Investigations On Fracture Mechanics Of Nonhomogeneous Materials With Complex Interfaces

Composite materials have been applied in more and more fields. Although composite materials have been designed with continuous and nonhomogeneous properties in macro scale, there are more or less material interfaces in various composite materials, especially, in particle reinforced composite materials (PRCMs). It is often found that although PRCMs can significantly improve the strength, stiffness and wear resistance of materials, the fracture toughness is significantly lower than that of the matrix material. Since composite materials are usually used in severe conditions, fracture is one of the most common failure modes. The material interfaces have to be taken into account when the fracture performance of these composites is concerned. Therefore, the mechanical behaviors of a crack in the environment containing complex interfaces are investigated in this thesis.In Chapter 1, the fracture problems of PRCMs are reviewed firstly. Then, the extended finite element method (XFEM) is introduced. Finally, the numerical methods are described for extracting fracture parameters, including the stress intensity factors (SIFs) and the T-stress. Since the XFEM allows cracks or material interfaces to be independent of the mesh, it can be used to deal with static crack problems and crack propagation problems of the materials with complex interfaces conveniently. However, up to the present day, there is no method which can not extract fracture parameters exactly and conveniently for the crack surrounded by complex interfaces. Accordingly, the aim of this article is to develop a method for extracting the fracture parameters easily when the crack tips lie in the vicinity of complex interfaces.In Chapter 2, a new domain expression of the interaction integral is derived for the computation of mixed-mode SIFs. This method is based on a conservation integral that relies on two admissible mechanical states (actual and auxiliary fields). Two improvements are provided for the interaction integral. First, by a suitable definition of the auxiliary fields, it is found that in the interaction integral, the terms related to the derivatives of material properties vanish. Second, we provide the proof that the formulation is still valid even when the integral domain contains material interfaces. Therefore, the interaction integral derived here can be used to solve the SIFs of a crack in nonhomogeneous materials with continuous or discontinuous properties. The interaction integral method combined with the XFEM is used to solve several representative fracture problems to verify the validation and domain-independence of the interaction integral. Then, the influences of material continuity on the mixed-mode SIFs are investigated by selecting four types of material properties. Numerical results show that the mechanical properties and their first-order derivatives affect mode I and II SIFs greatly, while the higher-order derivatives affect the SIFs slightly.In practice, a crack may grow in one material or along the material interface. Therefore, in Chapter 3, the interface crack problems are investigated. At the beginning of Chapter 3, the stress singularity of the interface crack between two nonhomogeneous materials is solved. Then, an interaction integral is derived for obtaining mixed-mode SIFs of an interface crack. Similarly to the expression in Chapter 2, the domain integral form of the interaction integral does not contain any derivatives of material properties and is valid when there are other material interfaces in the integral domain. Thus, the derived formulation can be applied to deal with interfacial fracture problems of the materials with complex interfaces. The interaction integral combined with the XFEM is employed to solve some fracture problems and the results show that the method is very reliable and domain-independent. Finally, several representative examples of complicated interface crack problems between nonhomogeneous materials are considered.There is no doubt that three-dimensional (3D) fracture problems are more significant in engineering fields compared with two-dimensional (2D) crack problems. In Chapter 4, the interaction integral for solving mixed-mode SIFs along a 3D curved crack front is discussed. A new 3D domain formulation without containing any derivatives of material properties is obtained. The interaction integral is still valid when the material properties in the integral domain are discontinuous. This method in conjunction with the finite element method (FEM) is employed to solve several representative 3D fracture problems. According to the comparison between the results and those from the published lectures, good agreement demonstrates the validation of the interaction integral. The domain-independence of the interaction integral is also shown in the results.Except for the SIFs, the T-stress is also an important fracture parameter. Therefore, in Chapter 5, the method for extracting the T-stress is described. Selecting the auxiliary field which is caused by a centralized force at the crack tip, we derived a new domain expression of the interaction integral for the computation of the T-stress. The interaction integral for extracting the T-stress has the same advantage as that for solving the SIFs, i.e., the interaction integral does not contain the terms related to the derivatives of material properties and does not require the material properties in the integral domain to be continuous. Then, the feasibility to use the interaction integral to extract the T-stress is proved rigorously. The interaction integral shows good validation and domain-independence by solving several representative fracture problems. Finally, the influences of material continuity on the T-stress are investigated. It can be found that the mechanical properties and their first-order derivatives affect the T-stress greatly, while the higher-order derivatives affect the T-stress slightly.