电可通纳米尺度孔边均布多裂纹的电弹断裂分析

解析研究了面内电载荷和反平面机械载荷作用下压电体中纳米尺度圆孔边均布电可通多裂纹问题的断裂性能。基于Gurtin-Murdoch表面弹性理论，利用保角映射方法和复变弹性理论给出了裂纹尖端电弹场分布、电弹场强度因子及能量释放率的解析结果。阐述了无量纲电弹场强度因子、无量纲能量释放率的尺寸依赖效应，讨论了裂纹数量和缺陷几何参数对无量纲场强度因子和无量纲能量释放率的影响。结果表明：无量纲电弹场强度因子和无量纲能量释放率具有显著的尺寸依赖效应；考虑表面效应，孔径和裂纹长度相当时，电弹场强度因子达到最大；裂纹/孔径比对电弹场强度因子随裂纹数量变化的制约会随着裂纹数量的增加而逐渐消失；过大或过小的裂纹孔径比会削弱裂纹长度对能量释放率的影响。

Electroelastic Fracture Analysis of Electrically Permeable Multiple Nano Cracks Emanating from A Circular Hole with Surface Effects

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.