Abstract
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.
Highlights
Mechanical twinning and martensitic transformations are known to form very rapidly, sometimes at the velocities close to the speed of sound; the atoms move collectively, and the product phase appear as plates, laths, or lenticles
The concept of simple shear has been the corner stone of the classical theories of the crystallography of martensitic transformations and deformation twinning for 150 years
The early models of the fcc-bcc transformations proposed by Young, Kurdjumov, Sachs, and Nishiyama, those of the bcc-hcp transformations made by Burgers, the phenomenological theory of martensitic transformations (PTMC) initiated by Greninger and Troiano and developed by Weschler, Read and Liebermann, and Bowles and Mackenzie, and lastly the theory of deformation twinning developed by Bilby, Bevis, and Crockers, among others, are all based on compositions of simple shears, or imply an invariant plane strain (IPS), which is a generalized form of shear that accounts for the volume change induced by the transformation
Summary
Mechanical twinning and martensitic transformations are known to form very rapidly, sometimes at the velocities close to the speed of sound; the atoms move collectively, and the product phase (martensite or twins) appear as plates, laths, or lenticles These transformations are called “displacive” in metallurgy (please note that the meaning of this term is different from the one used in physics, where “displacive” implies only small displacements of atoms without breaking the atomic bonds). Atoms, even with their simple hard-sphere image, are not explicitly present in the crystallographic theories of twinning and martensitic transformations, which are all based on the lattices and their transformation by shears, as in Mügge’s initial model.
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