基于可逆畴变的压电圆环多层致动器应变响应研究

压电致动器在现代工业中发挥着非常重要的作用。然而,目前应用的压电致动器均是基于线性压电效应,最大应变一般只有0.1-0.15%,实现大的致动应变一直是该领域学者追求的目标。本文中,我们提出了两种经过特殊设计的基于可逆非180°电畴翻转的PZT圆环多层致动器,一种是径向极化、部分电极（RPPE）的4层圆环,另一种是周期性正交极化（POP）的4层圆环,以期能够实现大的致动应变,而且圆环构型层数增加时也不容易发生失稳等问题。实验结果表明,在相同的驱动电场（2kV/mm,0.1Hz）下,4层RPPE最大致动应变为0.27%,约为普通PZT圆环的2倍,但表面变形很不均匀。相比之下,4层的POP圆环致动器的最大输出应变为0.36%,是普通PZT圆环的2.7倍。这两种致动器的致动应变都是随着频率的增加而减小, RPPE致动器在超过1Hz后稳定在0.19%, POP致动器在超过5Hz后稳定在0.2%。而且, POP圆环致动器重复性能很好,经过2万次致动循环后致动应变几乎不变。这种POP PZT多层圆环致动器具有结构稳定、输出应变大等优点,在致动领域具有很好的应用前景。     

基于可逆畴变的压电圆环多层致动器应变响应研究

压电致动器在现代工业中发挥着非常重要的作用。然而,目前应用的压电致动器均是基于线性压电效应,最大应变一般只有0.1-0.15%,实现大的致动应变一直是该领域学者追求的目标。本文中,我们提出了两种经过特殊设计的基于可逆非180°电畴翻转的PZT圆环多层致动器,一种是径向极化、部分电极（RPPE）的4层圆环,另一种是周期性正交极化（POP）的4层圆环,以期能够实现大的致动应变,而且圆环构型层数增加时也不容易发生失稳等问题。实验结果表明,在相同的驱动电场（2kV/mm,0.1Hz）下,4层RPPE最大致动应变为0.27%,约为普通PZT圆环的2倍,但表面变形很不均匀。相比之下,4层的POP圆环致动器的最大输出应变为0.36%,是普通PZT圆环的2.7倍。这两种致动器的致动应变都是随着频率的增加而减小, RPPE致动器在超过1Hz后稳定在0.19%, POP致动器在超过5Hz后稳定在0.2%。而且, POP圆环致动器重复性能很好,经过2万次致动循环后致动应变几乎不变。这种POP PZT多层圆环致动器具有结构稳定、输出应变大等优点,在致动领域具有很好的应用前景。     

Two-scale micromechanics-based probabilistic modeling of domain switching in ferroelectric ceramics

A two-scale micromechanics model is developed in this paper to analyze domain switching in ferroelectric ceramics, using a probabilistic domain switching criterion based on energetic analysis. The microstructure of ferroelectric ceramics at two distinct length scales, domains and grains, has been carefully analyzed. The interaction at domain level is accounted for by energy minimization theory, while the fluctuation at grain level is analyzed using ellipsoidal two-point correlation function. The model has been implemented by Monte Carlo method, and applied to simulate the electric poling and mechanical depoling of Pb(Zr_xTi_1-x)O₃ (PZT) ceramics across morphotropic phase boundary (MPB). The drastically different switching characteristics of PZT ceramics across MPB has been captured, and good agreement with experiments has been observed. The effects of the transformation strains and spontaneous polarizations are highlighted, confirming the proposition of Li et al. [2005. Domain switching in polycrystalline ferroelectric ceramics. Nature Materials 4, 776–781] that the strain compatibility plays a dominant role in domain switching in ferroelectric ceramics.     

Study on electroelastic field concentration around the electrode tip in multilayer ferroelectric actuators of two designs and their optimizations

Distribution of electromechanical field near electrode tips is closely related to the reliability of ferroelectric multilayer actuators. In this paper, the deformation and stress concentrations around the electrode tip in two multilayer actuator designs, partially and fully cofired, are investigated by means of experimental measurement and numerical simulations. The digital speckle correlation method (DSCM) is used to measure the full displacement field near the electrode tip with the high spatial resolution. The paths of electric breakdown and cracks initiated from the edge of electrodes were observed. With the proposed Double Gibbs free energy criterion, a fully coupled nonlinear electromechanical finite element method based on domain-switching mechanisms is developed and the simulation results agree well with the experiments. It is found that the crack-like “defects” in the partially cofired layered actuators, i.e. the interlayer gaps filled with soft insulating wax, can significantly reduce the maximum tensile stress level compared with that in “perfect” fully cofired actuators, which implies that the partially cofired design is more reliable than the fully cofired one. Further optimization on geometrical dimension of actuators is also carried out.     

Electroelastic field concentrations ahead of electrodes in multilayer piezoelectric actuators: experiment and finite element simulation

The effects of applied voltage on the electroelastic field concentrations ahead of electrodes in multilayer piezoelectric actuators were examined in a combined experimental and numerical investigation. Experiments were performed to measure the strain near internal and surface electrodes at various electrical loading conditions. The finite element method was also used to solve the coupled electro-elastic boundary value problem. The strain, stress and electric displacement concentrations were calculated and a non-linear behavior induced by localized polarization switching was discussed. A comparison of strain concentration was made between experiment and simulation.     

Micromechanics of ferroelectric domain switching behavior: Part II: Constitutive relations and hysteresis

A constitutive relation is developed to describe the nonlinear behavior of ferroelectric ceramics subjected to external stress and electric field. The theoretical development considers each domain as an inclusion. The Helmholtz and Gibbs free energy of the constituent element are derived by using a micromechanics approach. They are functionals of the orientation distribution function (ODF) that represents the domain distribution patterns. By applying the internal variable theory and expanding ODF in Fourier series, the yield condition, evolution of ODF, and constitutive relation are obtained. Theoretical results agree with experiments.     

An I-integral method for crack-tip intensity factor variation due to domain switching in ferroelectric single-crystals

In the present study, an I-integral method is established for solving the crack-tip intensity factors of ferroelectric single-crystals. The I-integral combined with the phase field model is successfully used to investigate crack-tip intensity factor variations due to domain switching in ferroelectricity subjected to electromechanical loadings, which exhibits several advantages over previous methods based on small-scale switching. First, the shape of the switching zone around a crack tip is predicted by the time-dependent Ginzburg–Landau equation, which does not require preset energy-based switching criterion. Second, the I-integral can directly solve the crack-tip intensity factors and decouple the crack-tip intensity factors of different modes based on superimposing an auxiliary state onto an actual state. Third, the I-integral is area-independent, namely, the I-integral is not affected by the integral area size, the polarization distributions, or domain walls. This makes the I-integral applicable to large-scale domain switching. To this end, the electro-elastic field intensity factors of an impermeable crack in PbTiO₃ ferroelectric single crystals are evaluated under electrical, mechanical, and combined loading. The intensity factors obtained by the I-integral agree well with those obtained by the extrapolation technique. From numerical results, the following conclusions can be drawn with respect to fracture behavior of ferroelectrics under large-scale switching. Under displacement controlled mechanical loading, the stress intensity factors (SIFs) decrease monotonically due to the domain switching process, which means a crack tip shielding or effective switching-induced toughening occurs. If an external electric field is applied, the electric displacement intensity factor (EDIF) increases in all cases, i.e., the formed domain patterns enhance the electric crack tip loading. The energy release rate, expressed by the crack-tip J-integral, is reduced by the domain switching in all examples, which underlines the switching-induced-toughening effect. In contrast, under stress controlled load, the SIF evolves due to large-scale switching to a stable value, which is higher than the non-switching initial value, i.e., fracture is promoted in this case.     

NUMERICAL SIMULATION OF OIL MIGRATION-ACCUMULATION OF MULTILAYER AND ITS APPLICATION

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｏｉｌｆｏｒｍａｔｉｏｎｉｎｓｅｄｉｍｅｎｔｂａｓｉｎｓ ,ｉｔｓｄｉｓｐｌａｃｅｍｅｎｔ,ｔｒａｎｓｐｏｒｔａｎｄａｃｃｕｍｕｌａｔｉｏｎ ,ａｎｄｔｈｅｆｉｎａｌｆｏｒｍａｔｉｏｎｏｆｏｉｌｄｅｐｏｓｉｔｓｈａｖｅｂｅｅｎｏｎｅｏｆｔｈｅｋｅｙｐｒｏｂｌｅｍｓｉｎｔｈｅｅｘｐｌｏｒａｔｉｏｎｏｆｏｉｌ＿ｇａｓｒｅｓｏｕｒｃｅｓ.Ｈｏｗｈａｓｏｉｌｂｅｅｎａｃｃｕｍｕｌａｔｅｄｉｎｔｈｅｐｒｅｓｅｎｔｌｏｏｐａｃｃｏｒｄｉｎｇｔｏｔｈｅｍｅｃｈａｎｉｃｓｏｆｉｍｍｉｓｃ…     

内爆压缩多层密绕螺线管的数值模拟

利用AUTODYN二次开发接口建立三维多层密绕螺线管数值模型,并实现周期性边界条件,应用光滑粒子动力学方法对内爆压缩多层密绕螺线管过程及其界面不稳定性开展数值模拟。计算结果表明,内爆压缩螺线管结构过程存在扰动快速增长至后期的界面失稳现象,与对应的实验结果较为相符。同时,计算显示螺线管结构参数对界面不稳定性发展具有显著影响,螺旋角度减小,结构压缩后期的界面不稳定性趋于严重;铜线直径减小,结构压缩后期的界面不稳定性趋于减弱。     

Finite element simulation of a polycrystalline ferroelectric based on a multidomain single crystal switching model

In this paper, we compute the constitutive behavior of a ferroelectric ceramic by a plane strain finite element model, where each element represents a single grain in the polycrystal. The properties of a grain are described by the microscopic model for switching in multidomain single crystals of ferroelectric materials presented by Huber et al. [J. Mech. Phys. Solids 47 (1999) 1663]. The poling behavior of the polycrystal is obtained by employing the finite element formulation for electromechanical boundary value problems developed by Landis [Int. J. Numer. Meth. Eng. 55 (2002) 613]. In particular, we address the influence of the single grain properties and the interaction between grains, respectively.     

Dynamic modeling,simulation and design of smart membrane systems driven by soft actuators of multilayer dielectric elastomers

Nonlinear Dynamics - A multilayer membrane element of absolute nodal coordinate formulation is proposed for dynamic modeling of multilayer dielectric elastomer actuators (DEAs). The coupled...     

A micromechanics method to study the effect of domain switching on fracture behavior of polycrystalline ferroelectric ceramics

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A study of electromechanical switching in ferroelectric single crystals

This article documents both modeling and experimental studies developed to investigate the switching behavior of ferroelectric single crystals. The theoretical model makes a priori ansatz that switching follows the evolution of a particular domain pattern. The choice of this configuration is dictated by the requirement that domains remain compatible during evolution, giving rise to a low-energy path for the overall switching. The construction of this pattern is achieved using multirank laminates. It offers an advantage of specifying different types of domain wall movements, leading to a distinction for the switching types. A loading experiment is performed on a barium titanate (BaTiO₃) single crystal with a constant compressive stress and a cyclic electric field. Both 180 and 90 coercive fields are measured as input parameters required for the theoretical framework. The simulation results show good agreement with the observed strains measured by the present and other available experiments. It is found that depolarization has a non-trivial influence on attainable actuation strains.     

The shift of Curie temperature and evolution of ferroelectric domain in ferroelectric crystals

A micromechanics-based thermodynamic model for the phase transition of ferroelectric crystals is developed and, with it, the shift of Curie temperature and evolution of ferroelectric phase upon cooling are examined. This approach differs from the classical phenomenological one in that the evolution of new domain concentration can be predicted. We start out by formulating the Gibbs free energy of a generic, two-phase crystal consisting of the parent paraelectric phase and the transformed ferroelectric phase, at a given level of temperature, stress, and electric field. The thermodynamic driving force for domain growth is then derived and, together with the resistance force, a kinetic equation is established. The derived driving force is found to arise from three different sources of Gibbs free energy: (i) the interaction energy due to the heterogeneity of electromechanical moduli of the parent and product phases, (ii) the energy dissipation due to spontaneous polarization, and (iii) the self-energy of the dual-phase system due to the existence of polarization strain and electric polarization. For a BaTiO₃ crystal the electromechanical heterogeneity is found to play a rather significant role that seems not to have been recognized before. The derived shift recovers to the Clausius-Clapeyron relation if such heterogeneity disappears. We have examined in detail several factors that affect the shift of Curie temperature, and calculated the evolution of overall polarization and dielectric constant of a BaTiO₃ crystal. The results are found to be consistent with available test data.     

Domain switching and non-linear coupling of ferroelectric composites

One of the most notable characteristics of ferroelectric materials is that they could undergo spontaneous polarization and spontaneous strain changes by applied fields. Reorientation of the spontaneous polarization and spontaneous polarization strain of ferroelectric inclusions in ferroelectric composites can change microstructures and affect effective electroelastic properties of ferroelectric composites. Based on orientation distribution function and its evolution as well as switching criterion, non-linear electromechanical coupling behaviour of ferroelectric composites is studied by application of micromechanics. A constitutive model of ferroelectric composites is developed. Comparison between analytical and experimental results shows that the model presented can describe many non-linear electromechanical coupling problems of ferroelectric composites such as polarization or depolarization, etc.     

An analytical model for electrode–ceramic interaction in multilayer piezoelectric actuators

The present paper develops an analytical model for multi-electrodes in multi-layered piezoelectric actuators, in which the electrodes are vertical to and terminated at the edges of the medium and electroelastic field concentrations ahead of the electrodes in the multilayer piezoelectric actuators are examined. By considering a representative unit in realistic multilayers, the problem is formulated in terms of electric potential between the electrode tips and results in a system of singular integral equations in which the electric potential is taken as unknown function. Effects are investigated of electrode spacing and piezoelectric coupling on the singular electroelastic fields at the electrode tips, and closed-form expressions are given for the electromechanical field near the electrode tips. Exact solution for un-coupled dielectrics is provided, where no piezoelectric coupling is present. The English text was polished by Yunming Chen.     

Electrical body forces and electrical tractions in the nonlinear response of ferroelectric actuators

The influence of the electrical body forces and electrical tractions on the nonlinear response of ferroelectric stack actuators is analytically investigated. While the role of the electrical body forces and tractions in the response of piezoelectric actuators is well documented (and in many cases is not significant), the questions of their effect on ferroelectric active materials is still of interest. To examine this influence, the analytical model for the electro-mechanical behavior of a ferroelectric stack actuator is augmented to account for the electrical body forces along the actuator and the electrical tractions at the material–electrode interfaces. Focusing on the effect of the electrical forces and tractions on the ferroelectric domain switching phenomenon, the model is used for the numerical analysis of a ferroelectric layer and for the comparison with the case that neglects the electrical body forces and traction. The comparison theoretically designates cases in which the effect of the electrical body forces and tractions may be prominent and other cases where the classical approach that neglects these effects can be adopted.     

On ferroelectric crystals with engineered domain configurations

This paper examines the engineered domain configurations and the macroscopic properties of ferroelectric crystals using an energy minimization theory. The energy minimizing domain configurations have been constructed, and their macroscopic properties have been calculated and compared well with experiments. The optimal domain configurations have also been identified.     

Analysis of piezoelectric ceramic multilayer actuators based on an electro-mechanical coupled meshless method

This paper presents an efficient meshless method for analyzing cracked piezoelectric structures subjected to mechanical and electrical loading. In this method, an element free Galerkin (EFG) formulation, an enriched basic function and some special shape functions that contain discontinuous derivatives are employed. Based on the moving least squares (MLS) interpolation approach, the EFG method is one of the promising methods for dealing with problems involving progressive crack growth. Since the method is meshless and no element connectivity data are needed, the burdensome remeshing procedure required in the conventional finite element method (FEM) is avoided. The numerical results show that the proposed method can yield an accurate near-tip stress field in an infinite piezoelectric plate containing an interior hole. In another example studying a ceramic multilayer actuator, the proposed model was found to be accurate in the simulation of stress and electric field concentrations arround the abrupt end of an internal electrode. The project supported by the National Natural Science Foundation of China (10025209, 10132010, and 90208002), and the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU 7203/03E). The English text was polished by Yunming Chen.     

Toughening under non-uniform ferro-elastic domain switching

The existing models of switch-toughening seldom consider the effect of non-uniform ferro-elastic domain switching in the vicinity of a crack. To explore this issue, an evolution law for the volume fraction of the switched portion under applied electromechanical loading is established from the minimum energy principle. Based on this law, a switching model capable of dealing with the non-uniform distribution of switching strain is developed. The domain switching zone is divided into a saturated inner core and an active surrounding annulus. Mono-domain solution of ferro-elastic toughening is obtained under the model of small scale domain switching. Toughening for ferroelectrics with different poling states is estimated via Reuss type approximation. Two sets of solutions are obtained according to spherical and cylindrical inclusions. The interval of toughening defined by these two models covers the range of experimental data. The same conclusion is reached for the size of the switching zone.