铁电陶瓷的电致失效力学
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摘要
铁电陶瓷作为新一代功能陶瓷的代表，其可靠性问题日益受到人们的关注。
铁电陶瓷在电场或力电耦合载荷作用下的典型失效模式为电致断裂和电致疲
劳。本文尝试采用断裂力学、畴变细观力学和介电物理学相结合的方法，从实验
和理论角度对铁电陶瓷的电致失效力学问题进行了研究。论文从电场驱动的裂尖
微结构演化导致电致失效这一基本思路出发，获得了裂尖集中电场诱发90°铁电
畴变的实验图像，提出了电致畴变断裂的理论模型，阐明了铁电陶瓷电致断裂，
疲劳裂纹扩展和裂纹偏折的失效机理。在铁电陶瓷电致失效研究这一新领域所完
成的主要工作有：
一、首次报道了裂尖集中电场诱发的90°铁电畴变的实验现象。利用不同取向铁
电畴的腐蚀速率不同的原理，获得了裂尖前方晶粒内电场诱发的90°a-c畴
结构的SEM照片。这一观测结果为电场驱动裂尖微结构演化的模型提供了
清晰的物理过程图像，并为进一步的理论分析提供了直接的实验依据。
二、提出了基于细观物理机制的小范围畴变模型。区别于传统的介电失效，揭示
了由裂尖集中电场引起畴变，畴变导致非协调应力，由应力驱动断裂的电致
失效机理。在此基础上，进行了电致断裂、断裂韧性的各向异性和断裂韧性
关于电场的非对称变化的理论分析。解决了基于线性压电本构的电致断裂分
析与实验观测不一致的矛盾。
三、观测了循环电场低于矫顽电场加载时，电致疲劳裂纹扩展的规律：首次阐明
了电致疲劳裂纹扩展的机理。不同于Cao和Evans的实验报道（矫顽电场以
下，裂纹不发生扩展），通过长焦距显微镜实时观测了循环电场的幅值低于
矫顽电场时，铁电陶瓷中疲劳裂纹扩展的规律。在实验基础上，理论分析了
铁电畴在交变电场作用下循环翻转而产生循环应力，以及由循环应力驱动裂
纹以起裂、扩展、止裂、再起裂的模式循环向前扩展的过程。定量给出了电
致疲劳裂纹扩展量与电场翻转次数的理论预测值，并与实验观测结果吻合较
好。
四、求解了铁电陶瓷中偏折裂纹的问题，讨论了电场对裂纹偏折的影响。基于线
性压电本构，将偏折裂纹等效为连续分布的位错和电偶极子，采用推广的
Stroh方法，建立了以位错密度和电偶极子密度为未知量的奇异积分方程
组。数值计算结果表明，1．在垂直拉应力和垂直正电场作用下，裂纹不发
生偏折，沿直线扩展；2．在混合型机械载荷作用下，垂直正电场将增加裂
纹偏折角度，3．沿水平侧向施加的正电场和水平拉应力促进裂纹偏折，而
沿水平侧向施加的负电场和水平压应力抑制裂纹偏折。
Reliability concerns of ferroelectric ceramics, as one of the most important
functional ceramics, call for a better understanding of their failure mechanisms. Under
an electric field or a combined electric and mechanical loading, the ferroelectric
ceramics are susceptible to electric fracture and electric fatigue. By the methods of
fracture mechanics, mesoscopic mechanics and dielectric physics, the problem of
electric field induced failure in ferroelectric ceramics is experimentally and
theoretically studied in this dissertation. We approach the problem based on the
perception that electric field induced microstructure evolution at the crack tip will
lead to fracture and fatigue. It follows that a micrograph of intensified electric field
induced 90° domain switching at the crack tip is obtained, a theoretical model of
domain switching induced fracture is proposed, and the failure mechanisms of electric
fracture, electric fatigue and crack kinking are revealed. The major works include:
1. Experimental observation on the electric field induced 9O° domain switching at
the crack tip is first reported. The difference in etch rates of domains with distinct
orientations gives rise to topographical contrast which can be used to identify the
domain configuration. A SEM micrograph of 90° a-c domain configuration in
the grain ahead of a crack tip is obtained. The result reveals a clear physical
picture of electric field induced microstructure evolution, and lends a direct
experimental support to the theoretical analysis.
2. A mechanism based small scale domain switching model is proposed in the
dissertation. In contrast to the conventional perception of dielectric failure, the
failure mechanism is revealed as follows: the intensified electric field in the
vicinity of a crack tip drives domains to switch, the switched domains induce
incompatible stress under the constraint of unswitched materials, and
consequently the induced stress leads to fracture. The model is capable of
explaining the experimental phenomena, such as electric fracture, fracture
toughness anisotropy, asymmetric variation of fracture toughness of poled
ferroelectrics under positive and negative electric fields. The inconsistency
between the experimental observation and the electric fracture analysis based on
the liner piezoelectric constitutive equations is resolved.
3. Electric field induced fatigue crack growth in ferroelectric ceramics is observed
and the mechanism of fatigue crack growth is revealed. In contrast to the
experimental report by Cao and Evans, we found that the crack would extend
under a cyclic electric field below the coercive field by the in-situ observation
through a long focal length optical microscope. The mechanism of fatigue crack
growth is understood as follows: under an alternating electric field, the field
concentrated around the crack causes the ferroelectrics to undergo cyclic local
domain switching, which generates a cyclic driving stress field near the crack tip.
Driven by the switching induced stress field, the crack extends in a repeated
process of initiation, growth, arrest and re-initiation. The prediction on the crack
growth versus electric field reversals agrees well with experimental
measurements.
4. Crack kinking in ferroelectric ceramics is explored within the framework of the
linear piezoelectric constitutive relation, with an emphasis on the effect of electric
field. The kink of a crack is mode
铁电陶瓷在电场或力电耦合载荷作用下的典型失效模式为电致断裂和电致疲
劳。本文尝试采用断裂力学、畴变细观力学和介电物理学相结合的方法，从实验
和理论角度对铁电陶瓷的电致失效力学问题进行了研究。论文从电场驱动的裂尖
微结构演化导致电致失效这一基本思路出发，获得了裂尖集中电场诱发90°铁电
畴变的实验图像，提出了电致畴变断裂的理论模型，阐明了铁电陶瓷电致断裂，
疲劳裂纹扩展和裂纹偏折的失效机理。在铁电陶瓷电致失效研究这一新领域所完
成的主要工作有：
一、首次报道了裂尖集中电场诱发的90°铁电畴变的实验现象。利用不同取向铁
电畴的腐蚀速率不同的原理，获得了裂尖前方晶粒内电场诱发的90°a-c畴
结构的SEM照片。这一观测结果为电场驱动裂尖微结构演化的模型提供了
清晰的物理过程图像，并为进一步的理论分析提供了直接的实验依据。
二、提出了基于细观物理机制的小范围畴变模型。区别于传统的介电失效，揭示
了由裂尖集中电场引起畴变，畴变导致非协调应力，由应力驱动断裂的电致
失效机理。在此基础上，进行了电致断裂、断裂韧性的各向异性和断裂韧性
关于电场的非对称变化的理论分析。解决了基于线性压电本构的电致断裂分
析与实验观测不一致的矛盾。
三、观测了循环电场低于矫顽电场加载时，电致疲劳裂纹扩展的规律：首次阐明
了电致疲劳裂纹扩展的机理。不同于Cao和Evans的实验报道（矫顽电场以
下，裂纹不发生扩展），通过长焦距显微镜实时观测了循环电场的幅值低于
矫顽电场时，铁电陶瓷中疲劳裂纹扩展的规律。在实验基础上，理论分析了
铁电畴在交变电场作用下循环翻转而产生循环应力，以及由循环应力驱动裂
纹以起裂、扩展、止裂、再起裂的模式循环向前扩展的过程。定量给出了电
致疲劳裂纹扩展量与电场翻转次数的理论预测值，并与实验观测结果吻合较
好。
四、求解了铁电陶瓷中偏折裂纹的问题，讨论了电场对裂纹偏折的影响。基于线
性压电本构，将偏折裂纹等效为连续分布的位错和电偶极子，采用推广的
Stroh方法，建立了以位错密度和电偶极子密度为未知量的奇异积分方程
组。数值计算结果表明，1．在垂直拉应力和垂直正电场作用下，裂纹不发
生偏折，沿直线扩展；2．在混合型机械载荷作用下，垂直正电场将增加裂
纹偏折角度，3．沿水平侧向施加的正电场和水平拉应力促进裂纹偏折，而
沿水平侧向施加的负电场和水平压应力抑制裂纹偏折。
Reliability concerns of ferroelectric ceramics, as one of the most important
functional ceramics, call for a better understanding of their failure mechanisms. Under
an electric field or a combined electric and mechanical loading, the ferroelectric
ceramics are susceptible to electric fracture and electric fatigue. By the methods of
fracture mechanics, mesoscopic mechanics and dielectric physics, the problem of
electric field induced failure in ferroelectric ceramics is experimentally and
theoretically studied in this dissertation. We approach the problem based on the
perception that electric field induced microstructure evolution at the crack tip will
lead to fracture and fatigue. It follows that a micrograph of intensified electric field
induced 90° domain switching at the crack tip is obtained, a theoretical model of
domain switching induced fracture is proposed, and the failure mechanisms of electric
fracture, electric fatigue and crack kinking are revealed. The major works include:
1. Experimental observation on the electric field induced 9O° domain switching at
the crack tip is first reported. The difference in etch rates of domains with distinct
orientations gives rise to topographical contrast which can be used to identify the
domain configuration. A SEM micrograph of 90° a-c domain configuration in
the grain ahead of a crack tip is obtained. The result reveals a clear physical
picture of electric field induced microstructure evolution, and lends a direct
experimental support to the theoretical analysis.
2. A mechanism based small scale domain switching model is proposed in the
dissertation. In contrast to the conventional perception of dielectric failure, the
failure mechanism is revealed as follows: the intensified electric field in the
vicinity of a crack tip drives domains to switch, the switched domains induce
incompatible stress under the constraint of unswitched materials, and
consequently the induced stress leads to fracture. The model is capable of
explaining the experimental phenomena, such as electric fracture, fracture
toughness anisotropy, asymmetric variation of fracture toughness of poled
ferroelectrics under positive and negative electric fields. The inconsistency
between the experimental observation and the electric fracture analysis based on
the liner piezoelectric constitutive equations is resolved.
3. Electric field induced fatigue crack growth in ferroelectric ceramics is observed
and the mechanism of fatigue crack growth is revealed. In contrast to the
experimental report by Cao and Evans, we found that the crack would extend
under a cyclic electric field below the coercive field by the in-situ observation
through a long focal length optical microscope. The mechanism of fatigue crack
growth is understood as follows: under an alternating electric field, the field
concentrated around the crack causes the ferroelectrics to undergo cyclic local
domain switching, which generates a cyclic driving stress field near the crack tip.
Driven by the switching induced stress field, the crack extends in a repeated
process of initiation, growth, arrest and re-initiation. The prediction on the crack
growth versus electric field reversals agrees well with experimental
measurements.
4. Crack kinking in ferroelectric ceramics is explored within the framework of the
linear piezoelectric constitutive relation, with an emphasis on the effect of electric
field. The kink of a crack is mode
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75．方菲，杨卫，朱廷．极化铁电陶瓷裂纹附近由电场诱发铁电畴变的实验观察．第九届全国疲劳与断裂学术会议论文集，昆明，1998，72～75
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82. Hwang S C, Huber J E, McMeeking R M, et al. The simulation of switching in polycrystalline ferroelectric ceramics. J Appl. Phy. 1998, 84:1530～1540
83. Hwang S C, McMeeking R M. A finite element model of ferroelastic polycrystals. Int. J. Solids Struct. 1999, 36(10): 1541～1556
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87．吕炜．铁电材料与形状记忆合金的宏细观本构研究：[博士学位论文]．北京：清华大学工程力学系，1998
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89．江冰，方岱宁．铁电本构关系及其相关问题的研究进展．力学进展，1998，28(3)：312～322
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74．朱廷，方菲，杨卫．铁电陶瓷电致疲劳的实验观测．第九届全国疲劳与断裂学术会议论文集，昆明，1998，68～71
75．方菲，杨卫，朱廷．极化铁电陶瓷裂纹附近由电场诱发铁电畴变的实验观察．第九届全国疲劳与断裂学术会议论文集，昆明，1998，72～75
76．杨卫，方菲，朱廷．铁电陶瓷的电致断裂与电致疲劳．第九届全国疲劳与断裂学术会议论文集，昆明，1998，50～53
77．许煜寰．铁电与压电材料．北京：科学出版社．1996
78．钟维烈．铁电物理学．北京：科学出版社．1996
79. McMeeking R M, Hwang S C. On the potential energy of a piezoelectric inclusion and the criterion for ferroelectric switching. Ferroelectrics, 1997, 200: 151～173
80. Hwang S C, McMeeking R M. The prediction of switching in polycrystalline ferroelectric ceracmics. Ferroelectrics, 1998, 207:465～495
81. Hwang S C, McMeeking R M. A finite element model of ferroelectric polycrystals. Ferroelectrics, 1998, 211:177～194
82. Hwang S C, Huber J E, McMeeking R M, et al. The simulation of switching in polycrystalline ferroelectric ceramics. J Appl. Phy. 1998, 84:1530～1540
83. Hwang S C, McMeeking R M. A finite element model of ferroelastic polycrystals. Int. J. Solids Struct. 1999, 36(10): 1541～1556
84. Chen X, Fang D N, Hwang K C. Micromechanics constitutive researches for ferroelectric single crystal with domain switching. In Wang T C, Chou T W, eds. Progress in Advanced Materials and Mechanics. Proc. of Int. Conference on Advanced Materials and Mechanics, Beijing. 1996, 465～470
85. Chen X, Fang D N, Hwang K C. Micromechanics simulation of ferroelectric polarization switching. Acta. Mater. 1998, 45(3): 3181～3189
86. Lu W, Fang D N, Hwang K C. Numerical analysis of ferroelectric/ferroelastic domain switching in ferroelectric ceramics. Comp. Mater. Sci. 1997, 8, 291～308
87．吕炜．铁电材料与形状记忆合金的宏细观本构研究：[博士学位论文]．北京：清华大学工程力学系，1998
88. Jiang B, Fang D N, Hwang K C. A unified model for the multiphase piezocomposites with ellipsoidal inclusion. Int. J. Solids Struct. 1999, 36: 2707～2733
89．江冰，方岱宁．铁电本构关系及其相关问题的研究进展．力学进展，1998，28(3)：312～322
90．江冰．铁电复合材料的本构关系：[博士学位论文]．北京：清华大学工程力学系，1998
91. Huo Y, Jiang Q. Modeling of domain switching in ferroelectric ceramics: an example. Int. J. Solids Struct. 1998, 35(13): 1339～1353
92. Jiang Q. On modeling of phase transformations in ferroelectric materials. Acta Mech. 1994, 102, 149～165
93. Hatano J, Lebihan F, Aikawa F, et al. Real-time observation of ferroelectric domains in NaNO_2 by nematic liquid crystal method. Ferroelectrics. 1990, 106: 33～38
94. Hu Y H, Chart H M, Zhang X W, et al. Scanning electron microscopy and transmission electron microscopy study of ferroelectric domains in doped BaTiO_3. J. Amer. Ceram. Soc. 1986, 69(8): 594～602
95. Mulvihill M L, Uchino K, Li Z, et al. In-situ observation of the domain configuration during the phase transitions in barium titanate. Phil. Mag. B. 1996, 74(1): 25～36
96. Park S B, Park S S, Carman G P, et al. Measuring strain distribution during mesoscopic domain reorientation in a ferroelectric material. J. Eng. Mater. Tech. ASME, 1998, 120(1): 1～6
97. McMeeking R M, Evans A G. Mechanics of transformation-toughening in brittle materials. J. Amer. Ceram. Soc. 1982, 65(5): 242～246
98. 杨卫．宏微观断裂力学．北京：国防工业出版社．1995
99. Bueckner H F. A novel principle for the computation of stress intesity factors. J. Appl. Math. Phys. 1970, 50:529～533
100. Rice J R. Some remarks on elastic crack-tip stress fields. Int. J. Solids Struct. 1972, 8(2):751～753
101. Tada H, Paris P C, Irwin G R. The stress analysis of cracks handbook. Del research, St. Louis, Mo. 1973
102． Lambropoulos J C. Shear, shape and orientation effects in transformation toughening. Int. J. Solids Struct. 1986,22(10) : 1083-1106
103． 李长青．铁电材料的本构关系和电致疲劳的实验研究：[硕士学位论文]．北 京：清华大学工程力学系，1998
104． Anstis G R, Chantikul P, Lawn B R, et al. A critical evaluation of indentation techniques for measuring fracture toughness: Ⅰ. Direct crack measurements. J. Am. Ceram. Soc. 1981, 64(9) : 533-538
105． Anstis G R, Chantikul P, Lawn B R, et al. A critical evaluation of indentation techniques for measuring fracture toughness: Ⅱ. Strength method. J. Am. Ceram. Soc. 1981,64(9) : 539-543
106． Zhang Z, Raj R. Influence of grain size on ferroelastic toughening and piezoelectric behavior of Lead Zirconate Titanate. J. Am. Ceram. Soc. 1995, 78(12) : 3363-3368
107． McHenry K D, Koepke B G. Electric field effects on subcritical crack growth in PZT. Frac Mech. Ceram. 1983, 5: 337-352
108． Barnett D M, Lothe J. Dislocations and line charges in anisotropic piezoelectric insulators. Phys. Status Solidi (b) 1975, 67: 105-111
109． Lo K K. Analysis of branched cracks. J. Appl. Mech., 1978, 45: 797-802
110． Obata M, Nemat-Nasser S, Goto Y. Branched cracks in anisotropic elastic solids. J. Appl. Mech. 1989, 56: 858-864
111． Azhdari A, Nemat-Nasser S. Hoop stress intensity factor and crack kinking in anisotropic brittle solids. Int. J. Solids Struct. 1996, 33: 2023-2037
112． Azhdari A, Nemat-Nasser S. Energy-release rate and crack kinking in anisotropic brittle solids. J. Mech. Phys. Solids 1996,44: 929-951
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