介电/压电/电致伸缩材料内缺陷放电及其效应研究
|
摘要
智能材料（如压电材料、电致伸缩材料等）及其器件在现代高科技领域具有广泛的应用。与传统的材料相比，智能材料具有独特的优越性。可是，在材料的生产和加工过程中不可避免的会产生各种缺陷，如孔洞、裂纹和孔隙等。当材料受到机械、电、磁、温度等多场载荷作用时，由于缺陷的存在，将引起电场集中与应力集中，导致夹杂裂纹的扩展。另一方面，当缺陷内的电场超过缺陷内的临界击穿电场时，可能导致缺陷内发生放电击穿，产生一系列的放电效应，从而致使材料产生破坏失效。
基于复变函数理论和Stroh公式，并利用Paschen定律作为临界放电击穿条件，本文研究了含孔洞和裂纹缺陷的介电材料、压电材料以及电致伸缩材料缺陷内的放电击穿问题，重点分析了缺陷内的电场、放电击穿判据和放电对缺陷的效应等。全文由七章组成，具体各章节的主要内容概括如下：
第一章介绍了介电材料、压电材料和电致伸缩材料电致失效的研究现状以及有待进一步探讨的问题。
第二章从气体放电形式、放电机理以及放电效应等方面对材料缺陷内的放电击穿做了简要的概述，并基于Paschen定律给出了含有孔隙或裂纹缺陷的介电材料、压电材料和电致伸缩材料缺陷内的临界击穿电场。
第三章主要研究了介电材料圆孔内由于放电击穿而产生的热应力问题。在分析过程中，将复杂的放电效应简化为以热效应为主，假设放电前孔洞内所存储的电能全部转化为热能并沿孔周均匀分布，最后得到由于放电释放的热量向材料四周耗散过程中而产生的孔洞放电热应力。
第四章分析了含裂纹缺陷的介电材料内的放电击穿以及放电对裂纹产生的效应。基于复势理论并采用半穿透电边界条件给出了裂纹内的电场，与临界击穿电场比较得到了裂纹内的放电击穿判据；考虑电场与放电对裂纹扩展的影响，计算了裂纹的能量释放率。
第五章研究了含椭圆孔和裂纹缺陷的压电材料内的放电击穿问题，并从理论上讨论了电场以及缺陷内放电对压电材料断裂的影响。利用Stroh公式给出了椭圆孔和裂纹内的电场，并引入临界击穿电场得到了缺陷内的放电击穿判据。同时，利用能量释放率准则分析了机械载荷、外加电场的正负以及裂纹内介质的介电常数对裂纹扩展的影响。
第六章讨论了外加机械载荷、外加电场以及环境与裂纹缺陷内的介电常数对电致伸缩材料内裂纹缺陷放电的影响以及放电产生的效应。利用半穿透电边界条件给出了电致伸缩材料裂纹内电位移的三次方程，进而得到裂纹内的电场，并与临界击穿电场比较得到了裂纹内的放电击穿判据。通过数值计算讨论了外载荷、环境与裂纹缺陷内介电常数对电致伸缩材料内裂纹扩展的影响。
最后，在第七章，对全文所做的研究工作做了总结并对未来的工作做了展望。
Smart materials (such as piezoelectric materials, electrostrictive materials) and the related deviceshave been widely used in the field of modern high technology, due to their unique advantagescompared with the traditional materals. However, a variety of defects, such as holes, cracks and pores,inevitably exist during the production and manufacturing process. Existence of those defects results inhigh electric field and stress concentration when the materials are subjected to the applied mechanical,electrical, magnetic and temperature loadings, and it may lead to crack growth. On the other hand, thepartial discharge and a series of discharge effects may be induced when the electric field inside thedefects exceeds the critical electric breakdown field, finally resulting in fracture or failure of thesematerials.
Based on the complex variable theory and combined with Stroh formalism and the critical electricbreakdown conditon in the view of Paschen law, in this paper we study the electric breakdown probemsin the dielectric materials, piezoelectric materials and electrostrictive materials containing differentdefects, respectively. The electric field inside the defects, the criteria for the occurrence of partialdischarge and the effects of discharge are analyzed, respectively. This paper consists seven chaptersand the main contents are as follows:
In the first chapter, a brief introduction to the electric induced failure problems of dielectricmaterial, piezoelectric materials and electrostrictive materials is given and the problems needed to besolved are outlined.
In the second chapter, the electric breakdown within the defects of those materials is summarizedfrom the different aspects of discharge, such as the discharge style, the discharge mechanism and thedischarge effects. And the critical condition for the dielectric materials, piezoelectric materials andelectrostrictive materials containing defects is introduced based on the law of Paschen.
In the third chapter, the thermal stress induced by partial discharge inside an air-containing cavityin an infinite dielectric material is studied. In the solution process, the complicate discharge effects aresimplified as the thermal effect, and then the thermal stress induced by the heat dissipation is calculatedunder the assumption that all the electric energy stored inside the cavity will completely be convertedto thermal energy, which is uniformly distributed along the whole surface of the cavity.
In the fourth chapter, the electric breakdown and its effects inside the crack of dielectric materialsare analyzed. According to the complex potential theory and the semi-permeable electric boundarycondition, the electric field inside the crack is derived, and then the critical condition for Townsend-type discharge is obtained. Considering the impact of the electric filed and discharge on thepropagation of the crack, the energy release rate of the crack is also given with and without theoccurrence of partial discharge.
In the fifth chapter, the electric breakdown in the piezoelectric materials containing elliptic holeand crack is studied, and the effects of discharge inside the defects on the fracture of piezoelectricmaterials are discussed. By using the Stroh formalism, the electric field and the criterion of electricbreakdown inside the elliptic hole and crack are derived. Meanwhile, based on the energy release rate,the impacts of mechanical stress and the applied positive or negative electric field on the propagation ofthe crack are investigated.
In the sixth chapter, the influences of the mechanical, electric loadings and the dielectric constantswithin the crack and the remote environment on the discharge in the electrostrictive materials arediscussed. According to the complex potential theory and the semi-permeable electric boundarycondition, the cubic equation containing the electric displacement inside the crack is first derived andthe electric field is obtained under the electric displacement and electric field relation. Then, the criticalbreakdown condition is derived. Finally, the numerical results are shown in the condition of differentenvironments under remote mechanical and electrical loadings to discuss the effects on the propagationof the crack.
Finally, in the seventh chapter, the present work is summarized and the future works on the topicare prospected.
基于复变函数理论和Stroh公式，并利用Paschen定律作为临界放电击穿条件，本文研究了含孔洞和裂纹缺陷的介电材料、压电材料以及电致伸缩材料缺陷内的放电击穿问题，重点分析了缺陷内的电场、放电击穿判据和放电对缺陷的效应等。全文由七章组成，具体各章节的主要内容概括如下：
第一章介绍了介电材料、压电材料和电致伸缩材料电致失效的研究现状以及有待进一步探讨的问题。
第二章从气体放电形式、放电机理以及放电效应等方面对材料缺陷内的放电击穿做了简要的概述，并基于Paschen定律给出了含有孔隙或裂纹缺陷的介电材料、压电材料和电致伸缩材料缺陷内的临界击穿电场。
第三章主要研究了介电材料圆孔内由于放电击穿而产生的热应力问题。在分析过程中，将复杂的放电效应简化为以热效应为主，假设放电前孔洞内所存储的电能全部转化为热能并沿孔周均匀分布，最后得到由于放电释放的热量向材料四周耗散过程中而产生的孔洞放电热应力。
第四章分析了含裂纹缺陷的介电材料内的放电击穿以及放电对裂纹产生的效应。基于复势理论并采用半穿透电边界条件给出了裂纹内的电场，与临界击穿电场比较得到了裂纹内的放电击穿判据；考虑电场与放电对裂纹扩展的影响，计算了裂纹的能量释放率。
第五章研究了含椭圆孔和裂纹缺陷的压电材料内的放电击穿问题，并从理论上讨论了电场以及缺陷内放电对压电材料断裂的影响。利用Stroh公式给出了椭圆孔和裂纹内的电场，并引入临界击穿电场得到了缺陷内的放电击穿判据。同时，利用能量释放率准则分析了机械载荷、外加电场的正负以及裂纹内介质的介电常数对裂纹扩展的影响。
第六章讨论了外加机械载荷、外加电场以及环境与裂纹缺陷内的介电常数对电致伸缩材料内裂纹缺陷放电的影响以及放电产生的效应。利用半穿透电边界条件给出了电致伸缩材料裂纹内电位移的三次方程，进而得到裂纹内的电场，并与临界击穿电场比较得到了裂纹内的放电击穿判据。通过数值计算讨论了外载荷、环境与裂纹缺陷内介电常数对电致伸缩材料内裂纹扩展的影响。
最后，在第七章，对全文所做的研究工作做了总结并对未来的工作做了展望。
Smart materials (such as piezoelectric materials, electrostrictive materials) and the related deviceshave been widely used in the field of modern high technology, due to their unique advantagescompared with the traditional materals. However, a variety of defects, such as holes, cracks and pores,inevitably exist during the production and manufacturing process. Existence of those defects results inhigh electric field and stress concentration when the materials are subjected to the applied mechanical,electrical, magnetic and temperature loadings, and it may lead to crack growth. On the other hand, thepartial discharge and a series of discharge effects may be induced when the electric field inside thedefects exceeds the critical electric breakdown field, finally resulting in fracture or failure of thesematerials.
Based on the complex variable theory and combined with Stroh formalism and the critical electricbreakdown conditon in the view of Paschen law, in this paper we study the electric breakdown probemsin the dielectric materials, piezoelectric materials and electrostrictive materials containing differentdefects, respectively. The electric field inside the defects, the criteria for the occurrence of partialdischarge and the effects of discharge are analyzed, respectively. This paper consists seven chaptersand the main contents are as follows:
In the first chapter, a brief introduction to the electric induced failure problems of dielectricmaterial, piezoelectric materials and electrostrictive materials is given and the problems needed to besolved are outlined.
In the second chapter, the electric breakdown within the defects of those materials is summarizedfrom the different aspects of discharge, such as the discharge style, the discharge mechanism and thedischarge effects. And the critical condition for the dielectric materials, piezoelectric materials andelectrostrictive materials containing defects is introduced based on the law of Paschen.
In the third chapter, the thermal stress induced by partial discharge inside an air-containing cavityin an infinite dielectric material is studied. In the solution process, the complicate discharge effects aresimplified as the thermal effect, and then the thermal stress induced by the heat dissipation is calculatedunder the assumption that all the electric energy stored inside the cavity will completely be convertedto thermal energy, which is uniformly distributed along the whole surface of the cavity.
In the fourth chapter, the electric breakdown and its effects inside the crack of dielectric materialsare analyzed. According to the complex potential theory and the semi-permeable electric boundarycondition, the electric field inside the crack is derived, and then the critical condition for Townsend-type discharge is obtained. Considering the impact of the electric filed and discharge on thepropagation of the crack, the energy release rate of the crack is also given with and without theoccurrence of partial discharge.
In the fifth chapter, the electric breakdown in the piezoelectric materials containing elliptic holeand crack is studied, and the effects of discharge inside the defects on the fracture of piezoelectricmaterials are discussed. By using the Stroh formalism, the electric field and the criterion of electricbreakdown inside the elliptic hole and crack are derived. Meanwhile, based on the energy release rate,the impacts of mechanical stress and the applied positive or negative electric field on the propagation ofthe crack are investigated.
In the sixth chapter, the influences of the mechanical, electric loadings and the dielectric constantswithin the crack and the remote environment on the discharge in the electrostrictive materials arediscussed. According to the complex potential theory and the semi-permeable electric boundarycondition, the cubic equation containing the electric displacement inside the crack is first derived andthe electric field is obtained under the electric displacement and electric field relation. Then, the criticalbreakdown condition is derived. Finally, the numerical results are shown in the condition of differentenvironments under remote mechanical and electrical loadings to discuss the effects on the propagationof the crack.
Finally, in the seventh chapter, the present work is summarized and the future works on the topicare prospected.
引文
[1]国家中长期科学和技术发展规划纲要.中华人民共和国国务院.2006年2月.
[2]宋道仁,肖鸣山编.压电效应及其应用.北京:科学普及出版社,1987.
[3] J.范兰德拉特, R.E.塞德林顿.压电陶瓷.北京:科学出版社,1981.
[4]贾菲(美).压电陶瓷,北京:科学出版社,1979:18.
[5] Mason W. E.. Piezoelectric crystals and their application to ultransonics．Von Nostrand，NewYork,1950．
[6]冯端等,材料科学导论.北京:化学工业出版社,2002．
[7]杨卫.电致失效力学.力学进展,1996,26:338-352.
[8]乔光利,宿彦京,乔利杰,褚武扬. PZT-5H导电缺口电致滞后开裂.科学通报,2006,51:1103~1104.
[9] Allen N.L., Boutlendj M., Lightfoot H.A.. Dielectric breakdown in nonuniform filed airgaps-ranges of applicability to dc voltage measurement. IEEE Transactions on ElectricalInsulation,1993,28:183-191.
[10] Bartnikas R.. Partial discharges: Their mechanism, detection and measurement. IEEETransactions on Dielectrics and Electrical Insulation,2002,9:763-808.
[11] Dissado L.A.. Predicting electrical breakdown in polymeric insulators: from deterministicmechanisms to failure statistics. IEEE Transactions on Dielectrics and Electrical Insulation,2002,9:860-875.
[12] Montanari G.C., Simoni L.. Aging phenomenology and modling. IEEE Transactions onElectrical Insulation,1993,28:755-776.
[13]王以田,郑晓泉, G Chen等.聚合物聚集态和残存应力对交联聚乙烯中电树枝的影响.电工技术学报,2004,19:44-48.
[14] Suwarno, Suzuoki Y., Komori F., et al. Partial discharges due to electrical treeing in polymers:phase-resolved and time-sequence observation and analysis. Journal of Physics D: AppliedPhysics,1996,29:2922-2931.
[15] Zheng X.Q., Chen. G.. Propagation mechanism of electrical tree in XLPE cable insulation byinvestigating a double electrical tress structure. IEEE Transactions on Dielectrics andElectrical Insulation,2008,15:800-807.
[16] Zein A.E., Talaat M., Bahy M.M.. A numerical model of electrical tree growth in solidinsulation. IEEE Transactions on Dielectrics and Electrical Insulation,2009,16:1724-1734.
[17] Suo Z., Kuo C.M., Barnett D.M., et al. Fracture mechanics for piezoelectric ceramics. Journalof the Mechanics and Physics of Solids,1992,40:739-765.
[18] Sosa H., Khutoryansky N.. New developments concerning piezoelectric materials withdefects. International Journal of Solids and Structures,1996,33:3399-3414.
[19] Fulton C.C., Gao H.. Electrical nonlinearity in fracture of piezoelectric ceramics. AppliedMechanics Review,1997,50: S56-S63.
[20] Uchino K.. Materials issues in design and performance of piezoelectric actuators: anoverview. Acta Materialia,1998,48:3745-3753.
[21]陈增涛,余寿文.压电介质损伤、断裂力学研究的现状.力学进展,1999,29:187-196.
[22] Setter N., Waser R.. Electroceramics materials. Acta Materialia,2000,48:151-178.
[23] Gabbert U., Tzou H.. Smart structures and structonic systems. In: Proceedings of IUTAM-Symposium Magdeburg2000, Dordrecht: Springer;2001.
[24] Hall D.A.. Nonlinearity in piezoelectric ceramics. Journal of Material Science,2001,36:4575-4601.
[25] Qin Q.H.. Fracture mechanics of piezoelectric materials. Southampyon: WIT Press,2001.
[26] Kamlah M.. Ferroelectric and ferroelastic piezoceramics: modeling of electromechanicalhysteresis phenomena. Continuum Mechanics and Thermodynamics,2001,13:219-268.
[27] Zhang T.Y., Zhao M.H., Tong P.. Fracture of piezoelectric ceramics. Advances in AppliedMechanics,2002,38:148-289.
[28]王保林著，压电材料及其结构的断裂力学，北京，国防工业出版社，2003.
[29] Zhang T.Y., Gao C.F.. Fracture behaviors of piezoelectric materials. Theoretical and appliedFracture Mechanics,2004,41:339-379.
[30] Yang W.. Mechanics and reliability of actuating materials. In: Proceedings of IUTAM-Symposium Beijing2004, Dordrecht: Springer;2006.
[31] Kuna M.. Fracture mechanics of piezoelectric materials-where are we right now. EngineeringFracture Mechanics,2010,77:309-326.
[32] Schneider G.A.. Influence of electrical field and mechanical stresses on the fracture offerroelectrics. Annual Review of Materials Research,2007,37:491-538.
[33] Gao C.F., Yu J.H.. Two dimensional analysis of a semi-infinite crack in piezoelectric media.Mechanics Research Communications,1998,25:695-700.
[34] Zhang T.Y., Qian C.F., Tong P.. Linear electro-elastic analysis of a cavity or a crack in apiezoelectric material. International Journal of Solids and Structures,1998,35:2121-2149.
[35] Gao C.F., Fan W.X.. An exact solution of crack problems in piezoelectric materials. AppliedMathematics and Mechanics,1999,20:51-58.
[36] Gao C.F., Wang M.Z.. Periodical cracks in piezoelectric media. Mechanics ResearchCommunications,1999,26:427-432.
[37] Zhu T., Yang W.. Crack kinking in a piezoelectric solid. International Journal of Solids andStructures,1999,36:5013-5027.
[38] Chao L.P., Huang J.H.. Fracture criteria for piezoelectric materials containing multiple cracks.Journal of Applied Physics,1999,85:6695-6703.
[39] Gao C.F., Wang M.Z.. Collinear permeable cracks between dissimilar piezoelectric Materials.International Journal of Solids and Structures,2000,37:4969-4986.
[40] Chen W.Q., Shioya T., Ding H.J.. A penny-shaped crack in piezoelectrics: resolved.International Journal of Fracture,2000,105:49-56.
[41] Sih G.C., Zuo J.Z.. Multiscale behavior of crack initiation and growth in piezoelectricceramics. Theoretical and Applied Fracture Mechanics,2000,34:123-141.
[42] Gao C.F., Wang M.Z.. General treatment of mode III interfacial crack problems inpiezoelectric materials. Archive of Applied Mechanics,2001,71:296-306.
[43] Yang F.Q.. Fracture mechanics for a Mode I crack in piezoelectric materials. InternationalJournal of Solids and Structures,2001,38:3813-3830.
[44] Soh A.K., Fang D.N., Lee K.L.. Fracture analysis of piezoelectric materials with defectsusing energy density theory. International Journal of Solids and Structures,2001,38:8331-8344.
[45] Huang Z.Y., Kuang Z.B.. A mixed electric boundary value problem for a two-dimensionalpiezoelectric crack. International Journal of Solids and Structures,2003,40:1433-1453.
[46] McMeeking R.M.. The energy release rate for a Griffith crack in a piezoelectric material.Engineering Fracture Mechanics,2004,71:1149-1163.
[47] Han J.C., Wang B.L.. Electromechanical model of periodic cracks in piezoelectric materials.Mechanics of Materials,2005,37:1180-1197.
[48] Li Q., Chen Y.H.. The coulombic traction on the surface of an interface crack indielectric/piezoelectric or metal/piezoelectric bimaterials. Acta Mechanica,2009,202:111-126.
[49] Wang B.. Three dimensional analysis of an ellipsoidal inclusion in a piezoelectric material.International Journal of Solids and Structures,1992,29:293-308.
[50] Chung M.Y., Ting T.C.T.. Piezoelectric solid with an elliptic inclusion or hole. InternationalJournal of Solids and Structures,1996,33:3343-3361.
[51] Shi W.. Rigid line inclusions under antiplane deformation and inplane electric field inpiezoelectric materials. Engineering Fracture Mechanics,1997,56:265-274.
[52] Zhong Z., Meguid S.A.. Interfacial debonding of a circular inhomogeneity inpiezoelectricmaterials. International Journal of Solids and Structures,1997,34:1965-1984.
[53] Wang X., Shen Y.P.. On double circular inclusion problem in antiplane piezoelectricity.International Journal of Solids and Structures,2001,38:4439-4461.
[54] Jiang C.P., Tong Z.H., Cheung Y.K.. A generalized self-consistent method for piezoelectricfiber reinforced composites under antiplane shear. Mechanics of Materials,2001,33:295-308.
[55] Wang X., Shen Y.P.. A solutions of the elliptic piezoelectric inclusion problem under uniformheat flux. International Journal of Solids and Structures,2001,38:2503-2516.
[56]王旭,沈亚鹏.面外剪切下各向异性三相椭圆夹杂中均匀应力.力学学报,2002,34:37-46.
[57] Gao C.F., Noda N.. Faber series method for two-dimensional problems of an arbitrarilyshaped inclusion in piezoelectric materials. Acta Mechanica,2004,171:1-13.
[58] Dai L., Guo W., She C.. Plane strain problem of piezoelectric solid with elliptic inclusion.Applied Mathematics Mechanics,2005,26:1615-1622.
[59] Yang B.H., Gao C.F., Noda N.. Interactions between N circular cylindrical inclusions in apiezoelectric matrix. Acta Mechanica,2008,197:31-42.
[60] Yang B.H., Gao C.F.. Anti-plane electro-elastic fields in an infinite matrix with Ncoated-piezoelectric inclusions. Composite Science and Technology,2009,69:2668-2674.
[61] Yang B.H., Gao C.F.. Plane problems of multiple piezoelectric inclusions in a nonpiezoelectric matrix. International Journal of Engneering Science,2010,48:518-528.
[62] Pak Y.E.. Elliptical inclusion problem in antiplane piezoelectricity: Implications for fracturemechanics. International Journal of Engineering Science,2010,48:209-222.
[63] Shang F.L., Wang Z.K., Li Z.H.. Thermal stresses analysis of a three-dimensional crack in athermopiezoelectric solid. Engineering Fracture Mechanics,1996,55:737-750.
[64] Qin Q.H., Mai Y., Yu S.. Some problems in plane thermopiezoelectric materials with holes.International Journal of Solids and Structures,1999,36:427-439.
[65] Qin Q.H.. General solutions for thermopiezoelectrics with various holes under thermalloading. International Journal of Solids and Structures,2000,37:5561-5578.
[66] Gao C.F., Wang M.Z.. A permeable interface crack between dissimilar thermopiezoelectricmedia. Acta Mechanica,2001,149:85-95.
[67] Gao C.F., Wang M.Z.. Collinear permeable cracks in thermopiezoelectric materials.Mechanics of Materials,2001,33:1-9.
[68]高存法,王敏中.热压电介质中的渗透型周期裂纹问题.力学学报,2001,33:630-637.
[69] Wang B.L., Mai Y.W.. Surface fracture of a semi-infinite piezoelectric medium undertransientthermal loading (poling axis parallel to the edge of the medium). Mechanics of Materials,2004,36:215-223.
[70] Dai H.L., Wang X.. Thermo-electro-elastic transient responses in piezoelectric hollowstructures. International Journal of Solids and Structures,2005,42:1151–1171.
[71] Chen F.M., Shen M.H., Chen S.N.. An exact thermopiezoelasticity solution for a three-phasecomposite cylinder. International Journal of Engineering Science,2006,44:1482-1497.
[72] Gao C.F., Fan W.X.. Green's functions for the plane problem in a half-infinite piezoelectricmedium. Mechanics Research Communications,1998,25:69-74.
[73] Gao C.F., Fan W.X.. Green's functions for generalized2D problems in piezoelectric mediawith an elliptical hole. Mechanics Research Communications,1998,25:685-693.
[74] Lu P., Williams F.W.. Green's functions of piezoelectric material with an elliptic hole orinclusion. International Journal of Solids and Structures,1998,35:651-664.
[75] Qin Q.H.. Thermoelectroelastic Green's function for a piezoelectric plate containing anelliptic hole. Mechanics of Materials,1998,30:21-29.
[76] Qin Q.H.. Thermoelectroelastic Green's function for thermal load inside or on the boundaryof an elliptic inclusion. Mechanics of Materials,1999,31:611-626.
[77] Lu P., Tan M.J., Liew K.M.. A further investigation of Green's functions for apiezoelectricmaterial with a cavity or a crack. International Journal of Solids and Structures,2000,37:1065-1078.
[78]王旭,沈亚鹏.平面弹性中双圆柱夹杂问题的格林函数.力学学报,2001,33:639-654.
[79] Gao C.F., Wang M.Z.. Green's function of an interfacial crack between two dissimilarpiezoelectric media. International Journal of Solids and Structures,2001,38:5323-5334.
[80] Ding H.J., Chen W.Q., Jiang A.M.. Green's functions and boundary element method fortransversely isotropic piezoelectric materials. Engineering Analysis with Boundary Elements,2004,28:975-987.
[81] Chen B.J., Liew K.M., Xiao Z.M.. Green's functions for anti-plane problems inpiezoelectricmedia with a finite crack. International Journal of Solids and Structures,2004,41:5285-5300.
[82] Khutoryansky N.M., Sosa H.. Dynamic representation formulas and fundamental solutionsfor piezoelectricity. International Journal of Solids and Structures,1995,32:3307-3325.
[83] Wang B.L., Han J.C., Du S.Y.. Dynamic response for non-homogeneous piezoelectricmedium with multiple cracks. Engineering Fracture Mechanics,1998,61:607-617.
[84] Wang B.L., Han J.C., Du S.Y.. Electroelastic fracture dynamics for multilayered piezoelectricmaterials under dynamic anti-plane shearing. International Journal of Solids and Structures,2000,37:5219-5231.
[85] Shen S.P., Kuang Z.B., Nishioka T.. Wave scattering from an interface crack in multilayeredpiezoelectric plate. European Journal of Mechanics A/Solids,2000,19:547-559.
[86] Gao C.F., Zhao Y.T., Wang M.Z.. Moving antiplane crack between two dissimilarpiezoelectric media. International Journal of Solids and Structures,2001,38:9331-9345.
[87] Wang X., Zhong Z., Wu F.L.. A moving conducting crack at the interface of two dissimilarpiezoelectric materials. International Journal of Solids and Structures,2003,40:2381-2399.
[88] Dai H.L., Wang X.. Dynamic responses of piezoelectric hollow cylinders in an axial magneticfield. International Journal of Solids and Structures,2004,41:5231-5246.
[89] Zhou Z.G., Sun Y.G., Wang B.. Investigation of the dynamic behavior of a Griffith crack in apiezoelectric material strip subjected to the harmonic elastic anti-plane shear waves by use ofthe non-local theory. Meccanica,2004,39:63-76.
[90] Wang X., Dong K., Wang X.Y.. Hygrothermal effect on dynamic interlaminar stresses inlaminated plates with piezoelectric actuators. Composite Structures,2005,71:220-228.
[91]王旭,王子昆.压电材料反平面应变状态的椭圆夹杂及界面裂纹问题.上海力学,1993,14:26-33.
[92] Gong S.X., Meguid S.A.. On the debonding of an elastic elliptical inhomogeneity underantiplane shear. International Journal of Fracture,1994,67,37-52.
[93] Gao C.F., Fan W.X.. An interface inclusion between two dissimilar piezoelectric materials.Applied Mathematics and Mechanics,2001,2:96-104.
[94] Xiao Z.M., Yan J., Chen B.J.. Electroelastic analysis for a Griffith crack interacting with acoated inclusion in piezoelectric solid. International Journal of Engineering Science,2005,43:639-654.
[95] Deeg W.F.. The analysis of dislocation, crack and inclusion problems in piezoelectric solids.Ph.D. Thesis, Stanford University, CA,1980.
[96] Pak Y.E.. Crack extension force in a piezoelectric material. Journal of Applied Mechanics,1990,57:647-653.
[97] Stroh A.N.. Dislocations and crack in anisotropic elasticity. Philosophical Magazine,1958,3:625-646.
[98] Sosa H.A.. On the fracture mechanics of piezoelectric materials. International Journal ofSolids and Structures,1992,29:2613-2622.
[99] Sosa H.A.. Plane problems in piezoelectric media with defects. International Journal ofSolids and Structures,1991,28:491-505.
[100] Ru C.Q.. Electric-field induced crack closure in linear piezoelectric media. ActaMaterialia,1999,47:4683-4693.
[101] Shen S., Nishoka T.. Fracture of piezoelectric materials energy density criterion. TheoreticalApplied Fracture Mechanics,2000,33:57-65.
[102] Park S., Sun C.T.. Fracture criteria for piezoelectric materials. Journal of American CeramicSociety,1995,78:1475-1480.
[103] Parton V.Z.. Fracture mechanics of piezoelectric materials. Acta Astronautica,1976,3:671-683.
[104] Dunn M.L.. The effects of crack face boundary conditions on the fracture mechanics.Engineering Fracture Mechanics,1994,48:25-39.
[105] Wang T.C., Han X.L.. Fracture mechanics of piezoelectric materials. International Journal ofFracture,1999,98:15-35.
[106] Gao C.F., Fan W.X.. Exact solutions for the plane problem in piezoelectric materials with anelliptic or a crack. International Journal of Solids and Structures,1999,36:2527-2540.
[107] Gao C.F., Fan W.X.. A general solution for the plane problem in piezoelectric media withcollinear cracks. International Journal of Engineering Science,1999,37:347-363.
[108] McMeeking R.M.. On mechanical stresses at cracks in dielectrics with application todielectric breakdown. Journal of Applied Physics,1987,62:3116-3122.
[109] Suo Z.. Models for breakdown-resistant dielectric and ferroelectric ceramics. Journal of theMechanics and Physics of Solids,1993,41:1155-1176.
[110] Ru C.Q., Mao X., Epstein M.. Electric-field induced interfacial cracking in multilayerelectrostrictive actuators. Journal of the Mechanics and Physics of Solids,1998,46:1301-1318.
[111] Heyer V., Schneider G.A., Balke H., et al. A fracture criterion for conducting cracks inhomogeneously poled piezoelectric PZT-PIC151ceramics. Acta Materialia,1998,46:6615-6622.
[112] Hao T.H., Shen Z.Y.. A new electric boundary condition of electric fracture mechanics andits applications. Engineering Fracture Mechanics,1994,47:793-802.
[113] McMeeking R.M.. Crack tip energy release rate for a piezoelectric compact tensionspecimen. Engineering Fracture Mechanics,1999,64:217-244..
[114] Crichton G.C., Karlsson P.W., Pedersen A.. Partial discharges in ellipsoidal and spheroidalvoids. IEEE Transactions on Dielectrics and Electrical Insulation,1989,24:335-342.
[115] Niemeyer L.. A generalized approach to partial discharge modeling. IEEE Transactions onDielectrics and Electrical Insulation,1995,2:510-528.
[116] Gutfleisch F., Niemeyer L.. Measurement and simulation of PD in epoxy voids. IEEETransactions on Dielectrics and Electrical Insulation,1995,2:729–743.
[117] Gao C.F.. Influence of mechanical stresses on partial discharge in a piezoelectric solidcontaining cavities. Engineering Fracture Mechanics,2008,75:4920-4924.
[118] Fu R., Qian C.F., Zhang T.Y.. Electrical fracture toughness for conductive cracks driven byelectric fields in piezoelectric materials. Applied Physics Letters,2000,76:126-128.
[119] Wang T.H., Zhang T.Y.. Electrical fracture toughness for electrically conductive deepnotches driven by electric field in depoled lead zirconate titanate ceramics. Applied PhysicsLetters,2001,79:4198-4200.
[120] Beom H.G., Jeong K.M., Park J.Y. et al. Electrical failure of piezoelectric ceramics with aconductive crack under electric fields. Engineering Fracture Mechanics,2009,76:2399-2407.
[121] Lin S., Beom H.G., Tao D.. Tubular channel growth in piezoelectric materials under electricfields. Acta Mechanica,2010,210:47-55.
[122] Zhang T.Y., Zhao M.H., Gao C.F.. The strip dielectric breakdown model. InternationalJournal of Fracture,2005,132:311-327.
[123] Dugdale D.S.. Yielding of steel sheets containing slits. Journal of the Mechanics and Physicsof Solids,1960,8:100-104.
[124] Gao C.F., Noda N., Zhang T.Y.. Dielectric breakdown model for a conductive crack andelectrode in piezoelectric materials. International Journal of Engineering Science,2006,44:256-272.
[125] Gao H.J., Zhang T.Y., Tong, P.. Local and global energy release rates for an electrically yieldcrack in a piezoelectric ceramic. Journal of the Mechanics and Physics of Solids,1997,45:491-510.
[126] Ru C.Q.. Effect of electric polarization saturation on stress intensity factors in apiezoelectric ceramics. International Journal of Solids and Structures,1999,36:869-883.
[127] Wang T.C.. Analysis of strip electric saturation model of crack problem in piezoelectricmaterials. International Journal of Solids and Structures.2000,37:6031-6049.
[128] Shen S., Nishioka T., Kuang Z.B., et al. Nonlinear electromechanical interfacial fracture forpiezoelectric materials. Mechanics of Materials,2000,32:57-64.
[129] Zhu T., Yang W.. Toughness variation of ferroelectrics by polarization switch undernon-uniform electric field. Acta Materialia,1997,45:4695-4702.
[130] Yang W., Zhu T.. Switch toughening of ferroelectrics subjected to electric fields. Journal ofthe Mechanics and Physics of Solids,1998,46:291-311.
[131] Wang B.L., Zhang X.H.. An electrical field based non-linear model in the fracture ofpiezoelectric ceramics. International Journal of Solids and Structures,2004,41:4337-4347.
[132] Wang B.L., Zhang X.H.. Fracture prediction for piezoelectric ceramics based on the electricfield saturation concept. Mechanics Research Communications,2005,32:411-419.
[133] Stratton J. A.. Electromagnetic Theory. McGraw-Hill, New York,1941．
[134] Landau L. D., Lifshitz E.M.. Electodynamics of Continous Media．Pergamon Press, Oxford,1960．
[135] Pao Y.H.. Eelectromagnetic force in deformable continua. Nemat-Nasser, Mechanics Today,Printed in Great Britain by Pitman. Bath,1978.
[136]匡震邦.非线性连续介质力学.上海:上海交通大学出版,2002.
[137] Yang W., Suo Z.. Cracking in ceramic actuators caused by electrostriction. Journal of theMechanics and Physics of Solids,1994,42:649-663.
[138] Knops R.J. Two-dimensional eletrostriction. Quarterly Journal of Mechanics and AppliedMathematics,1963,16:377-388.
[139] McMeeking R.M.. Electrostrictive stresses near crack-like flaws. Journal of AppliedMathematics and Physics (ZAMP),1989,40:615-627.
[140] Smith T.E., Warren W.E.. Some problems in two-dimesional electrostriction. Journal ofMathematical Physics,1966,45:45-51,1968(corrigenda)47:109-110.
[141]蒋泉.电致伸缩材料中二维问题的应力分析[博士论文].上海:上海交通大学,2005.
[142] Hao T.H., Gong X., Suo Z.. Fracture mechanics for the design of ceramic multilayeractuators. Journal of the Mechanics and Physics of Solids,1996,44:23-48.
[143] Beom H.G., Kim Y.H., Cho C., et al. Asymptotic analysis of an impermeable crack in anelectrostrictive material subjected to electric loading. International Journal of Solids andStructure,2006,43:6869-6886.
[144] Beom H.G., Kim Y.H., Cho C., et al. A crack with an electric displacement saturation zone inan electrostrictive material. Archive of Applied Mechanics,2006,76:19-31.
[145] Gao C.F., Mai Y.W., Zhang N.. Solution of a crack in an electrostrictive solid. InternationalJournal of Solids and Structures,2010,47:444-453.
[146] Gao C.F., Mai Y.W.. Fracture of electrostrictive solids subjected to combined mechanicaland electric loads. Engineering Fracture Mechanics,2010,77:1503-1515.
[147] Gao C.F., Mai Y.W., Zhang N.. Solution of collinear cracks in an electrostrictive solid.Philosophical Magazine,2010,90:1245-1262.
[148] Muskhelishvili N.I.. Some Basic Problems of the Mathematical Theory of Elasticity.Groningeng: Noordhoof,1963.
[149]杨津基.气体放电.北京:学出版社,1983.
[150]屠志健,张一尘.电气绝缘与过电压.北京:中国电力出版社,2005.
[151]高树香,陈宗柱.气体导电.南京:南京工学院出版社,1988.
[152] Bartinikas R.. Corna Measurement and Interpretation. Wilmington: ASTM Special TechnicalPublication,1984.
[153]王强,彭光辉,王小波.电晕对绝缘性能危害的探讨.机电元件,2005,25:19-20.
[154]刘尚合,武占成.静电放电及其危害防护.北京:北京邮电大学出版社,2004.66-68.
[155] Zeller H.R.. Breakdown and prebreakdown phenomena in solid dielectrics. IEEETransactions on Electrical Insulation,1987,22:115-122.
[156] Zhu H.S., Ding H.Z.. Recent advances in dielectric breakdown theory of solid insulators.Progress in Natural Science,1998,8:257-268.
[157] Salama M.M.A., Rizk M.S., Hackam R.. Electrical stress and inception voltage ofdischarges in gaseous cavities in an anisotropic dielectric material. Journal of AppliedPhysics,1986,60:2600-2608.
[158] Danikas M.G., Karafyllidis I., Thanailakis A., et al. Simulation of electrical tree growth insolid dielectrics containing voids of arbitrary shape. Modelling and Simulation in MaterialsScience and Engineering,1996,4:535-552.
[159] Vardakis G.E., Danikas M.G.. Simulation of tree propagation in polyethylene including airvoid by using cellular automata: The effect of space charges. Electrical Engineering,2002,84:211-216.
[160] Vardakis G.E., Danikas M.G... Simulation of electrical tree propagation using cellularautomata: the case of conducting particle included in a dielectric in point-plane electrodearrangement. Journal of Electrostatics,2005,63:129-142.
[161]徐芝纶.弹性力学.北京:高等教育出版社,1990.
[162]竹内洋一郎.热应力.北京:科学出版社,1977.
[163]杭斌.长输低温乙烯管道保冷设计浅析.保温材料与节能技术,1998,3:10-16.
[164]杜则裕,刘继元,张世林,等.工程材料简明手册.北京:电子工业出版社,1996.
[165] David E., Parpal J.L., Crine J.P.. Influence of internal mechanical stress and strain onelectrical performance of polyethylene. IEEE Transactions on Dielectrics and ElectricalInsulation,1996,3:248-257
[166] Wu K., Suzuoki Y., Mizutani T., et al. Model for partial discharges associated with treeingbreakdown: I. PDs in tree channels. Journal of Physics D: Applied Physics,2000,33：1197-1201.
[167] Wu K., Suzuoki Y., Mizutani T., et al. Model for partial discharges associated with treeingbreakdown: II. Tree growth affected by PDs. Journal of Physics D: Applied Physics,2000,33：1202-1208.
[168] Wu K., Suzuoki Y., Mizutani T., et al. Model for partial discharges associated with treeingbreakdown: III. PD extinction and re-growth of tree. Journal of Physics D: Applied Physics,2000,33：1209-1218.
[169]郑晓泉, Chen G..机械应力与电压频率对XLPE电缆电树的影响.高电压技术,2003,29:6-8.
[170] Dissado L.A.. Understanding electrical trees in solids: From experiment to theory. IEEETransactions on Dielectrics and Electrical Insulation,2002,9:483-497.
[171] Ding H.Z., Varlow B.R.. Thermodynamic model for electrical tree propagation kinetics incombined electrical and mechanical stresses. IEEE Transactions on Dielectrics andElectrical Insulation,2005,12:81-89.
[172]郑飞虎,张治文,肖春.应力对诱发空间电荷击穿的作用.电工技术学报,2006,21:31-34.
[173] McMeeking R.M.. Towards a fracture mechanics for brittle piezoelectric and dielectricmaterials. International Journal of Fracture,2001,108:25-41.
[174] Landis C. M.. Energetically consistent boundary conditions for electromechanical fracture.Internatiaonal Journal of Solids and Structure,2004,41:6291-6315.
[175] Gao C.F., Zhao M.H., Tong, P., et al. The energy release rate and the J-integral of anelectrically insulated crack in a piezoelectric material. International Journal of EngineeringScience,2004,42:2175-2192.
[176] Eshelby J. D.. The determination and the elastic field of an ellipsoidal inclusion and relatedproblems. Proceedings of the Royal Society London A,1957,241:376-396.
[177] Pedersen A., Crichton G.C., McAllister I.W.. The functional relation between partialdischarges and induced charge. IEEE Transactions on Dielectrics and Electrical Insulation,1995,2:535–543
[178] Kummar S., Singh R.N.. Effect of the mechanical boundary condition at the crack surfaceson the stress distribution at the crack tip in piezoelectric materials. Materials Science andEngineering,1998, A252:64-77.
[179] Fu R., Zhang T.Y.. Effects of an applied electric field on the modulus of rupture of poledlead Zirconate Titanate Ceramics. Journal of American Ceramic Society,1998,81:1058-1060.
[180] Fu R., Zhang T.Y.. Effects of an electric field on the fracture toughness of poled leadZirconate Titanate Ceramics. Journal of American Ceramic Society,2000,83:1215-1218.
[181] Gao C.F.. Further study on the generalized2D problem of an elliptical hole or a crack inpiezoelectric media. Mechanics Research Communications,2000,27:429-434.
[182] Winzer S.R., Shankar N.A., Ritter P.. Designing cofired multilayer electrostrictive actuaorsfor reliability. Journal of the American Ceramic Society,1989,72:2246-2257.
[183] Jiang Q., Kuang Z.B.. Stress analysis in two dimensional electrostrictive material with anelliptic rigid conductor. European Journal of Mechanics A/Solids,2004,23:945-956.
[2]宋道仁,肖鸣山编.压电效应及其应用.北京:科学普及出版社,1987.
[3] J.范兰德拉特, R.E.塞德林顿.压电陶瓷.北京:科学出版社,1981.
[4]贾菲(美).压电陶瓷,北京:科学出版社,1979:18.
[5] Mason W. E.. Piezoelectric crystals and their application to ultransonics．Von Nostrand，NewYork,1950．
[6]冯端等,材料科学导论.北京:化学工业出版社,2002．
[7]杨卫.电致失效力学.力学进展,1996,26:338-352.
[8]乔光利,宿彦京,乔利杰,褚武扬. PZT-5H导电缺口电致滞后开裂.科学通报,2006,51:1103~1104.
[9] Allen N.L., Boutlendj M., Lightfoot H.A.. Dielectric breakdown in nonuniform filed airgaps-ranges of applicability to dc voltage measurement. IEEE Transactions on ElectricalInsulation,1993,28:183-191.
[10] Bartnikas R.. Partial discharges: Their mechanism, detection and measurement. IEEETransactions on Dielectrics and Electrical Insulation,2002,9:763-808.
[11] Dissado L.A.. Predicting electrical breakdown in polymeric insulators: from deterministicmechanisms to failure statistics. IEEE Transactions on Dielectrics and Electrical Insulation,2002,9:860-875.
[12] Montanari G.C., Simoni L.. Aging phenomenology and modling. IEEE Transactions onElectrical Insulation,1993,28:755-776.
[13]王以田,郑晓泉, G Chen等.聚合物聚集态和残存应力对交联聚乙烯中电树枝的影响.电工技术学报,2004,19:44-48.
[14] Suwarno, Suzuoki Y., Komori F., et al. Partial discharges due to electrical treeing in polymers:phase-resolved and time-sequence observation and analysis. Journal of Physics D: AppliedPhysics,1996,29:2922-2931.
[15] Zheng X.Q., Chen. G.. Propagation mechanism of electrical tree in XLPE cable insulation byinvestigating a double electrical tress structure. IEEE Transactions on Dielectrics andElectrical Insulation,2008,15:800-807.
[16] Zein A.E., Talaat M., Bahy M.M.. A numerical model of electrical tree growth in solidinsulation. IEEE Transactions on Dielectrics and Electrical Insulation,2009,16:1724-1734.
[17] Suo Z., Kuo C.M., Barnett D.M., et al. Fracture mechanics for piezoelectric ceramics. Journalof the Mechanics and Physics of Solids,1992,40:739-765.
[18] Sosa H., Khutoryansky N.. New developments concerning piezoelectric materials withdefects. International Journal of Solids and Structures,1996,33:3399-3414.
[19] Fulton C.C., Gao H.. Electrical nonlinearity in fracture of piezoelectric ceramics. AppliedMechanics Review,1997,50: S56-S63.
[20] Uchino K.. Materials issues in design and performance of piezoelectric actuators: anoverview. Acta Materialia,1998,48:3745-3753.
[21]陈增涛,余寿文.压电介质损伤、断裂力学研究的现状.力学进展,1999,29:187-196.
[22] Setter N., Waser R.. Electroceramics materials. Acta Materialia,2000,48:151-178.
[23] Gabbert U., Tzou H.. Smart structures and structonic systems. In: Proceedings of IUTAM-Symposium Magdeburg2000, Dordrecht: Springer;2001.
[24] Hall D.A.. Nonlinearity in piezoelectric ceramics. Journal of Material Science,2001,36:4575-4601.
[25] Qin Q.H.. Fracture mechanics of piezoelectric materials. Southampyon: WIT Press,2001.
[26] Kamlah M.. Ferroelectric and ferroelastic piezoceramics: modeling of electromechanicalhysteresis phenomena. Continuum Mechanics and Thermodynamics,2001,13:219-268.
[27] Zhang T.Y., Zhao M.H., Tong P.. Fracture of piezoelectric ceramics. Advances in AppliedMechanics,2002,38:148-289.
[28]王保林著，压电材料及其结构的断裂力学，北京，国防工业出版社，2003.
[29] Zhang T.Y., Gao C.F.. Fracture behaviors of piezoelectric materials. Theoretical and appliedFracture Mechanics,2004,41:339-379.
[30] Yang W.. Mechanics and reliability of actuating materials. In: Proceedings of IUTAM-Symposium Beijing2004, Dordrecht: Springer;2006.
[31] Kuna M.. Fracture mechanics of piezoelectric materials-where are we right now. EngineeringFracture Mechanics,2010,77:309-326.
[32] Schneider G.A.. Influence of electrical field and mechanical stresses on the fracture offerroelectrics. Annual Review of Materials Research,2007,37:491-538.
[33] Gao C.F., Yu J.H.. Two dimensional analysis of a semi-infinite crack in piezoelectric media.Mechanics Research Communications,1998,25:695-700.
[34] Zhang T.Y., Qian C.F., Tong P.. Linear electro-elastic analysis of a cavity or a crack in apiezoelectric material. International Journal of Solids and Structures,1998,35:2121-2149.
[35] Gao C.F., Fan W.X.. An exact solution of crack problems in piezoelectric materials. AppliedMathematics and Mechanics,1999,20:51-58.
[36] Gao C.F., Wang M.Z.. Periodical cracks in piezoelectric media. Mechanics ResearchCommunications,1999,26:427-432.
[37] Zhu T., Yang W.. Crack kinking in a piezoelectric solid. International Journal of Solids andStructures,1999,36:5013-5027.
[38] Chao L.P., Huang J.H.. Fracture criteria for piezoelectric materials containing multiple cracks.Journal of Applied Physics,1999,85:6695-6703.
[39] Gao C.F., Wang M.Z.. Collinear permeable cracks between dissimilar piezoelectric Materials.International Journal of Solids and Structures,2000,37:4969-4986.
[40] Chen W.Q., Shioya T., Ding H.J.. A penny-shaped crack in piezoelectrics: resolved.International Journal of Fracture,2000,105:49-56.
[41] Sih G.C., Zuo J.Z.. Multiscale behavior of crack initiation and growth in piezoelectricceramics. Theoretical and Applied Fracture Mechanics,2000,34:123-141.
[42] Gao C.F., Wang M.Z.. General treatment of mode III interfacial crack problems inpiezoelectric materials. Archive of Applied Mechanics,2001,71:296-306.
[43] Yang F.Q.. Fracture mechanics for a Mode I crack in piezoelectric materials. InternationalJournal of Solids and Structures,2001,38:3813-3830.
[44] Soh A.K., Fang D.N., Lee K.L.. Fracture analysis of piezoelectric materials with defectsusing energy density theory. International Journal of Solids and Structures,2001,38:8331-8344.
[45] Huang Z.Y., Kuang Z.B.. A mixed electric boundary value problem for a two-dimensionalpiezoelectric crack. International Journal of Solids and Structures,2003,40:1433-1453.
[46] McMeeking R.M.. The energy release rate for a Griffith crack in a piezoelectric material.Engineering Fracture Mechanics,2004,71:1149-1163.
[47] Han J.C., Wang B.L.. Electromechanical model of periodic cracks in piezoelectric materials.Mechanics of Materials,2005,37:1180-1197.
[48] Li Q., Chen Y.H.. The coulombic traction on the surface of an interface crack indielectric/piezoelectric or metal/piezoelectric bimaterials. Acta Mechanica,2009,202:111-126.
[49] Wang B.. Three dimensional analysis of an ellipsoidal inclusion in a piezoelectric material.International Journal of Solids and Structures,1992,29:293-308.
[50] Chung M.Y., Ting T.C.T.. Piezoelectric solid with an elliptic inclusion or hole. InternationalJournal of Solids and Structures,1996,33:3343-3361.
[51] Shi W.. Rigid line inclusions under antiplane deformation and inplane electric field inpiezoelectric materials. Engineering Fracture Mechanics,1997,56:265-274.
[52] Zhong Z., Meguid S.A.. Interfacial debonding of a circular inhomogeneity inpiezoelectricmaterials. International Journal of Solids and Structures,1997,34:1965-1984.
[53] Wang X., Shen Y.P.. On double circular inclusion problem in antiplane piezoelectricity.International Journal of Solids and Structures,2001,38:4439-4461.
[54] Jiang C.P., Tong Z.H., Cheung Y.K.. A generalized self-consistent method for piezoelectricfiber reinforced composites under antiplane shear. Mechanics of Materials,2001,33:295-308.
[55] Wang X., Shen Y.P.. A solutions of the elliptic piezoelectric inclusion problem under uniformheat flux. International Journal of Solids and Structures,2001,38:2503-2516.
[56]王旭,沈亚鹏.面外剪切下各向异性三相椭圆夹杂中均匀应力.力学学报,2002,34:37-46.
[57] Gao C.F., Noda N.. Faber series method for two-dimensional problems of an arbitrarilyshaped inclusion in piezoelectric materials. Acta Mechanica,2004,171:1-13.
[58] Dai L., Guo W., She C.. Plane strain problem of piezoelectric solid with elliptic inclusion.Applied Mathematics Mechanics,2005,26:1615-1622.
[59] Yang B.H., Gao C.F., Noda N.. Interactions between N circular cylindrical inclusions in apiezoelectric matrix. Acta Mechanica,2008,197:31-42.
[60] Yang B.H., Gao C.F.. Anti-plane electro-elastic fields in an infinite matrix with Ncoated-piezoelectric inclusions. Composite Science and Technology,2009,69:2668-2674.
[61] Yang B.H., Gao C.F.. Plane problems of multiple piezoelectric inclusions in a nonpiezoelectric matrix. International Journal of Engneering Science,2010,48:518-528.
[62] Pak Y.E.. Elliptical inclusion problem in antiplane piezoelectricity: Implications for fracturemechanics. International Journal of Engineering Science,2010,48:209-222.
[63] Shang F.L., Wang Z.K., Li Z.H.. Thermal stresses analysis of a three-dimensional crack in athermopiezoelectric solid. Engineering Fracture Mechanics,1996,55:737-750.
[64] Qin Q.H., Mai Y., Yu S.. Some problems in plane thermopiezoelectric materials with holes.International Journal of Solids and Structures,1999,36:427-439.
[65] Qin Q.H.. General solutions for thermopiezoelectrics with various holes under thermalloading. International Journal of Solids and Structures,2000,37:5561-5578.
[66] Gao C.F., Wang M.Z.. A permeable interface crack between dissimilar thermopiezoelectricmedia. Acta Mechanica,2001,149:85-95.
[67] Gao C.F., Wang M.Z.. Collinear permeable cracks in thermopiezoelectric materials.Mechanics of Materials,2001,33:1-9.
[68]高存法,王敏中.热压电介质中的渗透型周期裂纹问题.力学学报,2001,33:630-637.
[69] Wang B.L., Mai Y.W.. Surface fracture of a semi-infinite piezoelectric medium undertransientthermal loading (poling axis parallel to the edge of the medium). Mechanics of Materials,2004,36:215-223.
[70] Dai H.L., Wang X.. Thermo-electro-elastic transient responses in piezoelectric hollowstructures. International Journal of Solids and Structures,2005,42:1151–1171.
[71] Chen F.M., Shen M.H., Chen S.N.. An exact thermopiezoelasticity solution for a three-phasecomposite cylinder. International Journal of Engineering Science,2006,44:1482-1497.
[72] Gao C.F., Fan W.X.. Green's functions for the plane problem in a half-infinite piezoelectricmedium. Mechanics Research Communications,1998,25:69-74.
[73] Gao C.F., Fan W.X.. Green's functions for generalized2D problems in piezoelectric mediawith an elliptical hole. Mechanics Research Communications,1998,25:685-693.
[74] Lu P., Williams F.W.. Green's functions of piezoelectric material with an elliptic hole orinclusion. International Journal of Solids and Structures,1998,35:651-664.
[75] Qin Q.H.. Thermoelectroelastic Green's function for a piezoelectric plate containing anelliptic hole. Mechanics of Materials,1998,30:21-29.
[76] Qin Q.H.. Thermoelectroelastic Green's function for thermal load inside or on the boundaryof an elliptic inclusion. Mechanics of Materials,1999,31:611-626.
[77] Lu P., Tan M.J., Liew K.M.. A further investigation of Green's functions for apiezoelectricmaterial with a cavity or a crack. International Journal of Solids and Structures,2000,37:1065-1078.
[78]王旭,沈亚鹏.平面弹性中双圆柱夹杂问题的格林函数.力学学报,2001,33:639-654.
[79] Gao C.F., Wang M.Z.. Green's function of an interfacial crack between two dissimilarpiezoelectric media. International Journal of Solids and Structures,2001,38:5323-5334.
[80] Ding H.J., Chen W.Q., Jiang A.M.. Green's functions and boundary element method fortransversely isotropic piezoelectric materials. Engineering Analysis with Boundary Elements,2004,28:975-987.
[81] Chen B.J., Liew K.M., Xiao Z.M.. Green's functions for anti-plane problems inpiezoelectricmedia with a finite crack. International Journal of Solids and Structures,2004,41:5285-5300.
[82] Khutoryansky N.M., Sosa H.. Dynamic representation formulas and fundamental solutionsfor piezoelectricity. International Journal of Solids and Structures,1995,32:3307-3325.
[83] Wang B.L., Han J.C., Du S.Y.. Dynamic response for non-homogeneous piezoelectricmedium with multiple cracks. Engineering Fracture Mechanics,1998,61:607-617.
[84] Wang B.L., Han J.C., Du S.Y.. Electroelastic fracture dynamics for multilayered piezoelectricmaterials under dynamic anti-plane shearing. International Journal of Solids and Structures,2000,37:5219-5231.
[85] Shen S.P., Kuang Z.B., Nishioka T.. Wave scattering from an interface crack in multilayeredpiezoelectric plate. European Journal of Mechanics A/Solids,2000,19:547-559.
[86] Gao C.F., Zhao Y.T., Wang M.Z.. Moving antiplane crack between two dissimilarpiezoelectric media. International Journal of Solids and Structures,2001,38:9331-9345.
[87] Wang X., Zhong Z., Wu F.L.. A moving conducting crack at the interface of two dissimilarpiezoelectric materials. International Journal of Solids and Structures,2003,40:2381-2399.
[88] Dai H.L., Wang X.. Dynamic responses of piezoelectric hollow cylinders in an axial magneticfield. International Journal of Solids and Structures,2004,41:5231-5246.
[89] Zhou Z.G., Sun Y.G., Wang B.. Investigation of the dynamic behavior of a Griffith crack in apiezoelectric material strip subjected to the harmonic elastic anti-plane shear waves by use ofthe non-local theory. Meccanica,2004,39:63-76.
[90] Wang X., Dong K., Wang X.Y.. Hygrothermal effect on dynamic interlaminar stresses inlaminated plates with piezoelectric actuators. Composite Structures,2005,71:220-228.
[91]王旭,王子昆.压电材料反平面应变状态的椭圆夹杂及界面裂纹问题.上海力学,1993,14:26-33.
[92] Gong S.X., Meguid S.A.. On the debonding of an elastic elliptical inhomogeneity underantiplane shear. International Journal of Fracture,1994,67,37-52.
[93] Gao C.F., Fan W.X.. An interface inclusion between two dissimilar piezoelectric materials.Applied Mathematics and Mechanics,2001,2:96-104.
[94] Xiao Z.M., Yan J., Chen B.J.. Electroelastic analysis for a Griffith crack interacting with acoated inclusion in piezoelectric solid. International Journal of Engineering Science,2005,43:639-654.
[95] Deeg W.F.. The analysis of dislocation, crack and inclusion problems in piezoelectric solids.Ph.D. Thesis, Stanford University, CA,1980.
[96] Pak Y.E.. Crack extension force in a piezoelectric material. Journal of Applied Mechanics,1990,57:647-653.
[97] Stroh A.N.. Dislocations and crack in anisotropic elasticity. Philosophical Magazine,1958,3:625-646.
[98] Sosa H.A.. On the fracture mechanics of piezoelectric materials. International Journal ofSolids and Structures,1992,29:2613-2622.
[99] Sosa H.A.. Plane problems in piezoelectric media with defects. International Journal ofSolids and Structures,1991,28:491-505.
[100] Ru C.Q.. Electric-field induced crack closure in linear piezoelectric media. ActaMaterialia,1999,47:4683-4693.
[101] Shen S., Nishoka T.. Fracture of piezoelectric materials energy density criterion. TheoreticalApplied Fracture Mechanics,2000,33:57-65.
[102] Park S., Sun C.T.. Fracture criteria for piezoelectric materials. Journal of American CeramicSociety,1995,78:1475-1480.
[103] Parton V.Z.. Fracture mechanics of piezoelectric materials. Acta Astronautica,1976,3:671-683.
[104] Dunn M.L.. The effects of crack face boundary conditions on the fracture mechanics.Engineering Fracture Mechanics,1994,48:25-39.
[105] Wang T.C., Han X.L.. Fracture mechanics of piezoelectric materials. International Journal ofFracture,1999,98:15-35.
[106] Gao C.F., Fan W.X.. Exact solutions for the plane problem in piezoelectric materials with anelliptic or a crack. International Journal of Solids and Structures,1999,36:2527-2540.
[107] Gao C.F., Fan W.X.. A general solution for the plane problem in piezoelectric media withcollinear cracks. International Journal of Engineering Science,1999,37:347-363.
[108] McMeeking R.M.. On mechanical stresses at cracks in dielectrics with application todielectric breakdown. Journal of Applied Physics,1987,62:3116-3122.
[109] Suo Z.. Models for breakdown-resistant dielectric and ferroelectric ceramics. Journal of theMechanics and Physics of Solids,1993,41:1155-1176.
[110] Ru C.Q., Mao X., Epstein M.. Electric-field induced interfacial cracking in multilayerelectrostrictive actuators. Journal of the Mechanics and Physics of Solids,1998,46:1301-1318.
[111] Heyer V., Schneider G.A., Balke H., et al. A fracture criterion for conducting cracks inhomogeneously poled piezoelectric PZT-PIC151ceramics. Acta Materialia,1998,46:6615-6622.
[112] Hao T.H., Shen Z.Y.. A new electric boundary condition of electric fracture mechanics andits applications. Engineering Fracture Mechanics,1994,47:793-802.
[113] McMeeking R.M.. Crack tip energy release rate for a piezoelectric compact tensionspecimen. Engineering Fracture Mechanics,1999,64:217-244..
[114] Crichton G.C., Karlsson P.W., Pedersen A.. Partial discharges in ellipsoidal and spheroidalvoids. IEEE Transactions on Dielectrics and Electrical Insulation,1989,24:335-342.
[115] Niemeyer L.. A generalized approach to partial discharge modeling. IEEE Transactions onDielectrics and Electrical Insulation,1995,2:510-528.
[116] Gutfleisch F., Niemeyer L.. Measurement and simulation of PD in epoxy voids. IEEETransactions on Dielectrics and Electrical Insulation,1995,2:729–743.
[117] Gao C.F.. Influence of mechanical stresses on partial discharge in a piezoelectric solidcontaining cavities. Engineering Fracture Mechanics,2008,75:4920-4924.
[118] Fu R., Qian C.F., Zhang T.Y.. Electrical fracture toughness for conductive cracks driven byelectric fields in piezoelectric materials. Applied Physics Letters,2000,76:126-128.
[119] Wang T.H., Zhang T.Y.. Electrical fracture toughness for electrically conductive deepnotches driven by electric field in depoled lead zirconate titanate ceramics. Applied PhysicsLetters,2001,79:4198-4200.
[120] Beom H.G., Jeong K.M., Park J.Y. et al. Electrical failure of piezoelectric ceramics with aconductive crack under electric fields. Engineering Fracture Mechanics,2009,76:2399-2407.
[121] Lin S., Beom H.G., Tao D.. Tubular channel growth in piezoelectric materials under electricfields. Acta Mechanica,2010,210:47-55.
[122] Zhang T.Y., Zhao M.H., Gao C.F.. The strip dielectric breakdown model. InternationalJournal of Fracture,2005,132:311-327.
[123] Dugdale D.S.. Yielding of steel sheets containing slits. Journal of the Mechanics and Physicsof Solids,1960,8:100-104.
[124] Gao C.F., Noda N., Zhang T.Y.. Dielectric breakdown model for a conductive crack andelectrode in piezoelectric materials. International Journal of Engineering Science,2006,44:256-272.
[125] Gao H.J., Zhang T.Y., Tong, P.. Local and global energy release rates for an electrically yieldcrack in a piezoelectric ceramic. Journal of the Mechanics and Physics of Solids,1997,45:491-510.
[126] Ru C.Q.. Effect of electric polarization saturation on stress intensity factors in apiezoelectric ceramics. International Journal of Solids and Structures,1999,36:869-883.
[127] Wang T.C.. Analysis of strip electric saturation model of crack problem in piezoelectricmaterials. International Journal of Solids and Structures.2000,37:6031-6049.
[128] Shen S., Nishioka T., Kuang Z.B., et al. Nonlinear electromechanical interfacial fracture forpiezoelectric materials. Mechanics of Materials,2000,32:57-64.
[129] Zhu T., Yang W.. Toughness variation of ferroelectrics by polarization switch undernon-uniform electric field. Acta Materialia,1997,45:4695-4702.
[130] Yang W., Zhu T.. Switch toughening of ferroelectrics subjected to electric fields. Journal ofthe Mechanics and Physics of Solids,1998,46:291-311.
[131] Wang B.L., Zhang X.H.. An electrical field based non-linear model in the fracture ofpiezoelectric ceramics. International Journal of Solids and Structures,2004,41:4337-4347.
[132] Wang B.L., Zhang X.H.. Fracture prediction for piezoelectric ceramics based on the electricfield saturation concept. Mechanics Research Communications,2005,32:411-419.
[133] Stratton J. A.. Electromagnetic Theory. McGraw-Hill, New York,1941．
[134] Landau L. D., Lifshitz E.M.. Electodynamics of Continous Media．Pergamon Press, Oxford,1960．
[135] Pao Y.H.. Eelectromagnetic force in deformable continua. Nemat-Nasser, Mechanics Today,Printed in Great Britain by Pitman. Bath,1978.
[136]匡震邦.非线性连续介质力学.上海:上海交通大学出版,2002.
[137] Yang W., Suo Z.. Cracking in ceramic actuators caused by electrostriction. Journal of theMechanics and Physics of Solids,1994,42:649-663.
[138] Knops R.J. Two-dimensional eletrostriction. Quarterly Journal of Mechanics and AppliedMathematics,1963,16:377-388.
[139] McMeeking R.M.. Electrostrictive stresses near crack-like flaws. Journal of AppliedMathematics and Physics (ZAMP),1989,40:615-627.
[140] Smith T.E., Warren W.E.. Some problems in two-dimesional electrostriction. Journal ofMathematical Physics,1966,45:45-51,1968(corrigenda)47:109-110.
[141]蒋泉.电致伸缩材料中二维问题的应力分析[博士论文].上海:上海交通大学,2005.
[142] Hao T.H., Gong X., Suo Z.. Fracture mechanics for the design of ceramic multilayeractuators. Journal of the Mechanics and Physics of Solids,1996,44:23-48.
[143] Beom H.G., Kim Y.H., Cho C., et al. Asymptotic analysis of an impermeable crack in anelectrostrictive material subjected to electric loading. International Journal of Solids andStructure,2006,43:6869-6886.
[144] Beom H.G., Kim Y.H., Cho C., et al. A crack with an electric displacement saturation zone inan electrostrictive material. Archive of Applied Mechanics,2006,76:19-31.
[145] Gao C.F., Mai Y.W., Zhang N.. Solution of a crack in an electrostrictive solid. InternationalJournal of Solids and Structures,2010,47:444-453.
[146] Gao C.F., Mai Y.W.. Fracture of electrostrictive solids subjected to combined mechanicaland electric loads. Engineering Fracture Mechanics,2010,77:1503-1515.
[147] Gao C.F., Mai Y.W., Zhang N.. Solution of collinear cracks in an electrostrictive solid.Philosophical Magazine,2010,90:1245-1262.
[148] Muskhelishvili N.I.. Some Basic Problems of the Mathematical Theory of Elasticity.Groningeng: Noordhoof,1963.
[149]杨津基.气体放电.北京:学出版社,1983.
[150]屠志健,张一尘.电气绝缘与过电压.北京:中国电力出版社,2005.
[151]高树香,陈宗柱.气体导电.南京:南京工学院出版社,1988.
[152] Bartinikas R.. Corna Measurement and Interpretation. Wilmington: ASTM Special TechnicalPublication,1984.
[153]王强,彭光辉,王小波.电晕对绝缘性能危害的探讨.机电元件,2005,25:19-20.
[154]刘尚合,武占成.静电放电及其危害防护.北京:北京邮电大学出版社,2004.66-68.
[155] Zeller H.R.. Breakdown and prebreakdown phenomena in solid dielectrics. IEEETransactions on Electrical Insulation,1987,22:115-122.
[156] Zhu H.S., Ding H.Z.. Recent advances in dielectric breakdown theory of solid insulators.Progress in Natural Science,1998,8:257-268.
[157] Salama M.M.A., Rizk M.S., Hackam R.. Electrical stress and inception voltage ofdischarges in gaseous cavities in an anisotropic dielectric material. Journal of AppliedPhysics,1986,60:2600-2608.
[158] Danikas M.G., Karafyllidis I., Thanailakis A., et al. Simulation of electrical tree growth insolid dielectrics containing voids of arbitrary shape. Modelling and Simulation in MaterialsScience and Engineering,1996,4:535-552.
[159] Vardakis G.E., Danikas M.G.. Simulation of tree propagation in polyethylene including airvoid by using cellular automata: The effect of space charges. Electrical Engineering,2002,84:211-216.
[160] Vardakis G.E., Danikas M.G... Simulation of electrical tree propagation using cellularautomata: the case of conducting particle included in a dielectric in point-plane electrodearrangement. Journal of Electrostatics,2005,63:129-142.
[161]徐芝纶.弹性力学.北京:高等教育出版社,1990.
[162]竹内洋一郎.热应力.北京:科学出版社,1977.
[163]杭斌.长输低温乙烯管道保冷设计浅析.保温材料与节能技术,1998,3:10-16.
[164]杜则裕,刘继元,张世林,等.工程材料简明手册.北京:电子工业出版社,1996.
[165] David E., Parpal J.L., Crine J.P.. Influence of internal mechanical stress and strain onelectrical performance of polyethylene. IEEE Transactions on Dielectrics and ElectricalInsulation,1996,3:248-257
[166] Wu K., Suzuoki Y., Mizutani T., et al. Model for partial discharges associated with treeingbreakdown: I. PDs in tree channels. Journal of Physics D: Applied Physics,2000,33：1197-1201.
[167] Wu K., Suzuoki Y., Mizutani T., et al. Model for partial discharges associated with treeingbreakdown: II. Tree growth affected by PDs. Journal of Physics D: Applied Physics,2000,33：1202-1208.
[168] Wu K., Suzuoki Y., Mizutani T., et al. Model for partial discharges associated with treeingbreakdown: III. PD extinction and re-growth of tree. Journal of Physics D: Applied Physics,2000,33：1209-1218.
[169]郑晓泉, Chen G..机械应力与电压频率对XLPE电缆电树的影响.高电压技术,2003,29:6-8.
[170] Dissado L.A.. Understanding electrical trees in solids: From experiment to theory. IEEETransactions on Dielectrics and Electrical Insulation,2002,9:483-497.
[171] Ding H.Z., Varlow B.R.. Thermodynamic model for electrical tree propagation kinetics incombined electrical and mechanical stresses. IEEE Transactions on Dielectrics andElectrical Insulation,2005,12:81-89.
[172]郑飞虎,张治文,肖春.应力对诱发空间电荷击穿的作用.电工技术学报,2006,21:31-34.
[173] McMeeking R.M.. Towards a fracture mechanics for brittle piezoelectric and dielectricmaterials. International Journal of Fracture,2001,108:25-41.
[174] Landis C. M.. Energetically consistent boundary conditions for electromechanical fracture.Internatiaonal Journal of Solids and Structure,2004,41:6291-6315.
[175] Gao C.F., Zhao M.H., Tong, P., et al. The energy release rate and the J-integral of anelectrically insulated crack in a piezoelectric material. International Journal of EngineeringScience,2004,42:2175-2192.
[176] Eshelby J. D.. The determination and the elastic field of an ellipsoidal inclusion and relatedproblems. Proceedings of the Royal Society London A,1957,241:376-396.
[177] Pedersen A., Crichton G.C., McAllister I.W.. The functional relation between partialdischarges and induced charge. IEEE Transactions on Dielectrics and Electrical Insulation,1995,2:535–543
[178] Kummar S., Singh R.N.. Effect of the mechanical boundary condition at the crack surfaceson the stress distribution at the crack tip in piezoelectric materials. Materials Science andEngineering,1998, A252:64-77.
[179] Fu R., Zhang T.Y.. Effects of an applied electric field on the modulus of rupture of poledlead Zirconate Titanate Ceramics. Journal of American Ceramic Society,1998,81:1058-1060.
[180] Fu R., Zhang T.Y.. Effects of an electric field on the fracture toughness of poled leadZirconate Titanate Ceramics. Journal of American Ceramic Society,2000,83:1215-1218.
[181] Gao C.F.. Further study on the generalized2D problem of an elliptical hole or a crack inpiezoelectric media. Mechanics Research Communications,2000,27:429-434.
[182] Winzer S.R., Shankar N.A., Ritter P.. Designing cofired multilayer electrostrictive actuaorsfor reliability. Journal of the American Ceramic Society,1989,72:2246-2257.
[183] Jiang Q., Kuang Z.B.. Stress analysis in two dimensional electrostrictive material with anelliptic rigid conductor. European Journal of Mechanics A/Solids,2004,23:945-956.