Andrei Artemev

Three-dimensional phase field model of proper martensitic transformation

Abstract The Phase Field Microelasticity theory is developed for proper multivariant martensitic transformations. The model is based on the exact solution of the elasticity problem in the homogeneous modulus approximation. The model takes into account the transformation-induced coherency strain and provides for the strain compatibility throughout the system. Computer simulations are performed for a dilatationless cubic→tetragonal martensitic transformation and for the transformation with parameters corresponding to a martensitic transformation Fe–31%Ni alloy. The development of the martensitic transformation through nucleation, growth and coarsening of orientation variants is simulated at different levels of undercooling. The simulated martensitic structure has a complex polytwinned morphology. Simulation demonstrates that the presence of a non-zero volumetric component in the transformation strain in the Fe–31%Ni system significantly affects the martensitic transformation.

Three-dimensional phase field model of low-symmetry martensitic transformation in polycrystal: simulation of ζ′2 martensite in AuCd alloys

A three-dimensional phase field model of the martensitic transformation that produces a low symmetry phase in polycrystals is developed. The transformation-induced strain mostly responsible for the specific features of the martensitic transformation is explicitly taken into account. The high computational efficiency of the model turns out to be almost independent of the complexity of the polycrystal geometry. An example of the cubic→trigonal transformation in AuCd alloys producing ζ′2 martensite is considered. The development of the transformation through nucleation, growth and coarsening of orientation variants is simulated for both single crystal and polycrystalline materials. The effect of an external load on the martensitic microstructure in the polycrystalline material is studied. It is shown that the elastic coupling between different transformed grains of the polycrystal drastically affects the microstructure and its response to the applied stress. The obtained self-accommodating morphologies of the multivariant martensitic structure are in agreement with those observed in the experiments.

THREE-DIMENSIONAL PHASE FIELD MODEL AND SIMULATION OF MARTENSITIC TRANSFORMATION IN MULTILAYER SYSTEMS UNDER APPLIED STRESSES

Abstract The phase field microelasticity theory is used to formulate a three-dimensional phase field model of a multivariant martensitic transformation under external load. The model is based on the exact solution of the elasticity problem in the homogeneous modulus approximation. The transformation-induced coherency strain and applied stress are explicitly taken into account. Computer simulations are performed for a generic cubic→tetragonal martensitic transformation in a multilayer system consisting of alternating active and inert layers. The development of the martensitic transformation through nucleation, growth and coarsening of orientation variants is simulated at different levels of the applied stress. The simulated martensitic structure has a complex polytwinned morphology. The simulation predicted such effects as the formation of texture and the stress-induced transformation that are in a general agreement with the experimental observations. The simulation produced realistic stress–strain hysteresis loops, which, in principle, can be used for the formulation of the constitutive equations of the macroscopic mechanics for the active system.

Thermodynamic analysis and phase field modeling of domain structures in bilayer ferroelectric thin films

The domain structure in bilayer ferroelectric films was studied by using an analytical thermodynamic theory and computer simulations utilizing the phase field model. It is demonstrated that in a low applied field, a self-poled state can be produced in a bilayer film with one layer in a polydomain state and the other layer in a single-domain state. The presence of the layer with a polydomain structure results in a higher dielectric constant and lower coercive field as compared to a bilayer in a single-domain state. The increase in the applied field results in the transition to a single-domain state in the whole bilayer. The thermodynamic potentials of the layers and the energies of electrostatic and elastic interactions determine the critical fields which can control the transitions between single-domain and polydomain states as well as polarization switching of bilayers. Different thermodynamic hysteresis loops are obtained depending on the relationship between these critical fields and the amplitude of t...

Morphological transitions of elastic domain structures in constrained layers

The phase transformation in a constrained layer is the subject of this article. The formation and evolution of polydomain microstructure under external stress in the constrained layer are investigated by phase-field simulation and analytically using homogeneous approximation. As a result of simulation, it has been shown that the three-domain hierarchical structure can be formed in the epitaxial films. Under external stress there are two types of morphological transitions: from the three-domain structure to the two-domain one and from the hierarchical three-domain structure to the cellular three-domain structure. The results of phase-field simulation are compared with conclusions of homogenous theory and with available experimental data.

Polydomain structures in ferroelectric and ferroelastic epitaxial films

A review of theoretical models, phase field modeling and experimental studies of domain structures in epitaxial films is presented. The thermodynamic theory of such domain structures is presented within the macroscopic thermo-mechanical framework. The theory allows for the evaluation of the main parameters of the domain structure using the energy minimization approach applied to the energy of elastic interactions. For homophase (polytwin) films, the thermodynamic theory provides a quantitative tool that can be used to estimate domain fractions in the film and the type of domain structure architecture. For heterophase films, the theory describes (a) the conditions under which two-phase structures can be obtained in epitaxial films, and (b) the phase and domain fractions in these films. The thermodynamic theory can also be used to describe the extrinsic contributions from domain structures to the functional properties of epitaxial ferroelectric films. The review of phase field modeling demonstrates that computational results reproduce the predictions of the thermodynamic theory. It is also shown that the phase field modeling that utilizes the energy minimization procedure for elastic and interfacial energies can be used to predict domain morphology for the films with two-phase structures produced either by phase transformation or through the co-deposition of immiscible phases. The experimental data presented in the review validate predictions of the thermodynamic model and the results of phase field modeling.

Phase field modeling of domain structures in ferroelectric thin films

Phase-field simulations were used to explore the effect of the characteristics of the Landau-Devonshire free energy and values of electrostatic and elastic interactions on the formation of different types of domain structures in ferroelectric thin films. Simulations were performed at different constant-applied electric fields and by using a cyclic continuously changing field. It is shown that the 180deg or 90deg domain structures can be produced depending on the relative strength of elastic interactions and the ratio of barrier heights that determine the energy of the 180deg and 90deg domain boundaries. It is shown that the applied field strength and the thickness of the dead layer can play a minor role in the transition between the 90deg and 180deg domain structures. It is also demonstrated that the poling history can affect the type of the domain structure.

Inverse electrostatic and elasticity problems for checkered distributions

We study the inverse electrostatic and elasticity problems associated with Poisson and Navier equations. These problems arise in a number of applications, such as diagnostic of electronic devices and analysis of residual stresses in materials. In microelectronics, piecewise constant distributions of electric charge having a checkered structure (i.e., that are constant on rectangular blocks) are of particular importance. We prove that the inverse electrostatic problem has a unique solution for such distributions. We also show that the inverse elasticity problem has a unique solution for checkered distributions of body forces. General necessary and sufficient conditions for the uniqueness of solutions of both inverse problems are discussed as well.

A Macro-Micro Model of Fusion Zone Microstructure Evolution in Mn-C Low-Alloy Steel Coupled With Thermal Stress Analysis

A macro-micro-model for microstructure evolution in the fusion zone of a l.2 Mn and 0.11 C low-alloy steel is described. The macro-model is a 3D transient thermal analysis of a welded structure that resolves the weld pool with element size greater than 1 mm and time steps greater than 1 second. The micro-model has cell size of about 1 micron and time step size of about 10 micro-seconds with a grid of about 80×80×500 cells. The micro model is positioned on the liquid-solid interface of the weld pool in the macro-model. The boundary conditions for the micro-model are mapped from the macro-model. The micro-model solves the 3D transient solute diffusion equations for Mn and C. The micro-model computes the liquid-solid interface movement with local velocities determined by local temperature, compositions of solid and liquid phases and interface curvature to predict columnar or dendritic solidification structures. As the solid cools from the melting point to room temperature, the evolution of austenite, ferrite, pearlite, bainite and martensite phases are computed. The 3D transient stress due to temperature and phase changes is computed in the micro-model as it cools from the melting temperature to room temperature. At room temperature a micro-model tensile test is run to 4% strain. The macro-stress and strain is compared to the micro-stress and strain distributions. The model is intended to be used to initialize models of fracture, fatigue and creep in weld fusion zones.© 2015 ASME

Domain structure and dielectric properties in nanocomposite ferroelectric thin layers with spherical dielectric inclusions

The phase field model was used to simulate the domain structure and polarization versus applied field hysteresis curves of a composite layer consisting of a ferroelectric matrix and spherical dielectric inclusions. Simulation results demonstrate that the introduction of dielectric inclusions into the ferroelectric matrix can lead to the stabilization of the polydomain structure in a wide range of applied fields. As a result a significant increase in susceptibility can be obtained due to the composite structure formation, which causes the addition of an extrinsic contribution into susceptibility. The composite structure can produce a number of different partially switched (partially poled) states with different values of the remnant polarization that are stable in wide ranges of the applied field producing a close to linear dielectric response with high susceptibility.