Effect of Thickness on Creep Relaxation of Stress Around the Crack Tip

Abstract

The Ct-integral has an equivalent role to the J-integral in the context of time-dependent creep behavior in quasi- static problems. Because of the time-dependent effects of creep deformation, there is no one parameter that characterizes the stress state around the crack tip for all circumstances. The appropriate parameter to use depends on the details of the constitutive law (whether the law describes primary, secondary, or tertiary creep) and on the stage of deformation of the material around the crack tip. In addition, creep deformation can occur in either an initially elastic or an initially plastic stress field. When the initial response of the material is linear elastic and secondary creep dominates the creep behavior, the stress intensity factor, KI, and the path independent integral, C*, are the relative loading parameters. For small-scale creep (that is, when elastic strains dominate almost everywhere in the specimen except in a small zone that grows around the crack tip), KI governs crack growth initiation. If, however, the creep zone becomes large compared to the specimen size and the elastic strains small compared to the creep strains, C* is the appropriate fracture parameter. For stationary cracks Ct characterizes the rate of growth of the crack-tip creep zone under small-scale creep conditions and is also related to the stress intensity factor KI. Under extensive secondary creep conditions, Ct→ C* and is path independent throughout the extensive creep region.This paper takes into account the evaluation of Ct-integral as a function of time for a shallow edge-crack in a half space subjected to constant Mode I far-field tensile loading. The effect of thickness on creep relaxation of stress around the crack tip has been also investigated. Similar to J-integral, the values of Ct-integral decrease as the thickness of the specimen decreases. The rate of the Ct-integral reduction reduces by decreasing the thickness.