Electroelastic interaction between a piezoelectric screw dislocation and an elliptical inclusion with interfacial cracks

Abstract

The electroelastic interaction between a piezoelectric screw dislocation, which is located inside either the inclusion or the matrix, and an elliptical inclusion with interfacial cracks under antiplane mechanical and inplane electrical loads is dealt with. An efficient and concise complex variable method for complex multiply connected region is developed, in terms of which general solutions of complex potentials in the matrix and the inclusion regions are derived. The explicit series-form solutions are then given for the interface with a finite crack. The image force on the piezoelectric screw dislocation due to the elliptical inclusion, interfacial crack and remote uniform loadings is calculated by using the generalized PeachKoehler formula. The influence of the curvature and the length of the crack, the shape of the inclusion and electroelastic mismatch between two materials on the image force is evaluated and discussed. Numerical examples show that the elliptical arc interfacial crack has significant effect on the equilibrium position of the dislocation near the interface. Further analysis implies that, when the curvature or the length of the crack goes up to a critical value, existence of the interfacial crack can change the interaction mechanism between a piezoelectric screw dislocation and the elliptical inclusion. In addition, a significative result is that there exists a same value of the crack angle to change the direction of the image force regardless of the shape of the inclusion as the area of the elliptical inclusion taking a constant. The present solutions contain a number of previously known results which can be shown to be special cases.

Size‐dependent elastic interaction between a screw dislocation and a circular nano‐hole with surface stress

“…Using Eq. (12) and referring to the work of Fang et al 6, the explicit expressions of the image force acting on the screw dislocation can be obtained: …”

Novel near-cloaking multicoated structures for screw dislocations

“…In particular, the elastic interaction of dislocations with inclusions is a classical topic that has attracted intensive interest from researchers (e.g. Dundurs, 1969;Srolovitz et al, 1984;Luo and Chen, 1991;Xiao and Chen, 2000;Li and Shi, 2002;Wang and Shen, 2002;Fan and Wang, 2003;Fang et al, 2005;Liu et al, 2004Liu et al, , 2006Jin and Fang, 2008;Fang et al, 2009;Markenscoff, 2010). In all the previous studies, the mobility of the dislocations was investigated in detail for given material and geometric parameters of the composites.…”

Analytical solution for a strained reinforcement layer bonded to lip-shaped crack under remote mode III uniform load and concentrated load

“…The strained reinforcement layer is bounded by two lip-shaped curves. The original problem can be mapped onto two concentric circles and be solved by using the method (unlike the work [10]) based on the complex potential method of conformal mapping and the technique of analytical continuation. The results of stress field and interfacial stress are obtained and described by numerical curves.…”