13th International Conference on Fracture June 16-21, 2013, Beijing, China 3. Analysis Examples 3.1. Analysis Model The isotropic hyper-elasticity model (St.Venant-Kirchhoff material) is used in the finite displacement assumption: SAB =CABCDECD, CABCD =2µδACδBD +λδABδCD, (15) where S and E are the second Piola-Kirchhoff stress tensor and the Green-Lagrange strain. The parameter λandµare Lame´’s constants. In this study, Poisson’s ratioν =λ/(2λ+2ν)issettobe0.4. Some results are compared with the analysis based on linear elasticity in the small displacement assumption: Ti j =Ci jklεkl, Ci jkl =2µδikδjl +λδi jδkl, (16) where T andεis Cauchy stress tensor and small strain tensor, respectively. Plane strain problems are assumed in a rectangular specimen of 100b × 20b, where b means the amount of unit discontinuous slip. The displacement on the left edge of the specimen is fixed and four different problems as shown in Fig. 2 are solved: Fig. 2(a) a dislocation dipole composed of two dislocations on 1-slip plane, (b) three dislocation dipoles on 3-slip planes, (c) some dislocation structures arranged on 3-slip planes, and (d) three dislocation dipoles on 3-slip planes under both compression and shear loading. u=0 u=0 u=0 u=0 100 b 20 b (a) 100 b 20 b (b) 100 b 20 b 100 b 20 b (c) u uy x (d) Figure 2. Schematics of model of analysis 3.2. Results of Analysis 3.2.1. Dislocation Dipoles on Slip Planes Figure 3 shows the distribution of stress σyy on deformed body for (a) one dislocation dipole on 1-slip plane model, and for (b) three dislocation dipoles on 3-slip plane model. In Fig.3(a), the dislocation on the left affects a repulsive image force due to the fixed boundary condition. On the other hand, the -4-
RkJQdWJsaXNoZXIy MjM0NDE=