压电体中考虑表面效应时开裂孔洞的断裂特征

研究了反平面机械载荷和面内电载荷作用下压电体中考虑表面效应时孔边双裂纹问题的断裂特征。基于Gurtin-Murdoch表面理论模型，通过构造映射函数，利用复势电弹理论获得了应力场和电位移场的闭合解答。给出了裂纹尖端应力强度因子、电位移场强因子和能量释放率的解析解。讨论了开裂孔洞几何参数和施加力电载荷对电弹场强因子和能量释放率的影响。

Fracture characteristics of cracked hole in piezoelectric solids considering surface effect

When defects (holes and cracks) in the piezoelectric material are on the order of nanometers, the surface properties of the defects have great influences on the distributions of the stress fields and the electric displacement fields, and the surface effects are not negligible. In this paper, the surface electroelastic constants of the defects are introduced to extend the size of the cracked circular hole in the piezoelectric solids to nanoscale. The fracture characteristics of piezoelectric solids containing two edge cracks emanating from a circular hole with surface under antiplane mechanical loads and inplane electric displacement loads was investigated theoretically. Based on the Gurtin-Murdoch surface model, the closed solutions of the stress field and electric displacement field of the problem are obtained using the complex potential function electroelastic theory via constructing a conformal mapping function. Analytical s of the stress intensity factor, electric displacement field factor and energy release rate at the crack tip are presented. The influences of the geometric parameters of the cracked hole, the applied mechanical load and electrical load on the electroelastic fields intensity factors and the energy release rate are discussed. The major results are as follows: The dimensionless stress intensity factor and the dimensionless electric displacement field factor of the nanoscale cracked hole are different, and both have significant size dependence. The dimensionless electroelastic field factors increase monotonously with the increase of the relative length of the crack to a fixed value. The dimensionless energy release rate of the nanoscale cracked hole has a significant size effect. The larger the hole and the longer the crack are, the greater the normalized energy release rate is. The effect of the mechanical loads on the normalized energy release rate is affected by the applied electrical loads. The normalized energy release rate increases first and then decreases with the increase of the electrical loads.