A Phase-Field Fracture Model of Ferroelectric Materials Under Electro-Mechanical Loading

2011 ◽  
Author(s):  
Amir Abdollahi ◽  
Irene Arias
Keyword(s):  
Phase Field ◽  
Phase Field Model ◽  
Ferroelectric Materials ◽  
Crack Face ◽  
Fracture Evolution ◽  
Main Challenge ◽  
Crack Interactions ◽  
Formation And Evolution ◽  
Crack Faces ◽  
Field Approaches

A phase-field model is proposed for the coupled simulation of microstructure and fracture evolution in ferroelectric materials. The model is based on energetic phase-field approaches for brittle fracture and ferroelectric domain formation and evolution. The variational nature of these approaches makes their coupling very natural. However the main challenge is to encode the electro-mechanical conditions of the sharp crack faces into the phase-field framework since the crack in this model is smeared and represented by an internal layer. We develope the model for different crack face boundary conditions. Simulations show the microstructure induced by the presence of the crack. Interactions between the microstructure and the crack are investigated under different electro-mechanical loadings.

scholarly journals Quantitative Shape-Classification of Misfitting Precipitates during Cubic to Tetragonal Transformations: Phase-Field Simulations and Experiments

Materials ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 1373
Author(s):  
Yueh-Yu Lin ◽  
Felix Schleifer ◽  
Markus Holzinger ◽  
Na Ta ◽  
Birgit Skrotzki ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Phase Field ◽  
Phase Field Model ◽  
Invariant Moments ◽  
Plane Normal ◽  
Plane Shape ◽  
Formation And Evolution ◽  
The Given ◽  
Good Agreement

The effectiveness of the mechanism of precipitation strengthening in metallic alloys depends on the shapes of the precipitates. Two different material systems are considered: tetragonal γ′′ precipitates in Ni-based alloys and tetragonal θ′ precipitates in Al-Cu-alloys. The shape formation and evolution of the tetragonally misfitting precipitates was investigated by means of experiments and phase-field simulations. We employed the method of invariant moments for the consistent shape quantification of precipitates obtained from the simulation as well as those obtained from the experiment. Two well-defined shape-quantities are proposed: (i) a generalized measure for the particles aspect ratio and (ii) the normalized λ2, as a measure for shape deviations from an ideal ellipse of the given aspect ratio. Considering the size dependence of the aspect ratio of γ′′ precipitates, we find good agreement between the simulation results and the experiment. Further, the precipitates’ in-plane shape is defined as the central 2D cut through the 3D particle in a plane normal to the tetragonal c-axes of the precipitate. The experimentally observed in-plane shapes of γ′′-precipitates can be quantitatively reproduced by the phase-field model.

scholarly journals Effects of Interface Trap on Transient Negative Capacitance Effect: Phase Field Model

Electronics ◽  
2020 ◽  
Vol 9 (12) ◽  
pp. 2141
Author(s):  
Taegeon Kim ◽  
Changhwan Shin
Keyword(s):  
Phase Field ◽  
Field Effect ◽  
Field Effect Transistor ◽  
Field Model ◽  
Phase Field Model ◽  
Ferroelectric Materials ◽  
Interface Trap ◽  
Negative Capacitance ◽  
Effect Transistor ◽  
The Impact

Ferroelectric materials have received significant attention as next-generation materials for gates in transistors because of their negative differential capacitance. Emerging transistors, such as the negative capacitance field effect transistor (NCFET) and ferroelectric field-effect transistor (FeFET), are based on the use of ferroelectric materials. In this work, using a multidomain 3D phase field model (based on the time-dependent Ginzburg–Landau equation), we investigate the impact of the interface-trapped charge (Qit) on the transient negative capacitance in a ferroelectric capacitor (i.e., metal/Zr-HfO2/heavily doped Si) in series with a resistor. The simulation results show that the interface trap reinforces the effect of transient negative capacitance.

Identifiability and Active Subspace Analysis for a Polydomain Ferroelectric Phase Field Model

2017 ◽  
Author(s):  
Lider S. Leon ◽  
Ralph C. Smith ◽  
William S. Oates ◽  
Paul Miles
Keyword(s):  
Domain Wall ◽  
Phase Field ◽  
Density Functional ◽  
Information Matrix ◽  
Synthetic Data ◽  
Phase Field Model ◽  
Ferroelectric Materials ◽  
Identifiability Analysis ◽  
Subspace Selection ◽  
Active Subspace

We consider subset selection and active subspace techniques for parameters in a continuum phase-field polydomain model for ferroelectric materials. This analysis is necessary to mathematically determine the parameter subset or subspace critically affecting the response, prior to model calibration using either experimental or synthetic data constructed using density functional theory (DFT) simulations. For the 180° domain wall model, we employ identifiability analysis using a Fisher information matrix methodology, and subspace selection to determine the active subspace. We demonstrate the implementation and interpretation of techniques that accommodate the model structure and discuss results in the context of identifiable parameter subsets and active subspaces quantifying the strongest influence on the model output. Our results indicate that the governing domain wall gradient energy exchange parameter is most identifiable.

Phase Field Simulation of Ferroelectric Single Crystals

Aerospace ◽  
2005 ◽  
Author(s):  
T. Liu ◽  
C. S. Lynch
Keyword(s):  
Phase Field ◽  
Wall Motion ◽  
Field Model ◽  
Landau Equation ◽  
Phase Field Model ◽  
Domain Wall Motion ◽  
Ferroelectric Materials ◽  
Time Dependent ◽  
Ginzburg Landau ◽  
Domain Structures

Ferroelectric materials exhibit spontaneous polarization and domain structures below the Curie temperature. In this study a cubic to tetragonal phase transformation and the evolution of domain structures in ferroelectric crystals are simulated by using the time-dependent Ginzburg-Landau equation. The effects of electric boundary conditions on the formation of domain patterns and field induced polarization switching are discussed. The phase field model is used to simulate the formation of domain structures, domain wall motion and the macroscopic response of ferroelectric materials under external fields.

A non-isothermal phase-field model for piezo–ferroelectric materials

2018 ◽  
Vol 31 (3) ◽  
pp. 741-750 ◽  
Author(s):  
A. Borrelli ◽  
D. Grandi ◽  
M. Fabrizio ◽  
M. C. Patria
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Ferroelectric Materials

scholarly journals Phase-field modelling and computing for a large number of phases

2019 ◽  
Vol 53 (3) ◽  
pp. 805-832
Author(s):  
Élie Bretin ◽  
Roland Denis ◽  
Jacques-Olivier Lachaud ◽  
Édouard Oudet
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Field Representation ◽  
High Resolution Data ◽  
Phase Field Models ◽  
Efficient Storage ◽  
Non Local ◽  
Discretization Point ◽  
Field Approaches

We propose a framework to represent a partition that evolves under mean curvature flows and volume constraints. Its principle follows a phase-field representation for each region of the partition, as well as classical Allen–Cahn equations for its evolution. We focus on the evolution and on the optimization of problems involving high resolution data with many regions in the partition. In this context, standard phase-field approaches require a lot of memory (one image per region) and computation timings increase at least as fast as the number of regions. We propose a more efficient storage strategy with a dedicated multi-image representation that retains only significant phase field values at each discretization point. We show that this strategy alone is unfortunately inefficient with classical phase field models. This is due to non local terms and low convergence rate. We therefore introduce and analyze an improved phase field model that localizes each phase field around its associated region, and which fully benefits of our storage strategy. To demonstrate the efficiency of the new multiphase field framework, we apply it to the famous 3D honeycomb problem and the conjecture of Weaire–Phelan’s tiling.

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