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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Energy scaling and branched microstructures in a model for shape-memory alloys with SO(2) invariance
Allan Chan,Sergio Conti +1 more
TL;DR: In this paper, a model for shape-memory alloys based on the full vectorial problem of nonlinear elasticity, including invariance under rotations, in the case of two wells in two dimensions was studied.
Journal ArticleDOI
An equilibrium theory of dislocation continua
TL;DR: It is proved that, in the absence of externally applied stresses, the only possible finite, simply connected distributions are ones in which all components of stress vanish everywhere.
Journal Article
Elastic micro-strain energy at the austenite-twinned martensite interface
TL;DR: In this article, a micromechanical scheme is developed for the analysis of elastic micro-strains induced by local incompatibilities at the austenite-twinned martensite interface.
Journal ArticleDOI
Numerical analysis of a relaxed variational model of hysteresis in two-phase solids
Carsten Carstensen,Petr Plecháč +1 more
TL;DR: The proposed scheme enables numerical simulations which show that the model allows for hysteresis, and an adaptive mesh-refining algorithm for efficient discretization is proposed.
Journal ArticleDOI
Micromechanical modeling of the martensitic transformation induced plasticity in steels
M Cherkaoui,M Berveiller +1 more
TL;DR: In this paper, a micromechanical model is developed to predict the overall behavior of a representative volume element (RVE) of a material undergoing non-thermoelastic martensitic phase transformation.
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.