The hardening behavior of materials in nonproportional cyclic process is related to the internal changes of materials, such as dislocation cell for wary slip material and ladder or vein substructures for planar slip material. The multiplicatively separated form of hardening function f, in terms of nonhardening region proposed by Ohno [1], and the measure of nonproportionality A proposed by Banallal and Marquis in 1987 [2], is then explained on this physical foundation. The new contributions of this hardening function are: (a) two parameters (f2 and f3) dependent on A are used to differentiate between the influence of latent hardening realized by a sudden change of loading direction, and hereditary hardening associated with nonproportional loading, (b) a general differential form fi (i = 1,2,3) is proposed, and memorial parameters a1 and a3 are introduced to describe different deformation history effects for wary and planar slip materials, (c) different hardening mechanisms through fi are embedded into thermomechanically constitutive relation. The stress responses of 304 and 316 stainless steels subjected to biaxial nonproportional loadings at room temperature are analyzed and compared with the experimental results obtained by Chaboche [3], Tanaka [4, 5] and Ohno [1].

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