压电材料裂纹顶端条状电饱和区 模型的力学分析1)

在线性压电本构方程框架下,对裂纹顶端条状电饱和区模型进行了严格的数学分析.完整地考虑了各向异性力电耦合效应.建立了电饱和区尺寸与外加电场的依赖关系.证实了当裂纹垂直极化轴时,压电材料的断裂应力随着外加正电场的增加而减小,随着外加负电场的增加而增加.当裂纹平行于极化轴时,与极化轴平行的外加电场对断裂应力无影响.     

双周期圆柱形压电夹杂反平面问题的精确解及其应用

研究无限压电介质中双周期圆柱形压电夹杂的反平面问题.借鉴Eshelby等效夹杂原理,通过引入双周期非均匀本征应变和本征电场,构造了一个与原问题等价的均匀介质双周期本征应变和本征电场问题.利用双准周期Riemann边值问题理论,获得了夹杂内外严格的电弹性解.作为压电纤维复合材料的一个重要模型,预测了压电纤维复合材料的有效电弹性模量.     

压电多层材料中的电极-陶瓷界面裂纹和椭圆夹杂

首先解析研究了压电多层材料中的电极-陶瓷界面裂纹,它是对Ru最近研究工作（见ASMB J·APPI.Mech.,2000年,67卷）的补充和完善.工作表明与 Ru的结论不同,对于一般的两相压电介质,仍可获得对于这种电极-陶瓷界面裂纹的精确解答.分析显示在界面处的电弹性场仍可显现出两类奇异性:振荡型奇异性一1/2土iε。和实指数型奇异性一1/2士 k,其中ε和k 由上下两相压电材料的本构常数加以确定.获得了界面电弹性场以及裂尖处能量释放率的显式和实形式解答.也讨论了在坐标变换下界面上物理量的一些不变性质.其次探讨了压电多层材料中的椭圆夹杂问题,并获得了当压电复合系统受到远场均布机电载荷时的通解.分析表明当压电基体受到远场均布机电载荷作用时,应力场和电场在压电夹杂体上仍然均匀分布井且整个夹杂体都为等电势体     

压电材料反平面应变状态的椭圆夹杂及界面裂纹问题

本文采用共法求解了压电材料反平面变形的椭圆夹杂及界面裂纹问题，前者的解答表明当远场外力均匀分布对夹杂内的应力场及电位移场是常量，后者解答表明在界面裂纹的裂尖处，应力及电位移都具有γ＾－１／２的奇异性。     

压电材料裂纹顶端条状电饱和区模型的力学分析

在线性压电本构方程框架下,对裂纹顶端条状电饱和区模型进行了严格的数学分析．完整地考虑了各向异性力电耦合效应．建立了电饱和区尺寸与外加电场的依赖关系．证实了当裂纹垂直极化轴时,压电材料的断裂应力随着外加正电场的增加而减小,随着外加负电场的增加而增加．当裂纹平行于极化轴时,与极化轴平行的外加电场对断裂应力无影响     

压电材料裂纹顶端条状电饱和区模型的力学分析

在线性压电本构方程框架下,对裂纹顶端条状电饱和区模型进行了严格的数学分析．完整地考虑了各向异性力电耦合效应．建立了电饱和区尺寸与外加电场的依赖关系．证实了当裂纹垂直极化轴时,压电材料的断裂应力随着外加正电场的增加而减小,随着外加负电场的增加而增加．当裂纹平行于极化轴时,与极化轴平行的外加电场对断裂应力无影响     

含刚性线夹杂及裂纹的各向异性压电材料耦合场分析

采用各向异性弹性力学中Ｓｔｒｏｈ方法对含刚性线夹杂及裂纹的无限大各向异性压电材料耦合的弹性场和电场进行了分析。并得到夹杂和基体界面间耦合场的实型显函表达式及夹杂尖端的１／２阶奇异性。     

力电耦合载荷作用下铁电陶瓷破坏行为的云纹干涉方法研究

本文介绍了如何用云纹干涉法实时地观察铁电陶瓷在力载荷和电载荷共同作用下裂尖的破坏行为．测量了三点弯试验中由电场和应力集中导致的裂尖的变形场．对变形的云纹图分析表明：当极化方向与裂纹扩展方向一致，且都与电场方向垂直，裂尖附近的正应变随电场的增加而增加，应变集中现象比较突出，电场促进和加速了裂纹的扩展．     

相变滞后对裂纹屏蔽效应的数值分析

论文针对奥氏体-马氏体双相材料,研究裂纹尖端区弥散分布的奥氏体颗粒在应变诱发时发生的相变对裂纹的屏蔽效应.鉴于实验中已发现的不同相变滞后对裂纹屏蔽效应的不同影响,研究通过在裂纹尖端区不同位置嵌入相变颗粒,考虑到裂纹尖端区应力应变场的奇异分布及其诱发的相变,将裂纹尖端区相变滞后问题转化为相变颗粒在裂纹尖端区的位置问题.计及奥氏体-马氏体相变的体积膨胀效应进行了平面应力裂纹问题数值模拟,得到了单个相变夹杂对裂纹屏蔽效应的影响规律.结果表明:裂纹尖端区相变夹杂的位置对裂纹的屏蔽效应在距裂尖2倍夹杂直径以内影响极大,且以裂尖86度方向为界.其影响规律与McMeeking和Evans理论预言的60度方向不同.     

压电界面裂纹裂尖强度因子的显式计算公式

对常见横观各向同性压电材料(TIP)中界面裂纹的裂纹面与压电材料的极化方向成任意夹角的一般情况进行了研究,通过推导得到了计算裂尖强度因子的显式外推公式,同时给出了裂纹面与极化方向垂直的典型情况下的外推公式.这些显式计算公式为常见数值方法如有限元法及边界元法在压电材料断裂力学中的应用提供了便利.     

Permeable cracks between two dissimilar piezoelectric materials

An interfacial crack with electrically permeable surfaces between two dissimilar piezoelectric ceramics under electromechanical loading is investigated. An exact expression for singular stress and electric fields near the tip of a permeable crack between two dissimilar anisotropic piezoelectric media are obtained. The interfacial crack-tip fields are shown to consist of both an inverse square root singularity and a pair of oscillatory singularities. It is found that the singular fields near the permeable interfacial crack tip are uniquely characterized by the real valued stress intensity factors proposed in this paper. The energy release rate is obtained in terms of the stress intensity factors. The exact solution of stress and electric fields for a finite interfacial crack problem is also derived.     

Antiplane deformation of a partially bonded elliptical inclusion

A new method that introduces two holomorphic potential functions (the two-phase potentials) is applied to analyze the antiplane deformation of an elliptical inhomogeneity partially-bonded to an infinite matrix. Elastic fields are obtained when either the matrix is subject to a uniform longitudinal shear or the inhomogeneity undergoes a uniform shear transformation. The stress field possesses the square-root singularity of a Mode III interface crack, which, in the special case of a rigid line inhomogeneity, changes in order, as the crack tip approaches the inhomogeneity end. In the latter situation the crack-tip elastic fields are linear in two real stress intensity factors related to a strong and a weak singularity of the stress field.     

压电体中裂纹与孤立电偶极子的相互作用

研究压电体裂纹与电偶极子的相互作用,得到问题的闭合解,包括应力-电位移场,裂纹张开位移和电势差,以及裂尖应力强度因子,结果表明,电偶极子的方向对裂纹场的影响可由压电体各向异性方向函数表示;当电偶极子位于裂尖附近时,在原点取在裂尖的局部极坐标系中电偶极子位置的极角对裂尖场的影响可由各向异性方向函数表示,电偶极子引起的裂尖应力强度因子与其距裂尖的距离的-3/2次幂成正比。     

Crack propagation along the interface of piezoelectric bimaterial

This paper is concerned with the propagation of a crack along the interface of a piezoelectric bimaterial, which can travel at subsonic or intersonic speed. The inertial effects are taken into account while the static approximation is applied to the electric fields. The effect of piezoelectricity on the asymptotic crack-tip field is discussed for an interface crack propagating subsonically and intersonically. An alternative method is used to avoid solving for the eigenvectors. This paper provides a unified method to analyze the crack-tip field of a crack propagating along a piezoelectric bimaterial interface.     

Effect of electric fields on fracture behavior of ferroelectric ceramics

The asymptotic problem of a semi-infinite crack perpendicular to the poling direction in a ferroelectric ceramic subjected to combined electric and mechanical loading is analyzed to investigate effect of electric fields on fracture behavior. Electromechanical coupling induced by the piezoelectric effect is neglected in this paper. The shape and size of the switching zone is shown to depend strongly on the relative magnitude between the applied electric field and stress field as well as on the ratio of the coercive electric field to the yield electric field. A universal relation between the crack tip stress intensity factor and the applied intensity factors of stress and electric field under small-scale conditions is obtained from the solution of the switching zone. It is found that the ratio of the coercive electric field to the yield electric field plays a significant role in determining the enhancement or reduction of the crack tip stress intensity factor. The fracture toughness variation of ferroelectrics under combined electric and mechanical loading is also discussed.     

各向异性压电材料平面裂纹的耦合场分析

用Stroh方法分析了各向异性压电材料电导通型裂纹问题的耦合场。结果表明,裂纹面上的切向电场强度和法向电位移均为常数,在裂纹尖端有由弹性场的耦事作用产生的奇异电导通裂纹模型中的静电场对裂纹尖端扩展的能量释放率不作贡献。     

Three-dimensional analysis of defects in a piezoelectric material

In this paper, the Green's function technique is used to develop a solution of an infinite, piezoelectric medium containing either an ellipsoidal cavity or a flat elliptical crack. The coupled elastic and electric fields both inside the cavity and on the boundary of the cavity are obtained, and the stress intensity factor and the electric field intensity factor are also obtained for an elliptical crack. It is found that; (1) the coupled elastic and electric fields inside the cavity keep uniform when the external elastic field and electric field are constant; (2) the behavior of the stress and electric field components in the neighborhood of the crack tip shows the classical type of singularity. The project supported by National Natural Science Foundation of China     

Dynamic response of a cracked piezoelectric ceramic under arbitrary electro-mechanical impact

The dynamic response of a cracked piezoelectric ceramic under in-plane electric and anti-plane mechanical impact is investigated by the integral transform method. The electric and mechanical loads are assumed to be arbitrary functions of time. It is shown that the dynamic crack-tip stress and electric displacement fields still have a square-root singularity. Numerical computations for the dynamic stress intensity factor show that the electric load has a significant influence on the dynamic response of stress field. On the other hand, the dynamic response of the electric field is determined solely by the applied electric field. The electric field will promote or retard the propagation of the crack depending on the time elapsed since the application of the external electro-mechanical loads.     

Coupled solution for anisotropic piezoelectric materials with cracks

The coupled elastic and electric fields for anisotropic piezoelectric materials with electrically permeable cracks are analyzed by using Stroh formula in anisotropic elasticity. It is shown from the solution that the tangent component of the electric field strength and the normal component of the electric displacement along the faces of cracks are all constants, and the electric field intensity and electric displacement have the singularity of type (1/2) at the crack tip. The energy release rate for crack propagation depends on both the stress intensity factor and material constants. The electric field intensity and electric displacement inside electrically permeable cracks are all constants.