Quantitative prediction of texture effect on Hall–Petch slope for magnesium alloys

The high texture dependence of a Hall–Petch slope (k) for Mg alloys has been frequently reported. Several important equations used to calculate k have been previously developed, and although they seem to work well for fcc and bcc materials, they often fail to predict the highly texture-dependent k in Mg alloys. A new equation based on the dislocation pile-up model was developed in this study. The validity of this new equation was tested through a comparison of the predicted k values with the experimental values as well as the calculations from older equations. The results indicate that the new equation can achieve an accurate prediction for several previously reported texture effects on k, whereas the k values predicted by the older equations often exhibit a clear deviation. The reasons for this were analyzed and discussed. The strong deformation anisotropy for Mg alloys leads to a complex texture effect on k, including the effects from both external and internal stresses. Both effects are well expressed in the new equation. In contrast, the old equations consider the external stress effect, but do not express well the internal stress effect. In addition, the old equations consider only the predominant deformation mode. However, our results indicate that the activation of a portion of another deformation mode other than the predominant one plays an important role in the k value. In the new equation, all possible deformation modes and their fractions are considered in the calculation. Using the important parameters of the new equation, the mechanisms for several texture effects on k as previously reported were discussed and new understandings were obtained.