表面荷载作用下半无限层状介质中的裂纹分析

Analysis of crack problems in layered half-spaces subject to uniform loadings over boundary surface

分析了半无限层状介质中的正方形裂纹。层状材料的层面互相平行,外部荷载作用在边界面上,正方形裂纹平行于层面。基于Yue基本解的数值方法和线弹性断裂力学叠加原理,首先采用一种数值方法获得无裂纹半无限层状介质的应力场,然后将计算得到的应力按叠加原理施加在裂纹面上,并采用另一种数值方法计算此情形下裂纹面的间断位移,最后采用裂纹面的间断位移计算应力强度因子。结果显示:I型和II型应力强度因子的变化与裂纹所处的位置关系密切;层状介质中的裂纹张开和滑移受到不同介质存在的影响,进而影响到裂纹的应力强度因子。建议的数值方法可用于分析复杂荷载作用下层状介质中裂纹的断裂力学特性。

This paper analyzes the square-shaped crack problems in layered half-spaces subject to uniform circular loadings on the boundary surface. The square-shaped cracks are parallel to the boundary surface and the interfaces of layered materials are also parallel to each other. The novel numerical methods to be used are based on the fundamental solutions of a layered elastic media. A numerical method is employed to analyze the stress fields of layered half-spaces without a crack, the superposition principle in linear elastic fracture mechanics is used to obtain the tractions on the crack surfaces and another numerical method is utilized to calculate discontinuous displacements on the crack surfaces. Finally, the discontinuity displacements are used to calculate the stress intensity factors. Results show that the variations of the stress intensity factors of I and II types are related to the positions of the crack in layered media. It can also be found that different layer in which the crack is located exerts an obviously different influence on the opening and sliding of the crack surfaces and induce the variations of the stress intensity factors. The proposed numerical methods can be used to analyze crack problems in layered materials under the action of complex loadings.