13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- initially tensioned film. 2. Theoretical formula and modeling The axis-symmetry model sketch is shown in Fig. 1, in which the symbol t_s=5mm and t_f =0.25mm represents the thickness of the substrate and film, respectively; r_s=50mm is the radius of the specimen, r_b=7.5mm indicates the coverage radius of the impact region. And l_c represents the interface crack length and will be set as 10~100 percent of the magnitude of r_b. Moreover, the two parameters defining the compressive pulse are τΔ =0.05μs and 0p =800MPa. The symmetry constraints are applied at the symmetry axis and the displacement at the boundary of the circular specimen are restricted as shown in Fig. 1. The densities of the substrate and film are 7850kg/m3 and 8800kg/m3, respectively. The ideal elasticity is assumed for the specimen and the elastic modulus of the substrate and film are 200e9 Pa and 210e9 Pa, respectively. The Poisson’s ratio of the substrate and film are 0.29 and 0.31 respectively. Fig. 1 Model sketch of the system of film and substrate with interface crack The discretized model is shown in Fig. 2. In detail, the film is divided as five segments through its thickness. Thus, the linear element size is nearly one fifth of the film thickness. The contact elements are adopted at the crack surface for both the film and substrate, for which the coulomb friction law is used to simulate the probable surface friction induced shearing between the crack surfaces. Fig. 2 Discretized model of the film and substrate As far as the initial stress state is considered, three cases are analyzed. That is, the results denoted by NRS represents the case of the initially stress free film; TRS represents the case of that the film
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