which the internal stress is small compared with the applied stress. The intensities of the singular stress and strain-rate fields are obtained rigorously for the case of β = n − 1. For the case of β < n − 1 and β > n − 1, the intensities are estimated by using a hypothesized path independence of the J-integral or the C*-integral. For any combination of n and β, the intensity of strain rate is very high immediately after load increase. Then the strain rate decreases and approaches its steady-state value. On the other hand, for load decrease the strain rate is low immediately after load decrease, and increases until it attains the steady-state value. From a survey of the values of n and β, the case of β < n − 1 seems to be prevailing for metallic creep. In this case C* can be a characterizing parameter of the near-tip fields. The observed acceleration and deceleration of crack growth rates under variable loads are found to be explained by the present analysis.