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.     

非均匀铁弹畴变对离面极化压电陶瓷应力强度因子的影响研究

基于文献中报道的试验结果，本文考虑非均匀的畴变过程区，它包含一个位于中心的饱和区和环绕饱和区的渐变区．为了描述外加应力引起的部分铁弹畴变，本文采用一个显式的基于最小能量原理的非均匀畴变准则．考虑离面极化的压电陶瓷，假设其初始极化矢量平行于离面方向．畴变后的电畴位于面内，具体方位由最大释放功来确定．基于非均匀畴变准则，本文给出了裂尖处非均匀畴变区几何及畴变体积分数的分布．并在静止裂纹和稳态扩展裂纹两种特殊情况下计算了铁弹畴变对裂尖处应力强度因子的影响．结果表明：(1) 静止裂纹尖端处的畴变减小了材料的起裂强度；(2) 准静态稳态裂纹附近的畴变增加了材料的断裂强度．且理论预测的R曲线渐近值与试验结果定量吻合．     

压电圆柱形夹杂对邻近裂纹三维应力场的影响

研究了压电复合材料薄板中压电圆柱形夹杂与邻近宏观钝裂纹间的相互作用。重点分析了外加电场，裂尖与压电圆柱形夹杂间韧带长度对裂尖三维应力场的影响。计算结果表明：在不同的外加电场作用下，压电体不仅能改变裂尖张开应力的大小，还能改变其分布。所得结果对进一步探讨线弹性介质中裂纹的启裂控制有参考价值。     

一维六方准晶压电材料反平面Ⅲ型裂纹电塑性分析

论文基于一维六方准晶压电材料反平面问题的基本方程,对Ⅲ型裂纹的电塑性区进行分析.采用条带模型并假设在电塑性区的切应力保持为常数,得到了电塑性区大小的表达式.这种假设方式消除了电场和应力在裂纹尖端的奇异性,这与实际情况相符合,也为一维六方准晶压电材料的断裂分析提供了理论基础.     

含电饱和区的压电双材料反平面界面Yoffe型运动裂纹问题研究

本文利用Fourier变换及Copson求解方法,得到了压电双材料中Yoffe型运动裂纹在裂纹尖端含有条状电饱和区条件下的相关解析解.结果表明电饱和尺寸只与电荷载有关,而与裂纹扩展速度无关;裂纹尖端的应力强度因子及电势跳变不仅与荷载及材料参数有关,而且还受到速度的影响,其中应力强度因子随着速度的增大而增大,而电势跳变随着速度的变化呈现递减趋势.     

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．     

多孔极化PZT95/5铁电陶瓷单轴压缩力学响应与放电特性

采用添加造孔剂的方法制备了四种不同孔隙率PZT95/5铁电陶瓷,对其进行电场极化,随后开展了准静态单轴压缩实验,讨论了畴变、相变以及孔隙率对极化PZT95/5铁电陶瓷的力学响应与放电特性的影响. 研究结果表明：(1)多孔极化PZT95/5铁电陶瓷非线性力学响应行为主要归因于畴变和相变的共同作用,与内部孔洞变形和坍塌基本无关;(2) 在准静态单轴压缩下极化PZT95/5铁电陶瓷的去极化机制是畴变和相变的共同作用;(3) 孔隙率对极化PZT95/5铁电陶瓷的弹性模量、压缩强度有明显的影响,而对断裂应变的影响较小;(4)极化PZT95/5铁电陶瓷畴变和相变开始的临界应力都随着孔隙率的增大而线性衰减,但相变开始的临界体积应变却不依赖孔隙率;(5)极化PZT95/5铁电陶瓷电荷饱和释放量随着孔隙率呈线性减小,但孔隙率对电荷释放速率基本没有影响。     

压电效应下一维六方准晶双材料孔边裂纹的反平面问题研究

利用复变函数方法和保角变换技术研究了压电效应下一维六方准晶双材料中圆孔边单裂纹的反平面问题．考虑电不可渗透型边界条件,运用保角变换和Stroh公式得到了弹性体受远场剪切力和面内电载荷作用下裂纹尖端应力强度因子和能量释放率的解析解. 数值算例分析了几何参数、远场受力、电位移载荷对能量释放率的影响．结果表明：裂纹长度、耦合系数和远场剪切力的减小可以抑制裂纹的扩展．不考虑电场时,声子场应力对能量释放率的影响较小．本文的研究结果可作为研究一维六方压电准晶双材料孔边裂纹问题的理论基础,同时为压电准晶及其复合材料的设计、制备、优化和性能评估提供理论依据．     

矩形压电体中反平面裂纹的电弹性场

基于线性压电理论,本文获得了含有中心反平面裂纹的矩形压电体中的奇异应力和电场。利用Fourier积分变换和Fourier正弦级数将电绝缘型裂纹问题化为对偶积分方程,并进一步归结为易于求解的第二类Fred-holm积分方程。获得了裂纹尖端应力、应变、电位移和电场的解析解,求得了裂纹尖端场的强度因子及能量释放率。分析了压电矩形体的几何尺寸对它们的影响。结果表明,对于电绝缘型裂纹,裂纹尖端附近的各个场变量都具有-1/2阶的奇异性,能量释放率与电荷载的方向及大小有关,并且有可能为负值。     

Effect of electric displacement saturation on the stress intensity factor for a crack in a ferroelectric ceramic

A crack in a ferroelectric ceramic with perfect saturation under electric loading is analyzed. The boundary of the electric displacement saturation zone ahead of the crack tip is assumed to be ellipse in shape. The shape and size of ferroelectric domain switching zone near a crack tip is determined based on the nonlinear electric theory. The stress intensity factor induced by ferroelectric domain switching under small-scale conditions is numerically obtained as a function of the electric saturation zone parameter and the ratio of the coercive electric field to the yield electric field. It is found that the stress intensity factor increases as the ratio of the semi-axes of the saturation ellipse increases.     

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.     

Effect of electrical polarization saturation on stress intensity factors in a piezoelectric ceramic

The electric-field induced stress intensity factor in a piezoelectric medium of limited electrical polarization is evaluated based on a strip-saturation model of the Dugdale-type. Particular emphasis is placed on the effect of the saturation condition on the near tip field and the stress intensity factor. To this end, the general solution is derived in terms of the (unspecified) normal electrical displacement distribution along the saturated strip. Since the saturated strip is representative of the unknown saturated zone, the normal electrical displacement may suffer discontinuity across the saturated strip. It is found that the crack-tip field and the stress intensity factors depend on the discontinuity of the normal electrical displacement across the saturated strip although this dependency disappears in some practically important cases. A crack perpendicular to the poling axis in a general poled ferroelectric is discussed in detail to illustrate the implications of the strip-saturation model for electric-field induced cracking. The results show that some discrepancies between theory and experiments, for which the classical linear piezoelectric model gives qualitatively incorrect results, can be explained clearly in terms of the stress intensity factor given by the strip-saturation model. In particular, these results are independent of the form of the saturation condition imposed on the saturated strip.     

Study on fracture behavior of ferroelectric ceramics under combined electromechanical loading by using a moiré interferometry technique

This paper discusses an in situ observation of fracture behavior around a crack tip in ferroelectric ceramics under combined electromechanical loading by use of a moiré interferometry technique. The deformation field induced by the electric field and the stress concentration near the crack tip in three-points bending experiments was measured. By analysis of the moiré images it is found that under a constant mechanical load, the electric field almost has no effect on the crack extension in the case that the directions of the poling, electric field and crack extension are perpendicular to each other. When the poling direction is parallel to the crack extension direction and perpendicular to the electric field, the strain decreases faster than that calculated by FEM with and without electrical loading as one goes away from the crack tip. In addition, as the electric field intensity increases, the strain near the crack tip increases, and the strain concentration becomes more significant. The project supported by the National Natural Science Foundation of China (10132010, 10025209, 10232023)     

Complex variable approach in studying modified polarization saturation model in two-dimensional semipermeable piezoelectric media

A modified polarization saturation model is proposed and addressed mathematically using a complex variable approach in two-dimensional(2 D) semipermeable piezoelectric media. In this model, an existing polarization saturation(PS) model in 2D piezoelectric media is modified by considering a linearly varying saturated normal electric displacement load in place of a constant normal electric displacement load, applied on a saturated electric zone. A centre cracked infinite 2D piezoelectric domain subject to an arbitrary poling direction and in-plane electromechanical loadings is considered for the analytical and numerical studies. Here, the problem is mathematically modeled as a non-homogeneous Riemann-Hilbert problem in terms of unknown complex potential functions representing electric displacement and stress components. Having solved the Hilbert problem, the solutions to the saturated zone length, the crack opening displacement(COD), the crack opening potential(COP), and the local stress intensity factors(SIFs) are obtained in explicit forms. A numerical study is also presented for the proposed modified model, showing the effects of the saturation condition on the applied electrical loading, the saturation zone length, and the COP. The results of fracture parameters obtained from the proposed model are compared with the existing PS model subject to electrical loading, crack face conditions, and polarization angles.     

Strip electric-magnetic breakdown model in a magnetoelectroelastic medium

Extending the polarization saturation model [Gao et al., 1997. Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic. J. Mech. Phys. Solids 45, 491-510] and the dielectric breakdown (DB) model [Zhang et al., 2005. The strip dielectric breakdown model. Int. J. Fract. 132, 311-327] in piezoelectric materials, the Strip Electric-Magnetic Breakdown (SEMB) model is proposed for electrically and magnetically impermeable crack in a magnetoelectroelastic medium to study the effect of the nonlinear character of electric field and magnetic field on fracture of magnetoelectroelastic materials. In the SEMB model, the electric field in the strip of the electric breakdown zone ahead of the crack tip is equal to the electric breakdown strength, while the magnetic filed in the strip of the magnetic breakdown zone is equal to the magnetic breakdown strength. By using the extended Stroh formalism and the extended dislocation modeling of a crack, the Griffith crack problem under the electrically and magnetically elastic-plastic condition in a magnetoelectroelastic medium is reduced to a set of dual integral equations. The sizes of the electric breakdown zone and the magnetic breakdown zone, the extended intensity factors and the local J-integral are obtained. The effect of the combined mechanical-electric-magnetic loadings on the local J-integral is studied.     

A Crack with an Electric Displacement Saturation Zone in an Electrostrictive Material

A crack with an electric displacement saturation zone in an electrostrictive material under purely electric loading is analyzed. A strip saturation model is here employed to investigate the effect of the electrical polarization saturation on electric fields and elastic fields. A closed form solution of electric fields and elastic fields for the crack with the strip saturation zone is obtained by using the complex function theory. It is found that the K _I -dominant region is very small compared to the strip saturation zone. The generalized Dugdale zone model is also employed in order to investigate the effect of the saturation zone shape on the stress intensity factor. Using the body force analogy, the stress intensity factor for the asymptotic problem of a crack with an elliptical saturation zone is evaluated numerically.     

Fatigue crack growth induced by domain switching under electromechanical load in ferroelectrics

Reliability calls for a better understanding of the failure of ferroelectric ceramics. The fracture and fatigue of ferroelectric ceramics under an electric field or a combined electric and mechanical loading are investigated. The small-scale domain-switching model is modified to analyze failure due to fracture and fatigue. Effects of anisotropy and electromechanical load coupling are taken into account. Analytical expressions are obtained for domain-switching regions near the crack tip such that of 90° domain switching can be distinguished from 180° domain switching in addition to different initial poling directions. The crack tip stress intensity variation of ferroelectric ceramics due to the domain switching is analyzed. A positive electric field tends to enhance the propagation of an insulating crack perpendicular to the poling direction, while a negative field impedes it. Fatigue crack growth under various coupling loads and effects of the stress field and electric field on near field stress intensity variation are analyzed. Predicted crack growth versus cyclic electric field agrees well with experiment.     

含直对称裂纹的一维六方压电准晶对SH波的散射Scattering of SH wave by a linear symmetric crack at one-dimensional piezoelectric hexagonal quasicrystals

利用积分变换技术,结合Copson方法,研究了含直线型对称裂纹的一维六方压电准晶对SH波的散射问题。通过求解对偶积分方程,得到声子场、相位子场应力、位移及电场电位移分量的解析解。定义了裂纹尖端应力强度因子及电位移强度因子,给出了电非渗透性条件下应力强度因子及电位移强度因子的解析解。此研究结果对压电准晶材料的工程应用有一定的理论价值。