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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Micromechanical modeling of martensitic transformation in random microstructures
TL;DR: In this article, a thermodynamic transformation criterion is used to describe the strain induced martensitic transformation (SIMT) in two different materials, namely in a dilute Cu-Fe alloy and in a low alloyed TRIP-steel.
Journal ArticleDOI
Grain size effects in multiphase steels assisted by transformation-induced plasticity
TL;DR: The influence of the grain size on the overall stress-strain behavior in a multiphase carbon steel is analyzed through three-dimensional finite element simulations in this article, where a recently developed multiscale martensitic transformation model is combined with a plasticity model to simulate the transformation-induced plasticity effects of a grain of retained austenite embedded in a ferrite-based matrix.
Journal ArticleDOI
Finite deformation beam models and triality theory in dynamical post-buckling analysis☆
TL;DR: In this paper, dual extremum principles in unstable dynamic systems are developed for post-buckling analysis and frictional contact problems, and a triality theory in postbuckle analysis is proved.
Journal ArticleDOI
The evolution of laminates in finite crystal plasticity: a variational approach
Dennis M. Kochmann,Klaus Hackl +1 more
TL;DR: In this article, an analytical partial relaxation of a Neo-Hookean energy formulation is proposed to model the time-continuous evolution of the laminate microstructure, and a numerical scheme is presented by means of which the micro-structure development can be computed, and show numerical results for particular examples in single and double-slip plasticity.
Journal ArticleDOI
The Regularity of Critical Points of Polyconvex Functionals
TL;DR: In this article, the question of regularity of critical points for functionals of the type eq1 was studied and a smooth, strongly polyconvex and Lipschitzian weak solution for eq2 to the corresponding Euler-Lagrange system was constructed.
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.