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A set of electrically conducting collinear cracks between two dissimilar piezoelectric materials
International Journal of Engineering Science ( IF 6.6 ) Pub Date : 2022-06-22 , DOI: 10.1016/j.ijengsci.2022.103725
V. Loboda , A. Sheveleva , F. Chapelle , Y. Lapusta

The plane problem of multiple collinear cracks between two piezoelectric semi-infinite spaces is considered. The cracks can have arbitrary lengths and distances between each other and they are assumed to be electrically conductive. The materials are polarized in the orthogonal to the interface direction. In-plane combined tension-shear loading and the electric field parallel to the crack faces are prescribed at infinity. The Riemann-Hilbert problems of linear relationship are formulated and solved analytically by using the presentations of electro-mechanical quantities via sectionally-analytic functions. The arbitrary constants are found from the conditions at infinity and the system of linear algebraic equations which dimension is equal to the number of cracks. Stresses, electric field outside cracks as well as mechanical and electrical displacement jumps along the crack regions are found in the relatively simple analytical forms. Special attention was devoted to the energy release rate (ERR) determination. Due to analysis of asymptotic fields at the tips of single and multiple

interface cracks, the analytical presentations of the ERR for any crack tips are obtained. Numerical illustrations for several interface cracks are presented. The variations of stresses, electric field and the crack opening along the interface are demonstrated. The ERR are given for different crack tips, loading, crack locations and different physical aspects of the interaction effect are discussed. The particular cases of purely elastic and purely electrically conductive states are considered and good agreement with known results is demonstrated.



中文翻译:

两种不同压电材料之间的一组导电共线裂纹

考虑了两个压电半无限空间之间多条共线裂纹的平面问题。裂纹可以具有任意长度和彼此之间的距离,并且假定它们是导电的。材料在与界面方向正交的方向上极化。平面内组合的拉剪载荷和平行于裂纹面的电场被规定为无穷大。线性关系的黎曼-希尔伯特问题是通过使用通过截面解析函数的机电量表示来解析地制定和解决的。任意常数是从无限大的条件和维数等于裂缝数量的线性代数方程组中找到的。强调,裂缝外的电场以及沿裂缝区域的机械和电位移跳跃在相对简单的分析形式中被发现。特别注意能量释放率(ERR)的确定。由于分析了单个和多个尖端的渐近场

界面裂纹,得到任何裂纹尖端的 ​​ERR 的分析表示。给出了几种界面裂纹的数值图解。展示了沿界面的应力、电场和裂纹开口的变化。给出了针对不同裂纹尖端、载荷、裂纹位置和相互作用效应的不同物理方面的 ERR。考虑了纯弹性和纯导电状态的特殊情况,并证明了与已知结果的良好一致性。

更新日期:2022-06-23
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