Fatigue Life Evaluation under Out-of-Phase Push-Pull and Torsion

Abstract

This paper discusses the stress-based evaluation of fatigue life under both in-phase and out-of-phase combined loading conditions. Load controlled fatigue tests were performed on a low carbon steel under combined push-pull and completely reversed torsion in the intermediate to high cycle regime. Phase differences between two loadings were 0°, 45° and 90°.
Experimental data showed that the increase of phase difference resulted in the increase of fatigue life under combined loadings. This may be explained by the decrease of plastic strain range due to material hardening in out-of-phase conditions.
Gough's ellipse quadrant was generalized to out-of-phase loadings by taking account of the phase differences. This criterion can be easily applied but slightly overstimates the actual life. A modification of Lee's criterion, which was also an extension of Gough's equation, showed good agreement with the observed life. Furthermore, Brown-Miller's theory expressed in terms of the shear and normal stresses on the maximum shear plane was applied to out-of-phase fatigue. As a result, the fatigue lives under push-pull, torsion and combined in- and out-of-phase loadings were well correlated by Brown-Miller's criterion.