航空学报 > 2018, Vol. 39 Issue (9): 221976-221987   doi: 10.7527/S1000-6893.2018.21976

无限板孔边裂纹问题的高精度解析权函数解

赵晓辰1, 吴学仁1, 童第华1, 徐武2, 陈勃1, 胡本润1   

  1. 1. 中国航发 北京航空材料研究院, 北京 100095;
    2. 上海交通大学 航空航天学院, 上海 200240
  • 收稿日期:2017-12-29 修回日期:2018-03-14 出版日期:2018-09-15 发布日期:2018-05-15
  • 通讯作者: 吴学仁 E-mail:xrwu621@163.com
  • 基金资助:
    国家自然科学基金(11402249)

Accurate analytical weight function solutions for crack at edge of circular hole in infinite plate

ZHAO Xiaochen1, WU Xueren1, TONG Dihua1, XU Wu2, CHEN Bo1, HU Benrun1   

  1. 1. AECC Beijing Institute of Aeronautical Materials, Beijing 100095, China;
    2. School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, China
  • Received:2017-12-29 Revised:2018-03-14 Online:2018-09-15 Published:2018-05-15
  • Supported by:
    National Natural Science Foundation of China (11402249)

摘要: 用Wu-Carlsson解析权函数法(WFM)求得了无限板孔边径向单裂纹和对称双裂纹的高精度解析权函数(WF)。分别用Shivakumar-Forman和Newman的解及基于复变函数泰勒级数展开的数值权函数WCTSE法结果,通过对相应格林函数(GF)的逐点比较验证了本文解析权函数的精度。该权函数不但精度高,而且作为裂纹长度的连续函数,能够高效准确地求解任意长度(a/R≤2)裂纹在任意复杂载荷作用下的断裂力学关键参量;且孔边单/双裂纹问题的权函数的形式和推导方法完全相同。作为示例,用该解析权函数计算了孔边裂纹在裂纹嘴楔形载荷、裂纹面幂函数,以及圆孔冷挤压残余应力等多种载荷形式下的应力强度因子。

关键词: 孔边裂纹, 权函数法, 格林函数, 应力强度因子, 裂纹张开位移

Abstract: Highly accurate Weight Functions (WFs) for the radial crack(s) at a circular hole are derived by using the Wu-Carlsson analytical Weight Function Method (WFM). Accuracy of the WFs proposed is verified and validated point-by-point by using Green's Functions (GFs) of Shivakumar-Forman and Newman, and also the Weight function Complex Taylor Series Expansion (WCTSE) method. It is shown that the WFs proposed are not only highly accurate, but also, as a continuous function for crack length, enable determination of key mechanical parameters of cracks of any length (a/R ≤ 2) under arbitrary loadings with high efficiency and accuracy. A unified approach is adopted for the derivations and expressions of WFs for single/double hole-edge crack(s). The analytical WFs proposed are also used to calculate stress intensity factors for various load cases including wedge-splitting forces at the crack mouth, crack face power stresses, and residual stress fields induced by cold-working of the circular hole.

Key words: crack at edge of circular hole, weight function method, Green's function, stress intensity factor, crack opening displacement

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