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The existing plasticity models recognize that ratchetting direction strongly depends on the loading path, the stress amplitude, and the mean stresses, but their predictions deviate from experiments for a number of materials. We propose an Armstrong-Frederick type hardening rule utilizing the concept of a limiting surface for the backstresses. The model predicts long-term ratchetting rate decay as well as constant ratchetting rate for both proportional and nonproportional loadings. To represent the transient behavior, the model encompasses a memory surface in the deviatoric stress space which recalls the maximum stress level of the prior loading history. The coefficients in the hardening rule, varying as a function of the accumulated plastic strain, serve to represent the cyclic hardening or softening. The stress level effect on ratchetting and non-Masing behavior are realized with the size of the introduced memory surface. Simulations with the model checked favorably with nonproportional multiaxial experiments which are outlined in Part 2 of this paper.

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AbstractÐStress±strain responses of single and polycrystals of Had®eld steel were modeled using a viscoplastic self-consistent approach. A unique hardening formulation was proposed in the constitutive model incorporating length scales associated with spacing between twin lamellae and grain boundaries. TEM observations lend further support to the length scales incorporated into the constitutive model. Many of the experimental ®ndings were made on " 111 and " 144 crystal orientations deformed in tension, displaying ®ne twin lamellae at small strains in addition to slip in intra-twin regions. A natural outcome of the model was the small deformation activity inside the twinned regions and higher deformations between the twins. The model utilized dislocation density as a state variable and predicted the stress±strain responses and texture evolution in single crystals accurately over a broad range of strains. The responses of polycrystals with three grain sizes (100, 300, and 1000 mm) were also captured closely with the model in addition to the twin volume fraction evolution with increasing deformation. Based on the simulations, it was possible to explain unequivocally the upward curvature in stress±strain curves in the single crystals and in coarse grained polycrystals of Had®eld steel. Overall, the combined experimental and modeling e orts provide a reliable tool to characterize slip±twin interaction in low stacking fault energy f