用Westergaard应力函数求解Ⅰ-Ⅱ复合型平面裂纹问题的研讨  

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

作　　者：蒋玉川[1] 蒲淳清 JIANG Yuchuan;PU Chunqing(School of Architecture and Environment,Sichuan University,Chengdu 610065,China;Sichuan Zhongheng Architectural Design Limited Liability Company,Chengdu 610072,China)

机构地区：[1]四川大学建筑与环境学院,成都610065 [2]四川众恒建筑设计有限责任公司,成都610072

出　　处：《力学与实践》2020年第4期504-507,共4页Mechanics in Engineering

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。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.

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 

分 类 号：O346[理学—固体力学]