13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- 4.2. Discussion on the ultimate bending striker displacement before perforation The ultimate bending striker displacement before perforation zb, is used to calculate the residual velocity for the analytical model. It can be determined by drop tests’ results and finite elements’ results, and is equal to the displacement of the striker before rupture. For an initial velocity of 5.8 m/s, zb is equal to 2.9 mm and 3.5 mm respectively for simulation and experiment. The hypothesis to take zb equal to 3 mm for the analytical model is in good agreement. 4.3. Velocity discussions Velocity’s results are discussed by plotting the residual velocity as a function of the initial velocity (Fig. 7). Analytical model’s results (N=4, zb=3mm) are in good agreement with drop tests’ results. Simulations tend to underestimate residual velocities, but results are close to experimental ones. A good ballistic limit velocity correlation is found. With the analytical model, it is equal to 5.0 m/s. With the finite elements model, it is between 5 and 5.5 m/s. The experimental ballistic limit velocity is about 5.0 m/s. Experimentally, the absorbed energy by the sheet during impact rises with the initial velocity until a maximal energy (about 161 J), reached for the ballistic limit velocity (Fig. 7). Drop tests’ results give an average maximal absorbed energy for perforation of 161 J. In the analytical model, this maximal absorbed energy for perforation is the addition of plastic work and fracture work and is equal to 168 J. Because of the use of a rate dependent model, simulations show that the absorbed energy continues to rise beyond the ballistic limit velocity and exceeds 180 J. Figure 7. Residual velocity versus initial velocity and absorbed energy versus initial velocity. 4.4. Discussion on the number of petals. More than four petals appear during perforation tests (Table 2). Because of the use of the “kill element” process, no petal is observed in FE simulations. It was already explained that results from the analytical model are number of cracks dependent. In this model, an evolution of the number of petals leads to an augmentation of the absorbed energy during impact and thus a decrease of the residual velocity. For example, for an initial velocity equal to 6.9 m/s the residual velocity is 4.7 m/s,
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