This paper presents a study of the crack arrest tendency under cyclic thermal stress for an inner-surface circumferential crack in a finite-length cylinder with its edges rotation-restrained, when the inside of the cylinder is cooled from uniform temperature distribution. The effects of structural parameters and heat transfer condition on the maximum transient SIF for the problem were investigated with the formerly developed systematical evaluation methods. Then, a tentative value of threshold stress intensity range $ΔKth$ being assumed as well as Paris law, the evaluation of crack length for crack arrest under cyclic thermal stresses was carried out. Finally, a map to find the crack arrest point for a cylinder with mean radius to wall thickness ratio $Rm/W=1$ and a specific length H under various heat transfer conditions could be originated. From the map, it was predicted that when the heat transfer coefficient and/or initial wall-coolant temperature differences become large enough, the nondimensional crack arrest length saturates to a specific value and is no longer affected by those conditions.

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