Beyond initial twin nucleation in hcp metals: Micromechanical formulation for determining twin spacing during deformation

Capturing twin nucleation in full-field crystal plasticity is a long-standing problem in materials science modeling. Pronounced efforts have been deployed to understand the nucleation event at the atomic level. Yet, it remains very challenging to appropriately scale up the inherently discrete mechanisms to the continuum scale. However, of significant implications for modeling of hardening and damage is not the embryonic/lamellar nucleation of an individual twin per say, but the spacing of the twins and their concomitant interactions with each other and active defects in the lattice. Thus, knowing when and where the next twin would nucleate or grow is certainly of significant consideration to crystal plasticity and would have been perhaps the primary goal of any model which would capture early site-specific nucleation. In this study, we develop an analytical model based on a micromechanical formulation, which is able to pinpoint where a second twin nucleates in an idealistic scenario in a homogeneous material. The model was probed with a three-point bending boundary value problem and predictions were compared to in-situ bending tests of an AZ31 Mg alloy. The alloy was chosen because it exhibited sharp textures which tend to develop twin patterns similar to single crystals. The analytical expression for the stress field was obtained for an ellipsoidal twin in an isotropic half-space. We show that the twin spacing depends primarily upon the height of the twin band, and the stress relaxation from twinning depends primarily upon the thickness of the twin domain. The solution compared well to experimental results.