The cyclic hardening behavior of metallic materials at a prescribed constant plastic strain rate is investigated. The development is within the framework of the endochronic theory of viscoplasticity. It has been shown that a cyclic steady state can be attained theoretically, in agreement with the experimental finding. A general expression for describing the stress-strain relation for all cycles of a fatigue test with fixed total strain amplitude is presented and the peak stress of each cycle at different specified total strain level is also investigated.

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