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Journal ArticleDOI

Fine phase mixtures as minimizers of energy

01 Mar 1987-Archive for Rational Mechanics and Analysis (Springer, Berlin, Heidelberg)-Vol. 100, Iss: 1, pp 13-52
TL;DR: 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.
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TL;DR: In this paper, a variational model of quasistatic crack evolution is proposed, which frees itself of the usual constraints of that theory : a preexisting crack and a well-defined crack path.
Abstract: A variational model of quasistatic crack evolution is proposed. Although close in spirit to Griffith’s theory of brittle fracture, the proposed model however frees itself of the usual constraints of that theory : a preexisting crack and a well-defined crack path. In contrast, crack initiation as well as crack path can be quantified, as demonstrated on explicitly computable examples. Furthermore the model lends itself to numerical implementation in more complex settings.

2,283 citations

Journal ArticleDOI
TL;DR: In this paper, a review of continuum-based variational formulations for describing the elastic-plastic deformation of anisotropic heterogeneous crystalline matter is presented and compared with experiments.

1,573 citations

Journal ArticleDOI
TL;DR: In this paper, the shape memory effect due to martensitic transformation and reorientation of polycrystalline shape memory alloy (SMA) materials is modeled using a free energy function and a dissipation potential.

848 citations

Journal ArticleDOI
TL;DR: Shape memory alloys (SMAs) with high transformation temperatures can enable simplifications and improvements in operating efficiency of many mechanical components designed to operate at tem... as mentioned in this paper, which can enable simplified and improved operating efficiency.
Abstract: Shape memory alloys (SMAs) with high transformation temperatures can enable simplifications and improvements in operating efficiency of many mechanical components designed to operate at tem...

694 citations

Journal ArticleDOI
TL;DR: In this paper, the authors make predictions based on an analysis of a new nonlinear theory of martensitic transformations introduced by the authors, where the crystal is modelled as a nonlinear elastic material, with a free-energy function that is invariant with respect to both rigid-body rotations and the appropriate crystallographic symmetries.
Abstract: Predictions are made based on an analysis of a new nonlinear theory of martensitic transformations introduced by the authors The crystal is modelled as a nonlinear elastic material, with a free-energy function that is invariant with respect to both rigid-body rotations and the appropriate crystallographic symmetries The predictions concern primarily the two-well problem, that of determining all possible energy-minimizing deformations that can be obtained with two coherent and macroscopically unstressed variants of martensite The set of possible macroscopic deformations obtained is completely determined by the lattice parameters of the material For certain boundary conditions the total free energy does not attain a minimum, and the finer and finer oscillations of minimizing sequences are interpreted as corresponding to microstructure The predictions are amenable to experimental tests The proposed tests involve the comparison of the theoretical predictions with the mechanical response of properly oriented plates subject to simple shear Additional crystallographic background is given for the model, and the theory is compared with the `linearized' model of Khachaturyan, Roitburd and Shatalov There are some similarities in the predictions of the two theories, but also some major discrepancies

694 citations

References
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Journal ArticleDOI
TL;DR: In this article, the Berechnung der dielektrizitatatkonstanten and der Leitfahigkeiten fur Elektriatitat and Warme der Mischkorper aus isotropen Bestandteilen behandelt.
Abstract: Es werden verschiedene physikalische Konstanten heterogener Korper aus den Konstanten ihrer homogenen Bestandteile nach einer einheitlichen Methode berechnet. In dieser ersten Arbeit wird die Berechnung der Dielektrizitatskonstanten und der Leitfahigkeiten fur Elektrizitat und Warme der Mischkorper aus isotropen Bestandteilen behandelt. Die Genauigkeit der alteren Formeln wird untersucht und die bis jetzt unbekannten Konstanten dieser Formeln werden berechnet. Sodann wird die Theorie gepruft an Messungen der Leitfahigkeit bei heterogenen Metallegierungen und an den DK. von gepresten Pulvern und Emulsionen; die verschiedenen Formeln werden bestatigt. Bei dieser Anwendung werden einige Widerspruche zwischen fruheren Untersuchungen aufgehoben und es wird versucht, einige ungenau bekannte DK. genauer zu bestimmen.

7,155 citations

Journal ArticleDOI

3,953 citations


"Fine phase mixtures as minimizers o..." refers background in this paper

  • ...It is easily shown that y is invertible on ~. It is probably significant that the equilibrium equations, when linearized about the deformation y = 7x, ~'E [2,/~], fail to satisfy the complementing condition of AGMON, DOUGLiS & NIRENBERG [ 2 ] with respect to boundary conditions of null traction....

    [...]

Book
01 Jan 1965
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.
Abstract: Part I General introduction. Formal geometry of crystal lattices. The theory of reaction rates. The thermodynamics of irreversable processes. The structure of real metals. Solids solutions. The theory of dislocations. Polycrystalline aggregates. Diffusion in the solid state. The classical theory of nucleation. Theory of thermally activated growth. Formal theory of transformation kinetics. Part II Growth from the vapour phase. Solidification and melting. Polymorphic Changes. Precipitation from supersaturated solid solution. Eutectoidal transformations. Order-disorder transformations. Recovery recrystalisation and grain growth. Deformation twinning. Characteristics of martensic transformations. Crystallography of martensitic transformations. Kinetics of martensitic transformations. Rapid solidification. Bainite steels. Shape memory alloys.

3,397 citations