Analysis of a Partially Debonded Elliptic Inhomogeneity in Piezoelectric Materials
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摘要: 利用复变函数方法，研究在反平面剪切和面内电场共同作用下压电材料椭圆夹杂的界面脱粘问题．假定夹杂界面脱粘导致了界面电绝缘型裂纹的产生．通过保角变换和解析延拓，将原问题化为两个黎曼-希尔伯特问题，获得了夹杂和基体复势的级数解，进而求得应力变形场以及夹杂-基体界面脱粘的能量释放率的一般表达式．通过理想粘结的椭圆夹杂、完全脱粘的椭圆夹杂、局部脱粘的刚性导体椭圆夹杂、局部脱粘的圆形夹杂等特例的分析说明了该解的有效性和通用性．Abstract: A generalized solution was obtained for the partially debonded elliptic inhomogeneity problem in piezoelectric materials under antiplane shear and inplane electric loading using the complex variable method.It was assumed that the interfacial debonding induced an electrically impermeable crack at the interface.The principle of conformal transformation and analytical continuation were employed to reduce the formulation into two Riemann-Hilbert problems.This enabled the determination of the complex potentials in the inhomogeneity and the matrix by means of series of expressions.The resulting solution was then used to obtain the electroelastic fields and the energy release rate involving the debonding at the inhomogeneity-matrix interface.The validity and versatility of the current general solution have been demonstrated through some specific examples such as the problems of perfectly bonded elliptic inhomogeneity,totally debonded elliptic inhomogeneity,partially debonded rigid and conducting elliptic inhomogeneity,and partially debonded circular inhomogeneity.
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Key words:
- piezoelectric material /
- elliptic inhomogeneity /
- debonding /
- energy release rate
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