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Protective effect of polymer coating on the circular steel plate response to near-field underwater explosions
Marine Structures 40 (2015) 247e266
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Marine Structures journal homepage: www.elsevier.com/locate/ marstruc
Protective effect of polymer coating on the circular steel plate response to near-field underwater explosions Yong Chen a, *, Feng Chen a, Zhi Peng Du b, Yu Wang b, Peng Duo Zhao b, Hong Xing Hua a a
State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai, 200240, PR China b The Navy Equipment Research Institute, Box 1303-14, Beijing, 100073, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 25 January 2014 Received in revised form 9 November 2014 Accepted 21 November 2014 Available online
To understand the intrinsic strong interaction between the soft coating and near-field underwater explosion, a series of comparative live fire tests are implemented. Nine steel circular plates with three configurations (i.e. rubber coated plate, foam coated plate and bare plate) are tested using 1.5 g PETN detonator. The stand-off between the plate center and explosive charge is ranged from 3.41 to 1.14 times of the maximum bubble radius. The transient strain history of the plate and acceleration history of the metal base fixture are monitored. The whole explosion process including local cavitation and bubble motion is recorded by an APX-RS high speed camera. Test results show that the compressibility of coating layer is the dominative factor that controls its protective performance in the shock wave loading phase. The more compressible foam coating distinctly reduce the shock wave intensity by local cavitation before enters the densification phase, while the explosion bubble shape and even the direction of water jet can also be changed. But the attenuation performance in the bubble loading phase is not as optimistic as that in the shock wave phase because more deformation space is required while the core has often entered the densification phase. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Polymer coating Compressibility Near-field underwater explosion Protective effects
* Corresponding author. Tel.: þ86 02134206813 818. E-mail address: [email protected] (Y. Chen).
http://dx.doi.org/10.1016/j.marstruc.2014.11.005 0951-8339/© 2014 Elsevier Ltd. All rights reserved.
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1. Introduction Sandwich structures are found to be capable of increasing the total anti-blast resistance. Their dynamic performance subjected to shock and impact loads becomes a hot topic in recent years. Early research works show that its good anti-blast resistance capability lies in two aspects. First, its good deflection capabilities provide volume to expand explosion gases and decrease the shock wave pressure [1,2]. And second, the progressive damage mode and energy absorbing mechanism of core permit relative small deformation of inner face plate [3e5]. The former merit may be more prominent if the blast medium is water. Xue [6] and Fleck [7] also estimated the momentum transmitted into a sandwich plate using the Taylor analysis [8] for a free standing front face sheet and drew some optimistically conclusions. Meanwhile, other research suggests that the benefits of employing sandwich construction for shock mitigation applications might be overestimated. E.g., Rabczuk [9] have investigated the response of sandwich beams subjected to underwater shocks by performing fully coupled FE fluid-structure interaction simulations. It is concluded that the final transmitted impulse is between the impulse according to the Taylor analysis if the face sheet is assumed to be free standing and that the entire sandwich structure is assumed to be free standing; and Liang [11] concluded that the classical Taylor model underestimates the mass of water by neglecting the reattachment process that occurs during stage II. Deshpande [12] made a deeply investigation on the one-dimensional shock response of sandwich plates subjected to an underwater pressure pulse. Both the propagation of an impinging acoustic shock wave within the fluid, and the propagation of a plastic shock wave within the sandwich core are accounted for. His analysis concluded that: (a) The momentum transmitted into the sandwich plates is substantially lower than that into a monolithic plate of same mass. (b) For a given core relative density, a smaller fraction of the shock impulse is transmitted into the sandwich plates with the bending-governed cores, which have lower compressive strength. Although the benefits of employing sandwich construction for shock mitigation applications might is not fully consistent, many experiment works still draw a positive conclusion. The experimental work by Wadley [13] showed that the impulse transferred to the fully supported sandwich structure is about 28% less than that transferred to a solid plate. In another test [14], the use of a crushable core in a fully back supported test configuration reduces the transmitted impulse by about 25% compared to that transmitted through a rigid, fully supported block. Schiffer [15] made a one-dimensional water tube test and concluded that the impulse imparted to water-backed sandwich plates can be dramatically reduced by increasing the initial hydrostatic pressure in the surrounding fluid. Although very promising in underwater explosion protection, the metal sandwich structure is difficult to use in practice nowadays for its complex fabrication process. Therefore, the nonmetal structure such as composite and polymer are also selected as potential candidates [16,17]. In some preceding researches, the idea that coats the ship hull with a layer of protective soft rubber sandwich coating is experimentally investigated [18,19]. It is shown that the protective rubber coating with soft core can improve the shock environment of ship equipment and moderate hull damage caused by the shock wave loadings. While for low frequency bubble loads, the mitigating effect is discounted. Above all these researches, the explosion loads considered are almost concentrated in far-field scenario. How the foam coating performs under near-field underwater explosions is seldom studied. In the near-field underwater explosions, the bubble effects and the strong local cavitation should be considered apart from the shock wave loading. Lee [20] showed that close-proximity charges can produce a complex shock interaction comprising several localized phenomena such as Mach reflection and rarefaction waves from the product bubble. In addition, the focused water jet from the bubble collapse was found to apply a much higher impulse than the shock in spite of the much smaller peak pressure. The bubble collapse phenomenon has been studied in more detail by Klaseboer [21] who examined the complex flow field and bubble dynamics associated with the collapse through both experiments and simulations. In addition to these phenomena, the well-known hull cavitation from shock-induced motion of the structure can also cause pressure cut-off, thus reducing the applied impulse [22]. Therefore, as the foam coating is easier to deform, the interaction between the soft foam and the bubble motion should be stronger and also needs to be considered. Aimed at the interaction between the soft foam and the bubble motion, a series of near-field live fire tests are made on foam coated metal plates in an artificial water tank using a detonator. The transient responses of steel
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circular plates with different coating configurations are compared as the stand-off changes. Details of the experiments are given and the test results are discussed. The main outline of this paper is as follows. Firstly, the structure and configuration of test models as well as the basic properties of two kinds of polymer coatings are introduced. Then, the main test procedure of the whole experiment is presented. In succession, the explosion pressure, acceleration, strain histories in different test events are discussed respectively. Finally, the video recorded by the high speed camera is also presented and analyzed. 2. Experimental research 2.1. Target plate and polymer coating Circular mild steel plate is used as the test specimen. All specimens are cut from the common sheet metal with the thickness being 3 mm. The nominal radius of the plates is 255 mm while the effective radius is 200 mm. The material of the specimen is SS41 steel, which is a kind of low carbon steel with good ductility. Its nominal static yielding strength is 235 MPa. Two kinds of polymer layers are applied as potential protective coating as shown in the right of Fig. 1. One is a natural rubber layer with 5 mm in thickness. The other is a layer of 16 mm thick PU foam plus a layer of 2 mm thick chloroprene rubber. The thin layer of chloroprene rubber face added to the foam is used to adding some weight and avoiding too early local deformation of the foam core. Both natural rubber and chloroprene layers have very limited compressibility compared with PU foam. The polymer foam layers are cut from some PE foam for industrial package use. The closed-cell foam is used for the watertight purpose. It is glued onto the outer face of test plate by epoxy resin glue. To guarantee enough adhesive strength, pyro acetic spirit is firstly used to clean the surface of both the coating and plate. After the glue being evenly smeared onto both faces, the plate and coating are combined together and compressed by a proper weight for about 12 h. The basic properties of three kinds of plates are listed in Table 1. Two kinds of coating layers almost have the same area density. Therefore, difference induced by the added mass effect on the response of steel plates brought by coatings can be eliminated. To understand the overall compressibility of two kinds of coatings, two circular specimens (shown in Fig. 2) are compressed in an INSTRON 693 material test machine. When the foam coating is tested, both the foam and the thin rubber layer are compressed at the same time. As the diameter of both test specimens is 8 cm, the ratio between diameter and height for pure rubber specimen reaches 16. The very large diameter to height ratio is selected because during tests, the thin rubber layer on the metal plate is confined by the plate and the outer boundary made by the supported basin when compressed by the shock loading. As the rubberlike materials have very little compressibility compared to their shear flexibility, large diameter to height ration specimen approaches its practical stress state. The compressive stressestrain curves of two kinds of coatings are plotted in Fig. 2. The compressive stress of rubber coating increases sharply when the compressive strain exceeds about 6%. It shows that the
Fig. 1. The test specimen and different coating configurations.
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Table 1 Some properties of different coatings. Test specimen
Bare plate
Rubber coated plate
Foam coated plate
Coating material Total thickness (mm) Area density (kg/m2)
/ 3 27.4
Rubber 3þ5 33.5
PU Foam þ Rubber 3 þ 16 þ 2 33.1
Fig. 2. The compressive strain-stress curve of two kinds of coating.
pure rubber coating is almost uncompressible. On the contrary, the PU foam has much better compressibility for its porous structure. It almost begins to enter the densification phases when the compressive strain is beyond 70%. But, as the PE foam used is a kind of closed-cell foam, no distinct stress plateau can be found. The tensile test of the material in the steel plate is also made in an INSTRON material test machine. Three pieces of specimen are cut from the backup test steel plates and then polished. The geometry and dimensions of the specimens is according to the metal material test standard GB/T 228-2002 of China. The tensile stressestrain curves of three specimens are plotted in Fig. 3. The consistence of different specimen is very good. The yielding stress of the material is about 235 Mpa and the maximum bearing stress can reach 330e335 Mpa. The final failure strain reaching 41.5%e45.2% shows good ductility of the material. 2.2. Underwater explosion tests and apparatus used The experiments are carried out in a steel water tank. The tank is 3 m in length, 2 m in width and 2.5 m in depth. It is welded by steel plates 8 mm in thickness. The top side of the tank is open (Fig. 4). The inner wall is covered by a layer of PU foam to decrease the shock wave reflected by the rigid wall. The maximum explosive allowed is 15 g TNT. A suite of apparatus is designed to properly fix the different specimens. As shown in Fig. 4, the main body of the fixture includes a steel drum, a vertical fixing arm and a transverse beam. The one-side opened steel drum is made by 20 mm thick steel panel to keep enough strength and stiffness. Its inner radius is 200 mm. The outer diameter is compatible with the specimen. At the open side of drum, a circle of twelve holes is drilled. Accordingly, twelve M18 bolts are used to fix the test specimen by a 22 mm thick annular plate to keep the plate boundary fixed. A vertical rectangular tube with the section 18 cm 18 cm is welded at the top of drum as a support arm. The signal wires also pass through
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Fig. 3. The tensile stressestrain curves of three specimen cut from test plates.
Fig. 4. The water tank and fixture used in the live fire test: ① steel drum ② observing window ③ horizontal supporting beam ④ detonator ⑤ watertight groove ⑥ accelerometer A3.
the hollow tube. A strong transverse steel beam is used as a supporting bridge spanning over the water tank. During tests, the strain gages are glued onto the inner face of test plate in advance. Then shielded cables are connected to the gages and accelerometers. A layer of asbestos paper is inserted between the plate and the front face of the supporting drum before the bolts are inserted and fastened. Once all bolts are fastened, the whole test apparatus is lifted into the water tank using a hoist. After the position has been adjusted, the detonator is placed into the water to the designed position and one test arrangements have completed. As one test finished, the whole apparatus is lifted up from the water tank to the open ground, and carefully checked to insure water-tightness. If plastic deformation or coating damage occurs, a new plate with the same coating configuration is replaced. After then, the next shot can be made. 2.3. Instrumentation The measured physical parameters include pressure, strain and acceleration histories. The pressure history indicates the explosion loading intensity. The strain and acceleration history gives the information about structure response.
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Two PCB 138A05 pressure transducers, linear within 2% up to 30 MPa, are applied to monitor the free-field and wall pressure change. The free-field transducer P1 is suspended at the same depth with that of denotation using nylon wire. It is kept 0.6 m distant from the explosive charge in the horizontal direction in all events. The other transducer is fixed at the face of the coating and planned to monitor the pressure fluctuation near the fluid structure interface. But, the large deformation of the coating makes it violently move back and forth. The pressure monitored is not consistent and abandoned in the later tests. Four unidirectional strain gages and two shock accelerometers are used for each plate to monitor the transient response. The 120-U resistance strain gages are glued onto the back surface of test plate after the measured points being polished and cleaned. The positions of the four gages from E1 to E4 are shown in Fig. 5. Considering the axisymmetric character of both loading and boundary, all gages are aligned with the radial direction. One accelerometer A1 is located at the center of the plate and the other A2 is located at the middle between the center and plate edge. In addition, an accelerometer A3 is mounted at the inner back plate of the supporting drum as illustrated in Fig. 4. It is used to measure the transient response of the drum. The shock response there can be considered as a shock environment measuring point considering much higher stiffness and greater mass of apparatus when compared with that of plate. All accelerometers are BK 4369 type piezoelectric transducer, which have a working range of 10,000 g, linear within 5% to 5000 g, and have a frequency range between 0.2 Hz and 6600 Hz. They were attached to the plate by a 5 mm steel stud in order to keep enough strength. Altogether nine channels are used for each test. Data are recorded with a maximum sampling frequency of 1 MHz/Ch and 18 bit resolution. The 100 ms recording span is sufficient to contain both the shock wave phase and the first bubble collapse for the 1.5 g charge. Since the strain signal decays much slower, 120 ms is set as the recording time span. The sampling rate is set to 10 KHz/Ch for both strain and acceleration records. The low-pass filter is set to 100 KHz for the pressure record and 5 KHz for acceleration and strain records respectively. An APX-RS high speed camera is used to observe the fluid-structure interaction process between the structure deformation and underwater explosion bubble. The camera is fixed before a transparent window that is located at the same height with the test plate center as shown in Fig. 4. The sunlight and two high power halogen lamps are used at the same time to enhance the luminance. The shooting frequency is set to 4500 frame per second (the time interval is 0.22222 ms) in order to capture the possible local cavitation accompanied by the shock wave. The focus of camera is aimed at the side face of the target plate center. When stand-off equals 0.6 m, the bubble motion is invisible because it is out of the view of the camera. When stand-off equals 0.4 m, only part of the bubble motion can be observed. The best images are captured in the nearest events when stand-off equals 0.2 m. Both the local cavitation and the whole bubble motion process can be observed.
Fig. 5. The position of the strain gages and accelerometers.
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For the convenience of data analysis, the camera and all other data recording devices are synchronously triggered by a rising pulse signal. The electric pulse is also used to ignite the detonator.
2.4. Charges and events The explosive charge consists of 1.5 g high explosive (70% PETN powder þ20% aluminum powder þ10% deterrent). The 1.5 g explosive is initiated with an exploding bridge wire detonator. A total of nine effective events are made at three stand-offs, i.e. 0.6 m, 0.4 m and 0.2 m. Charges in all tests are kept unchanged. The stand-off is defined as the distance between the detonator and the center of the steel plate. A then nylon string, with a 3 kg weight at the bottom end, is used to position the explosive charge. The peak pressure and first bubble period of all tests measured by the free pressure transducer are listed in Table 2. As the maximum stand-off is within 3.4 times of the theoretical maximum bubble radius (0.176 m), substantial interaction between the bubble and the target is expected. 3. Results and discussion Results are presented in four sections. First, the free-field pressure records are given to determine the shock loading intensity. Second, stain records are compared as the strain peak being a criterion on the protective performance of coating. Third, the acceleration history measured at the inner back of the supporting drum is presented. The shock response spectrum analysis is made to evaluate the dynamic performance of coating in frequency domain. Finally, some typical high speed camera images for the nearest stand-off events are given. The cavitation and bubble motion process are compared when the coating configuration changes.
3.1. Pressure-time profiles Generally speaking, two distinct phases can be observed in the free underwater explosion, i.e., shock wave and bubble pulse phase. The shock wave consists of an almost instantaneous rise in pressure to a peak pressure, followed by an exponential decay in pressure down to the hydrostatic pressure. The peak pressure and the decay constant depend upon the size of the explosive charge and the stand-off between the charge and measuring point. The following empirical equations is used to estimate the pressure history [23]
PðtÞ ¼ P0 eðtt0 Þ=q
(1)
Table 2 Nine effective test events and some test results of free-field pressure: measured at P1, 0.6 m distant from the explosion center. The theoretical value: P0 ¼ 7.98 MPa, q ¼ 0.123 ms, T ¼ 31.2 ms Event number
Charge size (g)
Stand-off (m)
Test specimen
Peak of the first shock (Mpa)
The first bubble motion period (ms)
1# 2# 3# 4#
1.5 1.5 1.5 1.5
0.6 0.4 0.2 0.6
8.1 8.2 8.0 8.2
33.5 34.1 34.1 33.3
5#
1.5
0.4
7.9
33.7
6#
1.5
0.2
8.2
34.7
7# 8# 9#
1.5 1.5 1.5
0.6 0.4 0.2
Pure plate Pure plate Pure plate Rubber coated plate Rubber coated plate Rubber coated plate Foam coated plate Foam coated plate Foam coated plate
8.1 8.3 8.2
33.6 33.3 32.4
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. A1 P0 ¼ K1 W 1=3 R
(2)
. A2 q ¼ K2 W 1=3 W 1=3 R
(3)
where P0 is the peak pressure in MPa and q the decay constant in milliseconds. W is the weight of charge in kilograms and R is the stand-off in meters. A1,A2,K1 and K2 are the coefficients related to different explosive. The gas bubble generated by the explosion is almost spherical during its initial stage of expansion and contraction. The maximum bubble radius and the time taken to reach the first bubble radius minimum can be calculated. Both vary with the size of the explosive charge and the depth at which the explosion occurs.
T ¼ K5 *W 1=3 ðD þ 9:8Þ5=6
(4)
. Rmax ¼ K6 *W 1=3 ðD þ 9:8Þ1=3
(5)
where T is the bubble period in seconds and Rmax is the bubble radius in meters. D is the explosion depth in meters. K5 and K6 are the coefficients related to different explosive. In our tests, 1.5 g PENT is used and the explosion depth is 1.4 m. For PENT, A1 ¼1.194, K1 ¼ 56.21 MPa, K2 ¼ 0.086 s, K5 ¼ 2.098 s, K6 ¼ 3.439 m [24], it can be computed as P0 ¼ 7.98 MPa, q¼0.123 ms, T ¼ 31.2 ms and Rmax ¼ 0.176 m. The three stand-offs 0.6 m, 0.4 m and 0.2 m are equivalent to 3.41Rmax, 2.27Rmax, and 1.14Rmax. Therefore, all test events can be regarded as near-field explosion environment. The typical pressure-time history recorded at P1 in test event 1#e3# are shown in Fig. 6(aec). For clarity the Y-axis is limited to 1 MPa. Several distinct phases can be distinguished in Fig. 6(a) as in common far-field free underwater explosions. The shock wave arrives at about 0.4 ms and the first reflective wave at about 3 ms. The first bubble pulse arrives at 34.2 ms, with the corresponding exciting frequency as 29.3 Hz. The period is a little longer than the theoretical value 31.2 ms. The second bubble pulse arrives at about 61 ms. There is no distinct difference between Fig. 6(a) and (b). It is shown that when stand-off changes from 3.41Rmax to 2.27Rmax, the influence of the structure deformation on the bubble is still not distinct. But when stand-off changes to 1.14Rmax, the peak of the first bubble pulse is clearly reduced as shown in Fig. 6(c). The second bubble pulse almost cannot be observed. The fact shows that when stand-off becomes nearer, the influence of the structure on the bubble loads is become more prominent. Table 1 lists the peak pressure induced by the shock wave and the period of the first bubble pulse in all nine test events. Totally speaking, the explosion process is stable and consistent. When the stand-off farer than 2.3Rmax, the plate deformation cannot effectively changes the bubble dynamics whether the plate is coated or not. But, when the stand-off decreases to 1.14Rmax, the first bubble motion can be altered. The phenomenon is also verified by the high speed camera images as discussed in Section 3.4. 3.2. Stain records and target deformation The strain peak measured on the plate can be used to evaluate the protective performance of different coatings. Though there is some difference between different records measured in four gages, the trend is similar as they all measure the strain in radial direction. Therefore, only strain history measured at E1 is detailed discussed as a typical record. The strain peaks of other records induced by both the shock wave and bubble pulse are extracted and compared in histogram. Typical strain history within 150 ms measured at E1 in all nine tests events are listed in Fig. 7. In Fig. 7(aec), the strain records measured at bare plates are compared when stand-off changes from 0.6 m to 0.2 m. The strain amplitude is closely related to the stand-off. As the stand-off decreases, the
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Fig. 6. Free-field pressure history measured at P1 that is 0.6 m distant from the detonator: (a) test event 1#, stand-off equals 0.6 m, (b) test event 2#, stand-off equals 0.4 m, (a) test event 3#, stand-off equals 0.2 m.
strain amplitude increases from 1011 mε to 3333 mε. This is due to the shock intensity is greatly enhanced when explosion becomes much nearer. For all records, the strain peaks induced by the first shock wave, the first and second bubble pulse can be easily distinguished and almost has the same order. Especially, the strain peak induced by the first bubble pulse at about 34 ms is always the maximum one in all three peaks. This phenomenon is different from that in far-field underwater
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Fig. 7. The typical strain history measured at E1 (low-pass filtered with cut-off frequency 5000 Hz): (aei)— event 1#e9#.
explosions, where the first shock wave is often the dominant factor if the natural frequency of the structure is not coincident with the bubble pulse frequency. In the near-field underwater explosions, the load of bubble pulse has much more energy than that of shock wave. For E1 in event 3, this trend is the most distinct, which the strain peak induced by shock wave is less than 2000 mε, while that induced by the first bubble pulse reaches 3333 mε, exceeding the nominal yielding strain of the material and obvious plastic strain can be observed. The fact verifies that the shock energy of the first bubble pulse is often the most important factor cause the structure failure, especially for thin-walled structures that has relatively wider span and lower natural frequency. The same trend can be observed in Fig. 7(def) for test event 4#e6#. In these three events, the target plates are rubber coated. Compared with that of bare plates, the peak values are correspondingly smaller than that in event 1#e3#. It should be attributed to the attached mass effect and some limited compressibility of rubber coating. The protective effect exists in all three events, no matter what intensity of the explosion load is. Fig. 7(geh) show the strain measured in event 7#e9# (foam coated plate). Some different trends can be observed. Firstly, obvious mitigation effect can be observed when stand-off equals 0.6 m. The peak strain is reduced from 1011 mε to 202 mε. It is shown that the foam coating has tremendous protective effect under this loading. But when the stand-off becomes 0.4 m, the mitigation effect is greatly discounted. The peak strain only reduces from 1520 mε to 1300 mε. The mitigation effect is only a little better than that of rubber coating. The fact is a little counter-intuitive before the high speed camera image carefully viewed. It is found that in test event 7#, the compressible level of coating is smaller when compared with that in test event 8#. Therefore, the fact can be explained as that the foam
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coating deforms in event 7#, but does not enter the densification phase. Therefore, the loading transmitted to the steel plate face is greatly mitigated by the compressible deformation of foam coating. But with the increasing of load intensity in test event 8#, the foam deforms greatly and enters the densification phase. Once densification occurs, the protective performance is greatly discounted. The similar trend can also be observed in test event 9#. The similar trend can be observed in the records measured at E2 to E4 though the magnitude may be different when the measuring location changes. As a more detailed comparison, the strain peaks measured at E1 to E4 in events that have the same stand-off are compared respectively. As the strain peaks in the shock wave and first bubble pulse phases can be distinctly divided, they are respectively compared. Only maximum tensile strain is considered, which is often used as a failure criterion for ductile metals. Fig. 8 compares the strain peaks measured at E1eE4 in event 1#, 4# and 7# when stand-off equal 0.6 m. The strain peaks in the bubble pulse phase is higher than that in the initial shock wave phase. The mitigation effect offered by the foam coating is very prominent in both phases. It is demonstrated under such loading, the compressibility of the foam coating takes effect. The loading is not intense enough to make the foam core enters densification phase. Fig. 9 compares the strain peaks measured at E1eE4 in event 2#, 5# and 8# when stand-off equal 0.4 m. Under this loading, the mitigation effect of both coating still exists. The foam coating still has the best performance. But its superiority is greatly discounted. This should be attributed to the densification of foam core when the shock loading is more intense. Compared with that in the shock wave phase, the protection performance in the bubble pulse phase is deteriorated. It is because that the bubble loading often has wider span and lower peak. More low-frequency ingredient contained in the bubble loading is than that in the shock wave loading. Therefore, more deformation space is needed in order to mitigate the bubble loading. Fig. 10 compares the strain peaks measured at E1eE4 in event 3#, 6# and 9# when stand-off equal 0.2 m. Though the loading is more intense in these three events as the stand-off decreases, the protection effects still exists in the shock wave phase. The foam coating still has the best effect for its better compressibility. While in bubble phase, the protection performance of foam coating seems better than that in the event when stand-off equals 0.6 m. The fact should be attributed to the influence of the coating deformation on the jet direction of bubble when stand-off reaches 0.2 m. More detailed discussion is made in Section 3.4. In all the test events, distinct plastic deformation occurs in the plate only in events 3#, 6# and 9#, when stand-off equals 0.2 m. In order to check the final deformation of the plates with different coating configuration, the specimens are cut into two halves. Fig. 11 gives lateral view of the cut specimens. Very distinctive deformation can be observed in the bare plate, the center deformation reaches 2.4 cm.
Fig. 8. Strain peaks comparison in event 1#, 4# and 7#, stand-off ¼ 0.6 m.
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Fig. 9. Strain peaks comparison in event 2#, 5# and 8#, stand-off ¼ 0.4 m.
Fig. 10. Strain peaks comparison in event 3#, 6# and 9#, stand-off ¼ 0.2 m.
The deformation of plates with coating is much smaller. The foam coated plate has the smallest deformation. The result is consistent with the strain records. The foam core deformation is checked by peeling the outer face of the foam coating after test event 9#. Distinct damage occurs at the center part of the plate as shown in Fig. 12. Considering the spherical wave effect, the center part of the plate should bear the most intense blast loading. Therefore, prominent gap occurs. The fact verifies the deduction that when stand-off equal 0.2 m, the blast loading is so intense that the foam enters densification phase. Better protection effect of foam coating can be anticipated if the strength of core is optimized aiming at the specific loading intensity. If the load becomes intense, the strength of core should be enhanced accordingly. 3.3. Acceleration records and shock environment Three accelerometers are used to monitor the response of plate and fixture. But, most records measure at A1 and A2 suffers to serious ‘zero-drifting’ and cannot be used. It is due to the direct loading on the plate are so intense and induces the resonance of the accelerometer. Fortunately, the strain record can be used as a comparative criterion. Therefore, these data is not compared. Only the acceleration record measured at A3 on the inner back of the supporting basin is used. The response
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Fig. 11. The final deformation of the plate in event 3#, 6#, 9# (stand-off equals 0.2 m), from the top to the bottom successively is: bare plate, rubber coated plate and foam coated plate.
Fig. 12. The damage mode of the foam coating in event 9#.
measured at this location contains much information such as the energy transmitted from the plate to the basin after being attenuated by the polymer coating. It can be regarded as a shock environment measuring point. As the information extracted from the signal in time domain is very limited, the Shock Response Spectrum (SRS) analysis is made to obtain more information. SRS is a graphical representation of an arbitrary transient acceleration input, such asshock in terms of how a Single Degree Of Freedom (SDOF) system (like a mass on a spring) responds to that input. It is a powerful tool in understanding the frequency component of the dynamic response of structure when subjected to shock input. In order to understand the spectrum distribution, the first natural frequency of test plate is estimated using the approximation calculation formula for the boundary fixed circular plate immersed in fluid [25]
0:4745 hc f ¼ pffiffiffiffiffiffiffiffiffiffiffiffi 21 1þb r
b ¼ 0:6689
r r r1 h
(6)
(7)
where f is the first natural frequency, h and r is the thickness and radius of the plate. r1 and c1 is the density and sound speed of the solid material. r is the density of the fluid. It can be computed that f equals 73.8 Hz for bare steel plate. It equals 59.7 and 60.2 Hz for rubber and foam coated plate respectively. The practical frequency should be less than the theoretical value for the inevitable elasticity of the fixed boundary. The SRS computed from the acceleration history of bare plate in event 1#e3# is compared firstly to understand the energy distribution in frequency domain. Fig. 13 shows the three SRS curves in a same logarithm coordinate. The spectrum acceleration, velocity and displacement can be read at the same
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Fig. 13. The SRS of A3 in event 1#, 2# and 3# (bare plate, stand-off equals 0.6, 0.4 and 0.2 m): red dotted line—event 1#, red dashed line—event 2#, red solid line—event 3#. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
time. The analyzing frequency bandwidth is between 1 Hz and 2 k Hz. With the decrease of stand-off, the maximum spectrum velocity monotonously increases from 0.28 m/s to 0.61 m/s. It indicates that the whole shock energy transmitted to the structure increases. Some typical frequency bands can be distinguished: (1) 1e40 Hz In this band, the SRS is mainly controlled by the bubble motion because the period of the first mode of plate is shorter than the first bubble motion period. The distinct peak can be found around 33e34 Hz, which is corresponding to the first bubble expansion and collapse motion period (about 33.5 ms). (2) 40e400 Hz In this band, the SRS is mainly controlled by the bubble motion excitation and the dynamic response of the plate. Several distinct peaks distributed from about 50 Hz to 300 Hz are corresponding to several lowest natural modes of the plate and fixture. (3) 400e2000 Hz In this band, the excitation of bubble motion is relatively weak and mainly controlled by the shock wave. A distinct peak lies around 700e800 Hz. This frequency should be corresponding to at least one of local natural frequency of fixture near the location where the accelerometer A3 mounted. When this mode is excited by the shock wave, a distinct peak appears in the SRS. The energy distribution in frequency domain is closely related to the stand-off distance. When stand-off equals 0.6 m (event 1#), the spectrum velocity induced by the shock wave reaches 0.3 m/s (800 Hz). But the spectrum velocity induced by bubble motion is below 0.2 m/s. This shows the energy transmitted to the plate by the shock wave is greater than that by the bubble motion. When stand-off becomes 0.4 m in event 2#, the maximum spectrum velocities induced by the bubble motion and shock
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wave are almost equal (0.31 m/s VS 0.30 m/s). When stand-off becomes 0.2 m in event 1#, the corresponding spectrum velocity becomes 0.6 m/s and 0.2 m/s respectively. The potential flow energy induced by the bubble motion becomes more and more prominent as the explosive charge becomes nearer and nearer, when compared with the shock wave energy transmitted by the compressive wave of water. For comparison, the SRS curves in the events that have the same stand-off but different coating configuration is plotted together. The SRS curves computed from the records in event 1#, 4# and 7# when stand-off equals 0.6 m are shown in Fig. 14. The blue dotted curves for event 7# (foam coated) is prominently lower than that of other two events in almost all frequency band except near 33 Hz, i.e. the bubble motion frequency. The difference between the red solid curve (bare plate) and green dashed curve (foam coated) is much smaller though the attenuation effects still can be observed in high frequency for rubber coating. Totally speaking, the foam coating has much better attenuation effect under such load density than that of rubber coating. The fact is consistent with the conclusion drawn from the strain analysis in Section. 3.2. The shock response spectrum curves of A1 in event 2#, 5# and 8# are shown in Fig. 15. When standoff becomes 0.4 m, some different trend can be observed. The attenuation effect of foam coating can be observed from 150 Hz to 2000 Hz, but some amplification effect exists between 20 and 100 Hz. It should be attributed to the densification behavior when the bubble loads exceeds its working strength. The suddenly increases caused by the densification excites the lower modes of plate. The attenuation effect of the rubber coating only exists in the high-frequency band between 700 and 1000 Hz. In other frequency band, the difference between rubber coating and bare plate is small. The fact tells us the compressibility of coating is the main control factor affects its attenuation performance in high-frequency band. The SRS curves computed from records in event 3#, 6# and 9# are shown in Fig. 16. When stand-off becomes 0.2 m, the most energy comes from the fluid flow induce by the bubble motion. Though the loading is more intense, the slight attenuation effect still exists for the foam coating between 40 and
Fig. 14. The SRS of A3 in event 1#, 4# and 7# (stand-off ¼ 0.6 m): red dotted line—event 1#, bare plate; blue dotted line—event 4#, rubber coated plate; green dotted line—event 7#, foam coated plate. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 15. The shock response spectrum of A3 in event 2#, 5# and 8# (stand-off ¼ 0.4 m): red dashed line—event 2#,bare plate; blue dashed line—event 5#,rubber coated plate; green dashed line—event 8#, foam coated plate. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
400 Hz. This is partly attributed the fact that the soft foam coating alter the bubble behavior and the jet direction as shown in the next section. The difference of maximum spectrum displacement between three models is more distinct than that in other events. The value of spectrum displacement plate with foam coating is 5 mm while the value of bare steel plate reaches 2 cm. This is also due to the fact that foam coating alters the flow induced by bubble motion as a different boundary. The maximum spectrum displacement of rubber coating lies between that of bare plate and foam coated plate. But in other frequency band, its attenuation effect is very limited. Totally speaking, the compressibility, not the mass effect, should be the supreme factor that controls the protective performance of coating, especially for the shock wave loading. Therefore, for far-field underwater explosion, the soft foam coating should performs better than in near-field scenario. It is due to the energy mainly exists in higher frequency band for shock wave loads. But when stand-off decreases, the bubble effect becomes dominant. The attenuation effect is discounted for energy concentrates in low-frequency band and more deformation space is often required. 3.4. Images shot by high speed camera As limited by the length of the article, only some typical images are selected for the test event 3#, 6 # and 9#. In these tree events, the stand-off is kept 0.2 m unchanged, but the coating configuration is changed. Two distinct stages can be observed: i. Shock wave loading and bubble expansion stage As shown in Fig. 17, the explosion process initiates in frame 1#. Then the bubble expands rapidly, accompanied by the shock wave transmission process. The time interval for the shock wave arrives at the face of the plate can be estimated as 0.2/1550 ¼ 0.129 ms. Therefore, in frame 2 (0.222 ms), the shock wave loading has been arrived at the surface of the target plate. As the theoretically decay constant for the first shock wave is q ¼ 0.123 ms, the shock wave loading should decays completely in
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Fig. 16. The shock response spectrum of A3 in event 3#, 6# and 9# (stand-off ¼ 0.2 m): red solid line—event 3#,bare plate; blue solid line—event 6#,rubber coated plate; green solid line—event 9#, foam coated plate. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
frame 2. The difference occurs at this moment can be observed in frame 2 of three test events. Slight local cavitation appears in test event 9# (foam coating plate). On the contrary, there is not any cavitation in both test event 3# and 6#. Only in the next frame (frame 3, 0.444 ms), local cavitation can be observed in all test events. This fact indicates that the motion of the target face with soft foam coating is much faster than that for other two plates. Four successive frames from 2# to 5# show that the cavitation expansion and closure process at the surface of the foam coating is the most obvious and durable. It sustains from frame 2# to 10# and lasts about 2 ms until the face motion caused by compression pressure is balanced by the force of structure deformation. As a comparison, this process in test event 3# and 6# sustains from frame 3# to 8#. The cavitation volume at the face of soft foam coating is also much greater than that for other two plates. The fact verifies the conclusion drawn in early researches [12,18]. The softer core with better compressibility can make the local cavitation take place much earlier and longer. This mechanism can cause the cut-off effect of the shock wave loading. The potential merit is that with the time span of the shock wave decreases and the total impulse transmitted into the hull could be reduced [18]. ii. Interaction stage between bubble motion and target deformation (Fig. 18) As stated in Section 3.1, the interaction between the bubble motion and target deformation is not so obvious when stand-off equals 0.6 m and 0.4 m. The maximum bubble radius can be estimated as Rmax ¼ 0.176 m when the influence of boundary neglected. Therefore, only when stand-off equal 0.2 m (1.14Rmax), the substantive interaction between the target deformation and bubble motion is anticipated. Some typical frames are presented in order to compare this interaction process. In frame 22#, at about 4.667 ms, the bubbles still expand but their left parts are almost stopped due to the existence of the target plate as a structure boundary. It can be estimated that the velocity of the potential flow between the left boundary of bubble and target plate outer surface almost become to zero at this moment. Then, the left boundary of the bubble begins to contract while the remaining part still expands because the neighboring fluid is not impeded as in the left part. The prominent difference
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Fig. 17. The high speed camera images in the shock phase of event 3#, 6# and 9# when stand-off equal 0.2 m, 1.14 Rmax.
appears when the bubbles in different boundary begin to contract. Once the bubble begins to contract, the fluid near the left boundary of the bubble is forced to move to the right. Therefor the cavitation region forms near the fluid structure interface as the water cannot sustain the negative pressure. There is great difference between the cavitation regions for different coatings. Like in the first shock wave stage, the cavitation region for the soft foam coating event is much wider and thicker than that for the rubber or no coating. As can be seen in frame 77# (16.88 ms), the dome shape cavitation region for the soft foam coating almost covers the whole plate. On the contrary, the cavitation in the other two events is similar, about 2/3 in radius around the center of the whole plate is cover with cavitation vapor. The bubble shape is flatter in test event 6# than that in event 3# and 9#. In frame 119# (26.22 ms), the difference still exists when the cavitation region partly close. Almost half of the bubble in event 9# is sunken to the right. The influence of the cavitation region on the bubble shape is so large that the left part of the bubble moves to the right until the bubble collapse. The cavitation region and the bubble separates and the reloading effect can be observed mainly caused by the cavitation closure. But in the
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Fig. 18. The high speed camera images in the bubble phase of event 3#, 6# and 9# when stand-off equal 0.2 m, 1.14 Rmax.
other two events, the cavitation is not large enough to cause the bubble moves to the right. Finally, a water jet is formed and hit the target plates as shown in frame 152#. The plastic deformation takes place in both these events. Therefore, the coating with high compressibility can also change the bubble shape even direction of the water jet when proper condition is satisfied. But the condition needs to be further investigated as only limited samples are presented in this paper. 4. Conclusions The transient response of polymer coated circular plates to the near-field underwater explosions is experimentally studied. Nine steel circular plates with three configurations (i.e. rubber coated plate, foam coated plate and bare plate) are tested using 1.5 g PETN detonator. Test results show that the compressible foam coating can distinctly influence the shock wave loading and the bubble behavior. The shock wave can be mitigated by local cavitation. But for the near-field bubble loading, more
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deformation space is often needed. Once the coating enters densification phase, the protective performance of coating is greatly discounted. Therefore, the mechanical behavior of the coating and the water loading-structure interaction effects should be considered if the optimal protective performance is anticipated. Acknowledgments The authors would like to thank the NSFC for financially supporting this research under the contract No. 11272215. References [1] Wadley HN, Dharmasena KP, Queheillalt DT, Chen Y, Dudt P, Knight D, et al. Dynamic compression of square honeycomb structures during underwater impulsive loading. J Mech Mater Struct 2007;2:2025e48. [2] Dharmasena KP, Wadley HNG, Williams K, Xue Z, Hutchinson JW. Response of metallic pyramidal lattice core sandwich panels to high intensity impulsive loading in air. Int J Impact Eng 2011;38:15. [3] Jackson M, Shukla A. Performance of sandwich composites subjected to sequential impact and air blast loading. Compos Part B Eng 2011;42:155e66. [4] Rathbun HJ, Radford DD, Xue Z, He MY, Yang J, Deshpande V, et al. Performance of metallic honeycomb-core sandwich beams under shock loading. Int J Solids Struct 2006;43:1746e63. [5] Xue Z, Hutchinson JW. Crush dynamics of square honeycomb sandwich cores. Int J Numer Methods Eng 2006;65:2221e45. [6] Xue Z, Hutchinson JW. A comparative study of impulse-resistant metal sandwich plates. Int J Impact Eng 2004;30: 1283e305. [7] Fleck N, Deshpande V. The resistance of clamped sandwich beams to shock loading. Trans Am Soc Mech Eng J Appl Mech 2004;71:386e401. [8] Taylor GI. The pressure and impulse of submarine explosion waves on plates. Cambridge, UK: Cambridge University Press; 1963. [9] Rabczuk T, Samaniego E, Belytschko T. Simplified model for predicting impulsive loads on submerged structures to account for fluid-structure interaction. Int J Impact Eng 2007;34:163e77. [11] Liang Y, Spuskanyuk AV, Flores SE, Hayhurst DR, Hutchinson JW, McMeeking RM, et al. The response of metallic sandwich panels to water blast. J Appl Mech Trans ASME 2007;74:81e99. [12] Deshpande V, Fleck N. One-dimensional response of sandwich plates to underwater shock loading. J Mech Phys Solids 2005;53:2347e83. [13] Wadley H, Dharmasen K, Chen Y, Dudt P, Knight D, Charette R, et al. Compressive response of multilayered pyramidal lattices during underwater shock loading. Int J Impact Eng 2008;35:13. [14] Dharmasen KP, Queheillalt DT, Wadley HNG, Dudt P, Chen Y, Knight D, et al. Dynamic compression of metallic sandwich structures during planar impulsive loading in water. Eur J Mech A Solids 2010;29:12. [15] Schiffer A, Tagarielli VL. One-dimensional response of sandwich plates to underwater blast: fluid-structure interaction experiments and simulations. Int J Impact Eng 2014;71:16. [16] Langdon G, von Klemperer C, Rowland B, Nurick G. The response of sandwich structures with composite face sheets and polymer foam cores to air-blast loading: preliminary experiments. Eng Struct 2012;36:104e12. [17] Gardner N, Wang E, Kumar P, Shukla A. Blast mitigation in a sandwich composite using graded core and polyurea interlayer. Exp Mech 2012;52:119e33. [18] Chen Y, Tong Z, Hua H, Wang Y, Gou H. Experimental investigation on the dynamic response of scaled ship model with rubber sandwich coatings subjected to underwater explosion. Int J Impact Eng 2009;36:318e28. [19] Chen Y, Zhang Z, Wang Y, Hua H, Gou H. Attenuating performance of a polymer layer coated onto floating structures subjected to water blasts. Eur J Mech A Solids 2009;28:591e8. [20] Lee JJ, Gregson J, Rude G, Paulgaard GT. Underwater shock and bubble interactions from twin explosive charges. In: €ttingen, Germany; July 15e20, 2007. Proceedings of the 26th international symposium on shock waves. Go [21] Klaseboer E, Hung KC, Wang C, Wang CW, Khoo BC, Boyce P, et al. Experimental and numerical investigation of the dynamics of an underwater explosion bubble near a resilient/rigid structure. J Fluid Mech 2005;537:26. [22] Slater J, Rude G, Paulgaard G. Experimental study of airbacked and water backed targets during near contact explosions. 2005. DRDC Suffield Technical Report # TR 2005152. [23] Cole RH. Underwater explosions. New York: Dover Publications; 1965. [24] Reid WD. The response of surface ships to underwater explosions. 1996. DTIC document. [25] Amabili M, Kwak M. Free vibrations of circular plates coupled with liquids: revising the lamb problem. J Fluids Struct 1996; 10:743e61.
Contents lists available at ScienceDirect
Marine Structures journal homepage: www.elsevier.com/locate/ marstruc
Protective effect of polymer coating on the circular steel plate response to near-field underwater explosions Yong Chen a, *, Feng Chen a, Zhi Peng Du b, Yu Wang b, Peng Duo Zhao b, Hong Xing Hua a a
State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai, 200240, PR China b The Navy Equipment Research Institute, Box 1303-14, Beijing, 100073, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 25 January 2014 Received in revised form 9 November 2014 Accepted 21 November 2014 Available online
To understand the intrinsic strong interaction between the soft coating and near-field underwater explosion, a series of comparative live fire tests are implemented. Nine steel circular plates with three configurations (i.e. rubber coated plate, foam coated plate and bare plate) are tested using 1.5 g PETN detonator. The stand-off between the plate center and explosive charge is ranged from 3.41 to 1.14 times of the maximum bubble radius. The transient strain history of the plate and acceleration history of the metal base fixture are monitored. The whole explosion process including local cavitation and bubble motion is recorded by an APX-RS high speed camera. Test results show that the compressibility of coating layer is the dominative factor that controls its protective performance in the shock wave loading phase. The more compressible foam coating distinctly reduce the shock wave intensity by local cavitation before enters the densification phase, while the explosion bubble shape and even the direction of water jet can also be changed. But the attenuation performance in the bubble loading phase is not as optimistic as that in the shock wave phase because more deformation space is required while the core has often entered the densification phase. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Polymer coating Compressibility Near-field underwater explosion Protective effects
* Corresponding author. Tel.: þ86 02134206813 818. E-mail address: [email protected] (Y. Chen).
http://dx.doi.org/10.1016/j.marstruc.2014.11.005 0951-8339/© 2014 Elsevier Ltd. All rights reserved.
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1. Introduction Sandwich structures are found to be capable of increasing the total anti-blast resistance. Their dynamic performance subjected to shock and impact loads becomes a hot topic in recent years. Early research works show that its good anti-blast resistance capability lies in two aspects. First, its good deflection capabilities provide volume to expand explosion gases and decrease the shock wave pressure [1,2]. And second, the progressive damage mode and energy absorbing mechanism of core permit relative small deformation of inner face plate [3e5]. The former merit may be more prominent if the blast medium is water. Xue [6] and Fleck [7] also estimated the momentum transmitted into a sandwich plate using the Taylor analysis [8] for a free standing front face sheet and drew some optimistically conclusions. Meanwhile, other research suggests that the benefits of employing sandwich construction for shock mitigation applications might be overestimated. E.g., Rabczuk [9] have investigated the response of sandwich beams subjected to underwater shocks by performing fully coupled FE fluid-structure interaction simulations. It is concluded that the final transmitted impulse is between the impulse according to the Taylor analysis if the face sheet is assumed to be free standing and that the entire sandwich structure is assumed to be free standing; and Liang [11] concluded that the classical Taylor model underestimates the mass of water by neglecting the reattachment process that occurs during stage II. Deshpande [12] made a deeply investigation on the one-dimensional shock response of sandwich plates subjected to an underwater pressure pulse. Both the propagation of an impinging acoustic shock wave within the fluid, and the propagation of a plastic shock wave within the sandwich core are accounted for. His analysis concluded that: (a) The momentum transmitted into the sandwich plates is substantially lower than that into a monolithic plate of same mass. (b) For a given core relative density, a smaller fraction of the shock impulse is transmitted into the sandwich plates with the bending-governed cores, which have lower compressive strength. Although the benefits of employing sandwich construction for shock mitigation applications might is not fully consistent, many experiment works still draw a positive conclusion. The experimental work by Wadley [13] showed that the impulse transferred to the fully supported sandwich structure is about 28% less than that transferred to a solid plate. In another test [14], the use of a crushable core in a fully back supported test configuration reduces the transmitted impulse by about 25% compared to that transmitted through a rigid, fully supported block. Schiffer [15] made a one-dimensional water tube test and concluded that the impulse imparted to water-backed sandwich plates can be dramatically reduced by increasing the initial hydrostatic pressure in the surrounding fluid. Although very promising in underwater explosion protection, the metal sandwich structure is difficult to use in practice nowadays for its complex fabrication process. Therefore, the nonmetal structure such as composite and polymer are also selected as potential candidates [16,17]. In some preceding researches, the idea that coats the ship hull with a layer of protective soft rubber sandwich coating is experimentally investigated [18,19]. It is shown that the protective rubber coating with soft core can improve the shock environment of ship equipment and moderate hull damage caused by the shock wave loadings. While for low frequency bubble loads, the mitigating effect is discounted. Above all these researches, the explosion loads considered are almost concentrated in far-field scenario. How the foam coating performs under near-field underwater explosions is seldom studied. In the near-field underwater explosions, the bubble effects and the strong local cavitation should be considered apart from the shock wave loading. Lee [20] showed that close-proximity charges can produce a complex shock interaction comprising several localized phenomena such as Mach reflection and rarefaction waves from the product bubble. In addition, the focused water jet from the bubble collapse was found to apply a much higher impulse than the shock in spite of the much smaller peak pressure. The bubble collapse phenomenon has been studied in more detail by Klaseboer [21] who examined the complex flow field and bubble dynamics associated with the collapse through both experiments and simulations. In addition to these phenomena, the well-known hull cavitation from shock-induced motion of the structure can also cause pressure cut-off, thus reducing the applied impulse [22]. Therefore, as the foam coating is easier to deform, the interaction between the soft foam and the bubble motion should be stronger and also needs to be considered. Aimed at the interaction between the soft foam and the bubble motion, a series of near-field live fire tests are made on foam coated metal plates in an artificial water tank using a detonator. The transient responses of steel
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circular plates with different coating configurations are compared as the stand-off changes. Details of the experiments are given and the test results are discussed. The main outline of this paper is as follows. Firstly, the structure and configuration of test models as well as the basic properties of two kinds of polymer coatings are introduced. Then, the main test procedure of the whole experiment is presented. In succession, the explosion pressure, acceleration, strain histories in different test events are discussed respectively. Finally, the video recorded by the high speed camera is also presented and analyzed. 2. Experimental research 2.1. Target plate and polymer coating Circular mild steel plate is used as the test specimen. All specimens are cut from the common sheet metal with the thickness being 3 mm. The nominal radius of the plates is 255 mm while the effective radius is 200 mm. The material of the specimen is SS41 steel, which is a kind of low carbon steel with good ductility. Its nominal static yielding strength is 235 MPa. Two kinds of polymer layers are applied as potential protective coating as shown in the right of Fig. 1. One is a natural rubber layer with 5 mm in thickness. The other is a layer of 16 mm thick PU foam plus a layer of 2 mm thick chloroprene rubber. The thin layer of chloroprene rubber face added to the foam is used to adding some weight and avoiding too early local deformation of the foam core. Both natural rubber and chloroprene layers have very limited compressibility compared with PU foam. The polymer foam layers are cut from some PE foam for industrial package use. The closed-cell foam is used for the watertight purpose. It is glued onto the outer face of test plate by epoxy resin glue. To guarantee enough adhesive strength, pyro acetic spirit is firstly used to clean the surface of both the coating and plate. After the glue being evenly smeared onto both faces, the plate and coating are combined together and compressed by a proper weight for about 12 h. The basic properties of three kinds of plates are listed in Table 1. Two kinds of coating layers almost have the same area density. Therefore, difference induced by the added mass effect on the response of steel plates brought by coatings can be eliminated. To understand the overall compressibility of two kinds of coatings, two circular specimens (shown in Fig. 2) are compressed in an INSTRON 693 material test machine. When the foam coating is tested, both the foam and the thin rubber layer are compressed at the same time. As the diameter of both test specimens is 8 cm, the ratio between diameter and height for pure rubber specimen reaches 16. The very large diameter to height ratio is selected because during tests, the thin rubber layer on the metal plate is confined by the plate and the outer boundary made by the supported basin when compressed by the shock loading. As the rubberlike materials have very little compressibility compared to their shear flexibility, large diameter to height ration specimen approaches its practical stress state. The compressive stressestrain curves of two kinds of coatings are plotted in Fig. 2. The compressive stress of rubber coating increases sharply when the compressive strain exceeds about 6%. It shows that the
Fig. 1. The test specimen and different coating configurations.
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Table 1 Some properties of different coatings. Test specimen
Bare plate
Rubber coated plate
Foam coated plate
Coating material Total thickness (mm) Area density (kg/m2)
/ 3 27.4
Rubber 3þ5 33.5
PU Foam þ Rubber 3 þ 16 þ 2 33.1
Fig. 2. The compressive strain-stress curve of two kinds of coating.
pure rubber coating is almost uncompressible. On the contrary, the PU foam has much better compressibility for its porous structure. It almost begins to enter the densification phases when the compressive strain is beyond 70%. But, as the PE foam used is a kind of closed-cell foam, no distinct stress plateau can be found. The tensile test of the material in the steel plate is also made in an INSTRON material test machine. Three pieces of specimen are cut from the backup test steel plates and then polished. The geometry and dimensions of the specimens is according to the metal material test standard GB/T 228-2002 of China. The tensile stressestrain curves of three specimens are plotted in Fig. 3. The consistence of different specimen is very good. The yielding stress of the material is about 235 Mpa and the maximum bearing stress can reach 330e335 Mpa. The final failure strain reaching 41.5%e45.2% shows good ductility of the material. 2.2. Underwater explosion tests and apparatus used The experiments are carried out in a steel water tank. The tank is 3 m in length, 2 m in width and 2.5 m in depth. It is welded by steel plates 8 mm in thickness. The top side of the tank is open (Fig. 4). The inner wall is covered by a layer of PU foam to decrease the shock wave reflected by the rigid wall. The maximum explosive allowed is 15 g TNT. A suite of apparatus is designed to properly fix the different specimens. As shown in Fig. 4, the main body of the fixture includes a steel drum, a vertical fixing arm and a transverse beam. The one-side opened steel drum is made by 20 mm thick steel panel to keep enough strength and stiffness. Its inner radius is 200 mm. The outer diameter is compatible with the specimen. At the open side of drum, a circle of twelve holes is drilled. Accordingly, twelve M18 bolts are used to fix the test specimen by a 22 mm thick annular plate to keep the plate boundary fixed. A vertical rectangular tube with the section 18 cm 18 cm is welded at the top of drum as a support arm. The signal wires also pass through
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Fig. 3. The tensile stressestrain curves of three specimen cut from test plates.
Fig. 4. The water tank and fixture used in the live fire test: ① steel drum ② observing window ③ horizontal supporting beam ④ detonator ⑤ watertight groove ⑥ accelerometer A3.
the hollow tube. A strong transverse steel beam is used as a supporting bridge spanning over the water tank. During tests, the strain gages are glued onto the inner face of test plate in advance. Then shielded cables are connected to the gages and accelerometers. A layer of asbestos paper is inserted between the plate and the front face of the supporting drum before the bolts are inserted and fastened. Once all bolts are fastened, the whole test apparatus is lifted into the water tank using a hoist. After the position has been adjusted, the detonator is placed into the water to the designed position and one test arrangements have completed. As one test finished, the whole apparatus is lifted up from the water tank to the open ground, and carefully checked to insure water-tightness. If plastic deformation or coating damage occurs, a new plate with the same coating configuration is replaced. After then, the next shot can be made. 2.3. Instrumentation The measured physical parameters include pressure, strain and acceleration histories. The pressure history indicates the explosion loading intensity. The strain and acceleration history gives the information about structure response.
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Two PCB 138A05 pressure transducers, linear within 2% up to 30 MPa, are applied to monitor the free-field and wall pressure change. The free-field transducer P1 is suspended at the same depth with that of denotation using nylon wire. It is kept 0.6 m distant from the explosive charge in the horizontal direction in all events. The other transducer is fixed at the face of the coating and planned to monitor the pressure fluctuation near the fluid structure interface. But, the large deformation of the coating makes it violently move back and forth. The pressure monitored is not consistent and abandoned in the later tests. Four unidirectional strain gages and two shock accelerometers are used for each plate to monitor the transient response. The 120-U resistance strain gages are glued onto the back surface of test plate after the measured points being polished and cleaned. The positions of the four gages from E1 to E4 are shown in Fig. 5. Considering the axisymmetric character of both loading and boundary, all gages are aligned with the radial direction. One accelerometer A1 is located at the center of the plate and the other A2 is located at the middle between the center and plate edge. In addition, an accelerometer A3 is mounted at the inner back plate of the supporting drum as illustrated in Fig. 4. It is used to measure the transient response of the drum. The shock response there can be considered as a shock environment measuring point considering much higher stiffness and greater mass of apparatus when compared with that of plate. All accelerometers are BK 4369 type piezoelectric transducer, which have a working range of 10,000 g, linear within 5% to 5000 g, and have a frequency range between 0.2 Hz and 6600 Hz. They were attached to the plate by a 5 mm steel stud in order to keep enough strength. Altogether nine channels are used for each test. Data are recorded with a maximum sampling frequency of 1 MHz/Ch and 18 bit resolution. The 100 ms recording span is sufficient to contain both the shock wave phase and the first bubble collapse for the 1.5 g charge. Since the strain signal decays much slower, 120 ms is set as the recording time span. The sampling rate is set to 10 KHz/Ch for both strain and acceleration records. The low-pass filter is set to 100 KHz for the pressure record and 5 KHz for acceleration and strain records respectively. An APX-RS high speed camera is used to observe the fluid-structure interaction process between the structure deformation and underwater explosion bubble. The camera is fixed before a transparent window that is located at the same height with the test plate center as shown in Fig. 4. The sunlight and two high power halogen lamps are used at the same time to enhance the luminance. The shooting frequency is set to 4500 frame per second (the time interval is 0.22222 ms) in order to capture the possible local cavitation accompanied by the shock wave. The focus of camera is aimed at the side face of the target plate center. When stand-off equals 0.6 m, the bubble motion is invisible because it is out of the view of the camera. When stand-off equals 0.4 m, only part of the bubble motion can be observed. The best images are captured in the nearest events when stand-off equals 0.2 m. Both the local cavitation and the whole bubble motion process can be observed.
Fig. 5. The position of the strain gages and accelerometers.
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For the convenience of data analysis, the camera and all other data recording devices are synchronously triggered by a rising pulse signal. The electric pulse is also used to ignite the detonator.
2.4. Charges and events The explosive charge consists of 1.5 g high explosive (70% PETN powder þ20% aluminum powder þ10% deterrent). The 1.5 g explosive is initiated with an exploding bridge wire detonator. A total of nine effective events are made at three stand-offs, i.e. 0.6 m, 0.4 m and 0.2 m. Charges in all tests are kept unchanged. The stand-off is defined as the distance between the detonator and the center of the steel plate. A then nylon string, with a 3 kg weight at the bottom end, is used to position the explosive charge. The peak pressure and first bubble period of all tests measured by the free pressure transducer are listed in Table 2. As the maximum stand-off is within 3.4 times of the theoretical maximum bubble radius (0.176 m), substantial interaction between the bubble and the target is expected. 3. Results and discussion Results are presented in four sections. First, the free-field pressure records are given to determine the shock loading intensity. Second, stain records are compared as the strain peak being a criterion on the protective performance of coating. Third, the acceleration history measured at the inner back of the supporting drum is presented. The shock response spectrum analysis is made to evaluate the dynamic performance of coating in frequency domain. Finally, some typical high speed camera images for the nearest stand-off events are given. The cavitation and bubble motion process are compared when the coating configuration changes.
3.1. Pressure-time profiles Generally speaking, two distinct phases can be observed in the free underwater explosion, i.e., shock wave and bubble pulse phase. The shock wave consists of an almost instantaneous rise in pressure to a peak pressure, followed by an exponential decay in pressure down to the hydrostatic pressure. The peak pressure and the decay constant depend upon the size of the explosive charge and the stand-off between the charge and measuring point. The following empirical equations is used to estimate the pressure history [23]
PðtÞ ¼ P0 eðtt0 Þ=q
(1)
Table 2 Nine effective test events and some test results of free-field pressure: measured at P1, 0.6 m distant from the explosion center. The theoretical value: P0 ¼ 7.98 MPa, q ¼ 0.123 ms, T ¼ 31.2 ms Event number
Charge size (g)
Stand-off (m)
Test specimen
Peak of the first shock (Mpa)
The first bubble motion period (ms)
1# 2# 3# 4#
1.5 1.5 1.5 1.5
0.6 0.4 0.2 0.6
8.1 8.2 8.0 8.2
33.5 34.1 34.1 33.3
5#
1.5
0.4
7.9
33.7
6#
1.5
0.2
8.2
34.7
7# 8# 9#
1.5 1.5 1.5
0.6 0.4 0.2
Pure plate Pure plate Pure plate Rubber coated plate Rubber coated plate Rubber coated plate Foam coated plate Foam coated plate Foam coated plate
8.1 8.3 8.2
33.6 33.3 32.4
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. A1 P0 ¼ K1 W 1=3 R
(2)
. A2 q ¼ K2 W 1=3 W 1=3 R
(3)
where P0 is the peak pressure in MPa and q the decay constant in milliseconds. W is the weight of charge in kilograms and R is the stand-off in meters. A1,A2,K1 and K2 are the coefficients related to different explosive. The gas bubble generated by the explosion is almost spherical during its initial stage of expansion and contraction. The maximum bubble radius and the time taken to reach the first bubble radius minimum can be calculated. Both vary with the size of the explosive charge and the depth at which the explosion occurs.
T ¼ K5 *W 1=3 ðD þ 9:8Þ5=6
(4)
. Rmax ¼ K6 *W 1=3 ðD þ 9:8Þ1=3
(5)
where T is the bubble period in seconds and Rmax is the bubble radius in meters. D is the explosion depth in meters. K5 and K6 are the coefficients related to different explosive. In our tests, 1.5 g PENT is used and the explosion depth is 1.4 m. For PENT, A1 ¼1.194, K1 ¼ 56.21 MPa, K2 ¼ 0.086 s, K5 ¼ 2.098 s, K6 ¼ 3.439 m [24], it can be computed as P0 ¼ 7.98 MPa, q¼0.123 ms, T ¼ 31.2 ms and Rmax ¼ 0.176 m. The three stand-offs 0.6 m, 0.4 m and 0.2 m are equivalent to 3.41Rmax, 2.27Rmax, and 1.14Rmax. Therefore, all test events can be regarded as near-field explosion environment. The typical pressure-time history recorded at P1 in test event 1#e3# are shown in Fig. 6(aec). For clarity the Y-axis is limited to 1 MPa. Several distinct phases can be distinguished in Fig. 6(a) as in common far-field free underwater explosions. The shock wave arrives at about 0.4 ms and the first reflective wave at about 3 ms. The first bubble pulse arrives at 34.2 ms, with the corresponding exciting frequency as 29.3 Hz. The period is a little longer than the theoretical value 31.2 ms. The second bubble pulse arrives at about 61 ms. There is no distinct difference between Fig. 6(a) and (b). It is shown that when stand-off changes from 3.41Rmax to 2.27Rmax, the influence of the structure deformation on the bubble is still not distinct. But when stand-off changes to 1.14Rmax, the peak of the first bubble pulse is clearly reduced as shown in Fig. 6(c). The second bubble pulse almost cannot be observed. The fact shows that when stand-off becomes nearer, the influence of the structure on the bubble loads is become more prominent. Table 1 lists the peak pressure induced by the shock wave and the period of the first bubble pulse in all nine test events. Totally speaking, the explosion process is stable and consistent. When the stand-off farer than 2.3Rmax, the plate deformation cannot effectively changes the bubble dynamics whether the plate is coated or not. But, when the stand-off decreases to 1.14Rmax, the first bubble motion can be altered. The phenomenon is also verified by the high speed camera images as discussed in Section 3.4. 3.2. Stain records and target deformation The strain peak measured on the plate can be used to evaluate the protective performance of different coatings. Though there is some difference between different records measured in four gages, the trend is similar as they all measure the strain in radial direction. Therefore, only strain history measured at E1 is detailed discussed as a typical record. The strain peaks of other records induced by both the shock wave and bubble pulse are extracted and compared in histogram. Typical strain history within 150 ms measured at E1 in all nine tests events are listed in Fig. 7. In Fig. 7(aec), the strain records measured at bare plates are compared when stand-off changes from 0.6 m to 0.2 m. The strain amplitude is closely related to the stand-off. As the stand-off decreases, the
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Fig. 6. Free-field pressure history measured at P1 that is 0.6 m distant from the detonator: (a) test event 1#, stand-off equals 0.6 m, (b) test event 2#, stand-off equals 0.4 m, (a) test event 3#, stand-off equals 0.2 m.
strain amplitude increases from 1011 mε to 3333 mε. This is due to the shock intensity is greatly enhanced when explosion becomes much nearer. For all records, the strain peaks induced by the first shock wave, the first and second bubble pulse can be easily distinguished and almost has the same order. Especially, the strain peak induced by the first bubble pulse at about 34 ms is always the maximum one in all three peaks. This phenomenon is different from that in far-field underwater
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Fig. 7. The typical strain history measured at E1 (low-pass filtered with cut-off frequency 5000 Hz): (aei)— event 1#e9#.
explosions, where the first shock wave is often the dominant factor if the natural frequency of the structure is not coincident with the bubble pulse frequency. In the near-field underwater explosions, the load of bubble pulse has much more energy than that of shock wave. For E1 in event 3, this trend is the most distinct, which the strain peak induced by shock wave is less than 2000 mε, while that induced by the first bubble pulse reaches 3333 mε, exceeding the nominal yielding strain of the material and obvious plastic strain can be observed. The fact verifies that the shock energy of the first bubble pulse is often the most important factor cause the structure failure, especially for thin-walled structures that has relatively wider span and lower natural frequency. The same trend can be observed in Fig. 7(def) for test event 4#e6#. In these three events, the target plates are rubber coated. Compared with that of bare plates, the peak values are correspondingly smaller than that in event 1#e3#. It should be attributed to the attached mass effect and some limited compressibility of rubber coating. The protective effect exists in all three events, no matter what intensity of the explosion load is. Fig. 7(geh) show the strain measured in event 7#e9# (foam coated plate). Some different trends can be observed. Firstly, obvious mitigation effect can be observed when stand-off equals 0.6 m. The peak strain is reduced from 1011 mε to 202 mε. It is shown that the foam coating has tremendous protective effect under this loading. But when the stand-off becomes 0.4 m, the mitigation effect is greatly discounted. The peak strain only reduces from 1520 mε to 1300 mε. The mitigation effect is only a little better than that of rubber coating. The fact is a little counter-intuitive before the high speed camera image carefully viewed. It is found that in test event 7#, the compressible level of coating is smaller when compared with that in test event 8#. Therefore, the fact can be explained as that the foam
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coating deforms in event 7#, but does not enter the densification phase. Therefore, the loading transmitted to the steel plate face is greatly mitigated by the compressible deformation of foam coating. But with the increasing of load intensity in test event 8#, the foam deforms greatly and enters the densification phase. Once densification occurs, the protective performance is greatly discounted. The similar trend can also be observed in test event 9#. The similar trend can be observed in the records measured at E2 to E4 though the magnitude may be different when the measuring location changes. As a more detailed comparison, the strain peaks measured at E1 to E4 in events that have the same stand-off are compared respectively. As the strain peaks in the shock wave and first bubble pulse phases can be distinctly divided, they are respectively compared. Only maximum tensile strain is considered, which is often used as a failure criterion for ductile metals. Fig. 8 compares the strain peaks measured at E1eE4 in event 1#, 4# and 7# when stand-off equal 0.6 m. The strain peaks in the bubble pulse phase is higher than that in the initial shock wave phase. The mitigation effect offered by the foam coating is very prominent in both phases. It is demonstrated under such loading, the compressibility of the foam coating takes effect. The loading is not intense enough to make the foam core enters densification phase. Fig. 9 compares the strain peaks measured at E1eE4 in event 2#, 5# and 8# when stand-off equal 0.4 m. Under this loading, the mitigation effect of both coating still exists. The foam coating still has the best performance. But its superiority is greatly discounted. This should be attributed to the densification of foam core when the shock loading is more intense. Compared with that in the shock wave phase, the protection performance in the bubble pulse phase is deteriorated. It is because that the bubble loading often has wider span and lower peak. More low-frequency ingredient contained in the bubble loading is than that in the shock wave loading. Therefore, more deformation space is needed in order to mitigate the bubble loading. Fig. 10 compares the strain peaks measured at E1eE4 in event 3#, 6# and 9# when stand-off equal 0.2 m. Though the loading is more intense in these three events as the stand-off decreases, the protection effects still exists in the shock wave phase. The foam coating still has the best effect for its better compressibility. While in bubble phase, the protection performance of foam coating seems better than that in the event when stand-off equals 0.6 m. The fact should be attributed to the influence of the coating deformation on the jet direction of bubble when stand-off reaches 0.2 m. More detailed discussion is made in Section 3.4. In all the test events, distinct plastic deformation occurs in the plate only in events 3#, 6# and 9#, when stand-off equals 0.2 m. In order to check the final deformation of the plates with different coating configuration, the specimens are cut into two halves. Fig. 11 gives lateral view of the cut specimens. Very distinctive deformation can be observed in the bare plate, the center deformation reaches 2.4 cm.
Fig. 8. Strain peaks comparison in event 1#, 4# and 7#, stand-off ¼ 0.6 m.
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Fig. 9. Strain peaks comparison in event 2#, 5# and 8#, stand-off ¼ 0.4 m.
Fig. 10. Strain peaks comparison in event 3#, 6# and 9#, stand-off ¼ 0.2 m.
The deformation of plates with coating is much smaller. The foam coated plate has the smallest deformation. The result is consistent with the strain records. The foam core deformation is checked by peeling the outer face of the foam coating after test event 9#. Distinct damage occurs at the center part of the plate as shown in Fig. 12. Considering the spherical wave effect, the center part of the plate should bear the most intense blast loading. Therefore, prominent gap occurs. The fact verifies the deduction that when stand-off equal 0.2 m, the blast loading is so intense that the foam enters densification phase. Better protection effect of foam coating can be anticipated if the strength of core is optimized aiming at the specific loading intensity. If the load becomes intense, the strength of core should be enhanced accordingly. 3.3. Acceleration records and shock environment Three accelerometers are used to monitor the response of plate and fixture. But, most records measure at A1 and A2 suffers to serious ‘zero-drifting’ and cannot be used. It is due to the direct loading on the plate are so intense and induces the resonance of the accelerometer. Fortunately, the strain record can be used as a comparative criterion. Therefore, these data is not compared. Only the acceleration record measured at A3 on the inner back of the supporting basin is used. The response
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Fig. 11. The final deformation of the plate in event 3#, 6#, 9# (stand-off equals 0.2 m), from the top to the bottom successively is: bare plate, rubber coated plate and foam coated plate.
Fig. 12. The damage mode of the foam coating in event 9#.
measured at this location contains much information such as the energy transmitted from the plate to the basin after being attenuated by the polymer coating. It can be regarded as a shock environment measuring point. As the information extracted from the signal in time domain is very limited, the Shock Response Spectrum (SRS) analysis is made to obtain more information. SRS is a graphical representation of an arbitrary transient acceleration input, such asshock in terms of how a Single Degree Of Freedom (SDOF) system (like a mass on a spring) responds to that input. It is a powerful tool in understanding the frequency component of the dynamic response of structure when subjected to shock input. In order to understand the spectrum distribution, the first natural frequency of test plate is estimated using the approximation calculation formula for the boundary fixed circular plate immersed in fluid [25]
0:4745 hc f ¼ pffiffiffiffiffiffiffiffiffiffiffiffi 21 1þb r
b ¼ 0:6689
r r r1 h
(6)
(7)
where f is the first natural frequency, h and r is the thickness and radius of the plate. r1 and c1 is the density and sound speed of the solid material. r is the density of the fluid. It can be computed that f equals 73.8 Hz for bare steel plate. It equals 59.7 and 60.2 Hz for rubber and foam coated plate respectively. The practical frequency should be less than the theoretical value for the inevitable elasticity of the fixed boundary. The SRS computed from the acceleration history of bare plate in event 1#e3# is compared firstly to understand the energy distribution in frequency domain. Fig. 13 shows the three SRS curves in a same logarithm coordinate. The spectrum acceleration, velocity and displacement can be read at the same
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Fig. 13. The SRS of A3 in event 1#, 2# and 3# (bare plate, stand-off equals 0.6, 0.4 and 0.2 m): red dotted line—event 1#, red dashed line—event 2#, red solid line—event 3#. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
time. The analyzing frequency bandwidth is between 1 Hz and 2 k Hz. With the decrease of stand-off, the maximum spectrum velocity monotonously increases from 0.28 m/s to 0.61 m/s. It indicates that the whole shock energy transmitted to the structure increases. Some typical frequency bands can be distinguished: (1) 1e40 Hz In this band, the SRS is mainly controlled by the bubble motion because the period of the first mode of plate is shorter than the first bubble motion period. The distinct peak can be found around 33e34 Hz, which is corresponding to the first bubble expansion and collapse motion period (about 33.5 ms). (2) 40e400 Hz In this band, the SRS is mainly controlled by the bubble motion excitation and the dynamic response of the plate. Several distinct peaks distributed from about 50 Hz to 300 Hz are corresponding to several lowest natural modes of the plate and fixture. (3) 400e2000 Hz In this band, the excitation of bubble motion is relatively weak and mainly controlled by the shock wave. A distinct peak lies around 700e800 Hz. This frequency should be corresponding to at least one of local natural frequency of fixture near the location where the accelerometer A3 mounted. When this mode is excited by the shock wave, a distinct peak appears in the SRS. The energy distribution in frequency domain is closely related to the stand-off distance. When stand-off equals 0.6 m (event 1#), the spectrum velocity induced by the shock wave reaches 0.3 m/s (800 Hz). But the spectrum velocity induced by bubble motion is below 0.2 m/s. This shows the energy transmitted to the plate by the shock wave is greater than that by the bubble motion. When stand-off becomes 0.4 m in event 2#, the maximum spectrum velocities induced by the bubble motion and shock
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wave are almost equal (0.31 m/s VS 0.30 m/s). When stand-off becomes 0.2 m in event 1#, the corresponding spectrum velocity becomes 0.6 m/s and 0.2 m/s respectively. The potential flow energy induced by the bubble motion becomes more and more prominent as the explosive charge becomes nearer and nearer, when compared with the shock wave energy transmitted by the compressive wave of water. For comparison, the SRS curves in the events that have the same stand-off but different coating configuration is plotted together. The SRS curves computed from the records in event 1#, 4# and 7# when stand-off equals 0.6 m are shown in Fig. 14. The blue dotted curves for event 7# (foam coated) is prominently lower than that of other two events in almost all frequency band except near 33 Hz, i.e. the bubble motion frequency. The difference between the red solid curve (bare plate) and green dashed curve (foam coated) is much smaller though the attenuation effects still can be observed in high frequency for rubber coating. Totally speaking, the foam coating has much better attenuation effect under such load density than that of rubber coating. The fact is consistent with the conclusion drawn from the strain analysis in Section. 3.2. The shock response spectrum curves of A1 in event 2#, 5# and 8# are shown in Fig. 15. When standoff becomes 0.4 m, some different trend can be observed. The attenuation effect of foam coating can be observed from 150 Hz to 2000 Hz, but some amplification effect exists between 20 and 100 Hz. It should be attributed to the densification behavior when the bubble loads exceeds its working strength. The suddenly increases caused by the densification excites the lower modes of plate. The attenuation effect of the rubber coating only exists in the high-frequency band between 700 and 1000 Hz. In other frequency band, the difference between rubber coating and bare plate is small. The fact tells us the compressibility of coating is the main control factor affects its attenuation performance in high-frequency band. The SRS curves computed from records in event 3#, 6# and 9# are shown in Fig. 16. When stand-off becomes 0.2 m, the most energy comes from the fluid flow induce by the bubble motion. Though the loading is more intense, the slight attenuation effect still exists for the foam coating between 40 and
Fig. 14. The SRS of A3 in event 1#, 4# and 7# (stand-off ¼ 0.6 m): red dotted line—event 1#, bare plate; blue dotted line—event 4#, rubber coated plate; green dotted line—event 7#, foam coated plate. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 15. The shock response spectrum of A3 in event 2#, 5# and 8# (stand-off ¼ 0.4 m): red dashed line—event 2#,bare plate; blue dashed line—event 5#,rubber coated plate; green dashed line—event 8#, foam coated plate. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
400 Hz. This is partly attributed the fact that the soft foam coating alter the bubble behavior and the jet direction as shown in the next section. The difference of maximum spectrum displacement between three models is more distinct than that in other events. The value of spectrum displacement plate with foam coating is 5 mm while the value of bare steel plate reaches 2 cm. This is also due to the fact that foam coating alters the flow induced by bubble motion as a different boundary. The maximum spectrum displacement of rubber coating lies between that of bare plate and foam coated plate. But in other frequency band, its attenuation effect is very limited. Totally speaking, the compressibility, not the mass effect, should be the supreme factor that controls the protective performance of coating, especially for the shock wave loading. Therefore, for far-field underwater explosion, the soft foam coating should performs better than in near-field scenario. It is due to the energy mainly exists in higher frequency band for shock wave loads. But when stand-off decreases, the bubble effect becomes dominant. The attenuation effect is discounted for energy concentrates in low-frequency band and more deformation space is often required. 3.4. Images shot by high speed camera As limited by the length of the article, only some typical images are selected for the test event 3#, 6 # and 9#. In these tree events, the stand-off is kept 0.2 m unchanged, but the coating configuration is changed. Two distinct stages can be observed: i. Shock wave loading and bubble expansion stage As shown in Fig. 17, the explosion process initiates in frame 1#. Then the bubble expands rapidly, accompanied by the shock wave transmission process. The time interval for the shock wave arrives at the face of the plate can be estimated as 0.2/1550 ¼ 0.129 ms. Therefore, in frame 2 (0.222 ms), the shock wave loading has been arrived at the surface of the target plate. As the theoretically decay constant for the first shock wave is q ¼ 0.123 ms, the shock wave loading should decays completely in
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Fig. 16. The shock response spectrum of A3 in event 3#, 6# and 9# (stand-off ¼ 0.2 m): red solid line—event 3#,bare plate; blue solid line—event 6#,rubber coated plate; green solid line—event 9#, foam coated plate. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
frame 2. The difference occurs at this moment can be observed in frame 2 of three test events. Slight local cavitation appears in test event 9# (foam coating plate). On the contrary, there is not any cavitation in both test event 3# and 6#. Only in the next frame (frame 3, 0.444 ms), local cavitation can be observed in all test events. This fact indicates that the motion of the target face with soft foam coating is much faster than that for other two plates. Four successive frames from 2# to 5# show that the cavitation expansion and closure process at the surface of the foam coating is the most obvious and durable. It sustains from frame 2# to 10# and lasts about 2 ms until the face motion caused by compression pressure is balanced by the force of structure deformation. As a comparison, this process in test event 3# and 6# sustains from frame 3# to 8#. The cavitation volume at the face of soft foam coating is also much greater than that for other two plates. The fact verifies the conclusion drawn in early researches [12,18]. The softer core with better compressibility can make the local cavitation take place much earlier and longer. This mechanism can cause the cut-off effect of the shock wave loading. The potential merit is that with the time span of the shock wave decreases and the total impulse transmitted into the hull could be reduced [18]. ii. Interaction stage between bubble motion and target deformation (Fig. 18) As stated in Section 3.1, the interaction between the bubble motion and target deformation is not so obvious when stand-off equals 0.6 m and 0.4 m. The maximum bubble radius can be estimated as Rmax ¼ 0.176 m when the influence of boundary neglected. Therefore, only when stand-off equal 0.2 m (1.14Rmax), the substantive interaction between the target deformation and bubble motion is anticipated. Some typical frames are presented in order to compare this interaction process. In frame 22#, at about 4.667 ms, the bubbles still expand but their left parts are almost stopped due to the existence of the target plate as a structure boundary. It can be estimated that the velocity of the potential flow between the left boundary of bubble and target plate outer surface almost become to zero at this moment. Then, the left boundary of the bubble begins to contract while the remaining part still expands because the neighboring fluid is not impeded as in the left part. The prominent difference
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Fig. 17. The high speed camera images in the shock phase of event 3#, 6# and 9# when stand-off equal 0.2 m, 1.14 Rmax.
appears when the bubbles in different boundary begin to contract. Once the bubble begins to contract, the fluid near the left boundary of the bubble is forced to move to the right. Therefor the cavitation region forms near the fluid structure interface as the water cannot sustain the negative pressure. There is great difference between the cavitation regions for different coatings. Like in the first shock wave stage, the cavitation region for the soft foam coating event is much wider and thicker than that for the rubber or no coating. As can be seen in frame 77# (16.88 ms), the dome shape cavitation region for the soft foam coating almost covers the whole plate. On the contrary, the cavitation in the other two events is similar, about 2/3 in radius around the center of the whole plate is cover with cavitation vapor. The bubble shape is flatter in test event 6# than that in event 3# and 9#. In frame 119# (26.22 ms), the difference still exists when the cavitation region partly close. Almost half of the bubble in event 9# is sunken to the right. The influence of the cavitation region on the bubble shape is so large that the left part of the bubble moves to the right until the bubble collapse. The cavitation region and the bubble separates and the reloading effect can be observed mainly caused by the cavitation closure. But in the
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Fig. 18. The high speed camera images in the bubble phase of event 3#, 6# and 9# when stand-off equal 0.2 m, 1.14 Rmax.
other two events, the cavitation is not large enough to cause the bubble moves to the right. Finally, a water jet is formed and hit the target plates as shown in frame 152#. The plastic deformation takes place in both these events. Therefore, the coating with high compressibility can also change the bubble shape even direction of the water jet when proper condition is satisfied. But the condition needs to be further investigated as only limited samples are presented in this paper. 4. Conclusions The transient response of polymer coated circular plates to the near-field underwater explosions is experimentally studied. Nine steel circular plates with three configurations (i.e. rubber coated plate, foam coated plate and bare plate) are tested using 1.5 g PETN detonator. Test results show that the compressible foam coating can distinctly influence the shock wave loading and the bubble behavior. The shock wave can be mitigated by local cavitation. But for the near-field bubble loading, more
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deformation space is often needed. Once the coating enters densification phase, the protective performance of coating is greatly discounted. Therefore, the mechanical behavior of the coating and the water loading-structure interaction effects should be considered if the optimal protective performance is anticipated. Acknowledgments The authors would like to thank the NSFC for financially supporting this research under the contract No. 11272215. References [1] Wadley HN, Dharmasena KP, Queheillalt DT, Chen Y, Dudt P, Knight D, et al. Dynamic compression of square honeycomb structures during underwater impulsive loading. J Mech Mater Struct 2007;2:2025e48. [2] Dharmasena KP, Wadley HNG, Williams K, Xue Z, Hutchinson JW. Response of metallic pyramidal lattice core sandwich panels to high intensity impulsive loading in air. Int J Impact Eng 2011;38:15. [3] Jackson M, Shukla A. Performance of sandwich composites subjected to sequential impact and air blast loading. Compos Part B Eng 2011;42:155e66. [4] Rathbun HJ, Radford DD, Xue Z, He MY, Yang J, Deshpande V, et al. Performance of metallic honeycomb-core sandwich beams under shock loading. Int J Solids Struct 2006;43:1746e63. [5] Xue Z, Hutchinson JW. Crush dynamics of square honeycomb sandwich cores. Int J Numer Methods Eng 2006;65:2221e45. [6] Xue Z, Hutchinson JW. A comparative study of impulse-resistant metal sandwich plates. Int J Impact Eng 2004;30: 1283e305. [7] Fleck N, Deshpande V. The resistance of clamped sandwich beams to shock loading. Trans Am Soc Mech Eng J Appl Mech 2004;71:386e401. [8] Taylor GI. The pressure and impulse of submarine explosion waves on plates. Cambridge, UK: Cambridge University Press; 1963. [9] Rabczuk T, Samaniego E, Belytschko T. Simplified model for predicting impulsive loads on submerged structures to account for fluid-structure interaction. Int J Impact Eng 2007;34:163e77. [11] Liang Y, Spuskanyuk AV, Flores SE, Hayhurst DR, Hutchinson JW, McMeeking RM, et al. The response of metallic sandwich panels to water blast. J Appl Mech Trans ASME 2007;74:81e99. [12] Deshpande V, Fleck N. One-dimensional response of sandwich plates to underwater shock loading. J Mech Phys Solids 2005;53:2347e83. [13] Wadley H, Dharmasen K, Chen Y, Dudt P, Knight D, Charette R, et al. Compressive response of multilayered pyramidal lattices during underwater shock loading. Int J Impact Eng 2008;35:13. [14] Dharmasen KP, Queheillalt DT, Wadley HNG, Dudt P, Chen Y, Knight D, et al. Dynamic compression of metallic sandwich structures during planar impulsive loading in water. Eur J Mech A Solids 2010;29:12. [15] Schiffer A, Tagarielli VL. One-dimensional response of sandwich plates to underwater blast: fluid-structure interaction experiments and simulations. Int J Impact Eng 2014;71:16. [16] Langdon G, von Klemperer C, Rowland B, Nurick G. The response of sandwich structures with composite face sheets and polymer foam cores to air-blast loading: preliminary experiments. Eng Struct 2012;36:104e12. [17] Gardner N, Wang E, Kumar P, Shukla A. Blast mitigation in a sandwich composite using graded core and polyurea interlayer. Exp Mech 2012;52:119e33. [18] Chen Y, Tong Z, Hua H, Wang Y, Gou H. Experimental investigation on the dynamic response of scaled ship model with rubber sandwich coatings subjected to underwater explosion. Int J Impact Eng 2009;36:318e28. [19] Chen Y, Zhang Z, Wang Y, Hua H, Gou H. Attenuating performance of a polymer layer coated onto floating structures subjected to water blasts. Eur J Mech A Solids 2009;28:591e8. [20] Lee JJ, Gregson J, Rude G, Paulgaard GT. Underwater shock and bubble interactions from twin explosive charges. In: €ttingen, Germany; July 15e20, 2007. Proceedings of the 26th international symposium on shock waves. Go [21] Klaseboer E, Hung KC, Wang C, Wang CW, Khoo BC, Boyce P, et al. Experimental and numerical investigation of the dynamics of an underwater explosion bubble near a resilient/rigid structure. J Fluid Mech 2005;537:26. [22] Slater J, Rude G, Paulgaard G. Experimental study of airbacked and water backed targets during near contact explosions. 2005. DRDC Suffield Technical Report # TR 2005152. [23] Cole RH. Underwater explosions. New York: Dover Publications; 1965. [24] Reid WD. The response of surface ships to underwater explosions. 1996. DTIC document. [25] Amabili M, Kwak M. Free vibrations of circular plates coupled with liquids: revising the lamb problem. J Fluids Struct 1996; 10:743e61.