Stress Intensity Factor of Surface Cracks in Anisotropic Tension Coil Springs

Abstract

In this study, 3D finite element analyses have been made on the stress intensity factors for semi-elliptic surface cracks in tension coil springs of generally anisotropic materials in order to investigate the effects of elastic anisotropy on the correction factors, F_i (i = I, II and III) for the three modes of the stress intensity factors. The generally anisotropic stiffness matrix was determined by changing the off-diagonal components C_ij (i ≠ j), except C₁₂, C₁₃, C₂₃, of the stiffness matrix modelled by a ferrous material. When the values of the off-diagonal components are changed simultaneously, the maximum value of the correction factors for all the three modes increased sharply as these components approaches to the values of one of Lamé's constants, or the shear modulus, G. The value of F_I, the correction factor for the mode I stress intensity factor takes local maxima in the vicinity of surface, i.e., ϕ = 0°∼90°and 150°∼180°, the F_II value at surface, i.e., ϕ = 0°and 180°, and the F_III value at ϕ = 45°and 135° where ϕ is the eccentric angle of the semi-elliptic crack. When only one of the off-diagonal components C_ij is set for near the G value and the others are 0, the variations of the correction factors with the value of ϕ are revealed to be similar to those for the case where all the values of the off-diagonal components are set for near the G value. These results imply that the correction factors for the mode I to III stress intensity factors of semi-elliptic surface cracks in generally anisotropic tension springs can be largely affected by the values of the off-diagonal components C₄₅ and C₄₆ of the stiffness matrix of the spring wire.