Stress Intensity Factors for Semi-elliptic Surface Cracks in Compression Coil Springs with Orthotropic Anisotropy and Those with Cylindrical Anisotropy

Abstract

This study has made 3D finite element analyses on the stress intensity factors for semi-elliptic surface cracks in compression coil springs of cylindrically anisotropic and orthotropic materials in order to clarify the effects of the anisotropies on the correction factors F_i (i = I, II and III) for the three modes of the stress intensity factors. The cylindrical anisotropy was modeled by the stiffness tensor composed of the same components as those of the orthotropic material plus the additional C₄₅ component. In the cylindrically anisotropic coil springs, the mode-I correction factor F_I was dominant being the order of 0.7-0.9 around the periphery of the cracks. As the C₄₅ value increased, the F_I value decreased around the periphery of the cracks except for the vicinity of the wire surface. The absolute values of F_II and F_III, however, increased locally beyond 1. In the orthotropic coil springs, F_I was also dominant being the order of 0.9. The absolute values of the other correction factors remained less than 0.2 and reached the highest value in the vicinity of the wire surface. Not only the values but also the distributions of the three kinds of correction factors around the crack periphery in the orthotropic coil springs were found not so different from those of the semi-elliptic surface cracks in the isotropic compression coil springs.