The cyclically symmetric anti-plane fracture analysis for the arc-shaped interface in a non-homogeneous bimaterial cylindrical structure

A hollow cylinder, which consists of an inner functionally graded elastic substrate and an outer functionally graded elastic layer with cyclically symmetric cracks (a special case of multiple cracks), is considered under anti-plane shear load. The method of variable separation is employed to reduce the mixed boundary value problems to a Cauchy singular integral equation, which is solved numerically by the Lobatto–Chebyshev quadrature technique. Numerical results are presented to show the effects of geometrical and physical quantities on the stress intensity factors (SIFs). Parametric studies are conducted on the SIFs, and practical guidelines are given for the optimization of the fracture performance: (a) the SIFs depend on the ratio between the outer and inner radii, and the ratio should be at least 1.1; (b) the outer elastic layer should be stiffer than the inner elastic substrate; (c) large non-homogeneity parameter of the outer graded layer and small non-homogeneity parameter of the inner graded substrate are beneficial to SIFs reduction; (d) there is a strong interference between the stress fields around multiple cracks when the cyclically symmetric parameter increases.