Issue34

M. Kikuchi et alii, Frattura ed Integrità Strutturale, 34 (2015) 318-325; DOI: 10.3221/IGF-ESIS.34.34 320 where G T GG G GG G K B D B d                     L T GL G LL L K B D B d                     (4) L T LL L LL L K B D B d                     G B     and L B     are displacement- strain matirces defined in global and local area, respectively. GG D     and LL D     are stress-strain matices which are described using young’s modulus and poisson’s ratio. These are material constants which may change in heterogenous material in each material. In Eq. (3), T T LG GL K K          , and the stiffness matrix is symmetric. GL K     expresses the relationship between local and global areas. By calculating this term with high accuracy, accurate FEM results are obtained. By solving Eq.(3), both displacement fields of local and global areas are obtained simultaneously. The detail of the theory was presented in the literature of one of the author [8]. This method is applied to crack growth in heterogeneous material. As shown in Fig.2, global model is made of two materials, and it is easy to define phase bounday in global model. Material properties are different from each other in material 1 and 2. But in local area, it is seen that it is difficult to arrange mesh in local area along phase boundary of global model. Local mesh is overlapped on global mesh. GL K     and LL K     are calculated by eq.(4), and LL D     , material properties in each material, are needed for these calculations. As shown in Fig.2, integrations are conducted using Gaussian numerical integration method in each local element, and material properties at these Gaussian points are needed for integration. In S-FEM analysis, all Gaussian points in local elements belong to some global element. Then, material properties of each Gaussian point is same as those of global element in which Gaussian point is located. For this meaning, local mesh needs not to have material properties, and it becomes easy to calculate eqs.(4) using material properties of global element. By this method, it becomes possible to apply S-FEM methodology to crack growth simulation in heterogeneous material. + = Global Mesh Global Mesh Local Mesh Local Mesh Interface Interface Figure 2 : Global mesh and local mesh in heterogeneous material. C RACK GROWTH IN BI - MATERIAL OF CFRP AND ALUMINUM ALLOY ig. 3 shows test specimen made of aluminum alloy, A2017 and CFRP. As shown in Fig. 4, fiber orientation of CFRP plate is 90 degree to loading direction. Initial notch is introduced in CFRP plate and grows toward to A2017. Phase boundary of two material is inclined about 80 degree to horizontal axis. Tensile load is subjected along x axis in Fig. 4. Mechanical properties of these two materials are shown in Tab. 1. Young’s modulus of A2017 is much larger than that of CFRP. Fig. 5(a) shows experimental result. Initial crack grows toward to phase boundary, and it changes growing direction a little to upper ward. This is the effect of mismatch of mechanical properties between two materials. As the Young’s modulus of A2017 is larger than that of CFRP, crack prefers to stay in CFRP side. Finally it reaches to the phase boundary, and separation occurred between two materials. Fig. 5 (b) shows result of numerical simulation. In this paper, crack growing direction is determined using the Maximum Tangential Stress (MTS) criterion [9], which determines the crack growth direction,  , to satisfy the following equation, F