孔洞对平面裂纹应力强度因子影响分析的广义参数Williams单元

本文采用圆形奇异区广义参数Williams单元（W单元）建立了中心裂纹与圆孔共存的平面应力模型，奇异区外围利用ABAQUS有限元软件自动网格离散技术与FORTRAN95编程前处理相结合，克服了自主编程中网格离散的局限性．算例分析了圆孔位置和几何参数对I-II混合型裂纹尖端应力强度因子(SIFs)的影响，并与扩展有限元法(XFEM)计算结果进行比较．结果表明：靠近圆孔一侧的裂尖SIFs大于远离圆孔一侧的裂尖SIFs；控制圆孔左边缘到裂纹中心的距离，则两侧裂尖SIFs随圆孔半径的增大而增大；圆孔中心与裂纹中心水平距离越远，圆孔对裂纹扩展的影响越小．同时，基于圆形奇异区的W单元直接计算得到的裂尖SIFs与扩展有限元法得到的解吻合较好，证明了W单元对奇异区离散形状不敏感，且具有高效率和高精度．

Finite Element Method with Generalized Degrees of Freedom for the Analysis of the Effect of Hole on the Crack Tip Stress Intensity Factor

This paper established a plane stress model with the central crack and the circular hole coexisting by adopting the finite element method with generalizaed degrees of freedom (W element) with circular singular region, and the periphery of the singular region was meshed through the combination of automatic grid dispersing function of ABAQUS finite element software and the preprocessing of FORTRAN95 programming, which overcomes the limitation of grid discretization in independent programming. The influences of the positions of the circular holes and the geometric parameters on the stress intensity factors (SIFs) of the mixed  model crack have been analyzed and compared with the results of the extended finite element method (XFEM). The results show that: The value of SIFs of the crack tip near the circular hole is larger than that far away from that the hole; if the distance between the left edge of the circular hole to the center of crack is kept constant, the SIFs of the crack tip on both sides increase with the radius of the circular hole; the larger the horizontal distance between the hole center and the  crack center is, the smaller the effect of the circular hole on the crack growth becomes. Meanwhile, the SIFs of the crack tip calculated directly from the W element based on the circular singular region is in good agreement with the results obtained by the extended finite element method, indicating that the W element method is insensitive to the dispersed shape of the singular region. In addition, it has high efficiency and good precision.