A critical review of the methods for evaluating fatigue of metals under simple (proportional) and complex (nonproportional) loadings indicates that most of the criteria are expressed in terms of either stresses or strains. In this paper a new approach to the evaluation of fatigue under these loadings is proposed. This approach is based upon the idea of relating fatigue life to the plastic work during a cycle of the loading. A procedure is outlined for the calculation of plastic work which involves explicit considerations of the material constitutive relations. It is based on the structure of modern plasticity theories and a new “hardening rule.” Validity of the constitutive relations to predict the cyclic stress-strain response is demonstrated for out-of-phase multiaxial loadings. Available experimental results of fatigue tests under out-of-phase loadings are shown to be in good agreement with the predictions using the new approach.

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