The problems of multiple inclined or curved cracks in circular positions is treated by using the hypersingular integral equation method. The cracks center are placed at the edge of a virtual circle with radius R. The first crack is fixed on the x-axis while the second crack is located on the boundary of a circle with the varying angle, θ. A system of hypersingular integral equations is formulated and solved numerically for the stress intensity factor (SIF). Numerical examples demonstrate the effect of interaction between two cracks in circular positions are given. It is found that, the severity at the second crack tips are significant when the ratio length of the second to the first crack is small and it is placed at a small angle of θ .

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The rolls are classified into two types; one is a single-solid type, and the other is a shrink-fitted construction type consisting of a sleeve and a shaft. The bimetallic work rolls are widely used in the roughing stands of hot rolling stand mills. Regarding a shrink-fitted construction type, the interfacial slip sometimes appears between the shaft and the shrink-fitted sleeve. This interfacial slip can be regarded as the relative displacement between the sleeve and the shaft. In this paper, the stress due to the interfacial slip is studied because the stress may cause the sleeve fracture. It is found that the stress in the shrink-fitted surface is slightly decreased with increasing number of rotations [Formula: see text]. Therefore, the stress obtained by the simulation at [Formula: see text] can be used to estimate the fatigue strength.

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