力学与实践 ›› 2020, Vol. 42 ›› Issue (4): 504-507.DOI: 10.6052/1000-0879-19-476

• 教育研究 • 上一篇    下一篇

用Westergaard应力函数求解I-II复合型平面裂纹问题的研讨

蒋玉川*,1), 蒲淳清   

  1. * 四川大学建筑与环境学院,成都610065;
    † 四川众恒建筑设计有限责任公司,成都 610072
  • 收稿日期:2019-12-18 出版日期:2020-08-20 发布日期:2020-08-25
  • 通讯作者: 1)蒋玉川,教授,主要研究方向为力学的教学和科研。E-mail: jiangyc@scu.edu.cn

THE PROBLEM OF I-II COMBINED PLANE CRACK SOLVED WITH WESTERGAARD STRESS FUNCTION

JIANG Yuchuan*,1), PU Chunqing   

  1. * School of Architecture and Environment, Sichuan University, Chengdu 610065, China;
    † Sichuan Zhongheng Architectural Design Limited Liability Company, Chengdu 610072, China
  • Received:2019-12-18 Online:2020-08-20 Published:2020-08-25

摘要: 直接获得I-II复合型平面裂纹问题裂纹尖端区域的应力场是一个比较复杂的问题,在此应用Westergaard应力函数求解I-II复合型平面裂纹问题,导出了裂纹尖端区域应力分量的表达式。该方法推导过程简单,物理概念清晰,其结果与一般断裂力学教材和文献中的结果一致。同时,应用叠加原理将裂纹面上的作用力转化为裂纹外边界的受力,给出了解决裂纹面上有作用力的I-II复合型平面裂纹问题的解题方法。

关键词: I-II复合型平面裂纹, Westergaard应力函数, 裂纹尖端应力分量, 叠加原理

Abstract: It is not easy to obtain directly the stress field at the crack tip of I-II combined mode plane crack problem. In this paper, the Westergaard stress function is used to solve the plane crack problem of I-II combined mode, complete with the expressions of the stress components at the crack tip. The method is simple in the derivation procedure and explicit in the physical concept, and the results are shown to agree well with available results in open literature. At the same time, the superposition principle is applied to transform the force on the crack surface into the force on the outer boundary for the problem of I-II combined plane crack with force on the crack surface.

Key words: I-II compound mode plane crack, Westergaard stress function, stress component near crack tip, superposition principle

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