Numerical studies of an array of equidistant semi-permeable inclined cracks in 2-D piezoelectric strip using distributed dislocation method

Abstract

An array of equidistant inclined cracks present in 2-D piezoelectric strip is numerically analyzed using distributed dislocation method (DDM). The piezoelectric strip is a cutout of an infinite domain so that the width-to-crack-length ratio is about 100 times larger than the aspect ratio of height-to-crack-length of the specimen. The inclined equidistant cracks are modeled as a continuous distribution of dislocations, and the problem is thus reduced into simultaneous Cauchy's type singular integral equations, which are then solved by the Gauss–Chebychev quadrature method. The study is carried out with respect to number of cracks, aspect ratio, inclination angle, inter-crack space distance, crack-face electrical boundary conditions and electrical loading. Various numbers of inclined equidistant cracks with different inclination angles under semi-permeable crack-face boundary conditions are examined. To show the accuracy and efficacy of DDM in modeling finite cracked piezoelectric problems, fracture parameters obtained by the DDM are validated against the results of extended finite element method under impermeable crack-face boundary conditions for two particular cases i.e., inclined crack and two unequal collinear cracks. The present results show the significant effects of aspect ratio, distance between cracks, inclination angle, crack face boundary conditions, and electrical loading on fracture parameters. The DDM developed to analyze an array of equidistant inclined cracks in 2-D piezoelectric strip can be extended to inclined periodic cracks in 2-D piezoelectric strip under various electrical boundary conditions.