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
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Geometry of adaptive martensite in Ni-Mn-based Heusler alloys
Robert Niemann,Sebastian Fähler +1 more
TL;DR: In this article, the Ni-Mn-based shape memory alloys were used to show the geometric rationale behind the concept of adaptive martensite, which regards all modulated phases as nanotwinned microstructures, and discussed the compatibility at the habit plane, the nature of high-order twin boundaries and the dependence of the lattice constants on different types of modulation.
Journal ArticleDOI
The failure of rank-one connections
TL;DR: In this paper, the authors considered the problem of computing the relationship between the sets of values of the differentials of the Cauchy-Riemann equations of the polyconvex hulls and the Jacobian estimates of the Jacobians in the course of solving the Monge-Ampere inequalities.
Journal ArticleDOI
Influences of granular constraints and surface effects on the heterogeneity of elastic, superelastic, and plastic responses of polycrystalline shape memory alloys
Harshad M. Paranjape,Harshad M. Paranjape,Partha P. Paul,Hemant Sharma,Peter Kenesei,Jun-Sang Park,Tom Duerig,L. Catherine Brinson,Aaron P. Stebner +8 more
TL;DR: In situ X-ray diffraction, specifically the far-field high energy diffraction microscopy (ff-HEDM) technique, was used to non-destructively measure the grain-averaged statistics of position, crystal orientation, elastic strain tensor, and volume for hundreds of austenite grains in a superelastically loaded nickel-titanium (NiTi) SMA.
Journal ArticleDOI
In situ scanning electron microscopy study of the thermoelastic martensitic transformation in Ti-Ni shape memory alloy
TL;DR: In this article, the thermoelastic martensitic transformation from the B2 to B19′ structures in the Ti-Ni shape memory alloy was observed by in situ scanning electron microscopy in order to investigate the self-accommodation microstructure.
Journal ArticleDOI
Relaxation of singular functionals defined on Sobolev spaces
TL;DR: In this paper, a Borel measurable function on the space of mn matrices f:Mmn! taking the value +1, such that its rank-one-convex envelope Rf is nite and satises for some xed p>1: c0Rf(F )c(1+kFk p ) for all F2M mn ; where c;c 0>0.
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.