In simulating cyclic plasticity with several existing “unified” constitutive equations, the predicted hysteresis loops are “oversquare” with respect to experimentally-observed behavior. To eliminate this shortcoming in the constitutive equations developed by the present author, the work-hardening coefficient in the equation controlling the back stress (R) has been made a function of the back stress itself and the sign of the effective modulus-compensated stress σ/E – R. This improvement results in simulated hysteresis loops whose curvature closely resembles that in experimental tests. The improvement preserves all of the previously demonstrated capabilities such as cyclic hardening, cyclic hardening, cyclic softening, etc. The same equations can also simulate some unusual experimentally-observed Bauschinger effects involving local reversals in curvature. The curvature reversals in the simulations result from strain softening of the isotropic work-hardening variable in the equations. The physical significance of the behavior of the constitutive equations is discussed in terms of annihilation of previously-generated dislocation loops by reversing dislocations and experimentally-observed decreases in dislocation density and dissolution of cell walls upon stress reversal.

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