This paper presents the prediction of the contours of plastic work for an AZ31 magnesium alloy sheet in the first quadrant of the stress space using a rate-dependent crystal plasticity finite-element method. The contour of plastic work was initially rather flat in the vicinity of equi-biaxial tension, but bulged severely thereafter. Evidently, the shapes of the contours changed as the plastic work increased, exhibiting a differential work-hardening behavior. The variation of the relative activity of each family of slip systems was examined to investigate the mechanism of the differential work-hardening behavior. During uniaxial tension, the work-hardening was determined mainly by the basal slip in the very beginning, whereas it was determined by both the prismatic and the basal slip in the subsequent deformation. On the other hand, during equi-biaxial tension, the relative activity of the prismatic slip systems was much smaller than that under uniaxial tension, whereas the relative activity of the basal slip systems played a dominant role in the work-hardening throughout the deformation. A simple analysis revealed that it was more difficult to activate the prismatic slip systems for equi-biaxial tension than uniaxial tension in rolled magnesium alloy sheets because the two biaxial stresses tended to cancel each other thus decreasing the relative activity as the biaxial stress ratio approached unity. On the other hand, the basal slip systems were much easily activated than the prismatic slip systems although their Schmid factors were small because the shear stress required for the activation of the basal slip systems was much lower than that of the prismatic slip systems. We concluded that such differences in the activities of the slip systems eventually resulted in the differential work-hardening behavior of the contour of plastic work.
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