This paper reports the effect of pre-strain on the work-hardening behavior of rolled AZ31 magnesium alloy sheets during in-plane cyclic loading. The work-hardening behavior of the alloy remained almost unchanged when tensile strain was applied before cyclic loading. However, the work-hardening behavior was significantly affected when a compressive strain was applied. First, the resulting stress-strain curve was not sigmoidal upon tension in some cases, depending on the magnitudes of the applied compressive pre-strain owing to the inversion of the loading direction from tension to compression before the second increase in the work-hardening rate. In other words, a sigmoidal stress-strain curve certainly arose upon tension when compressive pre-strain was applied and the loading direction was not inverted from tension to compression. It was found that the strain at the beginning of the second increase had a high correlation with the volume fraction of twins. Second, the change in the rate of work-hardening at the beginning of tension became sharp as compressive pre-strain increased, probably owing to the effect of activation of detwinning on the stress-strain curve, which became increasingly significant as the compressive pre-strain increased the volume fraction of twins.

The deformation behavior during unloading was examined under uniaxial tension in a mild steel sheet (body-centered cubic metal), an aluminum alloy sheet (face-centered cubic metal), and a magnesium alloy sheet (hexagonal close packed metal). A crystal plasticity finite-element method was also used to investigate the difference in the deformation behavior among on the materials. The nonlinearity during unloading was the largest in the magnesium alloy sheet, and the mild steel sheet showed a larger nonlinearity than the aluminum alloy sheet. On the other hand, the apparent elastic moduli determined from the linear approximation of unloading curves were not always consistent with the characteristics observed in the nonlinearity, and this inconsistency became pronounced as the degree of nonlinearity increased. It was found that the degree of nonlinearity would have a strong correlation with the strain rate sensitivity, suggesting that the apparent elastic modulus was not suitable to model the unloading behavior for materials with high strain rate sensitivity. The crystal plasticity analysis demonstrated that the nonlinearity was much larger in the magnesium alloy sheet than in the other two sheets as observed in the experimental results. The simulation results suggested that one of the reasons that gave rise to the nonlinearity during unloading would be the difference in the critical resolved shear stresses among the slip systems.