Abstract: The fracture performances of nano cracks emanating from circular holes under far-field antiplane shear were investigated. Based on the Gurtin-Murdoch surface elasticity theory and conformal mapping technique， an analytical solution of the whole-field stress for such heterogeneous materials was obtained by using complex elasticity theory. The closed-form formula for the mode Ⅲ stress intensity factors at tip of the nano cracks was presented. The stress field distributions of the hole were studied based on the obtained formulas. The size-dependence of the stress intensity factors and the influences of the relative size of the hole on the stress intensity factors at crack tips were also discussed. The numerical results reveal that the stress field of the hole shows a nonmonotonic distribution， and the influences of the surface effect on the stress are quite different at different positions on the holes. When the size of the hole-cracks is on the nanometer scale， the stress intensity factors at crack tips show a significant size dependent effect. The influences of the relative size of the holes on the stress intensity factors are restricted by the surface property. At the same time， the influences of the surface property on the stress intensity factors depend on the relative size of the holes too.

Key words: surface effect, nano cracked circular hole, mode Ⅲ crack, stress intensity factor

摘要： 研究了纳米尺度圆孔孔边裂纹在远场反平面剪切载荷作用下的断裂性能。基于Gurtin-Murdoch表面弹性理论和保角映射技术，利用复变弹性理论获得了该类非均匀材料应力场的解析解，给出了裂尖Ⅲ型应力强度因子的闭合解。基于所得解答，研究了孔边的应力场分布规律，讨论了裂尖应力强度因子的尺寸依赖效应以及圆孔相对尺寸对应力强度因子的影响。研究结果表明：孔边应力场呈现非单调分布，表面效应对孔边不同位置应力的影响程度不同；当圆孔裂纹的尺寸在纳米量级时，裂尖应力强度因子具有显著的尺寸依赖效应；圆孔相对裂纹尺寸对裂尖应力强度因子的影响规律受表面性能的制约，同时表面性能对应力强度因子的影响也取决于圆孔的相对尺寸。

关键词: 表面效应, 纳米尺度孔边裂纹, Ⅲ型裂纹, 应力强度因子