Multiaxial cyclic ratchetting under multiple step loading

Strain ratchetting responses of 1070 steel are reported for multiple step cyclic loading histories. The stress amplitude and mean stress are varied between loading steps in multiple step loading. Experimental results reveal that the material exhibits a strong memory of the previous loading history, and such memory plays a discerning role on the subsequent ratchetting. The material could ratchet in the opposite direction to the mean stress or could reverse its ratchetting direction with time. The origin of the ratchetting transients has been linked to the variation of the plastic modulus within the loading cycle for proportional loading and the noncoincidence of the plastic strain rate direction and yield surface translation direction for nonproportional loading. Many of the constitutive relations proposed for cyclic loading are not designed to handle the ratchetting evolution. Based on the Armstrong-Frederick hardening algorithm, the model forwarded by Bower can qualitatively predict the ratchetting directions for certain multiple step loading cases, but the predicted ratchetting rates differ from the experimental values. The Ohno-Wang model, which introduces threshold levels of dynamic recovery in nonlinear hardening, can simulate negative ratchetting under positive mean stress, or vice versa, as well as the ratchetting direction reversal during step loadings. This model can provide results that agree with experimental observations for a class of nonproportional cases, where the plastic strain rate direction and yield surface translation direction are noncoincident. Its performance deteriorates for proportional loading.