力学学报 ›› 2017, Vol. 49 ›› Issue (4): 848-857.doi: 10.6052/0459-1879-17-024

• 固体力学 • 上一篇    下一篇

半无限板边缘裂纹的权函数解法与评价

童第华, 吴学仁, 胡本润, 陈勃   

  1. 北京航空材料研究院, 北京 100095
  • 收稿日期:2017-01-20 出版日期:2017-07-15 发布日期:2017-08-01
  • 通讯作者: 吴学仁,研究员,主要研究方向:材料与结构的疲劳与断裂.E-mail:xrwu621@163.com E-mail:xrwu621@163.com
  • 基金资助:

    国家自然科学基金资助项目(11402249)

WEIGHT FUNCTION METHODS AND ASSESSMENT FOR AN EDGE CRACK IN A SEMI-INFINITE PLATE

Tong Dihua, Wu Xueren, Hu Benrun, Chen Bo   

  1. Beijing Institute of Aeronautical Materials, Beijing 100095, China
  • Received:2017-01-20 Online:2017-07-15 Published:2017-08-01
  • Contact: V215 E-mail:xrwu621@163.com

摘要:

权函数法是求解裂纹体在任意受载条件下的应力强度因子和裂纹面位移等断裂力学参量的高效、高精度方法,与有限元等数值方法相比,在求解效率和可靠性方面均具有明显优势.针对半无限板边缘裂纹,系统分析了在国际断裂力学界较有代表性的Wu-Carlsson、Glinka-Shen和Fett-Munz三种解析形式的权函数法,进而以在远端均匀加载下的半无限板边缘裂纹面位移Wigglesworth解析解导得的权函数及其对应的格林函数解(即裂纹面受一对单位集中力作用下的应力强度因子)为基准,沿整个裂纹长度对3种权函数的精度逐点进行比较,并与文献中基于其他方法求得的权函数做了广泛对比,包括Bueckner,Hartranft-Sih以及Wigglesworth利用不同解析方法推导出的高精度的权函数.研究了3种参考载荷(均布/正反向线性分布应力、集中力)及其不同组合,以及裂纹嘴位移的几何条件对权函数精度的影响.结果表明,基于一种参考载荷下的裂纹面张开位移比基于两种参考载荷下的应力强度因子所得到的权函数具有更高的精度,而且后一种方法的精度明显受到所选参考载荷组合的影响;裂纹面位移在裂纹嘴处三阶导数等于零的条件对基于一个参考解的权函数精度的改进效果较小.最后给出了利用各种权函数方法计算得到的4种载荷条件下的应力强度因子,并对结果进行了比较.

关键词:

半无限板|边缘裂纹|权函数法|格林函数|应力强度因子

Abstract:

Weight function method (WFM) is highly efficient and accurate for the determination of stress intensity factors (SIFs) and crack opening displacements (CODs) of cracked bodies under arbitrary load conditions. Comparing to the numerical methods such as the finite element method, WFMs have distinct advantage in terms of computational efficiency and reliability. This paper makes systematic analyses and comparisons of three WF approaches by Wu-Carlsson, Glinka-Shen and Fett-Munz, respectively, which are representative in the international fracture mechanics community. By employing the Wigglesworth analytical solutions to CODs of an edge crack in a semi-infinite plate under uniform tension, the WF and corresponding Green's function (SIF for a pair of point forces acting at an arbitrary location along the crack) are derived and used as the base for point-to-point comparison. The results are also compared with other existing WFs in the literature, including those by Bueckner, Hartranft-Sih and Wigglesworth using different analytical approaches. The study also includes the influence of selection of three reference load cases, including uniform, linear and reverse-linear stress distributions and their combinations, and geometric conditions related to CODs on the WF accuracy. Results show that the WF based on COD analytical expression for one reference load case are more accurate than that based on two SIFs due to two reference load cases. Furthermore, solution accuracy of the later approach is considerably affected by the selected reference load case(s). The geometric condition that the third derivative of COD vanishes at crack mouth has little effect on the accuracy of one-reference-load-case-based weight function. Finally, SIFs for four load cases calculated by using various WFMs are presented and compared.

Key words:

semi-infinite plate|edge crack|weight function method|Green's function|stress intensity factor

中图分类号: 

  • V215