【作者】 江冰；

【导师】 黄克智； 方岱宁；

【作者基本信息】 清华大学 ， 固体力学， 1998， 博士

【摘要】 本文系统地研究了铁电复合材料的宏细观力学行为、电学行为以及力电耦合行为。主要进行了以下五个方面的工作: 1.以Green函数方法研究了无穷大非压电介质中含有一个椭球状压电夹杂问题。建立了电弹Eshelby张量与弹性夹杂问题的Eshelby张量、介电夹杂问题的Eshelby张量之间的关系式。由于弹性及介电夹杂问题的Eshelby张量可以由弹性理论与电动力学求出,因此由本文所建立的这三类Eshelby张量之间的关系,可以很方便地求出力电耦合夹杂问题的电弹Eshelby张量。由电弹Eshelby张量的封闭形式解,我们可以得到当受外场及本征场作用时铁电夹杂内的约束电弹场的封闭形式解。此解可以用来分析外加电弹场与铁电夹杂内局部场之间的关系,从而为建立考虑夹杂之间相互作用和组分材料性能影响的畴变准则奠定基础。在这部分的工作中,我们还具体给出了横观各向同性圆柱夹杂和横观各向同性球形夹杂的电弹Eshelby张量的解析解。 2.以能量等效方法和本文第一部分的单个夹杂解,本文系统地研究了铁电复合材料的线性性质。得到了压电复合材料有效压电模量的封闭形式解。当采用不同的方法求解夹杂中平均应变与平均电场时,由此封闭形式解可以得到压电复合材料有效压电模量的稀疏解和Mori-Tanaka解。当椭球夹杂形状改变时,此解还可以分析具有不同连通性的压电复合材料有效性质。将此解推广,得到了含非压电相夹杂的压电复合材料有效性质的封闭形式解。在这部分的工作中,我们还具体给出了1-3型压电复合材料有效电弹模量的稀疏解和Moil-Tanaka解,以及0-3型压电复合材料有效电弹模量的稀疏解。理论预测值与实验值吻合较好。 3.考虑取向分布函数及其演化及铁电相材料的电畴反转,本文从宏观与细观相结合的角度系统地研究了铁电复合材料的非线性性质。建立了考虑铁电夹杂之间相互作用以及组分材料性能影响的畴变准则。以细观力学方法构造了铁电复合材料本构构元的能量,并以此建立了基于铁电畴变和铁弹畴变的铁电复合材料本构关系。此本构关系可以分析铁电复合材料的极化问题与非线性力电耦合问题。与实验结果的比较表明,本文建立的模型可以很好地描述铁电复合材料的主要性更多还原

【Abstract】 This dissertation studies the macroscopic and microscopic electric-mechanical coupling behavior of ferroelectric composites in systematic manner. The work is focused on the following five aspects:1. The problem of a ferroelectric ellipsoidal inclusion embedded in an infinite non-piezoelectric matrix is analyzed via the Green’s function technique. The closed-form solutions of the electroelastic Eshelby’s tensors can be expressed by the Eshelby’s tensors of the perfectly elastic inclusion problem and the perfectly dielectric inclusion problem. Since the closed-form solutions of the Eshelby’s tensors of the perfectly elastic inclusion problem and the perfectly dielectric inclusion problem can be given by theory of elasticity and electrodynamics respectively, the electroelastic Eshelby’s tensors can be gotten conveniently. Using these results, the closed-form solutions of the constraint elastic fields and constraint electric fields inside ferroelectric ellipsoidal are also obtained. The closed-form solutions can be readily utilized in analyzing the relations between the constraint electroelastic fields in the inclusion and applied electroelastic fields, which are the base of the switching criterion when the interactions among inclusions are considered, In this part, the analytical solutions of electroelastic Eshelby’s tensors are obtained for the cylinder inclusion and the spherical inclusion which are transversely isotropic.2. Based on the generalized Budiansky’s energy-equivalence framework and the results obtained in part I, the linear electric-mechanical coupling behavior of ferroelectric composites is studied systematically. The closed-form solutions of the effective properties of piezocomposites are given. The solutions can be used to analyze non-interaction or interaction among piezoelectric inclusions as well as the different connectivity patterns. The closed-form solutions of the effective properties of piezocomposites with non-piezoelectric inclusions are also obtained. In this part, the analytical solutions of the effective electroelastic moduli are obtained by means of the dilute solution for the 0-3 piezocomposite with the transversely isotropic piezoelectric spherical inclusion and by the dilute solution and the Mori-Tanaka’s method for the 1-3 piezocomposite with two kinds of transversely isotropicpiezoelectric cylinderical inclusions. The predicted results are compared with experimental data, which shows that the theoretical values agree quite well with the experimental ones.3. The non-linear electric-mechanical coupling behavior of ferroelectric composites is studied systematically by means of orientation distribution function (ODF) and its evolution and the domain switching of ferroelectric inclusions. The switching criterion which considers the interaction among the ferroelectric inclusions and the effect of material properties of constitutive phases is established. The free energy of the constitutive element is derived by micromechanics. Based on the above results, the constitutive law of ferroelectric composites is obtained, which can be used to analyze the poling problems and the non-linear electric-mechanical coupling problems of ferroelectric composites. The theoretical values are compared with experimental results, which shows that the constitutive law in this part can describe the principal properties of ferroelectric composites very well.4. The electric-mechanical coupling properties of the ferroelectric composites whose matrix is viscoelectric and exhibits dielectric relaxation are studied by means of Laplace transformation. The switching criterion and constitutive law is obtained which considers the interaction among the ferroelectric inclusions and the viscoelasticity and dielectric relaxations of the matrix. The predicted results are compared with experimental data, which shows that the constitutive law can describe the electric-mechanical coupling behavior of these kinds of ferroelectric composites.5. The experimental research for ferroelectric composites is carried out and new experimental data are obtained.更多还原