Statistic derivation of Taylor factors for polycrystalline metals with application to pure magnesium

We have investigated the Taylor factors of textured as well as texture-free polycrystalline aggregates. We begin with examining the Schmid factors of single crystals. A statistical model is then introduced to describe the distribution of grain orientations as well as the Schmid factor of individual grains of the polycrystalline system. The grains are classified into “soft” and “hard” ones. Based on this, a model is proposed for the derivation of the Taylor factors of textured as well as texture-free polycrystalline metals, and as a case study it is applied to polycrystalline magnesium. The model predictions are in very good agreement with the available experimental results. No free parameters have been involved in the development of this model, and the physical processes are clearly defined. Based on the fundamental assumption that grains can be classified into “soft” and “hard” in metals, this model should also be applicable to other hexagonal close packed metals such as α-titanium, beryllium and zirconium, as well as metals of other lattice structures such as face-centered cubic and body-centered cubic. It will also be interesting to see if this model can be incorporated into existing crystal plasticity models for the prediction of texture evolution under mechanical loading.