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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Book ChapterDOI
Energy Minimization for Isotropic Nonlinear Elastic Bodies
TL;DR: The microstructures accompanying phase transitions in solids are governed by the minimum energy principle as mentioned in this paper, and the occurrence of microstructure is connected with the incompatibility of individual solid phases and with the nonexistence of minimizers of energy.
Journal ArticleDOI
A bi-crystal aggregate model of pseudoelastic behaviour of shape-memory alloy polycrystals
TL;DR: In this paper, a multi-scale model of stress-induced phase transformation and martensite variant reorientation in shape memory alloy (SMA) polycrystals is developed.
Book ChapterDOI
Introduction: Fifty Years of Research on Evolving Phase Interfaces
TL;DR: A phase transition is a process in which a region occupied by one phase grows at the expense of another phase, with the essential physical activity occuring at the interfaces separating phases.
DissertationDOI
Energy-minimizing microstructures in multiphase elastic solids
TL;DR: In this paper, the authors considered the problem of determining the relaxation under fixed volume fraction of a two-well energy in two dimensions with no restrictions on the elastic moduli and transformation strains and showed that there always exist rank-I or rank-II laminates that are extremal.
Journal ArticleDOI
An adaptive finite element method for solving a double well problem describing crystalline microstructure
TL;DR: In this paper, an adaptive method is proposed and analyzed to give a more accurate resolution of laminated microstructure on arbitrary grids, which is based on discontinuous finite elements to reduce the pollution of a general triangulation on the computed minimizer.
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.