Journal ArticleDOI
Fine phase mixtures as minimizers of energy
TLDR
In this article, the authors explore a theoretical approach to these fine phase mixtures based on the minimization of free energy and show that the α-phase breaks up into triangular domains called Dauphine twins which become finer and finer in the direction of increasing temperature.Abstract:
Solid-solid phase transformations often lead to certain characteristic microstructural features involving fine mixtures of the phases. In martensitic transformations one such feature is a plane interface which separates one homogeneous phase, austenite, from a very fine mixture of twins of the other phase, martensite. In quartz crystals held in a temperature gradient near the α-β transformation temperature, the α-phase breaks up into triangular domains called Dauphine twins which become finer and finer in the direction of increasing temperature. In this paper we explore a theoretical approach to these fine phase mixtures based on the minimization of free energy.read more
Citations
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Journal ArticleDOI
A Quantization Property for Moving Line Vortices
Fanghua Lin,Tristan Rivière +1 more
Journal ArticleDOI
A variational model allowing both smooth and sharp phase boundaries in solids
John M. Ball,Carlos Mora-Corral +1 more
TL;DR: In this paper, the authors present models for solid-solid phase transitions with surface energy that allow both smooth and sharp interfaces, and show that a suitable scaling of the functional -converges to a pure sharp-interface model, as the parameters penalising the formation of interfaces go to zero.
Journal ArticleDOI
Evolution of martensitic microstructures in nanocrystalline NiTi wires deformed in tension
TL;DR: In this paper, an experimental method allowing for reconstruction of martensite variant microstructures evolving during tensile thermomechanical loading test on nanocrystalline NiTi wire is introduced.
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On the structure of quasiconvex hulls
TL;DR: In this paper, the authors define the set Kq,e ⊂ K of quasiconvex extreme points for compact sets K ⊆ MN×n and study its properties.
Journal ArticleDOI
Convex integration and infinitely many weak solutions to the perona-malik equation in all dimensions ∗
Seonghak Kim,Baisheng Yan +1 more
TL;DR: It is proved that for all smooth nonconstant initial data the initial-Neumann boundary value problem for the Perona-Malik equation in image processing possesses infinitely many Lipschitz weak solutions on smooth bounded convex domains in all dimensions.
References
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Journal ArticleDOI
Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen
TL;DR: In this article, the Berechnung der dielektrizitatatkonstanten and der Leitfahigkeiten fur Elektriatitat and Warme der Mischkorper aus isotropen Bestandteilen behandelt.
Book
The theory of transformations in metals and alloys : an advanced textbook in physical metallurgy
Journal ArticleDOI
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
Book
The theory of transformations in metals and alloys
J.W. Christian,H. M. Otte +1 more
TL;DR: In this paper, the authors present a general introduction to the theory of transformation kinetics of real metals, including the formation and evolution of martensitic transformations, as well as a theory of dislocations.