Abstract：The fracture characteristics of radial electrically permeable multi-cracks originating from a nanoscale circular hole in piezoelectric materials subjected to inplane electric loads and far-field antiplane mechanical loads were analytically investigated. Based on the Gurtin-Murdoch surface elasticity theory, the analytical solution of the electroelastic field, the electroelastic intensity factor and the energy release rate at the crack tip were obtained by using the conformal mapping technique and the complex elastic theory. The size effects of the dimensionless electroelastic intensity factor and the dimensionless energy release rate were revealed and the influences of the number of cracks and defect parameters (hole size, crack length, hole/crack ratio) on dimensionless electroelastic intensity factor and dimensionless energy release rate were discussed. The results indicate that the dimensionless electroelastic field intensity factor and the dimensionless energy release rate have a significant size-dependent effect. As the hole size increases, the size effect of the dimensionless field intensity factor and dimensionless energy release rate gradually disappear, and the dimensionless stress intensity factor is different from the dimensionless electric displacement intensity factor. The electroelastic field intensity factor can reach its maximum only when the crack length is close to the hole size, and overlarge or oversmall crack/hole ratio shields the dimensionless field intensity factor. When the number of cracks is 3, the dimensionless field intensity factor reaches its maximum value, and then gradually decreases with the increase of the number of cracks. The influence of the crack/hole ratio on the variation of the electroelastic field intensity factor with the number of cracks gradually weakens when the number of cracks increases. Overlarge or oversmall crack/hole ratio greatly weakens the effect of crack length on the energy release rate. When the ratio of hole size and crack length is in the range of (0.1, 10), the effect of the crack length on the dimensionless energy release rate is greater.
2020, Vol. 41 
