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杨昌锦 李尧臣. 压电体表面金属电极脱层的屈曲分析[J]. 力学学报, 2009, 41(4): 489-502. DOI: 10.6052/0459-1879-2009-4-2007-556
引用本文: 杨昌锦 李尧臣. 压电体表面金属电极脱层的屈曲分析[J]. 力学学报, 2009, 41(4): 489-502. DOI: 10.6052/0459-1879-2009-4-2007-556
Changjin Yang, Yaochen Li. Buckling analysis of the electrode delamination on the piezoelectric substrate[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(4): 489-502. DOI: 10.6052/0459-1879-2009-4-2007-556
Citation: Changjin Yang, Yaochen Li. Buckling analysis of the electrode delamination on the piezoelectric substrate[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(4): 489-502. DOI: 10.6052/0459-1879-2009-4-2007-556

压电体表面金属电极脱层的屈曲分析

Buckling analysis of the electrode delamination on the piezoelectric substrate

  • 摘要: 基于弹性有限变形理论和电弹性体偏场理论,对半无限压电体及其表面电极层间存在穿透脱层的屈曲问题进行了分析. 采用平面应变模型,在脱层远处作用有平行于脱层的应变载荷. 使用Fourier积分变换,应用脱层界面的连续条件和电极表面的边界条件将问题归为第2类Cauchy型奇异积分方程组. 利用Gauss-Chebyshev积分公式将奇异积分方程组变为齐次线性代数方程组,以确定临界应变载荷. 通过数值算例,给出了底层为PZT-4材料、电极为金属Pt在不同的脱层长厚比时的临界应变载荷和屈曲形状,分析了压电体的压电、介电效应对屈曲载荷的影响. 另外给出了脱层屈曲时,脱层尖端奇异性振荡因子随不同脱层长厚比的关系曲线.

     

    Abstract: The paper investigated the electrode delaminationbuckling of the layered system containing a through-the-width delaminationbetween the metallic electrode and the half-space piezoelectric substratebased on the finite deformation theory of elasticity and the biasing fieldtheory of the electroelastic body. The layered system in the plane strainproblem is subjected to the compressive strain-load parallel to the freesurface. Meanwhile, the theoretical model is reduced to the second kindCauchy-type singular integral equations by means of the Fourier integraltransform, the boundary conditions and the interfacial continuousconditions. The singular integral equations are solved numerically byutilizing Gauss-Chebyshev integral formulae. As an example, the layeredsystem of the metallic electrode Pt and piezoelectric substrate PZT-4 isconsidered. Numerical results for the critical strains of buckling and thecorresponding delamination buckling shapes are presented for, respectively,various ratios of the delamination length to thickness and the effect ofelectromechanical coupling in the piezoelectric substrate. The curves of thesingular oscillating factors in the delamination tip with respect to theratios of delamination length to thickness are also given.

     

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