The fracture behavior of multiple cracks emanating from a circular hole in piezoelectric materials

Abstract

Using the complex variable method and a new conformal mapping, the fracture behavior of multiple cracks emanating from a circular hole in piezoelectric materials is considered under remotely uniform in-plane electric and anti-plane mechanical loadings. The analytic solutions of the field intensity factors and the energy release rate are presented by taking the effect of dielectric permittivity into consideration. Known results can be derived as special cases from the general solutions. The results are illustrated with plots, showing that the piezoelectric material containing three radial cracks spaced equally at 120° apart originating from a circular hole is the easiest to fail for all cases of cracks originating from a circular hole under in-plane electric and anti-plane mechanical loadings. Moreover, if there exist multiple cracks (n ≥ 3) originating from a circular hole in piezoelectric materials, an increase in the number of cracks can enhance the reliability of these materials. The star-shaped cracks possess similar characteristics.