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
More filters
Journal ArticleDOI
Geometry of polycrystals and microstructure
John M. Ball,Carsten Carstensen +1 more
TL;DR: In this paper, the geometry of polycrystals is investigated and it is shown that the interior grains are polyhedral, while the set of triple points is small, and that a pure phase in either grain is impossible at minimum energy.
Book ChapterDOI
Applications in continuum mechanics and physics of solids
TL;DR: The theory of rate-independent processes has a large variety of applications in continuum mechanics of solids as mentioned in this paper, and rate independent effects typically can occur inside the bulk and at the surface or along interfaces.
Posted Content
Discontinuous order parameters in liquid crystal theories
John M. Ball,S. J. Bedford +1 more
TL;DR: In this paper, the authors focus on various issues surrounding the mathematical description of defects in models of liquid crystals, drawing on experience from solid mechanics, and highlight the roles played by a suitable choice of function space and by the growth properties of the free-energy density.
Computations of quasiconvex hulls of isotropic sets
Sebastian Heinz,Martin Kruzik +1 more
TL;DR: An algorithm for computations of quasiconvex hulls of isotropic compact sets in in the space of 2×2 real matrices has the time complexity of O(N logN) where N is the number of orbits of the set.
References
More filters
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.