a b s t r a c tA crystal-plasticity finite-element analysis of the loading-unloading process under uniaxial tension of a rolled magnesium alloy sheet was carried out, and the mechanism of the inelastic response during unloading was examined, focusing on the effects of basal and nonbasal slip systems. The prismatic and basal slip systems were mainly activated during loading, but the activation of the prismatic slip systems was more dominant. Thus the overall stress level during loading was determined primarily by the prismatic slip systems. The prismatic slip systems were hardly activated during unloading because the stress level was of course lower than that during loading. On the other hand, because the strength of the basal slip systems was much lower than that of the prismatic slip systems, the basal slip systems would be easily activated under the stress level during unloading in the opposite direction when their Schmid's resolved shear stresses changed signs because of the inhomogeneity of the material. These results indicated that one explanation for the inelastic behavior during unloading was that the basal slip systems were primarily activated owing to their low strengths compared to that of the prismatic slip systems. Numerical tests using the sheets with random orientations and with the more pronounced texture were conducted to further examine the mechanism.
This paper presents the work-hardening behaviors of a rolled AZ31B magnesium alloy sheet during in-plane cyclic loading. The overall trend of the stress-strain curve was as follows. As established before, the yield stress under compression was considerably less than that under tension, and an inflected shape was observed in the stress-strain curve during the subsequent tension. Furthermore, an asymmetric evolution of work-hardening was observed as follows. The rate of work-hardening in the late stage of compression became gradually large with an increase in the number of cycles. Owing to this increase in the rate of work-hardening, the stress at the end of compression increased as the number of cycles increased. On the other hand, the rate of work-hardening in the late stage of tension became small as the number of cycles increased, yielding a decrease in the stress at the end of tension with the increase in the number of cycles. The results were almost the same when the cyclic loading test was carried out after tensile strain was applied to the sheet. On the other hand, when the cyclic loading test was carried out after compressive strain was applied, the increase in the rate of work-hardening in the late stage of compression was significantly more pronounced, whereas the inflected shape of the curve during tension was considerably less pronounced. The mechanisms of the above macroscopic behaviors were investigated in terms of twinning.
We investigate the nonlinear response arising during unloading under in-plane uniaxial compression of a rolled magnesium alloy sheet using a crystal plasticity finite-element method, focusing on the effects of twinning and detwinning, and discuss the mechanism that causes the nonlinear response to be more pronounced under uniaxial compression than under uniaxial tension. In the simulation, we employed a twinning and detwinning model recently proposed by the authors. From numerical experiments, we confirmed that, as already noted in previous studies, detwinning activity plays an important role in the nonlinear response during unloading. However, we also found that the basal slip could become very active during unloading because of the dispersion of crystallographic orientations caused by twinning activity during loading, which is another factor in the pronounced nonlinear response during unloading under uniaxial compression. We conclude that the nonlinear response during unloading is more pronounced under uniaxial compression than under uniaxial tension because of these 2 factors-i.e., the detwinning activity and the pronounced basal slip activity-which are not present under uniaxial tension.
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