Abstract
Deformation twinning is observed in numerous engineering and naturally occurring materials. However, a fundamental law for critical twinning stress has not yet emerged. We resolve this long-standing issue by integrating twin-energy pathways obtained via ab initio density functional theory with heterogeneous, dislocation-based twin nucleation models. Through a hierarchical theory, we establish an analytical expression that quantitatively predicts the critical twinning stress in face-centered cubic metals without any empiricism at any length scale. Our theory predicts a monotonic relation between the unstable twin stacking fault energy and twin nucleation stress revealing the physics of twinning.
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