Extensive experiments were conducted on annealed copper under cyclic nonproportional strain histories. After cyclically stabilizing the material by uniaxial cycling, out-of-phase axial-shear strain cycling for the same effective strain range caused additional increases in stress amplitudes to restabilized levels. Following cyclic stabilization of the material under out-of-phase cycling, a cycle whose effective strain amplitude was comparable to those of previous cycles resulted in stress-strain behavior unique to that cycle and independent of prior stable deformation. The experimental verification of this material property, which has been the subject of much conjecture, allowed the design of a fundamental class of experiments that determined the subsequent yield surface and strain hardening behavior from only one specimen.
Experiments that demonstrate the basic quantitative and qualitative aspects of the cyclic plasticity of metals are presented in Part 1. Three incremental plasticity kinematic hardening models of prominence are based on the Prager, Ziegler, and Mroz hardening rules, of which the former two have been more frequently used than the latter. For a specimen previously fully stabilized by out of phase cyclic loading the results of a subsequent cyclic nonproportional strain path experiment are compared to the predictions of the above models. A formulation employing a Tresca yield surface translating inside a Tresca limit surface according to the Mroz hardening rule gives excellent predictions and also demonstrates the erasure of memory material property.
A model employing a modified Mroz kinematic hardening rule with a Tresca yield surface is derived for a state of plane stress, combining together successful attributes of previous nonproportional incremental plasticity theories. Results from several nonproportional tests on oxygen-free high-conductivity copper are compared with computer predictions. Solution sensitivity to the particular cyclic stress-stain curve used, its piecewise linearization for the Mroz-type hardening rule, and the magnitude of the effective strain increment in the analysis is studied. A trade-off between the number of surfaces used in the Mroz-type rule and the effective strain increment size is observed for optimum solution with respect to convergence and speed.
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