A measure of plastic anisotropy for hexagonal close packed metals: Application to alloying effects on the formability of Mg

Abstract

Mg is inherently plastically anisotropic and, over the years, alloying development efforts have sought to reduce the plastic anisotropy in order to enhance formability. To understand the relationship between alloy type and plastic anisotropy, we use a visco-plastic self-consistent (VPSC) polycrystal plasticity model to relate the macroscopic constitutive response to the underlying slip and twinning mechanisms in pure Mg and several Mg alloys. In the calculations, the influence of alloy type is represented by the differences in the CRSS values among the basal, prismatic, pyramidal slip and tensile twin systems. We show that for the same initial texture, this microscopic-level CRSS anisotropy can have a significant effect on the macroscopic indicators of formability, namely the anisotropy of the post-deformation polycrystal yield surface, tension-compression yield asymmetry, and Lankford coefficients. A plastic anisotropy (PA) measure is formulated to quantify the degree of single crystal plastic anisotropy acquired by the dissimilarities in the CRSS values of the slip and twinning modes for a given alloy. We demonstrate a strong correlation between the PA measure with the formability indicators mentioned above for multiple initial textures commonly enountered in processing. We find that alloys can be classified into two groups, those with a PA value below 2, which are more formable, less twinnable, and less sensitive to initial texture, where PA ∼2 for pure Mg, and those with a PA value above 2, which possess the opposite deformation response.