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  

Study on Two-dimensional Contact Problem of Piezoelectric Coating-functionally Graded Piezoelectric Interface Layer-substrate Structure

作　　者：崔智刚 刘铁军 Zhigang Cui;Tiejun Liu(Department of Mechanics,School of Science,Inner Mongolia University of Technology,Hohhot,010051)

机构地区：[1]内蒙古工业大学理学院力学系,呼和浩特010051

出　　处：《固体力学学报》2022年第3期284-295,共12页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(12062019);内蒙古自然科学基金项目(2020MS01022)资助。

摘　　要：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.论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方法,论文将压电涂层-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.论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.Sudden changes of material compositions and properties at the interface of multilayer elements often lead to stress concentration at the interface,resulting in cracking or creep of the interface layer,which severely shortens the service life of piezoelectric elements.As an interface layer,functionally graded piezoelectric materials can effectively alleviate the damage caused by interface material mismatch.This study focuses on the electromechanical response of the structure under the action of cylindrical indenter when the interface layer of functionally graded piezoelectric material is used to connect the piezoelectric coating and the substrate.Using the Fourier integral transform method,the two-dimensional plane strain contact problem of a structure consisting of a piezoelectric coating,a functionally graded piezoelectric interface layer,and a substrate under the action of rigid cylindrical indenter is transformed into a singular integral equation with the Cauchy kernel.Using the Gauss Chebyshev integration method,the singular integral equation is transformed into linear equations and solved numerically.The stress distribution and potential shift distribution in such a structure consisting of piezoelectric coating,a functionally graded piezoelectric interface layer,and a substrate under the action of cylindrical indenter are obtained.The numerical results show that the variations of gradient piezoelectric material parameters significantly influence the electromechanical response of the structure.Having important theoretical guiding significance for using the functionally graded piezoelectric interface layer to eliminate the failure due to stress discontinuity at the interface,the research results can provide help for the design of functionally graded piezoelectric interface layer.

关 键 词：接触力学 功能梯度压电材料 界面层应力 傅里叶积分变换 奇异积分方程 力电响应 

分 类 号：TB34[一般工业技术—材料科学与工程]