Research On Fracture Analysis Of Composite Materials By Extended Finite Element Method

Composite materials have characteristic of good thermal stability, higher specific strength and specific stiffness, hence, they have been used in lots of fields, such as aerospace,construction industry and automobile, etc. Due to the presence of cracks or inclusions,composite materials may failure or fracture in different degrees, which significantly influences their service lifetime. There are lots of methods to solve the problem of fracture or failure of composite materials, such as analytic method, experimental method and numerical method. The analytic method is suitable for the problem of having special geometric boundary and loading conditions, but for the problem of having complex boundary and loading conditions, the analytic method is ineffective. Due to the high cost of experimental method, it cannot be used widely. For simulating discontinuous problems of crack or inclusion,the frequently used numerical method requires remeshing.Therefore, there is greatly theoretical and practical significance to study the problems of fracture and damage of composite materials by developing new numerical method.The extended finite element method(XFEM) is a new numerical method to simulate discontinuous problems, for example, the problem of crack. This method inherits all the advantages of the traditional finite element method(FEM), and it overcomes the disadvantages on meshing in FEM. The study on the problem of fracture in thermoelastic orthotropy is relatively fewer than that in isotropic material, thus, there is significantly practical value for studying fracture in orthotropic material. Based on the facts, in this thesis, the extended finite element method is developed to study the problems of fracture or failure in isotropic and orthotropic composite. The orthotropic crack tip enrichment function is applied to the problems of orthotropic thermoelastic fracture, the isotropic thermoelastic crack tip enrichment function is applied to the problems of interaction between cracks and inclusions in isotropic medium. The main contents are given as follows:1. Basing on interaction integral for orthotropic medium, the formulations of interaction integral for isotropic and orthotropic mediums are given, by introducing thermal integral term,the expressions of the interaction integral for orthotropic thermoelastic material under static load are derived.The innovation of the expression lies in the term related to the variation of temperature being added, and the interaction integral for isotropic material being extended to the one for orthotropic material.2. Basing on the classical XFEM for isotropic materials, extending the XFEM for isotropic and elastic materials to analysis for problem in thermoelastic orthotropic materials,and then, the developed XFEM is applied to the problem of inclined crack in orthotropic composite materials plate under thermal loading, and the effects of different principal axises of orthotropy, mesh refinement, Gauss quadrature, crack tip enrichment functions and radius of J-integral domain on SIFs at crack tips are analyzed. The computed results are compared to those of results in literatures to justify the accuracy and validity of the developed XFEM.3. Due to the facts that the defects in material often take the form of multiple cracks and inclusions, there is importantly practical significance for studying the problem of multiple cracks and inclusions. Based on the known results on single crack and inclusion, the related governing equations on the problem of multiple cracks and inclusions under themoelastostaticload, the extended finite element discretization formulation, corresponding extended finite element displacement approximation for multiple cracks and multiple inclusions under themoelastostatic load are presented. Finally, three numerical examples focusing on the influence of the length of crack and distance between crack and inclusion on SIFs are shown to verify the accuracy of XFEM.4. After introducing the basic theories and methods on the problem of plane for anisotropic composite plate, by constructing proper conformal mapping and proper stress function, the analytic solutions of the SIFs at the crack tip are obtained for semi-infinite cracks in anisotropic composite plate with intensive loading at arbitrary point of the crack plane.