1、尽管31模式纵向应变比33模式小一半，但所需驱动电压仅需33模式的1/10或更少。传统的制备技术可以制备出壁厚在压电材料晶粒尺寸量级的中空纤维，但是长度仅有10mm或更短。混合共挤技术可以制备100mm以上的空心纤维。目前对中空压电纤维复合材料的研究大多限于利用短纤维的径向应变（水声听音设备），本文则研究利用纵向应变。目前对中空纤维的研究主要内容如下：（1）纤维壁内的电场分布（2）电场和应变之间的关系。本文主要研究（3）纤维和基体模量比、中空纤维壁厚与半径比及纤维体积分数对此类复合材料性能、制造及可靠性影响（4）中空纤维质量对复合材料制备和性能的影响。二、单个纤维及层板的有效性质中空纤维中的电
2、场： thin-wall approximation 在这篇文献里没有提到这个公式是近似的，还用这个公式计算了各种厚度的中空纤维的电场，但在后面Lin 和Sodano的文献中，似乎说为近似的。在一般情况，由该表达式电场内表面大外表面小，最大与最小差值随增加而增大，这样在外表面达到极化时，内表面处材料有可能由于大的电场产生的应力而损坏。同样在驱动中空纤维时，在外表面难以达到最大工作电压。因此，小的中空纤维是一个好的选择。纤维有效：，随着的增加而降低，即薄壁中空纤维可以产生高的应变。单层有效讨论：（1）纤维密度（纤维数/能放入的最大纤维数）代替纤维体积分数，通 过计算发现，thin-wall纤维虽
3、然d31最高，但由于体积分数的限制，不能使单层达到最高的d31；thick-wall纤维虽d31不及thin-wall，但由于可以达到高的体积分数，因而层板的d31较大。（2）层板d31随基体模量增加而降低。最大基体模量由单个纤维能承受的嵌入应力决定，嵌入应力由制备过层中基体与纤维的热应变差别引起（两种材料热膨胀系数不匹配）。纤维的环向、轴向和Von Mises应力由作者另一篇研究工作给出。研究表明：硬的基体容易导致纤维发生强度破坏，而软的环氧树脂基体容许各种和而不发生强度破坏。三、中空纤维制备与评估： 上面的研究表明，和材料性质（模量和d31）决定了中空复合材料的应变行为，而嵌入应力条件限制
4、了基体材料的选择。这节讨论microfabrication by coextrusion（MFCX），这种方法对各种陶瓷材料，制备晶粒尺度的任意横截面的纤维具有很高的成功率。（1）ovality（椭圆度）=最大直径偏差/名义直径（2）eccentriclty（偏心度）=孔的偏差/直径以上两个参数是重要的，它们直接影响壁厚，导致壁内电场的变化（3）straightness（直线度），由curvature（曲率）和waviness（波动）表示（4）material property evaluation：包括所制备材料的空隙率、密度、d31、和模量四、中空纤维制备与评估： Thin-wall纤维强
5、度较差因而会对复合材料可靠性带来影响。五、中空纤维与实心纤维的比较 实心纤维驱动电压要求很高，因而工程应用不方便。空心纤维如果电极破裂丧失了电连通性，纤维就失效了，在这种情况下，实心纤维比空心的强。2Beckert W, Kreher W, Braue W, Ante M. Effective properties of composites utilizing fibres with a piezoelectric coatingJ. Journal of the European Ceramic Society, 2001, 21（10-11）:1455-1458.hybird fiber
6、 with an inactive core and a piezoelectric coating, the piezoelectric inactive core provides the mechanical support, and improve mechanical stability. An electrical potential different between an inner and an outer electrode layer gives rise to an actuating electric field. A corresponding axial defo
7、rmation of the fiber is induced by the 31-coupling of the piezomaterial.core fiber: glass, SiC, steel结果：3种方法比较，d33与bulk fiber比较。 多几层薄的压电层（薄压电层驱动性能更好，在前面的文献中有讨论），然后加反向电压，控制起来灵活性更大（可实现双路反向控制）. 同时，与厚的压电层比较，用更多层薄的压电层，电场分布误差会很小，提供的夹持力比单层的要大，降低了压电材料中的应力。硕士研究,3Dai Q L, Ng K. Investigation of electromechani
8、cal properties of piezoelectric structural fiber composites with micromechanics analysis and finite element modelingJ. Mechanics of Materials, 2012,53:29-46. 用细观力学和有限元法（利用了双周期条件+能量方法）方法研究压电结构纤维复合材料（piezoelectric structural fiber composites），纤维纵向极化，芯材为SiC和C且不充当电极。 the monolithic piezoceramic material
9、s such as lead-based ceramics are brittle by nature. The fragile property makes them vulnerable to accidental breakage during operations, and difficult to apply to curved surfaces and harsh environments with reduced durability.（陶瓷材料易碎）。 金属芯：platinum，the metal core can reinforce the composite and ser
10、ve as electrode.但两者热膨胀性能的不匹配容易使涂层断裂（问题：热分析）。也可用导电的碳和碳化硅，但在碳和碳化硅表面的压电涂层如果太薄，使在采集轴向纤维的电场很困难，这也是本文的着眼点。 对有效性能预测，本文强调MT方法与实验结果最为接近。the aspect ratio, of PSF is defined as the shell thick, t divided by the outer radius, r. The volume fraction of the PSF is the volume ratio of fibers with the whole laminat
11、e. 传感模式的基本方程 驱动模式的基本方程如果3方向是极化方向，12方向是横观各向同性面，则本文利用驱动模式方程，由得到了传感模式方程的d33. Mori-Tanaka approach only considers the volume fraction and excludes the inclusion shape and size effects on the composite properties. Extended rule of mixture: the inclusion shape and size effects of each phase were considere
12、d.最初的混合率是对两相复合材料的，扩展的混合率用于研究三相复合材料，其实质就是应用两次针对两相材料的混合率。4Dinzart F, Sabar H. Electroelastic behabior of piezoelectric composites with coated reinforcements: micromechanical approach and applicationsJ. International Journal of Solids and Structures, 2009, 46（20）:3556-3564.5Lin Y, Sodano H A. Concept a
13、nd model of a piezoelectric structural fiber for multifunctional compositesJ. Composites Science and Technology, 2008,68（7-8）: 1911- 1918. 这篇文献intrduction写得好。 this paper introduces a novel active piezoelectric structural fiber that can be laid up in a in a composite material to perform sensing and a
14、ctuation, in addition to providing load bearing functionality. 建立了一维模型，结果表明，包含压电结构纤维的复合材料层板可以达到压电材料70%的耦合系数。 first,., additionality,. 实用单相压电材料有困难：易碎性，难以做成曲面形状。于是有了各种压电纤维复合材料PFC（包括active fiber composites（AFC）、macro-fiber composites（MFC）、1-3 composites, and hollow tube active fiber composite），这些压电复合材料
15、的典型应用为像一个patch粘贴在结构表面，或像一个active layers along with conventional fiber-reinforced lamina, While the PFCSs provide significant advantages over monolithic piezoceramic materials, they are still generally separate from the structural components and are not intended to provide any load bearing functional
16、ity.或者即使埋入材料内部，也不提供承受载荷的能力。 本文对压电纤维复合材料的工程应用有比较详细的介绍，但每个应用只有一个功能，这是的一个着眼点（本文为传感/驱动+承受载荷）。a one-dimensional micromechanics model. Prior efforts have characterized and developed accurate models for a solid piezoceramic fiber 7, however, these models are not applicable to the active fiber developed her
17、e, because the fiber is two phase. Prior efforts did not considered the coating aspect ratio, defined as the ratio of the piezoceramic coating thickness to the outside radius of the active fiber, or the non-uniform electric field, caused by different surface area between the inner and outer electrod
18、es. 这个等式假定压电层很薄，在压电层厚时是不准确的。由于按此分布压电壳内边界的电场高于外边界的电场，导致两个问题：（1）内边界处驱动应变高，限制了the magnitude of the electric field applied before depoling occurs（2）导致纤维与压电壳解除约束。只加电场时，一次压电效应无非均匀变形引起的约束应变？该点的应力为截面上总的piezoelectric force以上是为了求平均应变的一个虚拟（F是一个虚拟的力，只要有应变，就假象是由一个力引起的）的过程。其实可以如下式得到利用这个虚拟概念，可以类似得到压电结构纤维的上式也可以由静不定
19、求解得到：压电壳有一个平均应变，由于core的约束作用，core有一个伸长应变（假设由力FF引起），而压电壳有一个压缩应变（同样由力FF引起），由协调条件层板的 由将按照混合率换成即可。（工作：可以选用另一种混合率方法） 层板本构关系（在电场和机械场共同作用下），在平均意义下？算例：BAAQUS, 压电结构纤维及复合材料，core fibers 为carbon 和silicon carbonate，模型一端施加固定边界条件。用端部的平均位移计算平均应变。6Lin Y, Sodano H A. Electromechanical characterization of a active stru
20、ctural fiber lamina for multifucntional compositesJ. Composites Science and Technology, 2009,69（11-12）: 1825-1830.写论文参考！ the monolithic material is brittle making it difficult to apply to curved surfaces and reducing its durability in harsh environments subject to large strains or shock loading.压电纤维
21、复合材料（PFCs）包括以下四种：（1）active fiber composite（AFC）：实心圆截面压电纤维嵌入环氧树脂，电场施加困难。（2）macro fiber composite（MFC）：压电纤维为矩形，通过压电镜片切割获得。好处是能提供与电极好的电接触。Both the AFC and MFC use a separate interdigitated electrode pattern that is bonded to the surface of the fibers which can make embedding difficult. While the electr
22、ode pattern requires significantly higher voltages to achieve full actuation, it allows the electric field to be applied along the fiber length to capitalize on the higher d33 coupling coefficient.（3）hollow fiber composite（HFC）：Cannon and Brei 10,11 proposed the hollow fiber composite （HFC） in order
23、 to overcome the drawbacks of the solid fiber composites. In the HFC the electric field is applied through the thickness of the hollow fiber; from the inner and outer surfaces, significantly reducing the impedance of the material and the actuation voltage required 12. However, due to the hollow core
24、 and fragile nature of PZT greatly restricts its application and makes hollow fiber prone to cracking and failure under mechanical loading.（4）active structural fiber（ASF）：More recently, several research groups developed the metal core PFCs to overcome the disadvantage of the HFC by coating a metal f
25、iber （typical platinum fiber） with PZT to form the active piezoelectric fibers 1316. The metal core serves as one electrode for the PZT as well as carry part of the mechanical loading. Although metal core PFC provides significant advantages, the ductility and the high coefficient of thermal expansio
26、n of the metal conductor make the piezoceramic coating prone to cracking under mechanical strain and the sintering process.（工作：热分析） 本文制造了C和SiC芯材（能当电极）BaTiO3压电壳压电结构纤维，压电结构纤维复合材料达到70%的纯陶瓷材料的d31，这种高的耦合响应指示压电结构纤维复合材料的d31可以比其他一些纯压电材料的高，例如PZT-5H4E （d31 =320 pC/N） was used, the structural composite lamina
27、with an aspect ratio of and volume fraction of would have a bulk coupling coefficient of greater than _224 pC/N or more than four times that of pure unreinforced barium titanate （d31 =49 pC/N）. 单个压电结构纤维的有效d31已经通过试验验证，本文任务是验证压电结构纤维嵌入聚合物基体的试验验证。材料制备细节：For this effort silicon carbide fibers （Type SCS-6
28、, 140 lm diameter, Specialty Materials, Inc. Lowell, MA, USA） were used for the core and as the electrodes in the EPD process. Commercial barium titanate （BaTiO3） nano-powder（BaTiO3, %, average particle size: 100 nm, cubic phase, InframatAdvanced Materials, Farmington, CT, USA） was used as thepiezoc
29、eramic constituent because it is stable under high temperatures,has a high coupling coefficient and unlike PZT does not react with silicon carbide. Following the application of the green piezoceramic coating, the SiC fibers were sintered in a tube furnace （Thermolyne 79400） at 1200C under a nitrogen
30、 gas atmosphere as shown。After sintering the fibers, the outer surface of the BaTiO3 layerwas coated with silver paint （SPI Supplies, #5002） to form the outer electrode, schematically shown in Fig. 2c. The silver-coated fibers were heated to 600C，整个过程是芯材和压电壳在1200下烧结-然后在600度下制作银电极-然后在120度（居里温度，For bulk BaTiO3, the poling process can be done under a DC electric field （2 kV/ cm） at its curie temperature （120 C）下极化-在室温下按体积分数做环氧外层（为防止depole，温度要小于120） 试验结果对高aspect rat
