Dissertation
Dissertation > Mathematical sciences and chemical > Mechanics > Solid Mechanics > Strength theory > Fracture theory

Stress analysis of isotropic and orthotropic bi-material Ⅲ interface terminal

Author ZhaoJing
Tutor LiJunLin
School Taiyuan University of Science and Technology
Course Applied Mathematics
Keywords complex function isotropic and orthotropic bi-material ModeⅢinterface end singularity index stress fields displacement fields
CLC O346.1
Type Master's thesis
Year 2011
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With the rapid development of engineering technology, composite materials are used in production widely and all areas of life for its superior performance. In recent years ,with the depth research of composite materials, interface singular stress field has attracted great attention of many scholars at home and abroad. Singular stress field is the source of fracture mechanics. The fracture of bi-material occurs not only from the interface, thus obtain the analytical expression of stress field near the interface end is very important. Based on the analysis of bi-material interface crack, interface fracture mechanics has become mature. Stress field singularity of ModeⅢinterface end was studied widely, but the theory of fracture mechanics near the interface end has not yet formed.Boundary element method, integral transform method and complex function method are the mathematical methods for the fracture problem of composite material. The research of the stress field of isotropic bi-material interface end has achieved some important results. Recently, the use of complex function method on many research results of stress field near the tip of interface crack of orthotropic bi-material and ModeⅢorthotropic bi-material interface end with no oscillatory singularity has made some achievements. But for ModeⅢstress singularity analysis of isotropic and orthotropic bi-material near the interface end is seldom.In this paper, ModeⅢstress singularity of isotropic and orthotropic bi-material near the interface end is studied. By establishing complex functions on plane of z j, the problem of fracture is transformed into solving boundary value problem of partial differential equation. Based on the constructing stress function, with the boundary conditions, linear equations with four unknowns are obtained. Through the introduction of trigonometric functions, the characteristic equation is simplified. Ultimately, for an ModeⅢisotropic and orthotropic bi-material, the singularity index of interface end and its variation of the symmetric and asymmetric interface end and theoretical formula of stress and displacement fields are obtained.

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