Papers by Keyword: Landau Theory

Abstract: The continuum theory of dislocations, as developed predominantly by Kröner and Kosevich, views each dislocation as a source of incompatibility of strains. We show that this concept can be employed efficiently in the Landau free energy functional to develop a mean-field mesoscopic model of materials with dislocations. The order parameters that represent the distortion of the parent phase (often of cubic symmetry) are written in terms of elastic strains which are themselves coupled by incompatibility constraints. Since the “strength” of the incompatibility depends on the local density of dislocations, the presence of dislocations affects the evolution of the microstructure and vice versa. An advantage of this formulation is that long range anisotropic interactions between dislocations appear naturally in the formulation of the free energy. Owing to the distortion of the crystal structure around dislocations, their presence in multiphase materials causes heterogeneous nucleation of the product phase and thus also shifts of the transformation temperature. This novel field-theoretical approach is very convenient as it allows to bridge the gap in studying the behavior of materials at the length and time scales that are not attainable by atomistic or macroscopic models.

Abstract: The Landau theory has been developed for the description of martensite aging. The characteristic features of the theory are: i) the multicomponent non-scalar character of the order parameter describing the slow reconfiguration of lattice defects after martensitic transformation (MT); ii) the complete agreement with Symmetry-Conforming Short-Range-Order principle formulated by X. Ren and K. Otsuka; iii) the applicability to the different MT-s and various defects related to aging phenomena. The physical values interpreted as the components of internal stress, which stabilizes certain variant of martensitic phase, have been composed of the components of slow non-scalar order parameter. An applicability of the developed theory to the description of influence of aging on the MT temperature and yield stress was demonstrated.

Abstract: In the current paper, a macroscopic differential model for the hysteretic dynamics in shape memory alloy actuators is constructed by using the modified Landau theory of the first order phase transformation. An intrinsic thermo-mechanical coupling is achieved by constructing the free energy as a function depends on both mechanical deformation and the material temperature. Both shape memory and pseudoelastic effects are modeled. The hysteretic dynamics is linearized by introducing another hysteresis loop via nonlinear feedback strategy, which cancels the original one.

Abstract: The free energy function of martensitic transformation is established using Landau polynomial. According to the free energy function, the interfacial structural modification of austenite-martensite with the chemical driving force of martensitic transformation and elastic constants of materials is discussed. Some characteristics of martensitic transformation, such as the difference between thermoelastic and nonthermoelastic martensitic transformation, martensitic growth, are explained.