Bursting of a cylindrical vessel with an explosive charge at center
Analytical Service Pty Ltd
TECHNICAL NOTE 65
A set of simulations of such an event had been carried out, in which compact charges of TNT were placed at the center of the vessel (Fig.1) and detonated. The effects of such explosions are dependent on the amount of explosive used.
The computational model is shown in Fig.2. Apart from the charge and the shell the model also involves an air volume (black mesh), somewhat larger than shell, which facilitates observation of pressure changes and allows interaction between the explosive and the vessel. The shell is made from an aluminum alloy with the properties between those of 2024-T3 and 2024-T351. Although strength-wise these alloys are not regarded as particularly sensitive to the speed of deformation, the tests indicate that there is a large increase in the failure strain while under rapid loading. This was accounted for in the model. The properties vary somewhat, as indicated by the colors in Fig.3.
The smallest charge tried had 10.8 kg of TNT. It caused only swelling (Fig.4), but no rupture of the vessel. A larger charge of 14 kg had similar effect. Only 16 kg was effective in breaking the shell (Fig.5), but not to an excessive extent. The largest size tried, 20 kg, produced a thorough dismemberment of the vessel (Fig.6).
Finally, a charge of 6 kg was exploded at some 0.7m away from the surface, The charge was located at a 450 plane passing through the axis of the vessel. The resulting shock waves are illustrated in Fig.7, while the surface breakage is in Fig.8.
The over-all properties of the vessel are somewhat similar to those of a segment of fuselage of the aircraft Tu-154M. The diameter is the same and the material properties are similar. In the airplane the typical skin thickness is 1.5 mm. To provide an allowance for stringers in one direction and the frames in the other, 1mm of thickness was added, so that the total thickness of the isotropic skin in the model was 2.5mm. The tearing pattern is likely to be different from the fuselage, not only because of such an “equivalent thickness” does not reflect all possibilities of the breakup.
The other major difference is the presence of a floor in a fuselage. This makes the blast wave reflect thereby enhancing its effect. As far as breaking of skin, the same effect is achieved with less explosive. In spite of those differences some initial understanding of disintegration of a fuselage can be gained from studying such effects in a smooth vessel.
Because of multiple symmetry, only one-eighth of the vessel, charge and air was modeled for central explosion. The necessary planes of symmetry were included.
Fig. 1 (Left) Over-all view of the vessel.
There is a problem in modeling an axisymmetric body with an axisymmetric charge placed at the center. If the material properties are uniform, the disintegration will take place at once with all elements participating; a perfect, uniform breakup. This however, is possible only in a computer model, not in the real world. One of the reasons for it is that material properties vary from place to place, although the variations may be quite small. In our case such a failure is not possible, because of a somewhat irregular, blocky shape of the charge, which prevents pressure from being uniformly distributed around the circumference. Still, to be realistic, the properties, especially the failure strain were made variable along the surface. This was attained by assigning, at random, different material properties to circumferential as well as longitudinal strips depicted in Fig.3
Fig. 2 One quarter of vessel, computational model consisting of charge (center), shell and air volume somewhat larger than the shell. All components are shown with a semi-transparent mesh.
Fig. 3 Vessel alone. Different colors indicate different material properties. The wall thickness of 2.5 mm is constant. The material properties of strips (both longitudinal and circumferential) are different from those of the main shell.
Tests conducted for strain rates reaching 8000/s indicate that for these alloy types the strain at failure can reach some 28%, while for static conditions. It was not anticipated that such large rates would be reached here. We assumed the strain at failure as 20% for the basic shell material. The described simulations resulted in some 4000/s strain-rate peaks. The material was modeled as rate-insensitive.
Fig. 4 Deformation after the smallest charge of 10.8 kg was exploded. No failure was observed. Longitudinal one-half is shown.
The longitudinal and circumferential strips differed in two ways from the basic shell material. First, they were weaker, as the lower strain at failure was assigned, than that for the main shell. Secondly, they had a larger material density, to reflect overlapping of adjacent sheets.
One should also note that the model under-estimates the forces applied to the shell. This is because once the broken shell elements get outside the modeled air volume, no further “pushing” can take place and the motion results from inertia only.
Fig. 5 Deformation and partial splitting after a charge of 16 kg was exploded. There is not much separation between the end cap and the rest of vessel.
One of the important checks in such a project is to make certain that the pressure impulse applied to skin agrees with the experimental data. This, in our case, involves impulse averaging along the circumference, as the shape of the explosive is non-axisymmetric.
Fig. 6 Complete splitting after the large charge (20 kg) was detonated. Note that the ends are nearly broken off and that the side surface “unwraps”.
Fig. 7 Shock waves from the off-center charge illustrated by constant-pressure surfaces.
Fig. 8 Skin tearing from the off-center charge shown in a quarter-model. The 450 split appeared first. The other two splits, 00 and 900 may be exaggerated. Reason: Symmetry boundaries that pass through the longitudinal axis should have been removed and replaced by flow boundaries, which was not done.