Effective electromechanical properties of cellular piezoelectret: A review

Due to the large quasi-piezoelectric d 33 coefficient in the film thickness direction,cellular piezoelectret has emerged as a new kind of compliant electromechanical transducer materials.The macroscopic piezoelectric effect of cellular piezoelectret is closely related to the void microstructures as well as the material constants of host polymer.Complex void microstructures are usually encountered in the optimum design of cellular piezoelectret polymer film with advanced piezoelectric properties.Analysis of the effective electromechanical properties is generally needed.This article presents an overview of the recent progress on theoretical models and numerical simulation for the effective electromechanical properties of cellular piezoelectret.Emphasis is placed on our own works of cellular piezoelectret published in past several years.     

THE EFFECTIVE ELECTROMECHANICAL PROPERTIES OF CELLULAR PIEZOELECTRET FILM:FINITE ELEMENT MODELING

Cellular space-charge polymer film,also called cellular piezoelectret,has very large piezoelectric effect due to their unique microvoid structure.In this article,the cellular piezoelectret film is considered to be a periodic composite material with closed-cell microvoids aligned periodically.Three dimensional finite element modeling is carried out to obtain the effective elastic modulus and piezoelectric coefficients.Sensitivity analysis was presented by modeling the effective electromechanical properties with different individual variable,including material constants and void shape parameters.By assuming a relation between void shape and void volume fraction,the finite element model can simulate quite well the inflation experiments of the voided charged Polypropylene film published in literature.Finally,the finite element model is used to explore the voided charge polymer film with non-uniform distribution of the trapped charges on the internal surface of voids.It was found that the resultant overall piezoelectric coefficients will be more significant if charges are closely gathered in the central area,and sparse in the around area of the internal surface of voids.     

Three dimensional phase field study on the thickness effect of ferroelectric polymer thin film

The electromechanical behavior of poly(vinylidene fluoride-trifluoroethylene) [P(VDF-TrFE)] ferroelectric thin film was investigated using the three dimensional (3D) phase-field method. Various energetic contributions, including elastic, electrostatic, and domain wall energy were taken into account in the variational functional of the phase field model. Evolution of the microscopic domain structures of P (VDF-TrFE) polymer film was simulated. Effects of the in-plane residual stress, the film thickness and externally applied electric bias field on the electromechanical properties of the film were explored. The obtained numerical results showed that the macroscopic responses of the electric hysteresis loops are sensitive to the residual stress and electric bias field. It was also found that thickness has a great effect on the electric hysteresis loops and remanent polarization.     

Investigation into Electromechanical Properties of Biocompatible Chitosan-Based Ionic Actuator

Ionic actuators have attracted much attention due to their remarkably large strain under low-voltage stimulation. Here, we investigate a highly biocompatible ionic polymer actuator, which consists of multi-walled carbon nanotube (MCNT) film as a double electrode layer and an electrolyte layer equipped with chitosan polymer skeleton and ionic liquid. As a result, with the thickness increase of the electrolyte layer and the electrode layer, the membrane capacitance values are obviously improved, which are 0.01 F (membrane thickness of 1.3 mm) and 0.4 F (0.25 mm). The blocking force and its response speed show peak values of 5.75 mN (1.1 mm) and 5.1 mN (0.25 mm), while reverse increases for the displacement and its response speed are observed, which present maximum values of 10.3 mm (0.3 mm) and 13.3 mm (0.15 mm). Furthermore, for various thicknesses of the electrode layers under applied direct current of 5 V, the generated strain of 0.15 mm thickness (59%) is 4.92 times greater than that of the 0.25 mm thickness. This is against the strain difference on the electrode surface due to the growing stiffness of the electrode layer. Additionally, from the experiments of the electromechanical energy efficiency of various electrode layers and electrolyte layers, our actuator exhibits excellent electromechanical energy efficiency under a high electrical conductivity of the electrode layer, which enhance the specific electromechanical energy up to 9.95%.     

Vibration of quadrilateral embedded multilayered graphene sheets based on nonlocal continuum models using the Galerkin method

Free vibration analysis of quadrilateral multilayered graphene sheets(MLGS) embedded in polymer matrix is carried out employing nonlocal continuum mechanics.The principle of virtual work is employed to derive the equations of motion.The Galerkin method in conjunction with the natural coordinates of the nanoplate is used as a basis for the analysis.The dependence of small scale effect on thickness,elastic modulus,polymer matrix stiffness and interaction coefficient between two adjacent sheets is illustrated.The non-dimensional natural frequencies of skew,rhombic,trapezoidal and rectangular MLGS are obtained with various geometrical parameters and mode numbers taken into account,and for each case the effects of the small length scale are investigated.     

四面体无定型无氢非晶碳膜的制备及其摩擦学性能研究

采用磁过滤阴极真空弧系统分别在硅片[Si(100)]、W18Cr4V高速钢和Cr18Ni9不锈钢基体上沉积了一系列sp3键含量较高的四面体无定型无氢非晶碳膜(ta-C),研究了所合成薄膜的结构、硬度、附着强度和摩擦磨损性能,考察了基体和薄膜厚度对薄膜摩擦系数的影响,简要分析了相应ta-C膜的失效机理.结果表明,在高速钢基体上沉积的ta-C膜的显微硬度为76 GPa,结合力Lc值达42 N,具有优良的摩擦学性能,其摩擦系数为0.12,且摩擦系数可以在16 000 r范围内保持稳定.     

聚合物刷水润滑条件下水膜厚度和摩擦学行为的相关性研究

利用表面引发原子转移自由基聚合技术(SI-ARTP)在钢球和玻璃盘摩擦副表面分别接枝亲水性聚合物刷-聚甲基丙烯酸-3-磺酸丙酯钾盐(PSPMA),去离子水作为润滑剂,在球-盘式摩擦试验机和纳米级薄膜厚度测量装置上开展了其宏观摩擦学性能研究,探讨了流体动压效应介入下的聚合物刷水润滑机理. 利用光干涉技术观察了低卷吸速度下(4 mm/s)接触区域水膜分布情况,发现滚道两侧水膜的形状由初始状态的圆形随着时间逐渐沿着卷吸方向分布,证实了聚合物刷通过不断捕获周围的水分子形成了1层稳定的水膜;通过控制卷吸速度从1 mm/s连续增加512 mm/s实现了润滑状态的转变,低卷吸速度时处于薄膜润滑状态,膜厚不依赖于速度且稳定在35 nm左右,接触区内有效水膜的建立归功于聚合物刷的水合效应;当速度大于32 mm/s时处于弹流润滑状态,膜厚的测量值高于等黏弹膜厚公式的预测值(2~12 nm)和水合效应促成的膜厚值(约35 nm)之和,这意味着在流体动压润滑作用下聚合物刷表现出了优异的润滑增强作用, 是水合效应和流体动压效应协同作用的结果.      

A theoretical analysis of the breakdown of electrostrictive oxide film on metal

Oxide films that form to protect (passivate) metal substrates from corrosive environments can be severely damaged when they are subjected to sufficient levels of electric potential. A continuum mechanics model is presented that captures the intimate electromechanical coupling of the environment and the film responsible for either growth or dissolution of the oxide. Analytical solutions, obtained for a finite-thick film experiencing a uniform electric field, illustrate the existence of a critical combination of electric field strength, initial film thickness and shape, beyond which the passivating oxide can become thin enough to undergo dielectric breakdown, or the substrate can become exposed to the corrosive environment. An experimental procedure is proposed to measure combinations of material properties required by the theoretical model to predict the lifetime of the oxide or to avoid the critical state. Illustrative numerical examples are provided to describe the morphological evolution of oxide films with a periodically wavy surface.     

Effect of intrinsic stress gradient on the effective mode-I fracture toughness of amorphous diamond-like carbon films for MEMS

The influence of intrinsic stress gradient on the mode-I fracture of thin films with various thicknesses fabricated for Microelectromechanical Systems (MEMS) was investigated. The material system employed in this study was hydrogen-free tetrahedral amorphous diamond-like carbon (ta-C). Uniform gauge microscale specimens with thicknesses 0.5, 1, 2.2, and 3 μm, containing mathematically sharp edge pre-cracks were tested under mode-I loading in fixed grip configuration. The effective opening mode fracture toughness, as calculated from boundary force measurements, was 4.25±0.7 MPa√m for 0.5-μm thick specimens, 4.4±0.4 MPa√m for 1-μm specimens, 3.74±0.3 MPa√m for 2.2-μm specimens, and 3.06±0.17 MPa√m for 3-μm specimens. Thus, the apparent fracture toughness decreased with increasing film thickness. Local elastic property measurements showed no substantial change as a function of film thickness, which provided evidence for the stability of the sp²/sp³ carbon binding stoichiometry in films of different thicknesses. Detailed experiments and finite element analysis pointed out that the dependence of the effective fracture toughness on specimen thickness was due to the intrinsic stress gradient developed during fabrication and post-process annealing. This stress gradient is usually unaccounted for in mode-I fracture experiments with thin films. Thicker films, fabricated from multiple thin layers, underwent annealing for extended times, which resulted in a stress gradient across their thickness. This stress gradient caused an out-of-plane curvature upon film release from its substrate and, thus, combined bending and tensile mode-I loading at the crack tip under in-plane forces. Since the bending component cannot be isolated from the applied boundary force measurements, its contribution, becoming important for thick films, remains unaccounted for in the calculation of the critical stress intensity factor, thus resulting in reduced apparent fracture toughness that varies with film thickness and curvature. It was concluded that in the presence of a stress gradient, accounting only for the average intrinsic stresses could lead in an overestimate of the fracture resistance of a brittle film. Under these considerations the material fracture toughness of ta-C, as determined from specimens with negligible curvature, is K_IC=4.4±0.4 MPa√m.     

不同滑滚比下润滑油膜流变特性试验观察与数值模拟

通过在原有的球-盘接触光干涉润滑油膜测量装置上增设摩擦力测量单元,实现了任意滑滚比下油膜厚度和摩擦系数的同步测量与润滑状态的直观识别. 采用FVA3参考油,分析了不同滑滚比、速度和载荷下的摩擦系数变化规律,并结合油膜干涉图明确了润滑状态与热效应机制,推断出摩擦系数曲面在较低速工况存在混合润滑区域;通过采用基于恢复时间的流变模型对FVA3油品的流变润滑进行数值模拟,并与同等工况下的试验结果进行定量对比,两者取得了良好的吻合性,验证了试验测量的准确性和流变模型的适用性.      

Effect of disjoining pressure on the instability of a charged thin liquid film on a spherical rigid core

It is shown that the critical Rayleigh number which characterizes the stability of a thin charged viscous fluid film on the surface of a rigid spherical core develops rapidly with decrease in the film thickness to 100 nm when the effect of the disjoining pressure becomes significant. The dependence of the instability growth rate on the thickness of the fluid layer is obtained by analyzing the dispersion relation numerically. Yaroslavl’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 102–106, January–February, 1999.     

环境水氧对纳米氮化铝/聚四氟乙烯复合材料摩擦学性能的影响

采用超声分散法制备出纳米氮化铝/聚四氟乙烯(AlN/PTFE)复合材料,使用线性往复摩擦磨损试验机在大气和干燥氩气中对比测试了该复合材料摩擦学性能. 结果表明:大气环境下,纳米氮化铝质量分数为5%时可以将聚四氟乙烯磨损率降低4个数量级[1×10?7 mm3/(N·m)]. 而在同样摩擦测试条件的干燥氩气环境中,使用纳米氮化铝只能将聚四氟乙烯磨损率降低2个数量级[1×10?5 mm3/(N·m)]. 利用三维轮廓仪、扫描电镜、红外光谱仪和光电子能谱仪对金属对偶表面形成转移膜的形貌和化学成分进行分析. 研究发现:大气环境的摩擦过程中,聚四氟乙烯与环境水氧发生摩擦化学反应生成了富含羧酸盐的转移膜,显著提高了复合材料耐磨性能;干燥氩气中,水氧的缺失使复合材料无法在摩擦中生成富含羧酸盐的转移膜,影响材料耐磨性能的进一步提高.      

考虑膜厚影响薄膜磁致伸缩系数、泊松比和杨氏模量的同时测量

基于经典层合板理论,建立了一个能同时测量薄膜-基底系统中薄膜的磁致伸缩系数、杨氏模量和泊松比的板模型.以前的研究计算薄膜磁致伸缩系数时,大多假设薄膜的弹性属性与相应的块材一致,由此导致的磁致伸缩系数计算是不准确的.在目前大多数方法中仅仅在使用一个单一的弹性各向同性基底中能够避免这个问题.该文模型在各向异性基底下同样适用,并且不要求薄膜的厚度远远小于基底厚度,因此也能够用来计算磁致伸缩应变和设计微电机械系统和生物微电机械系统.对已有的铁基非晶薄膜的实验数据,在不同磁场强度下,磁致伸缩系数的计算结果与已有模型进行了比较,它们之间的差异得到了解释.同时,还可以得到薄膜的弹性常数.     

Piezoelectric composites with periodic multi-coated inhomogeneities

A new, robust homogenization scheme for determination of the effective properties of a periodic piezoelectric composite with general multi-coated inhomogeneities is developed. In this scheme the coating does not have to be thin, the shape and orientation of the inclusion and coatings do not have to be identical, their centers do not have to coincide, their properties do not have to remain uniform, and the microstructure can be with the 2D elliptic or the 3D ellipsoidal inclusions. The development starts from the local electromechanical equivalent inclusion principle through the introduction of the position-dependent equivalent eigenstrain and electric field. Then with a Fourier series expansion and a superposition procedure, the volume-averaged equivalent eigenstrain and electric field for each phase are obtained. The results in turn are used in an energy equivalent criterion to determine the effective properties of the composite. In this model the interphase interactions in each multi-coated particle and the long-range interactions between the periodically distributed particles are fully accounted for. To demonstrate its wide range of applicability, we applied it to examine the properties of several periodic composites: (i) piezoelectric PZT spherical particles in a polymer matrix, (ii) continuous glassy fibers with thin PZT coating in an epoxy matrix, (iii) spherical PZT particles coated by thick or functionally graded piezoelectric layer, (iv) spheroidal voids coated with a thick non-piezoelectric layer in a PZT matrix, and (v) spherical piezoelectric inhomogeneities with eccentric, non-uniform thickness coating. The calculated results reflect the complex nature of interplay between the properties of core, matrix, and coating, as well as whether the coating is uniform, functionally graded, or eccentric. The accuracy of this new scheme is checked against the double-inclusion and other micromechanics models, and good agreement is observed.     

Modulus prediction and discussion of reinforced syntactic foams with coated hollow spherical inclusions

The elastic properties of syntactic foams with coated hollow spherical inclusions have been studied by means of Mori and Tanaka‘s concept of average stress in the matrix and Eshelby‘s equivalent inclusion theories. Some formulae to predict the effective modulus of this material have been derived theoretically. Based on these formulae, the influences of coating parameters such as the thickness and Poisson‘s ratio on the modulus of the syntactic foams have been discussed at the same time.     

Global and local large-deformation response of sub-micron,soft- and hard-particle filled polycarbonate

Since polymers play an increasingly important role in both structural and tribological applications, understanding their intrinsic mechanical response is key. Therefore in the last few decades much effort has been devoted into the development of constitutive models that capture the polymers' intrinsic mechanical response quantitatively. An example is the Eindhoven Glassy Polymer model. In practice most polymers are filled, e.g. with hard particles or fibers, with colorants, or with soft particles that serve as impact modifiers. To characterize the influence of type and amount of filler particles on the intrinsic mechanical response, we designed model systems of polycarbonate with different volume fractions of small, order 100 nm sized, either hard or soft particles, and tested them in lubricated uniaxial compression experiments. To reveal the local effects on interparticle level, three-dimensional representative volume elements (RVEs) were constructed. The matrix material is modeled with the EGP model and the fillers with their individual mechanical properties. It is first shown that (only) 32 particles are sufficient to capture the statistical variations in these systems. Comparing the simulated response of the RVEs with the experiments demonstrates that in the small strain regime the stress is under-predicted since the polymer matrix is modeled by using only one single relaxation time. The yield- and the large strain response is captured well for the soft-particle filled systems while, for the hard-particles at increased filler loadings, the predictions are less accurate. This is likely caused by polymer–filler interactions that result in accelerated physical aging of the polymer matrix close to the surfaces. Modifying the S_a-parameter, that captures the thermodynamic state of the polymer matrix, allows us to correctly predict the macroscopic response after yield. The simulations reveal that all rate-dependencies of the different filled systems originate from that of the polymer matrix. Finally, an onset is presented to predict local and global failure based on critical events on the microlevel, that are likely to cause the over-prediction in the large-strain response of the hard-particle filled systems.     

Time dependence of effective properties of polycrystalline ferroelectric ceramics

In this paper, based on Merz[7] experimental results and classical nucleation theory, a micromechanics statistical model is proposed to describe the relation between the special microstructure-level evolution phenomena-domain switching and macro-response. The polycrystalline ferroelectric ceramics treated as a composition of switched domain and unswitched domain, the approaches of Eshelby's equivalent inclusion and Mori-Tanaka's mean field theory are used to analyze and predict its effective electroelastic properties. The model can incorporate the effects of time dependence of domain switching and shape of individual crystalline. To the BaTiO₃ polycrystalline ceramics, the analytical results are in good agreement with the experimental results.     

A coupled electromechanical analysis of a piezoelectric layer bonded to an elastic substrate: Part I,development of governing equations

This two-part contribution presents a novel and efficient method to analyze the two-dimensional (2-D) electromechanical fields of a piezoelectric layer bonded to an elastic substrate, which takes into account the fully coupled electromechanical behavior. In Part I, Hellinger–Reissner variational principle for elasticity is extended to electromechanical problems of the bimaterial, and is utilized to obtain the governing equations for the problems concerned. The 2-D electromechanical field quantities in the piezoelectric layer are expanded in the thickness-coordinate with seven one-dimensional (1-D) unknown functions. Such an expansion satisfies exactly the mechanical equilibrium equations, Gauss law, the constitutive equations, two of the three displacement–strain relations as well as one of the two electric field-electric potential relations. For the substrate the fundamental solutions of a half-plane subjected to a vertical or horizontal concentrated force on the surface are used. Two differential equations and two singular integro-differential equations of four unknown functions, the axial force, N, the moment, M, the average and the first moment of electric displacement, D₀ and D₁, as well as the associated boundary conditions have been derived rigorously from the stationary conditions of Hellinger–Reissner variational functional. In contrast to the thin film/substrate theory that ignores the interfacial normal stress the present one can predict both the interfacial shear and normal stresses, the latter one is believed to control the delamination initiation.     

压电智能复合材料层合梁的力电耦合模型及层间应力分析

由于非凡的物理性能,石墨烯纳米片(GPL)被认为是最有吸引力的复合材料增强材料之一.GPL增强材料可以明显提高聚偏氟乙烯(PVDF)压电性能和力学性能.在力电载荷作用下,对含均匀石墨烯薄片增强(GSR)智能压电复合材料层合梁层间应力预测至关重要.若对受到力电耦合作用且层与层之间材料性能突变的压电层合梁层间剪切变形预测有误,则其层间应力过大可能导致层间失效.因此,论文提出一种适于分析此类问题且满足层与层之间相容性条件的有效力电耦合模型,用于含GSR致动器的复合材料层合梁层间应力分析.应用Reissner混合变分原理(RMVT),可以提高考虑力电耦合效应的横向剪应力预测精度.三维(3D)弹性理论和所选模型计算结果将用于评估所提梁模型性能.此外,还从力电载荷、压电层厚度、石墨烯体积分数和长厚比等方面对含GSR致动器复合材料层合梁力学响应特性进行了系统的研究.     

A Model for Predicting Effective Properties of Piezocomposites with Non-piezoelectric Inclusions

Most piezocomposites, which have been widely used in engineering, consist of piezoelectric inclusions and a non-piezoelectric matrix. Due to the limits of fabrication technology, it is hard to avoid the matrix intermingling with other non-piezoelectric inclusions, such as cavities. The non-piezoelectric inclusions can substantially affect performance of piezocomposites. In this paper we study the electromechanical fields in piezocomposites which are composed of a non-piezoelectric matrix embedded with both piezoelectric and non-piezoelectric inclusions. Closed-form relations are obtained for the effective electroelastic moduli of a piezocomposite with both piezoelectric and non-piezoelectric inclusions. The effective properties of a 1-3 type piezocomposite with non-piezoelectric spherical inclusions are analyzed carefully and explicit formulae for the effective electroelastic properties of a 1-3-0 piezocomposite are also obtained. The analysis shows that the effect of non-piezoelectric inclusions on the electroelastic properties of piezocomposites is significant and should not be neglected. The model proposed in this paper is expected to be useful for predicting and analyzing the overall electromechanical properties of piezocomposites with a non-piezoelectric matrix containing both piezoelectric and non-piezoelectric inclusions.