Numerical Simulation On The Fracture Behaviors Of Functionally Graded Materials

Since functionally graded materials (FGMs) have many advantages in comparison with traditional materials, there are a lot of wide application prospects in various fields. Therefore, it is very important to investigate the fracture mechanics of FGMs for their design, manufacture and reliability. For functionally graded materials, only simplified models or models with rigid assumptions can be theoretically solved at present. Since there is the higher cost in the experimental characterization of FGMs, researchers have to use numerical methods to investigate the fracture behavior of FGMs. In order to simulate the mechanical behavior of nonhomogeneous materials numerically, the traditional finite element method (FEM) is improved in this dissertation and the finite element method with nonhomogeneous elements is developed. Since the actual material properties at integral points are adopted in the formation of the element stiffness matrix, nonhomogeneous material properties can be considered in each element. Thus, each element is a nonhomogeneous elment. For nonhomogeneous materials, FEM with nonhomogeneous elments improves numerical efficiency and accuracy compared to the traditional FEM.First, FEM with nonhomogeneous elements is used to analyze the fracture problem of two dimensional FGM strips with inner cracks or edge cracks in the plane strain condition. The influences of geometric parameters, material graded modality and nonhomogeneity constant of the structure on the stress intensity factors (SIFs) at crack tips are investigated. Then, the fracture problem of three dimensional FGM strips with center through cracks or edge through cracks is investigated. The corresponding SIFs are compared with two dimensional results in the plane strain state and similar characters of SIFs are found. Because of the limited thickness of three dimensional FGM strip, the corresponding SIFs increase in comparison with ones in the plane strain, particularly near the free surface. In addition,the fracture problem of FGM strps with semi-elliptical surface cracks is investigated and the SIFs of FGMs are compared with ones of homogeneous materials. Finally, the influences of the free surface on SIFs are investigated. Numerical results show that the meshing refinement near free...