多场耦合下铁电薄膜非线性行为的畴变模型

铁电薄膜在外加力场, 电场和温度场的作用下表现出明显的非线性, 为了更好的描述这种现象, 本文提出了一个热-电-力耦合场铁电薄膜下的畴变模型。该模型基于细观力学模型, 认为电畴自由能的改变提供电畴翻转的动力, 且180°电畴翻转由两步90°翻转构成。在本构关系中加入了铁电薄膜制备过程中产生的残余应变项, 以区别于块体铁电材料, 通过该模型计算出了铁电薄膜在不同外场下的响应, 结果与实验和其他模型的结果较为符合。     

Micromechanical modeling and simulation of rate-dependent effects in ferroelectric polycrystals

In this contribution, rate-dependent switching effects of ferroelectric materials are studied by means of a micromechanically motivated approach. The onset of domain switching is thereby initiated based on the reduction in Gibbs free energy by means of energy-based criterion. The subsequent nucleation and propagation of domain walls during switching process are incorporated via a volume fraction concept combined with a simple linear kinetics theory. The key aspect in modeling of the interaction between the individual grains (intergranular effects) are incorporated in this model by making use of a probabilistic ansatz; to be specific, a phenomenologically motivated Weibull distribution function is adopted. The developed framework is incorporated into a finite element formulation whereby each domain is represented by a single finite element and initial dipole directions are randomly oriented so that the virgin state of the particular bulk ceramics of interest reflects an un-poled material. Based on a staggered iteration technique and straightforward volume averaging concept, the model is simulated to capture the non-linear behavior for different loading, for various loading amplitudes and frequencies. Attributes of the model, both symmetric major loops and biased minor loops are illustrated through examples. Simulation results for the rate-independent case are in good agreement with experimentally measured data reported in the literature and, moreover, are extended to rate-dependent computations which captures some important insights.     

A phenomenological multi-axial constitutive law for switching in polycrystalline ferroelectric ceramics

A phenomenological constitutive law for ferroelectric switching due to multi-axial mechanical and electrical loading of a polycrystalline material is developed. The framework of the law is based on kinematic hardening plasticity theory and has a switching surface in the space of mechanical stress and electric field that determines when non-linear response is possible. The size and shape of the switching surface in a modified electric field space remains fixed during non-linear behavior but its center moves around and thus is controlled by a kinematical hardening process. In general, the remanent polarization and the remanent strain are used as the internal variables that control how the center of the switching surface moves. However, the form presented in this paper has a one-to-one relationship between the remanent strain and the remanent polarization, simplifying the constitutive law and allowing remanent polarization to be used as the only internal variable controlling the kinematic effects. The constitutive law successfully reproduces hysteresis and butterfly loops for ferroelectric ceramics. The hysteresis and butterfly loops respond appropriately to the application of a fixed compressive stress parallel to the electric field. In addition, the law successfully handles remanent polarization rotation due to the application of electric field at an angle to the polarization direction.     

Toughening due to domain switching in single crystal ferroelectric materials

In this paper Mode I steady state crack growth in single crystal ferroelectric materials is investigated. Specifically, the fracture toughness enhancement due to domain switching near a steadily growing crack tip is analyzed. For this purpose, an incremental phenomenological constitutive law for single crystal ferroelectric materials is implemented within a finite element model to calculate the stress and remanent strain fields around the crack tip. Also, the ratio of the far field applied energy release rate to the crack tip energy release rate, i.e. the toughening, is calculated. The numerical computations are carried out for single crystal ferroelectric materials of tetragonal or rhombohedral structure with different switching hardening and irreversible remanent strain levels. Toughening levels for crack growth along different crystallographic directions and planes are obtained and compared. Results from numerical computations for the toughening anisotropy for both tetragonal and rhombohedral crystals are presented and discussed.     

Multiaxial behavior of ferroelectric single and polycrystals with pressure dependent boundary effects

The external electric and mechanical fields applied at angles to the initial poled direction of the ferroelectric ceramics produce a significantly different nonlinear behavior to that of external fields applied parallel to the poling direction. This angle dependent response of ferroelectric single and polycrystals are predicted by the model proposed based on irreversible thermodynamics and physics of domain switching. The dissipation associated with boundary constraints in thin ferroelectric single crystals are incorporated in the model. As well, the pressure dependent constraints imposed by the surrounding grains on the grain of interest at its boundary during domain switching is correlated with the resistance experienced by a ferroelectric single crystal on its boundary during domain switching. Taking all the domain switching possibilities, the volume fractions of each of the variants in a grain are tracked and homogenized for macroscopic behavior. Numerical simulations were carried out for the multiaxial behavior of ferroelectric single and polycrystals under electrical, mechanical and electromechanical loading conditions.     

Numerical analysis of ferroelectric/ferroelastic domain switching in ferroelectric ceramics

A numerical approach predicting the behavior of ferroelectric ceramics under electric field and mechanical loading is proposed in this paper. In the model, macroscopic properties of ferroelectric ceramics are determined by microscopic structures. Ferroelectric ceramics are seen to be composed of many domains with different orientations, and domain switching is the source of the nonlinear constitutive behavior of the ferroelectric ceramics. Numerical calculations based on the model were carried out, and the computational results are compared with the experimental results, which shows the two sets of results consist with each other. The calculation approach can provide a guidance for the ceramics component design.     

Temperature-dependent ferroelectric hysteresis properties of modified lead zirconate titanate ceramics

Temperature-dependent ferroelectric hysteresis properties of modified lead zirconate titanate ceramics have been investigated in a wide temperature range from 300 to 433 K. It is observed that remnant polarization, saturation polarization, and coercive field are increasing with an increase of the temperature in a low-field region and decreasing in a high-field region. Such behavior is explained by the competition between switching and backswitching mechanisms. A three-stage dependence of the logarithm of the hysteresis loop area on the logarithm of the electric field is identified. The temperature dependence of backswitching properties has been studied. The obtained results indicate that the temperature dependence of the polarization backswitching can be well described by the Arrhenius law. The activation energy for the domain switching determined from the fitting results exhibits decreasing tendency with the increase of the electric field.     

Visco-elastic behavior through fractional calculus: An easier method for best fitting experimental results

In capturing visco-elastic behavior, experimental tests play a fundamental rule, since they allow to build up theoretical constitutive laws very useful for simulating their own behavior. The main challenge is representing the visco-elastic materials through simple models, in order to spread their use. However, the wide used models for capturing both relaxation and creep tests are combinations of simple models as Maxwell and/or Kelvin, that depend on several parameters for fitting both creep and relaxation tests. This paper, following Nutting and Gemant idea of fitting experimental data through a power law function, aims at stressing the validity of fractional model. In fact, as soon as relaxation test is well fitted by power law decay then the fractional constitutive law involving Caputo’s derivative directly appears. It will be shown that fractional model is proper for studying visco-elastic behavior, since it may capture both relaxation and creep tests, requiring the identification of two parameters only. This consideration is assessed by the good agreement between experimental tests on creep and relaxation and the fractional model proposed. Experimental tests, here reported are performed on two polymers having different chemical physical properties such that the fractional model may cover a wide range of visco-elastic behavior.     

Electrical and optical modulation on ferroelectric properties of P(VDF-TrFE) thin film capacitors

Modulating the ferroelectric properties of P(VDF-TrFE) polymers both electrically and optically could open up new opportunities for their applications in non-volatile memories and sensors. Here by using the Nb:SrTiO₃ semiconductor as electrode compared with metal Au electrode, we report on the modulation of ferroelectric properties of P(VDF-TrFE) thin film capacitors both by electric field and UV light. A ferroelectric hysteresis loop shift together with the asymmetric switching behavior has been observed when using semiconducting electrode, which could be explained by the band alignment model based on interfacial charge screening. On the basis of band bending near the ferroelectric/semiconductor interface, we could further modulate the ferroelectric switching behaviors reversibly by UV light illumination. Our research provides a new route to engineer the ferroelectric properties of P(VDF-TrFE) polymer thin film capacitors, promising their applications in optoelectronic devices.     

A model based creep equation for 9Cr–1Mo–0·2V (P91 type) steel

Abstract

The isothermal constant stress creep tests data for a 9Cr–1Mo–0·2V (P91 type) steel were submitted for a phenomenological analysis in order to obtain the relevant creep equation for such steel. Namely, the minimum creep strain rate of P91 type steel cannot be described by the simple Arrhenius type power law constitutive model. The incorporation of the threshold stress concept in the analysis of creep data leads to a modified power law, which satisfactorily describes the creep behaviour of the examined P91 steel. However, the threshold stress is not a good material parameter, as it often varies with temperature and/or applied stress. This adds uncertainty to the extrapolation of the creep rates into ranges where experimental data are not available. Besides the fact that the physical foundation for a threshold stress is questionable from a scientific point of view, this is a serious practical limitation of the modified power law creep equation. The second creep equation proposed in the present paper is the improved stress dependent energy barrier model. The improvement of the standard model is based on two assumptions: first, on the hypothesis that the application of a stress also affects the energy barrier to be overcome when a local region transitions from the initial to the final state, and second, by applying a simple power function of stress instead of a hyperbolic sin function in the model based equation. The obtained value of stress exponent, n=5·5, is too high for entirely climb controlled creep. The apparent activation energy of approximately 510 to 545 kJ mol^?1, which is considerably higher than the activation energy for lattice diffusion, is the stress dependent activation energy of the slowest, dominant rate controlling process of the supposed multiple creep mechanisms.     

2D and 3D Multiphysics Voronoi Cells,Based on Radial Basis Functions,for Direct Mesoscale Numerical Simulation (DMNS) of the Switching Phenomena in Ferroelectric Polycrystalline Materials

In this paper, 2D and 3D Multiphysics Voronoi Cells (MVCs) are developed, for the Direct Mesoscale Numerical Simulation (DMNS) of the switching phenomena in ferroelectric polycrystalline materials. These arbitrarily shaped MVCs (arbitrary polygons in 2D, and arbitrary polyhedrons in 3D with each face being an arbitrary polygon) are developed, based on assuming radial basis functions to represent the internal primal variables (mechanical displacements and electric potential), and assuming linear functions to represent the primal variables on the element boundaries. For the 3D case, the linear functions used to represent the primal variables on each of the polygonal surfaces of the polyhedral VCs are the Barycentric Washspress functions. The present 2D MVC is denoted as MVC-RBF, while the 3D MVC is denoted as MVC-RBF-W. Each MVC can represent a single grain or crystallite, with an irregular polygonal shape for the 2D case, and an irregular polyhedral shape for the 3D case. In this work, a nonlinear constitutive model is used to describe the evolution of volume fractions of the constitutive-variants in each grain, as the electric or mechanical loading changes. This constitutive model is based on satisfying a local dissipation inequality in each grain in the polycrystalline that yields the minimum Gibbs free energy in this grain. This requirement should always hold in order to be consistent with the second law of thermodynamics and is used to govern the switching process in each grain in each simulation step. Since the interaction between the grains during the loading cycles has a profound influence on the switching phenomena, it is important to simulate the grains with geometrical shapes that are similar to the real shapes of the grains as seen in the lab experiments. Hence the use of 3D MVCs, which allow for the presence of all the six variants of the constitutive relations, together with the randomly generated crystallographic axes in each grain (or MVC), as done in the present paper, is considered to be the most realistic analytical model that can be used for the direct mesoscale numerical simulation of polycrystalline ferroelectric materials.     

Analysis of creep and modulus loss of the wood cell wall

This paper proposes a nonlinear constitutive model for the wood cell wall based on the nonequilibrium thermodynamics. The wood cell wall is modeled as a long fiber-reinforced composite with cellulose microfibril enclosed by hemicellulose and lignin. An internal variable is introduced into the Helmholtz free energy of the cell wall system, to describe the modulus loss of hemicellulose due to moisture absorption. The viscoelastic behavior of the wood cell wall changes with its moisture content, which leads to different creep evolutions even under the same loading level. To account for this phenomenon, another internal variable is introduced to depict the creep behavior of the wood cell wall, which is correlated with the irreversible energy dissipation processes such as stick–slip mechanism in the wood cell wall. Based on five elastic coefficients of transverse isotropy predicted by the present model, the creep behaviors of the wood cell wall with different microfibril angles are theoretically analyzed and show good agreements with experiment results.     

考虑围压对粗粒土蠕变特性影响的Burgers模型参数修正方法研究

传统的Burgers模型假设只有偏应力引起蠕变,而没有考虑围压对蠕变特性的影响,因此其主要用于描述岩石的蠕变特性。但不同于岩石,堆石料等粗粒土是由颗粒集合而成的摩擦型材料,其蠕变特性与围压密切相关。为了考虑围压对粗粒土蠕变特性的影响,该文首先推导了Burgers模型的三轴蠕变理论解,并根据各参数物理意义,提出一套简便实用的参数反演方法,用于获取同一围压不同偏应力下粗粒土的Burgers模型参数;进而总结并分析不同粗粒土的三轴蠕变实验结果,发现幂函数能较好地描述Burgers模型各参数随围压变化的规律;在此基础上,提出考虑围压对粗粒土蠕变特性影响的Burgers模型参数修正方法,并通过三组粗粒土的蠕变实验结果验证了所提方法的有效性。     

Defect-Enhanced Polarization Switching in the Improper Ferroelectric LuFeO3

Results of switching behavior of the improper ferroelectric LuFeO₃ are presented. Using a model set of films prepared under controlled chemical and growth-rate conditions, it is shown that defects can reduce the quasi-static switching voltage by up to 40% in qualitative agreement with first-principles calculations. Switching studies show that the coercive field has a stronger frequency dispersion for the improper ferroelectrics compared to a proper ferroelectric such as PbTiO₃. It is concluded that the primary structural order parameter controls the switching dynamics of such improper ferroelectrics.     

Defect‐Mediated Polarization Switching in Ferroelectrics and Related Materials: From Mesoscopic Mechanisms to Atomistic Control

The plethora of lattice and electronic behaviors in ferroelectric and multiferroic materials and heterostructures opens vistas into novel physical phenomena including magnetoelectric coupling and ferroelectric tunneling. The development of new classes of electronic, energy‐storage, and information‐technology devices depends critically on understanding and controlling field‐induced polarization switching. Polarization reversal is controlled by defects that determine activation energy, critical switching bias, and the selection between thermodynamically equivalent polarization states in multiaxial ferroelectrics. Understanding and controlling defect functionality in ferroelectric materials is as critical to the future of oxide electronics and solid‐state electrochemistry as defects in semiconductors are for semiconductor electronics. Here, recent advances in understanding the defect‐mediated switching mechanisms, enabled by recent advances in electron and scanning probe microscopy, are discussed. The synergy between local probes and structural methods offers a pathway to decipher deterministic polarization switching mechanisms on the level of a single atomically defined defect.     

A rate-dependent thermo-electro-mechanical free energy model for perovskite type single crystals

The three-dimensional electro-mechanical free energy potential developed by Kim and Seelecke [S.J. Kim and S. Seelecke, A rate-dependent three-dimensional free energy model for ferroelectric single crystals, Int. J. Solids Struct. 44 (2007) 1196-1209] is generalized to model various thermal aspects of perovskite type single crystals. A total of seven energy potentials are described in the 10-dimensional space of electric displacement vector, strain tensor and temperature, the first six of them representing the six distinct types of ferroelectric tetragonal variants and the seventh the paraelectric cubic phase of the materials. Energy barrier expressions given as functions of thermodynamic driving forces are combined with evolution equations to determine the phase fractions based on the theory of thermally activated processes, thus allowing for a natural treatment of rate-dependent effects. The thermodynamic Clausius-Clapeyron relation is derived from the energy potential and the double polarization hysteresis loops near Curie temperature observed by Merz [W.J. Merz, Double hysteresis loop of BaTiO₃ at the Curie point, Phys. Rev. 91 (1953) 513-517] are predicted and compared. Besides, various nonlinear coupling behavior, such as variation of spontaneous polarization over temperature, mechanical depolarization, and rate-dependent hysteresis loops, are calculated and discussed.     

Monte Carlo Study of Long-Range Interactions of a Ferroelectric Bilayer with Antiferroelectric Interfacial Coupling

By the use of Monte Carlo simulation, we have studied the critical behavior of a ferroelectric bilayer with antiferroelectric interfacial coupling using the transverse spin- $\frac{1}{2}$ Ising model. We discuss the effects of long-range interactions for the internal energy, specific heat, free energy, dielectric susceptibility, and polarization. The dependence of the Curie temperature on the thickness of the bilayer, long-range interactions, and the transverse field was also investigated. It is assumed that the long-range interaction decays with the distance between the pseudo-spins as a power law.     

Phase field simulation of domain structures in ferroelectric materials within the context of inhomogeneity evolution

A phase field model for simulating the domain structures in ferroelectric materials is proposed. It takes mechanical and electric fields into account, thus allowing for switching processes due to mechanical and/or electrical loads. The central idea of the model is to take the spontaneous polarisation as an order parameter and to provide an evolution law for this parameter. The concept of evolving inhomogeneities (configuratioanl forces) can be used in this context, as the Spatial distribution of the spontaneous polarisation describes the inhomogeneity of the system. The evolution is found to be in agreement with the second law of thermodynamics and to resemble the (classical) Ginzburg-Landau equation. Numerical simulations show the features of the model and the interaction of domain structures with defects.     

Creep behavior of unidirectional composites

The creep behavior of the continuous fiber reinforced unidirectional composites due to the viscoelasticity of the resin matrix is investigated assuming that the constituent matrix obeys the nonlinear creep law and the fiber is the linear elastic materials. Utilizing a quasi three-dimensional finite element method, the macroscopic creep behavior of the composites with regular fiber packing is obtained, giving the orthotropic creep law for the composites. Then, the creep of the composites with random fiber packing is estimated applying the random model proposed by Kondo and Saito in which the neat matrix cylinders are embedded in the regular array composites. The theoretical predictions for the creep behavior are compared with the experimental results.