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  • The explosive was ignited at one end of the


    The explosive was ignited at one end of the cylinder at time zero. The density of the explosive was 1.87 g/cm3, and the detonation velocity was 8820 m/s. The AUTODYN “burn on time” model was used for the explosive. The total length of the cylinder with explosive is 10.2 cm. The length of the steel ring is 1 cm and its thickness is 0.3 cm. Two different shots (loadings) were studied (Table 1).
    Results Fig. 3 shows a picture of the 3D simulation of the experimental setup in AUTODYN. The simulations were performed in 3D using quarter symmetry. In AUTODYN and IMPETUS the unstructured grid with 4-noded tetrahedral elements are used. The SPH algorithm was used for the explosive, brass and ring. The very same simulation was performed in IMPETUS Afea; however, here the corpuscular model was used for the explosive and the Lagrange model for the steel ring and the brass. The node splitting algorithm was used for the steel ring only. Fig. 4 compares the streak camera recordings with the simulations for two different shots. The fragmentation pattern may depend on the numerical solver. Only the rings were used in a numerical study. The expansion velocities of the rings in Fig. 4 were input to new simulations where we apply different numerical techniques. 190 m/s expansion velocity was used for the low velocity and 630 m/s for the high velocity shot. For the low velocity we apply an JAK STAT Compound Library size of 600 microns in 3D as baseline. For the high velocity we apply quarter of symmetry in 3D and an element size of 400 microns. The experimental results are compared with the numerical simulations using the AUTODYN, IMPETUS Afea and the regularized smooth particle (RSPH) method. In AUTODYN, we used element erosion at the strain of 1.5. In the IMPETUS Afea, erosion by material failure was used for the brass tube. The mass of the steel ring is preserved due to the node splitting algorithm. However, for the high velocity case (only), erosion due to falling time step had to be utilized in order to avoid the numerical problems, only about 1.4% was eroded in this case. No erosion was used for the steel ring in the low velocity case and hence the fracturing of the ring is solely due to the node splitting algorithm. Figs.5–8 show the simulation results for baseline parametric values with T = . We apply symmetry and only simulate half of the ring along the axial axes. Fig. 5 shows the results after 6 μs for the high velocity shot. In AUTODYN, a layer connected to the inner surface of the ring is severely damaged and failed. Failure develops from this region and spreads outwards by tensile, or shear, failure. In IMPETUS Afea, the node splitting algorithm controls the fracture. The node splitted region spreads outwards JAK STAT Compound Library and radially. The RSPH shows much the same behavior as in AUTODYN although the severe damaged region at the inner surface is not observed. Fig. 6 shows the results after 20 μs. The symmetry plane is clearly seen. The number of the larger fragments is around 30–300. Figs.7 and 8 show the similar results for the low velocity shot in IMPETUS Afea and RSPH. AUTODYN did not show any fractures. In general, the number of fragments is much lower than that for the high velocity shot. The reduced number of fragments can be explained. The fragmentation process starts with the initiation of shear or tensile fractures at some random points. After fractures are initiated, loads decrease so stresses are not sufficient to trigger the multiple fracture surfaces. However, when the same ring is deformed at high strain rate, the fragmentation number increases since a fracture that develops at one location can only influence the stress and strain at a neighboring location after a finite delay time. This delayed interaction between initiation sites provides time for crack growth at neighboring sites. For strain rates up to 103/s, it is believed that the dislocation motion is controlled by thermal activation, and a linear logarithmic relationship has traditionally been used for strength as a function of strain rate [16]. Above the rate of 103/s, the strength of materials are often significantly enhanced [16,18,31] due to the changes of the microstructure rate controlling mechanisms. Enhanced strain rate dependency may be due to resistance to dislocation motion in the lattice itself by phonon viscosity [32]. The stress is here found to be linearly proportional to the strain rate [33]. In Ref. [20], the ring material was studied, and it was found that the simulation results worsen when the strength increases with strain rate.