Non-linear Deformation Behavior during Unloading in Various Metal Sheets

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.