This paper presents a new design criterion for fully reversed out-of-phase torsion and bending fatigue. This criterion, similar in spirit to that proposed by Kanazawa, Miller, and Brown, is derived as an extension of Gough's ellipse quadrant.

Theories and tests under “in-phase” torsion and bending fatigue are briefly reviewed. A few commonly used fatigue theories for “out-of-phase” multiaxial loadings are critically evaluated. Tests were performed with cantilever type SM45C structural steel specimens under fully reversed out-of-phase combined torsion and bending loadings in the intermediate cycle regime. Available fatigue data under high-cycle out-of-phase torsion and bending are plotted on constant life diagrams calculated according to the new criterion.

For multiaxial out-of-phase loadings, generated by fully reversed combined torsion and bending, both the present test results and data in the literature are in good agreement with the new fatigue criterion. The criterion predicts fatigue life under fully reversed bending with out-of-phase or in-phase torsion at intermediate to high cycles.