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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Finite element procedure and simulations for a multiphase phase field approach to martensitic phase transformations at large strains and with interfacial stresses
TL;DR: Basak and Levitas as discussed by the authors developed a finite element procedure for a new phase field approach to temperature and stress induced multivariant martensitic transformations at large strains and with interfacial stresses.
Journal ArticleDOI
Structure of stable solutions of a one-dimensional variational problem
TL;DR: In this article, the periodicity of all H 2 -local minimizers with low energy for a one-dimensional higher order variational problem was studied and a bilinear double well potential function was used to analyze the intricate interactions between the phase boundaries.
Journal ArticleDOI
Young measure solutions and instability of the one-dimensional Perona–Malik equation
TL;DR: In this paper, a variational approach to the one-dimensional version of the widely used Perona-Malik equation in image processing is presented. But it is not shown that the solution of this problem is stable under small W-1,W- infinity perturbations.
Journal ArticleDOI
Interfacial stresses within boundary between martensitic variants: Analytical and numerical finite strain solutions for three phase field models
TL;DR: In this article, the origin of a large elastic stress within an interface between martensitic variants (twins) within a finite strain phase field approach has been determined, and an analytical finite-strain solution has been found for an infinite sample for tetragonal martensite under plane stress condition.
Journal ArticleDOI
Relaxation and regularization of nonconvex variational problems
Robert V. Kohn,Stefan Müller +1 more
TL;DR: In this paper, the authors consider variational problems of the form min √ W(∆u) dx, with W nonconvex and show the behavior of the regularized solution in the limit as e→0.
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.