导电压头作用下的功能梯度压电涂层二维黏附接触问题研究  

The 2D Adhesive Contact of the Functionally Graded Piezoelectric Coating Under a Conducting Indenter

作　　者：韩立夫[1,2] 刘铁军[1] HAN Lifu;LIU Tiejun(College of Science,Inner Mongolia University of Technology,Hohhot 010051,P.R.China;Hetao College,Bayannur,Inner Mongolia 015000,P.R.China)

机构地区：[1]内蒙古工业大学理学院,呼和浩特010051 [2]河套学院,内蒙古巴彦淖尔015000

出　　处：《应用数学和力学》2024年第2期227-244,共18页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11662011);内蒙古自然科学基金(2020MS01022)。

摘　　要：纳米压痕实验是研究材料的力学性能和表面形貌的重要手段,当接触区尺寸减小时,压头与试件接触表面间的黏附作用将无法忽视,因此,考虑黏附作用对压头作用下的接触问题具有重要的价值.功能梯度压电材料(FGPM)兼具梯度材料和压电材料的优点,用作涂层可有效地抑制接触损伤和破坏.该文将针对梯度压电材料在导电压头作用下的黏附接触问题开展研究,假设功能梯度压电涂层的材料参数按照指数形式变化,基于Maugis黏附模型,利用Fourier积分变换获得了功能梯度压电涂层在导电压头作用下的二维无摩擦黏附接触问题的控制奇异积分方程,并采用Erdogan-Gupta的数值方法求解,获得了黏附应力、梯度参数和压头所带电荷对力-电耦合响应的影响.研究结果为利用功能梯度压电材料涂层改善材料表面的接触行为提供了理论依据,同时可为压电结构及器件的设计提供帮助.Nano-indentation experiments are an important means of studying the mechanical properties and surface morphology of materials.With the decrease of the contact area,the adhesion between the indenter and the contact surface of the specimen cannot be ignored.Therefore,the adhesion effect plays an important role in the contact problem under the action of the indenter.The functional graded piezoelectric material(FGPM)has the advantages of both graded and piezoelectric materials,and can effectively avoid contact damage and failure of coatings.The adhesive contact problem of FGPMs under conducting indenters was studied.With exponentially changing material parameters of the FGPM coating,based on the Maugis adhesive model,the control singular integral equation for the 2D frictionless adhesive contact problem of the FGPM coating under the conducting indenter,was obtained through the Fourier integral transform,and the Erdogan-Gupta numerical method was used to solve the equation.The effects of the adhesive stress,the graded parameter and the charge of the indenter on the electro-mechanical coupling response were obtained.The results provide a theoretical basis for improving the contact behavior of material surfaces with FGPM coatings,and help design piezoelectric structures and devices.

关 键 词：功能梯度压电涂层 黏附 Fourier积分变换 奇异积分方程 

分 类 号：O34[理学—固体力学]