Mechanics of indentation for piezoelectric thin films on elastic substrate

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:49

Article

Wu, Y. F.²  Yu, H. Y.^2,3  Chen, W. Q.¹ 

[1] Zhejiang Univ, Dept Engn Mech, Hangzhou 310027, Peoples R China

[2] Zhejiang Univ, Dept Civil Engn, Hangzhou 310058, Zhejiang, Peoples R China

[3] Natl Tsing Hua Univ, Dept Mat Sci & Engn, Hsinchu 30013, Taiwan

关键词: Indentation;    Piezoelectric film;    Green's function;    Integral equations;   

DOI  :  10.1016/j.ijsolstr.2011.09.014

来源: Elsevier

【 摘 要 】

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. (C) 2011 Elsevier Ltd. All rights reserved.

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