Stress Field and Modified J-Integral Near a Crack Tip under Condition of Confined Creep Deformation

Abstract

This paper deals with the stress and strain fields and the modified J-integral near a crack tip under the condition of incipient creep deformation. It was assumed in this analysis that (1) the total strain can be divided into the elastic and creep strains, (2) the crack does not grow (a stationary crack), (3) the elastic strain prevails except for a region near the crack tip where the creep strain is predominantly large compared with the elastic strain, and (4) the definition of the modified J-integral, J', is valid in this region.
Analytical expressions for the stress and strain fields and the J' evaluation near the crack tip were derived for the Norton-type steady-state creep, the time-hardening creep and the strain-hardening creep hypotheses. The validity of the proposed expressions was confirmed numerically by using the finite element analysis. It was found that the values of stress, strain and J' were very high in the vicinity of the crack tip during incipient creep deformation. For example, under constant loading the J' value near the crack tip was inversely proportional to loading time. J' approached to its steady-state value J'_st as the creep deformation increased. As a measure of this transition, a characteristic time t_tr was defined, which is proportional to J_el/J'_st where J_el denotes the elastic J-value. This transition time t_tr was evaluated for a type 304 stainless steel and a Cr-Mo-V steel using the data available in the literature. It was shown that this transition should be taken into account for predicting the initial phase of creep crack growth of low ductility Cr-Mo-V steel. The effect of plastic strain was also discussed and it was suggested that the plastic J-integral J_pl divided by J'_st could be taken as another characteristic time.