Buckling Analysis And Stoney Formula Of Piezoelectric Thin Film-elastic Substrate Structure

With the growing development of science and technology,in the micro nano electromechanical system,flexible electronic devices,aerospace and human health monitoring,some structures that need high integration,high efficiency,low energy consumption and other characteristics to complete some specific work,the thin film basement structure plays an important role.Piezoelectric materials were also widely used in sensors and low power transistors because of their unique mechanical and electrical coupling properties.However,this structure often had mechanical failure such as membrane buckling,fracture and delamination,because of the existence of residual stress and the complex working environment.It is of great significance to further study these mechanical failure problems for the further application and optimization of this structure.Based on the basic theory of piezoelectric and the base of nonlinear elastic thin plate theory,the problem of warpage and deformation of piezoelectric thin film elastic substrate was first analyzed;Secondly,based on the minimum energy principle,the buckling problem of piezoelectric thin film elastic substrate was systematically studied;Then the bilayer structure is extended to the 3 layer structure,and the buckling proplem of the 3 layer structure was studied by a similar method;Finally,the Stoney's work on metal thin films is extended to piezoelectric materials,and the Stoney formula of piezoelectric thin film elastic substrate structure was obtained.The main work was summarized as follows:(1)The warpage problem of piezoelectric thin film elastic substrate structure was analyzed theoretically,and the critical condition and amplitude of warpage were obtained.When the piezoelectric material is degenerated into elastic material,the result is consistent with the results obtained in the literature.Compared with elastic thin films,it was found that piezoelectric effect can improve the buckling stability of piezoelectric thin film elastic substrate system.(2)The problem of buckling and post buckling of piezoelectric thin film elastic substrate under the action of force electric coupling load(pre strain and voltage)was studied systematically.The influence of material parameters,soft and hard degree of elastic substrate,pre strain and voltage on buckling behavior was emphatically analyzed.On the assumption of small strain,based on the theory of thin film and piezoelectricity,the analytical expressions of the wavelength,amplitude and critical strain of the buckling of the piezoelectric film,as well as the analytical expression of the wavelength and amplitude of post buckling were obtained by the energy method.Under the finite deformation hypothesis,the buckling and post buckling problems were further analyzed.The analytical expressions of the amplitude,wavelength and critical strain of the buckling of the piezoelectric thin film elastic substrate structure were obtained,and the analytical expressions for the amplitude and wavelength of the post buckling were obtained.Based on the error analysis of the two deformation hypotheses,it was found that when the strain is not more than 5%,the two error is less than 5%.(3)The buckling problem of 3 layer structure of piezoelectric thin film was studied theoretically.Based on the energy method,the critical strain,wave number,wavelength and amplitude of the 3 layer structure buckling of piezoelectric thin film were obtained.When the 3 layer structure is degraded to the bilayer structure,the analytical expression of its buckling characteristic is exactly the same as that of the bilayer structure.By comparing and analyzing the 3 layer structure of the piezoelectric thin film and the 3 layer structure of the elastic film,it was found that the piezoelectric material can improve the capacity of the structure to resist the buckling deformation because of its piezoelectric effect.(4)The problem of bending deformation due to mismatch of piezoelectric bilayer structure was studied.The Stoney formula for the piezoelectric thin film elastic substrate structure was obtained by energy analysis.By comparing and analyzing the difference between the elastic thin film and the piezoelectric thin film Stoney formula,it was found that the piezoelectric effect can reduce the bending curvature of the bilayer structure,and the greater the coupling coefficient of the force and electricity,the smaller the curvature.A simple method for estimating transverse piezoelectric constant was proposed by applying the Stoney formula.