Energetic contributions to deformation twinning in magnesium

TL;DR

This work addresses the energetics of heterogeneous nucleation of the $\{10\overline{1}2\}$ tension twin in magnesium by combining molecular dynamics with a micromechanical energy framework. MD reveals nucleation from an asymmetrically tilted grain boundary, forming CTB/PB facets and $I_1$ stacking faults, with a significant energy contribution from the prior grain boundary transformation. An Eshelby-based elastic-field analysis, together with PCA-derived twin geometry, estimates the elastic energy, but a full description requires incorporating end-dislocation interactions at fault boundaries. The revised model shows that the change in grain boundary character can offset other energetic costs, and that grain boundary inclination plays a key role, pointing to improved predictive capabilities for twin nucleation sites in Mg polycrystals.

Abstract

Modeling deformation twin nucleation in magnesium has proven to be a challenging task. In particular, the absence of a heterogeneous twin nucleation model which provides accurate energetic descriptions for twin-related structures belies a need to more deeply understand twin energetics. To address this problem, molecular dynamics simulations are performed to follow the energetic evolution of $\{10\overline{1}2\}$ tension twin embryos nucleating from an asymmetrically-tilted grain boundary. The line, surface and volumetric terms associated with twin nucleation are identified. A micromechanical model is proposed where the stress field around the twin nucleus is estimated using the Eshelby formalism, and the contributions of the various twin-related structures to the total energy of the twin are evaluated. The reduction in the grain boundary energy arising from the change in character of the prior grain boundary is found to be able to offset the energy costs of the other interfaces. The defect structures bounding the stacking faults that form inside the twin are also found to possibly have significant energetic contributions. These results suggest that both of these effects could be critical considerations when predicting twin nucleation sites in magnesium.

Figures (14)

• Figure 1: Schematic of the periodic quasi-2D simulation cell with honeycomb grains. The $xyz$ coordinate axes are referred to as the global coordinate system in the text. The $[\overline{1}\overline{1}20]$ crystal axes of all grains are aligned with the global $z$-axis. Grains 2, 3 and 4 are tilted with respect to Grain 1 by a rotation of $\phi$ about the global $z$-axis, i.e., $\phi$ is the angle between the grain's $c$-axis and the global $x$-axis. The $(\overline{1}102)$ and $(1\overline{1}02)$ planes associated with the activated $\{10\overline{1}2\}$ tension twin system are highlighted in the central unit cell, with the respective twinning directions indicated by red arrows.
• Figure 2: A sketch of (a) the simulation cell after initial equilibration, (b) the deformed simulation cell with a twin in G1 (the deformation is exaggerated), (c) the simulation cell after the removal of far-field strain. The initial dimensions $l_i$, $h_i$, $t_i$ are 692 $\text{\AA}$, 600 $\text{\AA}$ and 25.6 $\text{\AA}$ respectively.
• Figure 3: Snapshots of the simulation box and twin nuclei at representative states of the MD simulation after the removal of the far-field strain, with the reported strain values given in reference to the corresponding load step. (a,b) Snapshots of the simulation box at LP0 ($\varepsilon_{yy}^0 = -0.0208$) and LP40 ($\varepsilon_{yy}^0 = -0.0286$). (c-h) Snapshots of the twinned G1-G3 boundary at LP0, LP9, LP19, LP24, LP32 and LP40 ($t = 104$, $113$, $123$, $128$, $136$ and $144$ ps respectively). N1, N2 and N3 indicate the three distinct twin nuclei on the G1-G3 boundary at $113$ ps. White and blue indicate atoms in hcp and fcc environments, whereas black denotes a disordered structure on an interface.
• Figure 4: The change in potential energy of the simulation cell relative to values at LP0 ($t = 104$ ps) (i) after the first energy minimization, (ii) after removal of the far-field strain $\varepsilon^0$, (iii) after the second energy minimization.
• Figure 5: The change in potential energy relative to the values at LP0 ($t = 104$ ps) of (i) the entire simulation cell, (ii) G1, and (iii) the region occupied by the twin at $140$ ps.