Research on dynamic response of explosion containment vessels

1 Introduction

Containment vessels are used for a wild range of activities in both civil and military field, from the temporary storage of explosive materials to explosive forming of metals to experimental investigation on explosion and many more. In the process of application, explosion containment vessels have significant effects on restricting the area of influence of explosion waves and products, protecting experimental staffs and equipment, and preventing environmental pollution.

Recently, some explosion containment vessels with new style materials and structures have been designed which have many advantages, such as feasibility in manufacture, safety in application, convenience in transportation and easy inspection in service, and many data on their dynamic response were obtained. Zheng [1, 2] have theoretically and experimentally analyzed the elastic dynamic response of discrete multilayered vessels under internal explosion. Jagadeep Thota [3] presented a generalized optimization technique for the three-layer composite blast containment vessel to reduce the peak strains resulting from internal blast loading. Qi Dong [4] designed and manufactured three cylindrical shells employed carbon fiber, and the dynamic behaviour and the failure modes under internal blast loading were presented based on the tests. Zamani [5] demonstrated an analytical solution for elastic thin-walled cylinder-truncated cone shell intersection under internal pulse pressure.

With the development of blasting technology, the application of underwater blasting is more and more widely. Because the surrounding medium and environment are very complex, especially in deep water environment, the output energy and the blasting effect also change when the depth of the explosives into the water changes. Underwater explosion is very important and complex problem in both civil and military applications. Phenomena of underwater explosion have been clarified since World War II. The sudden release of energy associated with the explosion of a high explosive leads to generation of a shock wave and formation of a superheated, highly compressed gas bubble in the surrounding water. Two crucial and distinct phenomena are usually involved in an underwater explosion. The first phenomenon is the quick propagation of an underwater shockwave in the water. The second phenomenon involves the motion of high temperature and pressure gas bubble, which occurs over a longer period. Many studies have examined underwater explosion using experiments and simulations, and many semi-empirical equations for predicting shockwave propagation and bubble motion have been developed in the succeeding decades.

In order to research the underwater blasting technology, we often use explosion vessel to do some experiment, which can simulate the explosion experiment of different depth of the water environment by changing the water pressure. Explosive containment vessels filled water can be used to experimentally investigate some problems about underwater explosion, such as the characteristics of shock wave propagation and bubble pulsation, as well as the dynamic response of submarines subjected to underwater explosion, which have been researched through costly and time-consuming process of underwater explosion testing that is although useful, is extremely limited, in addition in which environmental safety cannot be guaranteed. There exist lots of differences between water and air medium due to their different physical properties, and the key among them is that the water has a much lower compressibility than air. Some previous works have been punished on the analysis of the dynamic behaviour of water-filled vessels subjected to internal blast loading. Dalrymple and Johnson [6] present an analytical model to predict the formed shape of thin-walled tubes filled water based on the energy flux density. Proctor [7] summarized the formulation of explosion-containment equations for idealized water-filled right-circular cylinders. Rusak, Ryzhanskii and Ivanov [8–10] found that shell failure develops a strong scale effect in the form of a sharp reduction in explosion resistance with an increase in dimensions by experimental study of cylindrical shells filled water under internal explosive loading, and revealed a significant effect of the filling medium on the response of the container and the ratio of its mass to the mass of deformable walls of the container based on the experimental study and numerical calculation of the system “explosive-filling medium-container”.

The dynamic response of a structure subjected to underwater explosion is very complicate, and some works have been done about this. Kwon and Fox [11] studied the nonlinear dynamic response of a cylinder subjected to a side-on, far-field underwater explosion using both numerical and experimental techniques, and the study showed improvements of the numerical results compared to the experimental data and the dynamic motion of the cylinder has an accordion mode, a breathing mode and a whipping mode. Schiffer and Tagarielli [12] studied the dynamic response of composite plates to underwater blast, and the results of the study shown that an impulsive description of the loading can lead to large errors. Yong Chen [13] carried out a series of comparative tests to comprehend the dynamic performance of the protective layer when both shock wave and bubble pulse loading were considered, and the detailed discussions on test results showed that the protective rubber layer is capable of moderating damage of the ship body caused by shock wave while not very effective in reducing the whipping damage excited by bubble pulse. Hung, Lin, Hwang-Fuu, Hsu [14] investigated the linear and nonlinear dynamic responses of three cylindrical shells subjected to underwater small charge explosions in a water tank, and found that the plastic deformation of the upper side of the cylinder occurred at smaller distances. Jian Li and Ji-li Rong [15] found that the artificial bulk viscosity had a significant effect on the peak pressure of the shock wave and discussed the effects of the length-to-diameter ratio and the angle to the peak pressure of the shock wave for a cylindrical explosive. Schiffer and Tagarielli [16] observed that early deformation of the plates, by propagation of flexural waves, results in the emergence of a localised cavitations zone at the fluid–structure interface and in the central portion of the plates. Schiffer and Tagarielli [17] concluded that the impulse imparted to double hulls by underwater explosions can be dramatically reduced by employing the sandwich construction of the outer skin and the reductions are scarcely sensitive to the thickness of the water layer. Schiffer and Tagarielli [18] examined the one-dimensional response of water-backed and air-backed sandwich plates subject to blast loading in either deep or shallow water and concluded that the advantages of using the sandwich construction over the monolithic one are maximised for the case of water-backed sandwich plates in deepwater. Zhenhua Zhang [19] discovered the damage mechanism and mode of hull girder subjected to near field explosion below the midship, and discussed the coupling effect between whole motion of hull girder and distortion of local structure.

When the charge explodes under the water, it suffers from two parts of pressure. One part is the hydraulic pressure, and the other part is the outer atmospheric pressure. The hydraulic pressure is related to the water depth of the charge location, according to the physics theory, it of 10 m water depth equals to an atmosphere. Hence, the water-filling explosion containment vessels, loaded corresponding hydraulic pressure, can be used to experimentally investigate deep-water explosion.

The dynamic response of the simulated deep water explosion pressure vessels must be paid more attention for their serious consequences in accidental explosions, yet it appears that no detailed study is available on it. James F and Proctor A [20] summarized the formulation of basic explosion-containment equations for idealized water-filled right-circular cylinders. Ryzhanskii, Ivanov and Kovalev [21] had an experimental study of the response of cylindrical steel containers to internal explosive loading and a significant effect of the filling medium on the shape and deformation of the container was found. With an eye to this, in order to gain confidence in the dynamic characteristics of the response of a filled water vessel subjected to outer hydraulic pressure and internal explosion loading, this study included an explosion test which used an cylindrical explosive chamber comprising a cylindrical shell and elliptical ends filled water under the action of blast loading resulting from a concentrated explosive charge set in the geometrical centre of the vessel. The results in this paper were obtained from an initial study of an ongoing project about the water-filling explosion containment vessels to improve the understanding of law of the dynamic response, to determine the carrying capacity and failure modes, and to present, on this basis, the theory of optimization design of the water-filling explosion containment vessels.

2 Experimental

2.1 Description of the explosive containment vessel

Explosive vessels generally are intended to provide containment for multiple impulsive loading events for many years. The structural response is relevant to safety evaluation and working limits, so experiments must be carried out to examine the dynamic strain. The horizontal explosive containment welding together by a cylindrical shell with two elliptical end caps, is shown in Fig. 1.

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Fig.1

The explosion containment vessel in test.

The length of the cylindrical portion of the vessel is 1950 mm, and the total length of the vessel is 3000 mm. The inner diameter of the vessel is 2000 mm, with a wall thickness of 35 mm. The material of the cylindrical shell and the elliptical end caps is steel of 16MnR, while the connection flange and load-bearing components are all forgings of 16 Mn. Table 1 lists the material properties. The total weight of the vessel is approximately 8500 kg. The real multiple-use cylindrical explosion containment vessel fully filled with water, designed to withstand internal blast loading from the detonation of an explosive charge equivalent to 10 g TNT and 2 hydraulic pressure, is can be employed to simulate underwater explosion up to 200 m depth.

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Table 1

The material properties

Material	Density (ρ) kg/m3	Modulus of elasticity (E) G Pa	Tensile strength (σ b ) M Pa	Yield strength (σ s ) M Pa	Allowable stress (T < 100°C) M Pa
16 MnR Steel	7850	200	490	325	163
16 Mn Forging	7850	200	450	275	150

2.3 Experiment and sensor layout

The experimental investigation on the cylindrical explosive containment vessel with elliptical end caps was conducted using static strain test and underwater explosion test, as described in this section.

Before the explosion test, static strain test was conducted on the vessel. When the vessel fully filled with water was under 0, 0.5, 1, 1.5 and 2 Mpa static pressure, the static strain were recorded at two positions, namely at the central cross-section and at the pole point on the end closure. The explosion test performed a series of underwater explosion experiments under different blast loading from TNT spherical high explosives located at the centre of the vessel, and static pressure conditions. Experiments were carried out at three levels of explosive loading corresponding to 1, 3, and 10 g of TNT, respectively, and the high explosives were detonated from the centre. At the same time, the test simulate deep water explosion of different water depths by changing the static pressure loaded to the vessel. The detailed parameters of the explosive are shown in Table 2.

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Table 2

Experimental events

Event number	Charge mass (g)	Loading static pressure (MPa)	Acceleration peak (g)		Strain peak (μɛ)
			A1	A2	S1	S2
1	1	0	664.36	1155.17	101.61	173.98
2	1	0.5	2443.72	2990.73	190.87	434.01
3	1	1	2008.5	2715.73	339.37	421.29
4	1	1.5	1336.03	2060.58	309.25	549.13
5	1	2	2039.01	2731.77	324.48	634.31
6	3	0	957.42	4054.43	181.59	256.15
7	3	1	2785.94	5368.54	362.85	759.71
8	3	2	3043.57	4605.77	408.21	834.47

The underwater explosion tests were conducted to find the rule of the dynamic response of the simulated deep water explosion containment vessel by measuring the overpressure on the inner surface as well as accelerations and dynamic strains on the shell. One PCB138A01 pressure transducer (dynamic sensitivity 5.128 mV/PSI) was placed on the inner surface of the central cross-section to capture the time history of the incident pressure for understanding the characters of pulsing loading. Two accelerometers and two dynamic strain gauges mounted on the outer surface of the shell to measure dynamic response. Figure 2 shows the sensor layout.

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Fig.2

Locations of sensors.

Results are presented in four sections. We begin with an analysis of the static strain of the vessel under different static pressure. Then the pressure records are analyzed for all events to explore the characteristics of blast loading. This is followed by a detailed presentation of the acceleration response to both blast loading and static pressure. The response spectrum analysis is also made to evaluate dynamic performance of vessel in frequency domain. Finally, strain records are compared and discussed. Like acceleration, strain peaks are also selected as a main evaluation criterion.

3.2 Overpressure on the inner surface

The shock wave recorded at P in third event is shown in Fig. 3. It can be seen that the incident shock wave arrived on the inner surface of the vessel, with peak at 4.617 Mpa, decayed rapidly within about 0.061 ms. The shock wave followed at about 4 ms by first bubble pulse, having a broader profile and lower maximum pressure (2 Mpa). All pressure peaks and their function time recorded at P are given in Table 4. It is shown that as the charge mass from 1 g TNT to 3 g TNT, The maximum pressure increases distinctly. For equal charge-mass, the difference of pressure peak in different events do not exceed 8% (excepting event 1). No comparison was made on the peaks of bubble pulse considering their broad profile characteristics.

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Fig.3

Typical pressure records at P when charge-mass = 1 gTNT and static-pressure = 1 Mpa.

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Table 4

The peak pressure (MPa)

Charge mass (TNT)	1 g					3 g
Static pressure (Mpa)	0 MPa	0.5 MPa	1 MPa	1.5 MPa	2 MPa	0 MPa	1 MPa	2 MPa
Peak overpressure (MPa)	3.868	4.605	4.617	4.650	4.557	6.829	7.459	6.850
Function time (ms)	0.02	0.053	0.061	0.053	0.048	0.085	0.062	0.053

3.3 Acceleration records

Acceleration is selected as a main criterion to evaluate the damage of inertial force that is generated by explosion shock vibration on the wall of the vessel. All acceleration peaks recorded at A1 and A2 are given in Table 2. It is shown that as the static pressure is constant, the maxim acceleration increases with mass of the charge at all measure points, while for equal charge mass, the rule of acceleration peak changing with the static pressure cannot be observed. In opposition to what is expected, it is shown that the acceleration peak of A2 at the pole point on the elliptical end cap is much larger than A1 at the central cross-section in all experimental events, although the distance between A2 and explosion source is greater than that between A1 and explosion source, which demonstrates that the inertial response of the end cap is larger. It is attributed by the concentration efficiency of the elliptical end cap.

The acceleration history curves within 50 ms are given in Figs. 4 and 5 while the charge-mass = 1 g TNT and charge-mass = 3 g TNT respectively. Denser signal can be seen in the acceleration records of events with larger static pressure, which indicates higher frequency signals exist in these events.

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Fig.4

Acceleration history when charge-mass = 1 gTNT, left column for A1 and right column for A2.

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Fig.5

Acceleration history when charge-mass = 3 gTNT, left column for A1 and right column for A2.

3.4 Strain records

The peak strains given in Table 2 are the sum of the static strain excited by hydraulic pressure and the dynamic strain excited by the blast loads. Like acceleration records, although the peak strain at the pole point on the end cap is much larger than that at the central cross-section which caused by the concentration efficiency of the elliptical end cap, both of them are not exceed the yield limit, demonstrating the response of the containment vessel remained within elastic range during underwater explosion impact. By comparison, it can be found that the peak strains at positions S1 and S2 increase in different extent, when the charge mass increased from 1 g to 3 g while the static pressure loaded to the vessel kept unchanged. On the other hand, no distinct relation can be found between the strain and the static pressure when the charge mass remained stable.

Figures 6 and 7 display the time history of measured dynamic strains within 50 ms picked from the strain rosette S1 at the central cross-section and S2 at the pole point on the elliptical end cap when the charge-mass = 1 g TNT and charge-mass = 3 g TNT respectively. It can be found that the magnitude of dynamic strain is determined not only by incident impulse, but measurement locations and static pressure loaded to vessel. It is difficult to evaluate the actual effects of static pressure loaded to vessel from only a few events. However, the Denser signal can be observed in the dynamic strain records of events with larger static pressure, which indicates higher frequency signals exist in these events.

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Fig.6

Dynamic strain history when charge-mass = 1 gTNT, left column for S1 and right column for S2.

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Fig.7

Dynamic strain history when charge-mass = 3 gTNT, left column for S1 and right column for S2.

This study performed underwater explosion experiments on a cylindrical explosive containment vessel with elliptical end caps under different blast loading from TNT spherical high explosives located at the center of the vessel and static pressure conditions, and measured dynamic responses, including acceleration and strains. Based on the results, the following conclusions are drawn:

The overpressure on the inner surface of the vessel should mainly depends on the charge mass. For the same charge mass, the maximum peak pressure almost keeps unchanged when the static pressure loaded on the vessel increased.