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1、1 Brei D, Cannon B J. Piezoceramic hollow fiber active compositesJ. Composites Science andTechnology, 2004, 64(2):245-261.Poluig diei2ticii (radial)Outer electrodeElectrnde pHlcli, connected to fiber imteriarLongimdijial dcibniiahonactivationAspect R:itio - 0.3图1中空压电纤维Aspect Ratio = 0.42Aspect Ratio
2、 = 0.52、背景介绍一般压电纤维复合材料中的压电纤维为实心截面，当驱动该类压电复合材料时，电极放 在基体表面，电场因需要穿透非导电基体因而其达到压电纤维时产生大的损耗，因而需要高 的驱动电压。另外，该类复合材料的基体必须用不导电材料，这限制了其的应用范围。中空 压电纤维复合材料可以降低驱动电压，并且基体材料选择广泛，可以涵盖不导电的环氧树脂 和各类导电的金属材料。本文讨论了中空圆环形截面压电纤维的制造和应用，以及纤维和基 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、制造及可靠性问题。Thin-wall纤维最理想，但存在严重的可靠性问题。总之，对中空压电纤维复合材料，要
3、同时考虑压电纤维品质、制造及可靠性问题。空心压电纤维复合材料驱动用 31模式，实心压电纤维复合材料用33模式。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
4、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场：Etw=v/t thin-wall approximationE（r）=_、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r ln（1 ：.）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a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，a小的中空纤维是一个好的选择。纤维有效d3
5、1 :J2 Etw =df Etw , d；.随着口的增加而降低，即薄壁中空纤维可以产生ln（1 - : ）（1/ : 一0.5）高的应变。3,eff Yf X单层有效d31 ：d，Etw,Ylam =YfV +Ym(1-Vf)I 2,3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，Vf 过计算发现，thin-wall纤维虽然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
6、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Vf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，U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(椭圆度尸最大直径偏差/名义直径(2) ec
7、centriclty(偏心度尸孔的偏差/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：包括所制备材料白空隙率、密度、 d31、和模量四、中空纤维制备与评估：Thin-wall纤维强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。2 Beckert W, Kreher
8、 W, Braue W, Ante M. Effective properties of composites utilizing fibreswith a piezoelectric coatingJ. Journal of the European Ceramic Society, 2001, 21(10-11):1455-1458.一core fibrehybird fiber with an inactive core and a piezoelectric coating, the piezoelectric inactive core provides the mechanical
9、 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 deformation of the fiber is induced by the 31-coupling of the piezomaterial. core fiber: glass, SiC, steel结果：3种
10、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，3 Dai Q L, Ng K. Investigation of electromechanical properties of piezoelectric structural fibercomposites with micromechanics analysis and finite eleme
11、nt modelingJ. Mechanics of Materials, 2012,53:29-46.Electrodes（与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 composite ,纤维纵向极化，芯材为 SiC和C且不充当电极。the monolithic piezoceramic materials such as lead-based ceramics are brittle by nature. The fragile property makes them vulnerabl
12、e to accidental breakage during operations, and difficult to apply to curved surfaces and harsh environments with reduced durability!（瓷材料易碎）。金属芯：platinum , the metal core can reinforce the composite and serve as electrode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
13、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, a 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 laminate.传感模式的基本方程司=Sjmn mn d nijE nDi-dimn - mn YEn驱动模式的基本方程二ijDi-Cijmn -mn - enij E n=eimn =mn, I
14、n E n如果3方向是极化方向，12方向是横观各向同性面，则悒2总3 信 悒 际 D1D23jc*1* cl2* c1300000* c12*cl1 c c1300000* e31一* c13*c13*c3300000*e33000* c44000* el500000* c440* e150000000* c660000000*50,* k1100000*e15000,* k110-e311*-e31*-e3300000Q -2翦32盘32&12名2EiE2后Jc66 =Xc；）本义利用驱动模式方程由ekq=dkpCpq ,dijk=（BmnC京卜得到了传感模式方程的d33.Mori-Tana
15、ka 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 sizeeffects of each phase were considere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。4 Dinzart F, Sabar H. Electroe
16、lastic behabior of piezoelectric composites with coated reinforcements: micromechanical approach and applicationsJ. International Journal of Solids and Structures, 2009, 46(20):3556-3564.dijk - eimn Cmnjk5 Lin Y, Sodano H A. Concept and model of a piezoelectric structural fiber for multifunctional c
17、ompositesJ. 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 actuation, in addition to providing load bearing functionality.建立了
18、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 f
19、iber-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 functionality.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
20、 是的一个着眼点（本文为传感/驱动+承受载荷）Electrode1Piezoelectric MaterialGarbon Fibera 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 here, because the fiber is
21、 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 electrodes.E(r- -V区个等式假定压电层很薄，在
22、压电层厚时是不准确的。由于r l n (-1-)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。ij - Sijmn - mn d nijE nDi = dimn : mn - 3n En如果3方向是极化方向，12方向是横观各向同性面，则自1、sl2sl300000d31k i投2sl2sl1sl300000d31522髭3sl3sl3s3300000d33633 2 /3000s440
23、00d1500232 &1二0000s440d150051-2 3-200000s56000仇D10000d150kl100EiD2仙)000d15000k0E21d31d31d3300000k33 19 J只加电场时，一次压电效应配=d31E(r)无非均匀变形引起的约束应变?该点的应力为PP _c(r) =Y (r) =Y d/。)截面上总的 piezoelectric force2 rPNd31YPVtn tYPd31E(r)rdrd - 31P0r0 工ln(1 -1 / r0)YP =AF;=(ln(1 _：.)(1/ ：. _0.5)国=31年以上是为了求平均应变非勺一个虚拟（F旦T
24、H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2 - r00，(r)rdrd1=2 - r0d31E(r)rdrd 日222=(-r0 -(r0 -t) (1/ 10.5)ln(1 -:)Etw ,effEtw利用这个虚拟概念，可以类似得到压电结构纤维的 dmuefyniuhi = yprv +(一评)卜-twd 3T仇 一0.5) ln(l - ”啕EiiuJli,multi _y multi - ym Lilli上式也可以由静不定求解得到:有一个伸长应变骂（假设由力压电壳有一个平均应变=d；1,eff Etw ,由于core的约束作用，coreFF引起），而压
25、电壳有一个压缩应变（第同样由力FF引起），由协调条件；=d31,eff EtwFFmulti YA，一六段 d31,eff EtwYPAPYf Af YfAfYmuitiA_FF(YpApYfAf) : FFYmultiA一YpApYfAf-YpApYfAfd31,eff YP vP. multiEtw - d31,effEtwY multi层板的d3imeff由 deffd31,effY multivP将Ymulti按照混合率换成YpVp +YfVf +Ym(1-Vp-Vf）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?Free Strain
26、：Blocked Force: Fbl = 乂泮屈步宏算例：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。6 Lin Y, Sodano H A. Electromechanical characterization of a active structural fiber lamina for multifucntional compositesJ. Composites Science and Technology, 2009,69(11-12): 1825-1830
27、.写论文参考！AFM tipSiC fiberBaTiOa coatingEpoxy matrixAFMSample holderthe 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.压电纤维复合材料(PFCs饱括以下四种：(1)active fiber composite(AFC),实心圆截面压电纤维
28、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 electrode pattern requires significantly higher voltages to ac
29、hieve 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 to overcome the drawbacks of the solid fiber composite
30、s. 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 and fragile nature of PZT greatly restricts its applic
31、ation 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 corePFCs to overcome the disadvantage of the HFC by coating a metal fiber (typical platinum fiber)with PZT to form the acti
32、ve piezoelectric fibers 13 T6. The metal core serves as one electrode forthe 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 expansion of the metal conductor make the piezoceramic coating
33、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 with an aspect ratio of 0.8 and volume fraction of
34、0.6 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, 140 lm diameter, Specialty Materials, In
35、c. Lowell, MA, USA) were used for the core and as the electrodes in the EPD process. Commercial barium titanate (BaTiO3) nano-powder(BaTiO3, 99.95%, average particle size: 100 nm, cubic phase, InframatAdvanced Materials, Farmington, CT, USA) was used as thepiezoceramic constituent because it is stab
36、le 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 gas atmosphere as shown After sinter
37、ing the fibers, the outer surface of the BaTiO3 layer was coated with silver paint (SPI Supplies, #5002) to form the outer electrode, schematically shown in Fig. 2c. The silver-coated fibers were heated to600C， 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
38、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 ratioW较大误差，本文分析了其中的原因。The results demonstrate that composites fabricated form the ASF can achieve coupling levels as high as 50% of the piezoelectric constituent with volume fr
39、actions as low as 30%.7 Jian Liu, Jinhao Qiu, Weijie Chang, Hongli Ji, Kongjun Zhu. Metal-core piezoelectric fibers forthe detection of lamb waves. Proceedings of the ASME 2010 Conference on Smart Materials,Adaptive Structures and Intelligent Systems, September 28 - October 1,2010, Philadelphia,Penn
40、sylvania, USA.Ekctrodefpt) EkctwdcCcraniic冷Longitudlinall modeElctrole(pt) ElecfrodeOramkbending mode（b）本文将金属芯压电结构纤维 MPF作为超声Lamb波（应力波）的接收器（传感器），获得 MPT的电压响应。AFC和MFC使用方式是制成复合材料，而不能直接使用纤维，更进一步， 由于电极被放置在基体表面，电场损失很大，因此它们作为传感器和驱动器是低效率的。金属芯压电结构纤维的优点：直径小、重量轻、易于与host structure结合。压电层厚度50-150微米，MPF直径范围150-400微
41、米，长度20毫米，因此可以与结构 host-structure结合，且由于有金属芯增强，可以克服压电壳的脆性。压电结构纤维可用作传 感器和驱动器。当外电极全涂时，此时称为金属芯（本文为铝）压电纤维MPF,被用于纵向模式。当外电极半 涂（必须半涂吗）时，称为半涂金属芯压电纤维 HMPF。被用于弯曲模式。本文MPF作为传 感器，工作于3-1模式。Consider an MPF sensor bonded on the surface of a structure and deforms with it. Since the radius of the fiber is much smaller t
42、han its length, we can neglect all the lateral stresses. Due to axial symmetry there is no shear stress in the fiber. Under the electrical boundary conditions of an open circuit, the total charge on the electrode of an MPF sensor is zero, andcm r小阳二=0thus ”（零还是常量？ ）, where the integration is perform
43、ed over each electrode 23. Because there is no free charge inside the ceramics, the same expression is valid for any cylindrical area of radius satisfying RrRc.8 M. Bayat, M.M. Aghdam. A micromechanics based analysis of hollow fiber composites usingDQEM. Composites: Part B, 2012, 43:2921-2929.hollow
44、 fiber: a high stiffness/strength-to-weight ratio is a key advantage of composites compared to other materials.multilayered hollow-cored inclusion.本文研究由于利用广义平面微结构模型研究了应力、应变及有效弹性性质，以及冷却过程中产生的残 余应力和空心纤维与实心纤维的能量吸收，纤维方形排列。求解利用A Least-squares based differentialquadrature element method （DQEM , 一种快速、简单、准确
45、求解线性和非线性微分方程的解法）求解，结 果与ANSYS进行了对比。in which superscript C refers to the overall property of the composite.本文的特色为将不规则求解域映射成矩形域，利用 DQEM方法求解（将不规则求解域映射成矩形域， 周期边界条件和应力协调条件+位移连续条件）位移型控制方程（以位移表示的平衡方程）。由于采用方形排列，有效弹性性质可由简单的方法求出。冷却过程中的热残余应力给一个-AT即可。而能量吸收则由施加应力求位移决定。绝缘体：又称电介质，是一种阻碍电荷流动的材料，或不善于传导电流的物质称为绝缘体。 在绝缘体
46、中，价带电子被紧密的束缚在其原子周围。绝缘体和导体，没有绝对的界限。绝缘 体在某些条件下可以转化为导体。这里要注意：导电的原因：无论固体还是液体，内部如果 有能够自由移动的电子或者离子，那么他就可以导电。没有自由移动的电荷，在某些条件下， 可以产生导电粒子，那么它也可以成为导体。电介质：所有可被电极化的绝缘体为介电质，是一种可被电极化的绝缘体。假设将介电质置 入外电场，则束缚于其原子或分子的束缚电荷不会流过介电质，只会从原本位置移动微小距 离，即正电荷朝着电场方向稍微迁移位置，而负电荷朝着反方向稍微迁移位置。这会造成介 电质电极化，从而在介电质内部产生反抗电场，减弱整个介电质内部的电场。假若介电质是 由弱键结的分子构成，则这些分子不但会被电极化，也会改变取向，试着将自己的对称轴与 电场对齐。自发极化：在一定温度范围内、单位晶胞内正负电荷中心不重合，形成偶极矩，呈现极性。 这种在无外电场作用下存在的极化现象称