Shifting the Shear Paradigm in the Crystallographic Models of Displacive Transformations in Metals and Alloys

Deformation twinning and martensitic transformations are characterized by the collective displacements of atoms, an orientation relationship, and specific morphologies. The current crystallographic models are based on the 150-year-old concept of shear. Simple shear is a deformation mode at constant volume, relevant for deformation twinning. For martensitic transformations, a generalized version called invariant plane strain is used; it is associated with one or two simple shears in the phenomenological theory of martensitic crystallography. As simple shears would involve unrealistic stresses, dislocation/disconnection-mediated versions of the usual models have been developed over the last decades. However, a fundamental question remains unsolved: how do the atoms move? The aim of this paper is to return to a crystallographic approach introduced a few years ago; the approach is based on a hard-sphere assumption and linear algebra. The atomic trajectories, lattice distortion, and shuffling (if required) are expressed as analytical functions of a unique angular parameter; the habit planes are calculated with the simple “untilted plane” criterion; non-Schmid behaviors associated with some twinning modes are also predicted. Examples of steel and magnesium alloys are taken from recent publications. The possibilities offered in mechanics and thermodynamics are briefly discussed