Shakedown of a cracked body consisting of kinematic hardening material

Abstract In this paper, the shakedown behaviour of a cracked body is studied. The main idea is to consider the crack as a notch. Then no singular stresses appear at crack tip. Due to the local character of the problem, Melan's shakedown theorem is used. By solving shakedown as an optimization problem, the limited stress intensity factor (SIF) for shakedown Ksh is obtained. It is found that the shakedown limit SIF of a cracked body is proportional to the initial yield stress σy of the material times the square root of the effective crack tip radius π, i.e. Ksh ∝ σy√ϱ. Comparison of shakedown limit SIFs with fatigue thresholds for certain materials, so far as can be found in literature, shows that these two quantities agree well with each other. This agreement indicates that shakedown of the cracked body is one of the reasons for arrest of the crack under cyclic loads. Shakedown investigation is then a new method for predicting the fatigue threshold of a cracked body. Thus, a transition from shakedown to cyclic fracture mechanics has been achieved.

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