13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- Fig. 2. is the photomicrograph of the 2D plain weave C/SiC by SEM. According to the micrograph the geometry of the fiber yarns is determined, AB=0.25mm, AE=AD=1.8mm, with the woven hole in the square of 0.2mm×0.2mm. The periodic boundary conditions meets the requirement of displacement periodicity and continuity of the proper boundary conditions, which implies that no separation or overlap will be found between neighboring of RVEs. Each RVE in the composites has the same deformation mode. As stated by Z.Xia[18], the periodic conditions on the boundary V is where, ik are the average strains, i u is the periodic part of the displacement components on the boundary surfaces and it is related to the applied global loads. Aboudi has developed a unified micromechanical theory based on the study of interacting periodic cells, and its boundary conditions, plane-remains-plane, were applied to the RVE models in the normal traction loading conditions. Now based on these the proper boundary conditions are the planes ABFE and CDGH keeps plane during the loading in x direction on EFHG plane. The ABCD plane keeps zero displacement in X direction. And to avoid the rigid motion, the displacement components of the center point of the ABCD plane are assumed to be zero. 3. The meso-model In the model, RVE that used to investigate the 2D woven C/SiC under tension loading, is shown in Fig. 3. The matrix, fiber and the yarn/matrix interface are taken into account with their specific damage behavior. (a) Matrix (b) Interface (c) Fiber bundles Figure 3. The RVE model and its constituents 3.1. Matrix The elastic constants for the matrix material SiC: Young's modulus E, Poisson's ratio v are found to be E=430Gpa, v=0.3. The brittle cracking material constitutive in ABAQUS is chosen to describe the damage and failure behavior of the isotropic brittle matrix. The failure stress and displacement are 200Mpa and 0.02mm, respectively. In order to consider void in matrix, the elastic constants is assumed to reduced to 10% of the original matrix, and the model with void is shown in Fig. 3(a), the small squares in the RVE is the void region. 3.2. Fiber yarns The fiber bundles in C/SiC is regarded as transverse isotropic materials. And the properties are listed in Table 1. Table 1. The mechanical properties of the fiber yarns E1(Gpa) E2(Gpa) v12 v23 G12(Gpa) G23(Gpa) f(Mpa) f 220 13.8 0.2 0.18 9 4.8 800 1.5%
RkJQdWJsaXNoZXIy MjM0NDE=