压电涂层-功能梯度压电界面层-基底结构的二维接触问题研究

在多层压电元件中,由于界面处材料成分和性质的突变,常常导致界面处应力集中,使得界面处出现开裂或蠕变现象,从而大大缩短了压电元件的使用寿命。功能梯度压电材料作为界面层,可有效的缓解界面材料不匹配导致的破坏。本文主要研究利用功能梯度压电材料界面层连接压电涂层和基底,分析三层结构在圆柱型压头作用下的力电响应。利用傅里叶积分变换技术,本文将压电涂层-功能梯度压电层-基底结构在刚性圆柱压头作用下的二维平面应变接触问题转化为带有柯西核的奇异积分方程。运用高斯-切比雪夫积分公式,将奇异积分方程转化为线性方程组并对其进行数值求解,得到压电涂层-功能梯度压电层-基底结构在圆柱形压头作用下的应力分布和电位移分布。数值结果表明,梯度压电材料参数的变化对结构中的力电响应具有重要的影响。本文研究结果对于利用功能梯度压电界面层消除界面处的应力不连续导致的界面破坏具有重要的理论指导意义,研究结果可为功能梯度压电材料界面层的设计提供帮助。     

Winkler地基模型上功能梯度材料涂层的摩擦接触问题

研究Winker地基模型上功能梯度材料涂层在一刚性圆柱形冲头作用下的摩擦接触问题。功能梯度材料涂层表面作用有法线向和切线向集中作用力。假设材料非均匀参数呈指数形式变化,泊松比为常量,利用Fourier积分变换技术将求解模型的接触问题转化为奇异积分方程组,再利用切比雪夫多项式对所得奇异积分方程组进行数值求解。最后,给出了功能梯度材料非均匀参数、摩擦系数、Winker地基模型刚度系数及冲头曲率半径对接触应力分布和接触区宽度的影响情况。     

一类功能梯度材料表面接触力学研究进展

针对一类杨氏模量梯度变化的功能梯度材料, 考虑摩擦、微动磨损和黏附等因素, 综述了梯度材料有限尺寸、梯度变化规律、梯度涂层厚度、界面摩擦热、压头形状等对表面接触力学性能的影响; 根据不同接触模型中接触界面应力场分布, 分析多种因素影响下功能梯度材料表面抵抗磨损的能力; 最后给出了功能梯度材料接触力学研究中仍存在的主要科学问题及进一步研究展望.      

刚性圆形压头作用下热电材料半平面的无摩擦接触问题

热电材料可以将热能转化为电能,反之亦然,这一优良的性质将有助于研发更具成本效益的设备和器件。本文研究了刚性圆形压头作用在热电材料半平面的无摩擦接触问题。假定压头为电导体、热导体,且压头压入深度及与材料的接触区域宽度未知。首先求解电场和温度场,利用傅里叶变换得到了电势函数、温度、电流密度和能量通量的解析表达式。然后求解弹性场,利用积分变换和边界条件,将该热弹性接触问题转化为第一类奇异积分方程并数值求解。数值结果讨论了压头半径和热电载荷对法向接触应力、电流强度因子和能量通量强度因子的影响。结果表明,对于圆压头,热电材料的法向电流密度、法向能量通量在接触边缘表现出奇异性,而表面法向接触应力在接触边缘为零。本文建立的研究模型有助于更深层次的了解热电材料的接触行为。     

功能梯度材料涂层平面运动裂纹分析

研究粘结于均匀材料基底上功能梯度材料涂层平面运动裂纹问题,假设功能梯度材料剪切模量和密度为坐标的指数函数,而泊松比为常数.采用Fourier变换和传递矩阵法将该混合边值问题转化为一对奇异积分方程,通过数值求解奇异积分方程组获得功能梯度材料涂层平面运动裂纹的应力强度因子.考察了结构几何尺寸、裂纹运动速度以及材料梯度参数对运动裂纹的应力强度因子的影响,发现材料梯度参数、结构几何尺寸、裂纹长度以及运动速度均对功能梯度材料动态断裂行为有显著影响.     

功能梯度材料涂层平面裂纹分析

研究粘接于均质基底材料上功能梯度涂层平面裂纹问题. 假设功能梯度材料剪切模量的倒数为坐标的线性函数，而泊松比为常数. 采用Fourier变换和传递矩阵法将该混合边值问题化为奇异积分方程组，通过数值求解获得 应力强度因子. 考察了材料梯度变化形式、结构几何尺寸和材料梯度参数对裂纹应力强度因子的影响，发现 功能梯度材料涂层尺寸、裂纹长度以及材料梯度参数均对应力强度因子有显著影响.     

任意梯度分布功能梯度涂层平面裂纹分析

提出可以分析任意梯度功能梯度材料的分层模型,并采用该模型研究功能梯度涂层平面裂纹问题.采用Fourier变换和传递矩阵法将该混合边值问题化为奇异积分方程组,通过数值求解获得应力强度因子.考察了分层模型的有效性,以及材料梯度变化形式、结构几何尺寸和材料梯度参数对裂纹应力强度因子的影响,发现结构几何尺寸、材料梯度变化形式、...     

功能梯度层与弹性层间的单退让接触问题

基于所有接触面间光滑的假设,研究了同时受压的功能梯度层与弹性层间的单退让平面接触问题.假设功能梯度层是各向同性的非均匀材料,其剪切模量按照指数函数形式变化.利用Fourier积分变换把问题转化为求解奇异积分方程.然后利用Gauss-Chebyshev求积公式和迭代法得到下层接触应力和退让接触半径的数值解.最后在数值算例中,分别讨论了两层间的厚度比值,功能梯度层的硬度参数,以及上层接触半径对退让接触半径与下层接触应力的影响.     

功能梯度压电压磁材料粘结的Ⅲ型裂纹问题

利用奇异积分方程方法研究两个半无限大的功能梯度压电压磁材料粘结,在渗透和非 渗透边界条件下的III型裂纹问题. 首先通过积分变换构造出原问题的形式解，然 后利用边界条件通过积分变换与留数定理得到一组奇异积分方程， 最后利用Gauss-Chebyshev方法进行数值 求解，讨论材料参数、材料非均匀参数以及裂纹几何形状等对裂纹尖端应力 强度因子的影响. 从结果中可以看出，压电压磁复合材料中反平面问题的应力奇异性 形式与一般弹性材料中的反平面问题应力奇异形式相同，但材料梯度参数对功能梯度压电压 磁复合材料中的应力强度因子和电位移强度因子有很大的影响.     

自适应无网格法在生物涂层接触问题中的应用

自适应无网格法是针对有限元法无法求解或者不易求解的复杂问题,利用无网格法节点排布灵活、易于增删节点、便于自适应分析等优点发展起来的. 在对自适应无网格法理论基础和发展进行总结基础上,采用基于应变能梯度的自适应无网格—— 有限元耦合方法,对等离子喷涂制备的HA 生物涂层材料的无摩擦接触问题进行分析,对制备的两种不同厚度的生物涂层材料进行求解,分别给出了von Mises 应力分布云图. 结果表明,自适应无网格法能较好地应用于生物涂层接触问题中.     

The axisymmetric partial slip contact problem of a graded coating

In this paper, the axisymmetric contact problem with the partial slip condition for a functionally graded coated half-space which is indented by a rigid spherical indenter is considered. The material properties are assumed to vary along the thickness of the coating. A series of linear functions of the thickness are used to model the functionally graded coating with the arbitrarily varying shear modulus. The contact problem is formulated in terms of a set of Cauchy singular integral equations by employment of Hankel integral transforms technique and transfer matrix method. By using the uncoupled solution and the coupled solution,the coupled equations are solved. The effect of the coating’s gradient on the normal and radial tractions in the whole contact region is presented. The results show that the contact tractions and the size of the stick zone can be altered by adjusting the gradient of the coating. This may have potential applications in the resistance of contact deformation and damage.     

Contact vibration analysis of the functionally graded material coated half-space under a rigid spherical punch

This paper studies the contact vibration problem of an elastic half-space coated with functionally graded materials (FGMs) subject to a rigid spherical punch. A static force superimposing a dynamic time-harmonic force acts on the rigid spherical punch. Firstly, we give the static contact problem of FGMs by a least-square fitting approach. Next, the dynamic contact pressure is solved by employing the perturbation method. Lastly, the dynamic contact stiffness with different dynamic contact displacement conditions is derived for the FGM coated half-space. The effects of the gradient index, coating thickness, internal friction, and punch radius on the dynamic contact stiffness factor are discussed in detail.     

Analytical solution of the spherical indentation problem for a half-space with gradients with the depth elastic properties

The contact problem for the impression of spherical indenter into a non-homogeneous (both layered and functionally graded) elastic half-space is considered. Analytical methods for solving this problem have been developed. It is assumed that the Lame coefficients vary arbitrarily with the half-space depth. The problem is reduced to dual integral equations. The developed methods make it possible to find the analytical asymptotically exact problem solution, suitable for a PC. The influence of the Lame coefficients variation upon the contact stresses and size of the contact zone with different radius of indenter as well as values of the impressing forces are studied. The effect of the non-homogeneity is examined. The developed method allows to construct analytical solutions with presupposed accuracy and gives the opportunity to do multiparametric and qualitative investigations of the problem with minimal computation time expenditure.     

Axisymmetric frictionless contact of functionally graded materials

The main interest of this study is a new method to solve the axisymmetric frictionless contact problem of functionally graded materials (FGMs). Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into a series of sub-layers with shear modulus varying linearly in each sub-layer and continuous at the sub-interfaces. With this model, the axisymmetric frictionless contact problem of a functionally graded coated half-space is investigated. By using the transfer matrix method and Hankel integral transform technique, the problem is reduced to a Cauchy singular integral equation. The contact pressure, contact region and indentation are calculated for various indenters by solving the equations numerically. An erratum to this article can be found at     

Two-dimensional contact mechanics of functionally graded materials with arbitrary spatial variations of material properties

A multi-layered model for frictionless contact analysis of functionally graded materials (FGMs) with arbitrarily varying elastic modulus under plane strain-state deformation has been developed. Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into several sub-layers and in each sub-layers the shear modulus is assumed to be linear function while the Poisson’s ratio is assumed to be a constant. With the model, the frictionless contact problem of a functionally graded coated half-space is investigated. By using the transfer matrix method and Fourier integral transform technique, the problem is reduced to a Cauchy singular integral equation. The contact pressure, contact region and indentation are calculated for various indenters by solving the equations numerically.     

Two-dimensional sliding frictional contact of functionally graded materials

A multi-layered model for sliding frictional contact analysis of functionally graded materials (FGMs) with arbitrarily varying shear modulus under plane strain-state deformation has been developed. Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into several sub-layers and in each sub-layers the shear modulus is assumed to be a linear function while the Poisson's ratio is assumed to be a constant. In the contact area, it is assumed that the friction is one of Coulomb type. With this model the fundamental solutions for concentrated forces acting perpendicular and parallel to the FGMs layer surface are obtained. Then the sliding frictional contact problem of a functionally graded coated half-space is investigated. The transfer matrix method and Fourier integral transform technique are employed to cast the problem to a Cauchy singular integral equation. The contact stresses and contact area are calculated for various moving stamps by solving the equations numerically. The results show that appropriate gradual variation of the shear modulus can significantly alter the stresses in the contact zone.     

The axisymmetric torsional contact problem of a functionally graded piezoelectric coated half-space

In this article, we study the axisymmetric tor-sional contact problem of a half-space coated with func-tionally graded piezoelectric material (FGPM) and subjected to a rigid circular punch. It is found that, along the thick-ness direction, the electromechanical properties of FGPMs change exponentially. We apply the Hankel integral trans-form technique and reduce the problem to a singular integral equation, and then numerically determine the unknown con-tact stress and electric displacement at the contact surface. The results show that the surface contact stress, surface azimuthal displacement, surface electric displacement, and inner electromechanical field are obviously dependent on the gradient index of the FGPM coating. It is found that we can adjust the gradient index of the FGPM coating to modify the distributions of the electric displacement and contact stress.     

Indentation of a Rigid Sphere into an Elastic Half-Space in the Direction Orthogonal to the Axis of Material Symmetry

In this work a contact problem for a transversely isotropic half-space indented by a rigid sphere is considered. The axis of symmetry of the half-space is orthogonal to the axis of the applied contact load, which makes the problem fully three-dimensional. An exact solution to this contact problem is constructed. Stresses and strains are obtained in the form of contour integrals in the complex plane with explicitly determined dimensionless integrands. As an illustrative application of the constructed solution, failure beneath the indenter in a unidirectional composite is analyzed.     

Mechanics of indentation for piezoelectric thin films on elastic substrate

Frictionless normal indentation problem of rigid flat-ended cylindrical, conical and spherical indenters on piezoelectric film, which is either in frictionless contact with or perfectly bonded to an elastic half-space (substrate), is investigated. Both conducting and insulating indenters are considered. With Hankel transform, the general solutions of the homogeneous governing equations for the piezoelectric layer and the elastic half-space are presented. Using the boundary conditions for a vertical point force or a point electric charge, and the boundary conditions on the film/substrate interface, the Green’s functions can be obtained by solving sets of simultaneous linear algebraic equations. The solution of the indentation problem is obtained by integrating these Green’s functions over the contact area with unknown surface tractions or electric charge distribution, which will be determined from the boundary conditions on the contact surface between the indenter and the film. The solution is expressed in terms of dual integral equations that are converted to a Fredholm integral equation of the second kind and solved numerically. Numerical examples are also presented. The comparison between two film/substrate bonding conditions is made. It shows that the indentation rigidity of the film/substrate system is lower when the film is in frictionless contact with the substrate. The effects of the Young’s modulus and Poisson’s ratio of the elastic substrate, indenter electrical condition and indenter prescribed electric potential on the indentation responses are presented.