【作者】 姚迪；

【导师】 洪家旺；

【作者基本信息】 北京理工大学 ， 力学， 2018， 硕士

【摘要】 挠曲电效应是描述材料中电极化强度和应变梯度相互作用的一种新型的力电耦合效应。该效应可存在于所有介电材料中,并且随着材料尺寸的减小而增加,因此在微纳米尺度下具有重要的应用前景。挠曲电效应系数的定量表征是挠曲电效应发展与应用的前提和基础。本论文基于理论推导和数值分析,对挠曲电系数表征方法进行了较为系统的理论研究,提出了结合弯曲实验与压缩实验获得单晶立方相材料的全部挠曲电系数张量分量的测量方法,为挠曲电系数实验表征奠定了理论基础。本论文的主要工作包括:(1)建立了变截面悬臂梁的挠曲电系数表征模型。通过结合变截面悬臂梁弯曲模型与不同晶向的等截面弯曲梁测试方法,从理论上获得了立方相材料三个挠曲电系数张量分量,为实验测量挠曲电系数张量分量提供了一种新方法。(2)建立了变截面体压缩的挠曲电系数精确表征模型。理论推导出受压缩变截面体内部的精确应变场,通过结合单晶三点弯曲实验,计算得到了立方相材料的挠曲电系数张量分量值。并将该模型与变截面体压缩的挠曲电系数近似表征模型进行了对比研究,验证了在挠曲电系数测量中采用精确表征模型的必要性。(3)发展了微纳尺度下压电材料挠曲电系数的测试表征方法。通过建立变截面压电纳米锥在考虑挠曲电效应下的压缩刚度模型,提出了基于纳米压缩技术,通过测量等截面和变截面压电体的压缩刚度变化,获得材料的等效纵向挠曲电系数。同时通过数值模拟计算对纳米压缩试样尺寸进行了优化,提高了挠曲电系数定量表征的准确性。以上研究工作从理论上发展了挠曲电效应系数的表征方法,为实验上定量表征挠曲电系数张量分量奠定了理论基础。更多还原

【Abstract】 The flexoelectric effect is a new type of electro-mechanical coupling effect,which describes the coupling between electric polarization and strain gradient.Such an effect exists in all dielectric materials and enhanced as the sample size reduces,thus leading to potential applications at nanoscale.The characterization of the flexoelectric coefficients is critical for the development and application.In this thesis,we establish systematic characterization methods of the flexoelectric coefficients based on the theoretical deduction and numerical analysis.We propose the method of measuring all the flexoelectric coefficients tensor components by combining the bending and compression experiments in single crystalline sample with cubic symmetry,which paves the path for the experimental measurement of flexoelectric coefficients.This thesis is organized as following:(1)A characterization model of the variable cross-section cantilever beam for measuring the flexoelectric coefficients is established.Through the combination of the models of the variable cross-section cantilever beam and constant-section bending beam with different crystal orientations,we theoretically obtain three flexoelectric coefficient tensor components for the cubic structure,which provides a novel method to experimentally measure the flexoelectric coefficient tensor components..(2)An accurate characterization model for compression of the variable cross-section sample is established.We theoretically obtained the precise strain distribution.The flexoelectric coefficient tensor components in cubic materials are calculated by the compression model,combining with the available three-point bending experiments.Meanwhile,by comparing the results with the approximate characterization model,we reveal the significance of accurate characterization model in flexoelectric coefficient measurement.(3)A nanoscale measurement of the flexoelectric coefficients is proposed.Based on the nano-compression technique,the compression model of stiffness of piezoelectric nano cone is established,taking flexoelectric effect into account.The equivalent longitudinal flexoelectric coefficients is obtained by measuring the stiffness change of the constant and variable cross-section pillars.Meanwhile,the size of the sample for nanocompression is optimized by the numerical approach,which improves the accuracy of the measurement of the flexoelectric coefficients.In summary,we develop the theoretical characterization methods of flexoelectric coefficients,which enlighten the experimental measurement of the flexoelectric coefficient tensor components.更多还原