铁电材料非线性力电耦合关系研究
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摘要
二十一世纪是新技术和新材料飞速发展的世纪。随着计算机技术、通讯技术、生物技术以及微电子技术等的日益发展，人们对组成各个系统与结构的基本部分的性能提出了新的要求，不仅要求材料可靠与安全，更希望材料能根据其周围环境的变化来调整自身的某些参数以达到最优化的要求。关于“智能材料与结构”的研究正顺应这一趋势而蓬勃发展起来。铁电材料不仅是重要的电子功能材料，而且被认为是最有应用前景的智能基础材料。人们虽然对铁电现象很早就有了认识，但对其基本性能的认识还远未完善，对材料的微结构、疲劳、损伤、断裂、破坏失效的机理也不十分明了，迫切希望进行更深入、更全面的了解。本论文就是针对铁电材料的非线性力电耦合性能进行研究与分析，以期能对其本构关系作出简单明确的描述，为铁电元器件的材料设计、结构分析及寿命估计等提供依据。
本文主要进行了以下研究工作：
①提出了新的铁电材料力电耦合模型，以描述复杂的力电耦合效应。其工作包括：
——在分析铁电材料电畴翻转基本特征的基础上，引入电畴的“连续翻转”模型，克服了“完全反转”假设对铁电特性描述的局限性，使电畴翻转模型的物理意义更为明确。
——建立了以电畴翻转时的体积分数增量为中心的，基于铁电畴壁运动特性的剩余应变及电位移的增量形式的演化方程，在其中包含有材料参数、畴壁运动、电畴形式、电畴体积分数及基体与夹杂、夹杂与夹杂等相互间能量作用等影响因素。
——依据晶体塑性理论，将铁电材料中的电畴翻转类比于晶体位错滑移面上的滑移系，定义铁电材料中相应的电畴反转系；采用电畴的体积分数表述电畴翻转的变化量，得到了电畴翻转的饱和特性的简单描述。
②初步提出了跨多尺度的铁电陶瓷材料的力电耦合分析方法，得到与实验结果相符合的铁电陶瓷本构行为的计算结果。主要内容包括：
——建立基于铁电材料微结构的夹杂单元体的均匀化方法，不但将材料的宏、细观力电响应关系连接起来，而且将材料细／微观结构的几何及材料特性与材料的宏观性能相统一，使对铁电多晶材料的损伤、疲劳及破坏等的研究更直接有效。
——通过采用基于Hill理论的扩展的自洽计算方法，将其从一般多晶材料、复合材料的纯力学性能描述，扩展到具有力电耦合的复杂情况，建立其整体迭代和局部迭代的计算方法，得到铁电多晶材料的非线性力电耦合关系的描述。
重庆大学博士学位论文
③应用提出的模型与方法，针对层状微结构铁电材料的具体特点，进行了计算与
分析，包括:
建立了层状铁电材料的力电场边界条件，推导出在外加力电场作用下的各层
材料的局部力电响应的表达关系。
对各层材料的体积百分比及相对弹性模量对材料整体性能的影响进行了计算
与分析。
分析了不同空间取向分布的铁电夹杂体，获得了其等效应力及等效应变的分
布情况与演化关系，指明因夹杂的空间分布而引起的非均匀性因素对损伤与破坏
的影响。
④发展了能采用多轴加载方式的计算程序。该程序不仅适用于四方—立方结构
相变的钙钦矿型铁电材料，而且通过简单修改，就可应用于其它结构相变形式的
铁电材料电畴翻转的描述之中。
New technology and advanced materials are developing rapidly in the 21st century. With the development of computer, communication, biology and microelectronic technology, people now expect a common system and structure with moderate activity or intelligence to adapt itself to the changes of its surroundings. This is known as "Smart or Intelligent Material and Structure". Ferroelectric materials are not only vital electronic functional materials, but are thought of as the most interesting and promising intelligent materials of the future. Though ferro-electricity was recognized in the early 1920's, people still do not clearly understand even its basic characteristics and microstructure because descriptions of the behavior of ferro-electric ceramics remain in their infancy. The mechanism of damage, fatigue, crack and fracture of ferro-electrics should be studied more concretely not only in theory but also in application. The purpose behind this thesis is to study the nonlinear electro-mechanical coupling perfo
rmance, and to have relatively simple yet substantial constitutive relations of ferro-electrics, that can eventually provide guidance for material design, sensor or actuator structural analysis and life expectancy for ferro-electric structure and system. The main work and result of this dissertation include the following aspects: (1) A new mechanical-electric model of ferro-electric materials is proposed to describe the complicated electromechanical coupling phenomena.
_Based on the domain switching behavior of ferroelectrics, a model of "Successive
Switching" for ferroelectric domains is introduced. This may help to avoid some of the intrinsic limitations of the "Complete Switching" hypothesis, and be a more physical representation.
_Incremental form of evolution law of domain switching is developed by taking the
volume fraction of domains as key intrinsic factors. The main factors that have great influence on domain switching are material parameters, domain wall motion, domain volume fraction and the interaction energy between inclusion and matrix. Inclusion and its neighbors could be addressed in the description as well.
_The phenomenon of saturation or "lock up" when all of the grains have transformed,
is described in a rattier simple form through domain volume fractions by the proposed model, in which domain switching in ferro-electrics is analogous to that of dislocation movement on crystal slip planes in metals.
(2) A primary multi-scale method for the electromechanical coupling analysis of ceramics is developed and show good agreement between the calculated results and the related experiments.
The equivalent inclusion method is modified to include the geometrical and physical parameters of the ferroelectric inclusion units, and be expanded into piezo/ferro-electric media. The inclusion cell is the bridge of macro and micro mechanical-electrical responses, but also provides a direct relationship between meso/micro grain characteristic parameters and between globe macro performance, which could become a great help for the study on damage, fatigue and fracture mechanism of ferro-electrics.
The self-consistent method based on Hill's theory is extended to be applicable to ferroelectrics. The introduction of global iteration and local iteration under loading of electric and/or stress fields calculate the nonlinear electromechanical coupling behavior.
(3) The electro-mechanical coupling behavior of layer-structured ferroelectric composites is investigated and predicted.
The electrical and mechanical boundary conditions are obtained considering the characteristics of layered ferroelectrics; the local electric-mechanical response equations of each structural layer of units are derived under the coupling of electric and mechanical loads.
Various calculations are conducted when the volume fraction of each layer differs, as well as when the ratio of Yang's modular between layers changes. The influence of these factors to material performance is studied.
The distributi
本文主要进行了以下研究工作：
①提出了新的铁电材料力电耦合模型，以描述复杂的力电耦合效应。其工作包括：
——在分析铁电材料电畴翻转基本特征的基础上，引入电畴的“连续翻转”模型，克服了“完全反转”假设对铁电特性描述的局限性，使电畴翻转模型的物理意义更为明确。
——建立了以电畴翻转时的体积分数增量为中心的，基于铁电畴壁运动特性的剩余应变及电位移的增量形式的演化方程，在其中包含有材料参数、畴壁运动、电畴形式、电畴体积分数及基体与夹杂、夹杂与夹杂等相互间能量作用等影响因素。
——依据晶体塑性理论，将铁电材料中的电畴翻转类比于晶体位错滑移面上的滑移系，定义铁电材料中相应的电畴反转系；采用电畴的体积分数表述电畴翻转的变化量，得到了电畴翻转的饱和特性的简单描述。
②初步提出了跨多尺度的铁电陶瓷材料的力电耦合分析方法，得到与实验结果相符合的铁电陶瓷本构行为的计算结果。主要内容包括：
——建立基于铁电材料微结构的夹杂单元体的均匀化方法，不但将材料的宏、细观力电响应关系连接起来，而且将材料细／微观结构的几何及材料特性与材料的宏观性能相统一，使对铁电多晶材料的损伤、疲劳及破坏等的研究更直接有效。
——通过采用基于Hill理论的扩展的自洽计算方法，将其从一般多晶材料、复合材料的纯力学性能描述，扩展到具有力电耦合的复杂情况，建立其整体迭代和局部迭代的计算方法，得到铁电多晶材料的非线性力电耦合关系的描述。
重庆大学博士学位论文
③应用提出的模型与方法，针对层状微结构铁电材料的具体特点，进行了计算与
分析，包括:
建立了层状铁电材料的力电场边界条件，推导出在外加力电场作用下的各层
材料的局部力电响应的表达关系。
对各层材料的体积百分比及相对弹性模量对材料整体性能的影响进行了计算
与分析。
分析了不同空间取向分布的铁电夹杂体，获得了其等效应力及等效应变的分
布情况与演化关系，指明因夹杂的空间分布而引起的非均匀性因素对损伤与破坏
的影响。
④发展了能采用多轴加载方式的计算程序。该程序不仅适用于四方—立方结构
相变的钙钦矿型铁电材料，而且通过简单修改，就可应用于其它结构相变形式的
铁电材料电畴翻转的描述之中。
New technology and advanced materials are developing rapidly in the 21st century. With the development of computer, communication, biology and microelectronic technology, people now expect a common system and structure with moderate activity or intelligence to adapt itself to the changes of its surroundings. This is known as "Smart or Intelligent Material and Structure". Ferroelectric materials are not only vital electronic functional materials, but are thought of as the most interesting and promising intelligent materials of the future. Though ferro-electricity was recognized in the early 1920's, people still do not clearly understand even its basic characteristics and microstructure because descriptions of the behavior of ferro-electric ceramics remain in their infancy. The mechanism of damage, fatigue, crack and fracture of ferro-electrics should be studied more concretely not only in theory but also in application. The purpose behind this thesis is to study the nonlinear electro-mechanical coupling perfo
rmance, and to have relatively simple yet substantial constitutive relations of ferro-electrics, that can eventually provide guidance for material design, sensor or actuator structural analysis and life expectancy for ferro-electric structure and system. The main work and result of this dissertation include the following aspects: (1) A new mechanical-electric model of ferro-electric materials is proposed to describe the complicated electromechanical coupling phenomena.
_Based on the domain switching behavior of ferroelectrics, a model of "Successive
Switching" for ferroelectric domains is introduced. This may help to avoid some of the intrinsic limitations of the "Complete Switching" hypothesis, and be a more physical representation.
_Incremental form of evolution law of domain switching is developed by taking the
volume fraction of domains as key intrinsic factors. The main factors that have great influence on domain switching are material parameters, domain wall motion, domain volume fraction and the interaction energy between inclusion and matrix. Inclusion and its neighbors could be addressed in the description as well.
_The phenomenon of saturation or "lock up" when all of the grains have transformed,
is described in a rattier simple form through domain volume fractions by the proposed model, in which domain switching in ferro-electrics is analogous to that of dislocation movement on crystal slip planes in metals.
(2) A primary multi-scale method for the electromechanical coupling analysis of ceramics is developed and show good agreement between the calculated results and the related experiments.
The equivalent inclusion method is modified to include the geometrical and physical parameters of the ferroelectric inclusion units, and be expanded into piezo/ferro-electric media. The inclusion cell is the bridge of macro and micro mechanical-electrical responses, but also provides a direct relationship between meso/micro grain characteristic parameters and between globe macro performance, which could become a great help for the study on damage, fatigue and fracture mechanism of ferro-electrics.
The self-consistent method based on Hill's theory is extended to be applicable to ferroelectrics. The introduction of global iteration and local iteration under loading of electric and/or stress fields calculate the nonlinear electromechanical coupling behavior.
(3) The electro-mechanical coupling behavior of layer-structured ferroelectric composites is investigated and predicted.
The electrical and mechanical boundary conditions are obtained considering the characteristics of layered ferroelectrics; the local electric-mechanical response equations of each structural layer of units are derived under the coupling of electric and mechanical loads.
Various calculations are conducted when the volume fraction of each layer differs, as well as when the ratio of Yang's modular between layers changes. The influence of these factors to material performance is studied.
The distributi
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