A HIGH‐CYCLE FATIGUE CRITERION APPLIED IN BIAXIAL AND TRIAXIAL OUT‐OF‐PHASE STRESS CONDITIONS

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Abstract
A high‐cycle fatigue criterion suitable for multiaxial non‐proportional stress loading is proposed in this paper. The criterion is based on some microscopic considerations related to the crystalline structure of metals. The purpose of the present paper is mainly the application of this criterion in two loading cases: (a) biaxial loads involving two normal stresses or one normal and one shear stress, and (b) triaxial load with two normal stresses and one shear stress. Stress states of these kinds are very common in piping assemblies. Application of the proposed criterion in the case of triaxial loading, where the three stress components are of the same frequency, but out‐of‐phase, leads to a simple analytical formula. This formula is the equation of a bounding surface that delimits in the space of the above three stresses the safety domain against fatigue crack initiation. A remarkable theoretical result concerns the phase difference of the shear stress, which does not appear in the derived formula. Consequently, according to our proposal the safety domain (i.e. the limiting fatigue endurance) under combined out‐of‐phase biaxial normal stress loading and torsion is independent of the phase difference of the torsion. Obviously this result holds also for the simpler case of axial load and torsion. On the contrary the phase difference between the two normal stresses has a strong detrimental effect on the fatigue endurance of a metal. As is shown these theoretical conclusions are in good agreement with fatigue limit test data found in the scientific literature.

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