13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- available at this moment. However, as mentioned above, the variability of the parameters can be presented by the disturbance in mesh configuration. Table 1. Material properties of epoxy resin Young's modulus (Mpa) 3300 Poisson's ratio 0.38 Tensile strength (Mpa) 35.0 Epoxy density (kg/m3) 1180 8 5 140.0 24.5 Y Z X Unit(mm) B.C.: Uniform tensile Fixed end 0.6 Figure 2. Analysis model The force boundary condition is posed. The bottom end of the model is fixed, and the top end is pulled up in longitudinal direction. The loading rate is set to be 5N/s. Since the loading rate is small, the initial load of simulation is set to be 135N to save computation time. No element failure exists under this initial load. Following the PDS-FEM discretization, the crack tip is modeled as a notch with 0.6 mm height; the vertical surface of the notch is discretized by using 2 elements. The average mesh size is 1.0 mm at the top and bottom surfaces of the model to save computational overload. The time increment is set to be t = 5.0x10-9s. 200 samples with slightly different mesh configurations or distributions of candidate crack path for PDS-FEM are prepared for Monte-Carlo simulation. The number of samples is decided by checking the convergence of average crack path position through the specified cross-sections. 4.2. Simulation results and experimental comparison For numerical simulation, the crack patterns can be classified into two groups: (1), the crack paths are symmetrically distributed; (2), one crack is fully developed horizontally from either of the notches. Fig. 3 shows eight typical crack path solutions of the model with small heterogeneity. Bifurcation is also observed in the simulation results; see Fig. 3.5~Fig.3.8. In order to record the development of crack growth and stress changes of the epoxy resin thin plate, an ultra high speed video camera, which can capture images at the rate of 1 million frames per second, is used herein [18]. The photo-elastic technology [19] is used to show the stress distribution of experimental samples. Fig. 4 shows the final stages of four typical photo-elastic fringe patterns.
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