Effects of Pitch on the Correction Factors of the Stress Intensity Factors for Semielliptic Surface Cracks in Compression Coil Springs

Abstract

This study has investigated the effects of spring pitch on the principal stresses and the correction factors, F_i(i=I, II and III) of the three modes of the stress intensity factors for semielliptic surface cracks on the surface of compression coil springs both inside and outside of the coils. For this purpose, 3D finite element stress analyses have been made on compression coil springs with and without surface cracks having normalized pitch p/R=0.8, 1.2 and 1.8, or the pith angle α=7.3°, 10.8°, 16.0°, respectively where p is the spring pitch and R the coil radius. The principal stresses calculated by FEM were compared with those calculated by the formula proposed by A. M. Wahl with the pitch angle α taken into consideration. The results obtained by FEM and by the formula showed good agreement, revealing that both the maximum and minimum principal stresses σ₁ (>0) and σ₃ (<0) were the lowest on the wire surface inside of the coil and increased linearly with the distance from the axis of the wire and reached their maxima on the outer surface of the coil. The differences between the maximum and minimum values of σ₁ and σ₃ increased as the value of p/R became larger probably due to the bending stress. The correction factor F_I of the mode I stress intensity factor was larger on the wire surface outside of the coil than on that inside of the coil. The maximum F_I value was 0.66 outside for p/R=1.8 whereas 0.34 inside for p/R=0.8 at the eccentric angles of Φ=30° and 150°. The F_I value became larger with increase in the p/R value outside whereas it became smaller with increasing p/R value inside. The F_I value was found dominant among the three modes of correction factors; i.e., both the F_II and the F_III values were nearly zero and slightly varied along the periphery of the crack.