功能梯度压电界面层在球形压头作用下的接触问题  

Contact problem of functionally graded piezoelectric interface layer under a spherical punch

作　　者：臧炜煜 刘铁军 ZANG Weiyu;LIU Tiejun(Department of Mechanics,School of Science,Inner Mongolia University of Technology,010051 Hohhot,China)

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：《应用力学学报》2024年第5期1175-1185,共11页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金资助项目(No.12062019);内蒙古自然科学基金资助项目(No.2020MS01022)。

摘　　要：材料参数的不连续变化是导致界面处裂纹萌生和分层现象的重要原因。将材料参数连续变化的功能梯度压电材料用作界面层是抑制界面处裂纹萌生和分层的重要方法。主要研究了压电涂层-功能梯度压电界面层-压电基底结构在刚性绝缘球形压头作用下的轴对称无摩擦接触问题。首先,假设涂层和基底为均匀压电材料,建立材料参数沿厚度方向按照指数函数形式变化的功能梯度压电界面层的接触力学分析模型;其次,利用Hankel积分变换方法,将刚性球形压头作用下压电涂层-功能梯度压电界面层-压电基底结构的轴对称无摩擦接触问题转化为奇异积分方程并求解;最后,得到材料非均匀参数对涂层、梯度压电界面层、基底结构内部及界面处的力电响应的影响。研究结果表明:功能梯度压电材料作为界面层连接压电涂层和基底时,可以消除界面处的材料参数不连续导致的界面应力不连续;梯度压电材料参数的变化对界面层的应力与电位移分量有显著影响。The discontinuous variation of material properties is an important reason for the crack initiation and delamination at the interface.Therefore,using functionally graded piezoelectric materials with continuous variation of material properties as the interfacial layer is an important method to affect the crack initiation and delamination at the interface.In this paper,the axisymmetric frictionless contact problem of piezoelectric coating-functionally graded piezoelectric interfacial layer-piezoelectric substrate structure under a rigid insulating spherical punch is studied.First,assuming that the coating and substrate are homogeneous piezoelectric materials,the contact mechanics analysis model of functionally graded piezoelectric interfacial layer with material properties varying in the form of exponential function along the thickness direction is established.Then,the axisymmetric frictionless contact problem of piezoelectric coating-functionally graded piezoelectric interfacial layer-piezoelectric substrate structure under a rigid spherical punch is transformed into a singular integral equation by using Hankel integral transformation method and solved by numerical integration method.Finally,the effects of material inhomogeneous properties on the electromechanical responses of coating,gradient piezoelectric interfacial layer,substrate structure and interface are obtained.The results show that when the functionally graded piezoelectric materials can be used as the interfacial layer to connect the piezoelectric coating and substrate,the interface stress discontinuity caused by the discontinuity of material properties at the interface can be eliminated.The variation of gradient piezoelectric material properties in the interfacial layer has a significant effect on the stress and electric displacement components of the interface layer.

关 键 词：接触 奇异积分方程 功能梯度压电材料 界面层 力电响应 

分 类 号：O343.3[理学—固体力学]