Variations of Stress Intensity Factors of Surface Cracks with Wrapping Location in Compression Coil Springs

Abstract

This study has investigated the effects of coil turn position on the principal stresses and the correction factors, Fi (i=I, II and III) of the three modes of the stress intensity factors for a semi-elliptic surface crack on the outer surface of a compression coil spring. For this purpose, 3D finite element stress analyses have been made on a compression coil spring having a surface crack on the outer surface of its wire at every 0.5 turn from n=0.5 to n=4.5. The maximum principal stress, σ1, was also calculated by FEM and found to vary as cosine function of number of turns, n. The value of σ1 took maxima for half integer coil turns, i.e., n=0.5, 1.5, 2.5, …, whereas minima for every coil turn, i.e., n=1, 2, 3, … The principal stress fluctuation range was found as small as 4.6 % of its center value. The correction factor FI for the mode I stress intensity factors of the semi-elliptic surface crack also varied as cosine functions of n in the same manner as σ1 at all the positions of crack peripheries investigated. The largest mode I correction factor fluctuation range was as large as 22.9 % of its fluctuation center value. The variations of FI value with n can be distinguished into 5 groups according to the distance from the wire surface. This tendency was caused by the variations of FI value with the eccentric angle φ of the crack which are expressed as quartic functions of φ almost symmetric with the φ=90° (deepest point). The FI value took minima at the wire surface and second minima at the deepest point of the crack, and the value increased as the point got closer to the surface. The FI value varied from 0.47 to 0.69 with the geometrical parameters n and φ. The FI value was found dominant among the three modes of correction factors, since the values of the correction factors of the other modes, i.e., FII and FIII, were at most 8.3 % and 14.3 % of the FI value, respectively.