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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A Variational View of Partial Brittle Damage Evolution
TL;DR: In this article, the authors established the existence of a relaxed variational evolution where, at each time, the two states of the material combine to form a fine mixture, optimal from the standpoint of the applied load at that time, yet preserving the irreversibility of the damaging process.
Journal ArticleDOI
Micromechanical modelling of ferroelectrics
TL;DR: In this article, a review of recent micromechanical models of ferroelectric switching is presented, from discrete switching models that neglect grain-to-grain interaction, through to incremental switching model that account for interaction between grains.
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Heterogeneous Thin Films of Martensitic Materials
TL;DR: In this paper, the effective behavior of heterogeneous thin films with three competing length scales: the film thickness and the length scales of heterogeneity and material microstructure was studied, and the effective energy density was derived as all length scales tend to zero with given limiting ratios.
Journal ArticleDOI
Inter-martensitic transitions in Ni–Fe–Ga single crystals
TL;DR: In this article, the role of inter-martensitic transformation in creating intersecting heating and cooling segments was investigated and the authors used a thermo-mechanical formulation to rationalize the role.
Journal ArticleDOI
Atomistic to continuum limits for computational materials science
TL;DR: In this paper, an overview of some mathematical results, which provide elements of rigorous basis for some multiscale computations in materials science, is presented, focusing on atomistic to continuum limits for crystalline materials.
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.