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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Piecewise affine stress-free martensitic inclusions in planar nonlinear elasticity
TL;DR: This work considers a partial differential inclusion problem which models stress-free martensitic inclusions in an austenitic matrix, based on the standard geometrically nonlinear elasticity theory, and shows that for specific parameter choices there exist piecewise affine continuous solutions for the square-to-oblique and the hexagonal-to -oblique phase transitions.
Journal ArticleDOI
A computational micro-sphere model applied to the simulation of phase-transformations
TL;DR: In this article, an efficient model for the simulation of polycrystalline materials undergoing solid to solid phase transformations is presented, which is embedded into a micro-sphere formulation in order to simulate three-dimensional boundary value problems.
Journal ArticleDOI
Coarse-grained models of materials with non-convex free-energy: two case studies
TL;DR: In this article, the use of modern techniques from (nonconvex) calculus of variations in developing coarse-grained models of microstructure-driven material response is presented.
Journal ArticleDOI
Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Dirichlet Problem with Affine Data in int(K^{lc})
TL;DR: In this paper, the authors study the higher Sobolev regularity of convex integration solutions to differential inclusions arising from applications in materials sciences and present a method to compute the higher-Sobolev-regularity of these solutions.
Journal ArticleDOI
The Two Well Problem With Surface Energy
TL;DR: In this article, the authors consider a bounded Lipschitz domain in IR, and consider the functional properties of the functional matrix with det (H) = 1, where H is a 2 × 2 diagonal matrix.
References
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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.