The paper is concerned with the theoretical prediction of cyclic hardening and cyclic softening of metals under conditions of cyclic straining. First, a constitutive equation of a hereditary type is proposed, which is based on the notion of intrinsic time, introduced recently by the author. In essence, the intrinsic time is the cumulative sum of “deformation increments” experienced by a material in the past, weighted with respect to a weighing function which is a material property. The theory predicts that an annealed metal will harden upon cyclic straining until a critical value of the intrinsic time is reached whereupon the metal will begin to soften. It is also shown that an initial strain prehistory will accelerate the onset of softening in accord with experimental observation. Finally, the “fading memory” of metals with respect to the intrinsic time scale is demonstrated and its consequences are shown to be in agreement with observation.

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