A one-step mechanism for new twinning modes in magnesium and titanium alloys modelled by the obliquity correction of a (58°,<b>a</b>+ 2<b>b</b>) prototype stretch twin

Cayron, Cyril

doi:10.1107/s2053273317015042

Cited by 15 publications

(2 citation statements)

References 26 publications

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“…We recently found, by EBSD, a new and unconventional twin in a magnesium single crystal [150] that is incompatible with simple shear but corresponds exactly to this case. This twin is a cousin of the usual (1122 ) and (1126 ) twins; actually, the three twins derive from the same prototype "Bain" stretch detailed in [151], and differ only by their obliquity correction.…”

Section: Application Of the Distortive Model To Other Twinning Modesmentioning

confidence: 94%

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

Cayron

2018

Crystals

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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.

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Section: Application Of the Distortive Model To Other Twinning Modesmentioning

confidence: 94%

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

Cayron

2018

Crystals

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“…To explain them, Friedel [50] at the end of his life proposed a model based on diperiodic multiple "lattice" that replaces the triperiodic one, but these developments were largely ignored by the scientific community, probably because of the rareness of these unconventional twins. For the last decade, we have used the atomic hard-sphere assumption to establish some simple crystallographic models of martensitic transformations in steels and other alloys [40][41][42][43][44][45] and of deformation twinning in magnesium alloys [23,30,51,52]. We came to conclude that the habit plane is not fully invariant during the lattice distortion.…”

Section: Epitaxial Twinningmentioning

confidence: 99%

Complements to Mügge and Friedel’s Theory of Twinning

Cayron

2020

Metals

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The crystallography of twinning is based on the concepts of simple shear and obliquity introduced by Mügge, Mallard and Friedel at the turn of the last century, with tensor mathematics later developed by Bilby, Bevis and Crocker in the 1960s. We propose a synthesis of these works by writing the three transformations (distortion, orientation and correspondence) as matrices in dyadic product forms. We show that a "normal" Friedelian mode is implicitly assumed. We introduce another mode called "tilted" that explains, with the simple twin index q = 1, some twins that were previously oddly reported with q = 2. We also interpret the type II twins, which are usually presented as the conjugate twins of type I twins, as simple shears a rational reciprocal plane, exactly as the type I twins are simple shears a rational direct plane. Finally, we explain why the term "twin" for variants inherited from a phase transformation is not appropriate, and we call for a generalization of the crystallography of twinning by considering epitaxial distortions and iso-orientation shears.Metals 2020, 10, 231 2 of 32 plane for the twin edifice; it is also the interface between the two individual crystals. For type II twins, the direction η 2 is a 180 • rotation for the edifice. Many growth twins of type II do not exhibit a clear straight interface, or if it exists, it is the plane K 2 or a rational plane closest to K 2 containing η 2 . It is assumed that the plane K 1 for type I twins and the direction η 2 for type II twins cannot be symmetry elements of the individual crystals. After Mügge, the mathematics inherited from these concepts were developed by Kihô [11], Jaswon and Dove [12], and later by Bilby, Bevis and Crocker [13][14][15].In parallel to Mügge's work on deformation twins, Mallard [16] introduced important concepts for the crystallography of growth twins in the period 1876-1886: (a) "twinning by merohedry" where the crystal and its twin share the same lattice but the orientation of the motif is different; and (b) "twinning by pseudo merohedry" in which a reticular plane is "nearly" a mirror plane of the crystal or a reticular direction is nearly a 180 • rotation (see also [17,18]). A plane can become a mirror symmetry for the twin edifice when its normal is close to a reticular direction, and a direction can become a 180 • rotation when its normal plane is close to a reticular plane. In such cases, the lattice of the crystal and that of its twin are "close", which means that a slight distortion is sufficient to transform one into the other. An example is shown in Figure 1b. The direction n normal to the plane K 1 = (0, 1) is close to the reticular direction η 2 = [0, 1]; twinning can occur because the obliquity θ, i.e., the misorientation angle between the two directions, is small. The parent and twin lattices are in mirror orientation through their common K 1 plane. We took the liberty to use here Mügge's notations of deformation twinning K 1 and η 2 , whereas Friedel never used them to describe the growth twins. Note that the...

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Determination of twinning path from broken symmetry: A revisit to deformation twinning in bcc metals

Gao

Zhang

2020

Acta Materialia

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A one-step mechanism for new twinning modes in magnesium and titanium alloys modelled by the obliquity correction of a (58°,a+ 2b) prototype stretch twin

Cited by 15 publications

References 26 publications

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

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

Complements to Mügge and Friedel’s Theory of Twinning

Determination of twinning path from broken symmetry: A revisit to deformation twinning in bcc metals

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