Fig shows the randomly forming process of fragments with

Fig. 4 shows the randomly forming process of fragments with different sizes. The donor was initiated from the top, and the detonation waves propagated from up to down to make the shell expanding. When the shell expanded at a certain extent, there were breaking holes on the shell formed randomly, and then the holes extended to be fracture belts along the vertical direction, as shown in Fig. 4(b). Along with the shell deformation, elements separated and formed fragments, as shown in Fig. 4(c). After the donor charge detonated completely, the shell ruptured to form the random size fragments, as shown in Fig. 4(d). Since the failure values of node groups were random, the fragments of donor shell formed random fragments with different size. Even at the same distance between the donor and the acceptor, each calculation could result to different results. This would lead to the random gdc-0980 of the acceptor, which was the same as in practical test. Therefore, the multiple calculations at the same distance were required to get the statistical results. In order to reduce computation time and gain more data in each calculation, a four acceptors model was developed. 4 acceptors were placed around the donor in the calculation. There were contacts between fragments of the donor and the acceptors, and no interaction between acceptors. Here we can gain four experiments results in one calculation. Then every calculation equals to 4 parallel tests. Fig. 5 shows the positions of the donor and the acceptor, four acceptors took the same distance from the donor. Because the effects of the shock waves and the products are much smaller than the effect of fragments on acceptors, the air field was not considered in the model, and the propagation of the shock waves in the air was ignored, the description of shell fragments was only focused on. The Lagrangian method was used in the model in order to observe the distortion and the reaction of the acceptors. Fig. 6 shows the model of the sympathetic reaction tests, without considering the performance of the detonator, and the initiation point was set in the center of the top surface of donor. The sympathetic detonation tests were simulated by using an explicit finite element hydrocode LS-DYNA [5]. The elastic plastic hydrodynamic material model was used for the mechanical behaviors of the donor and the acceptors, and the Ignition and Growth reactive (I&G) model [6] was used to describe the GHL explosive detonation. The parameters for Ignition and Growth reactive model for GHL explosives were listed in Table 1[7]. The reaction rate equation in Ignition and Growth model is of the form:where λ is the reacted fraction, t is time, ρ is current density, ρ0 is initial density, P is pressure, and I, G1, G2, a, b, x, c, d, y, e, g are constants.
Results and discussion Fig. 7 shows the deformation of the witness plate under the acceptor for 225 mm charge distance. It can be seen from Fig. 7 that a hole was formed by the acceptor detonation, which was slightly smaller than the diameter of explosive charge. Fig. 8 is the photo of acceptor remnants at 273.4 mm charge distance. It can be seen that there were some residual explosives and fragments; the charge was only partial reacted, and did not detonate completely. Fig. 9 is the photo of acceptor remnants for 300 mm charge distance. It can be seen from Fig. 9 that the lower part of the acceptor charge was destroyed but the upper part was almost intact, a lot of GHL explosives are left in the shell, It meant that the main impaction of the fragments was on the lower part of the acceptor. The results of tests with different charge distances are listed in Table 2. When the charge distance was less than 150 mm, the acceptors detonated completely; when the distance was in the range from 150 to 300 mm, the acceptors detonate randomly. When the charge distance was exceeds 300 mm, acceptors would not react. The distance from 150 to 300 mm could be considered the critical distance rang.