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A combined experimental and numerical investigation on projectiles penetrating into water-filled container
Thin-Walled Structures 143 (2019) 106230
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Full length article
A combined experimental and numerical investigation on projectiles penetrating into water-filled container
T
Peng Rena,*, Lu Shia, Renchuan Yea, Dongliang Chaia, Wei Zhaoa, Jie Wua, Wei Zhangb, Zhongcheng Muc a
School of Naval Architecture & Ocean Engineering, Jiangsu University of Science and Technology, Jiangsu, 212003, PR China High Velocity Impact Dynamics Lab, Harbin Institute of Technology, Harbin, 150080, PR China c School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, 200240, PR China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Water-filled container Fluid-structure interaction Hydrodynamic ram Failure mode Finite element analysis
The experiments and numerical simulations of projectile penetrating into water-filled container with aluminum target plates were conducted. The motion of projectile and cavity evolution of hydrodynamic ram in water were assessed. The results show the propagation characteristics of initial shock wave of hydrodynamic ram in the container. The study presents that the plugging with outward deformation was the main failure mode of the target plates when the velocity of projectile was below 270 m/s. With the velocity of projectile increasing, the ultimate deformation of plates increased linearly and the petaling failure appeared on the rear plates. Four kinds of typical failure modes for plates of water-filled container were concluded through the combining results of experiment and simulation. In addition, the effect of plate thickness on the plastic deformation were discussed, and the quantitative relation among the deformation of target plates, velocity of projectile and plate thickness were established.
1. Introduction The serious damages of fluid-filled tank was generated when the structures were impacted by high-velocity projectiles and fragments [1]. Compared to the empty structure, the hydrodynamic ram (HRAM) in the fluid-filled tank played an important role in the damage of the container [2]. Hence, it is inevitable to investigate the failure mechanism of the tank under the coupling effect of impact and HRMA. The process of HRAM can be divided into four stages, including initial shock wave, drag, cavity and exit [3]. Firstly, the propagation of initial shock wave from the impacting of projectile caused the slight deformation of the container. Then, the projectile penetrated into water, the velocity decay of the projectile could be observed due to the drag force of fluid. The partial kinetic energy of the projectile transferred to fluid in this stage. Meanwhile, a cavity was formed behind the projectile. Finally, the projectile penetrated the rear wall and exited the fluid-filled container. In order to illustrate the mechanism of HRAM, the scholars have investigated the phenomenon of HRAM by experiments, numerical simulations and theoretical analysis over half of the century. The earlier experimental tests were performed by McMillen [4] on the propagation characteristic of initial shock. The negative correlation between the *
measured pressure and the angle along the arc of the shock wave away from the shot line was found. Based on the research, Swanson [5] conducted a series of experiments to measure the pressure of the initial shock wave by using the fixed transducers in the container, and the shock wave was also visualized through the shadowgraph technique. Using the similar experimental method, Huang [6] obtained the attenuation characteristic of shock wave from the experimental results, and concluded the effect of projectile shape on the peak pressure. According to Minhyung [7], the initial shock wave could be divided into ballistic wave and collapse wave. The ballistic wave was produced by the projectile penetrating into fluid and collapse waves generated from the cavity collapse. The analysis showed that the pressure of ballistic waves increased with the initial velocity of projectile increasing, while the collapse waves was irrelevant to the initial velocity of projectile. Then, Lecysyn [8–10] investigated the cavity stage of HRAM by utilizing the high-speed photography. The relationship among the velocity decay of projectile, the cavitation parameters (cavity radius, cavity wall velocity, cavity collapse time) and the initial velocity of projectile were analyzed. Meanwhile, Shi [11,12] found that the deflection of projectile trajectory in water depended on the distance of penetration, and the cavity behind the projectile was strongly chaotic. Deletombe [13] also observed the evolution of cavity and measured the cavity geometry
Corresponding author. E-mail address: [email protected] (P. Ren).
https://doi.org/10.1016/j.tws.2019.106230 Received 14 December 2018; Received in revised form 23 May 2019; Accepted 29 May 2019 Available online 08 June 2019 0263-8231/ © 2019 Elsevier Ltd. All rights reserved.
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Fig. 1. Sketch of the experimental device.
contributed great to the damage of fluid-filled container, and HRAM was affected by the shape and velocity of projectiles. Meanwhile, it can be found that the damage of fluid-filled tank was caused by the combination of penetration and HRAM loads, which is obviously different from the damage of metallic structures resulted from impulsive or impact loading. Although there are many studies on failure modes of the metallic structures, the research on the critical conditions for failure modes of water-filled container subjected to projectiles was still shortage. Additionally, the ballistic limit velocity for most empty aluminum tank was only approximate 200 m/s [23], however the velocity of projectile used in the mentioned researches almost above 600 m/s. Hence, the studies on the deformation and failure of water-filled tank subjected to projectile impact with initial velocity from 100 to 400 m/s was also shortage. The relevant results can provide supports for promoting the protective performance of the fluid-filled container effective. In the present work, a series of experiments were conducted to investigate the damage of the water-filled container impacted by flat projectiles with the different velocities from 100 to 300 m/s. The motion of projectile and cavity evolution in water were measured by using the high-speed photography. The deformation and failure modes of the water-filled container were assessed. Additionally, the numerical simulation was performed to analyze the dynamic response of the waterfilled container. The critical values among failure modes of the fluidfilled container were also identified, and the quantitative relations between the deformation of target plates, velocity of projectile and plate thickness were established. The future work will involve the structure optimization of the container to alleviate the damage of structures.
during the growth stage according to the images recording in tests. The fluid-filled container can be seriously damaged by the coupling action of HRAM and projectile impact. Based on the phenomenon, Townsend [14] investigated the failure of water-filled container impacted by projectiles, and designed a new kind of container with air baffles, which could effectively alleviate damage of container. At the same time, the research of Disimile [15] showed that triangular bars in the container could also weaken the damage of rear wall of the container because the triangular bars can effectively prevent the cavitation expanding. In order to study the failure mechanism of the container under the fluid-structure interaction, Ren [16] carried out experiments to analyze the failure modes of water-filled vessel subjected to projectile impact. The results show that the ogive-nose projectile can produce more severe failure of vessel walls. Recently, the composite materials were applied to enhance the impact resistance of fluid-filled container. Varas [17] analyzed the deformation of the water-filled carbon fiber reinforced plastics (CFRP) tube impacted by projectiles and found that the CFRP panels could improve the protective properties of the water tube, due to the delaminated of CFRP panels which can effectively absorption energy of projectile. Tian [18] presented that the sandwich plates with flexible core could be used as bulkhead of the water-filled container because of the good performance of energy absorption on the initial shock wave. Numerical simulation as a useful method was applied to reproduce all the stages of HARM. Firstly, the lagrangian method was used to simulate the hydrodynamic ram phenomenon and the results showed that the meshes might be distorted during the simulation [19]. Then, the Coupling Euler-Lagrange method was introduced to solve the problem, and good results were obtained [20]. Recent years, Varas [21–23] used two commercial finite element code ABAQUS and LS-DYNA to simulate the hydrodynamic ram events. The numerical results were compared with the experimental results to assess the accuracy of finite element technique in performing such a complex phenomenon of hydrodynamic ram. Guo [24] conducted the numerical simulation to descript the effect of different nose shapes of projectiles on drag phase and cavity phase of hydrodynamic ram. Three major parameters in the cavity model were determined both in the theoretical and experimental studies. Moreover, a drag coefficients model independent of the cavitation number was proposed based on the experimental and numerical results. The similar work was conducted by Li [25,26] that the effects of initial velocity, radius and length of long-rod projectiles on HARM were analyzed in the numerical study. Guerrero [27] carried out the numerical simulations to investigate the influence of the fluid filling level in container on the hydrodynamic ram phenomenon and found that the rear wall of the container presented the largest plastic deformation when the container was filled in fluid. Comprehensively, the researches showed that HRAM
2. Experimental study 2.1. Experimental device A one-stage light gas gun was employed to perform the experiments, and the sketch of the experimental device was shown in Fig. 1. The diameter of the launch tube of light gas gun was 16 mm. The lab-scaled water-filled container was designed to provide a variety of structure configurations. In order to achieve a perpendicular impact of the projectile, the water-filled container was fixed in the protective tank with fixture, which can keep the axis of launch tube perpendicular to front wall of the container. The distance between the muzzle of the launch tube and the container is 60 mm. Meanwhile, a 50 mm thickness wood block was fixed on the back wall of the protective tank to prevent the spring back of projectile after exiting from the water-filled container. Fig. 2(a) shows the geometry of the container frame, in which the length, width and height of the container were 300 mm, 298 mm and 2
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Fig. 3. Dimension of blunt projectiles (unit: mm). Table 2 The experimental results of flat projectiles. Test number
mp(g)
vi(m/s)
Ff
Fr
1 2 3 4 5 6 7 8 9 10
44.51 44.49 44.52 44.53 44.51 44.55 44.56 44.51 44.55 44.57
134.32 142.75 151.85 178.61 184.37 191.85 200.12 217.14 234.92 241.67
Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation
Crack+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation
alloy. The mechanics properties of 5A06 aluminum alloy at the strain rates from 10−3 s−1 to 2000 s−1 were obtained by experimental tests [29]. The constitutive model of 5A06 aluminum alloy is taken as Johnson-Cook model that accounts the equivalent stress σeq as a function of effective strain, strain rate and temperature, given as
Fig. 2. Geometry of the water-filled container, (a) The structure of container, (b, c) The sketch of the specimen.
n * )(1 − T *m) σeq = (A + Bεeq )(1 + C ln ε˙eq
290 mm, respectively. The container frame was made from high strength steel. For the direct observation of the projectile motion and cavity evolution during the whole test, two transparent PMMA windows with 20 mm thickness were installed on the laterals of the container by using bolts. The Photron SA-Z high-speed camera was employed to record the travelling process of the projectile in the container. Based on previous researches [6,24], the frame rate of the high-speed camera selected in the experiments was 30000 per second, and the resolution was 256 × 256 pixels. Meanwhile, two 1200 W lamps as backlighting were utilized to light the water-filled container for accurately capturing profile of the cavity shape. The settings exhibited an optimal trade-off between the available lighting and minimization of blur in the images. The measurement accuracy of camera used in the tests was within 3% [16,28].
(1)
* is the non-dimensionalized effective where εeq is the effective strain, ε˙eq plastic strain rate, T*=(T-Tr)/(Tm-Tr) is the non-dimensionalized temperature, Tr and Tm are the reference temperature and melt temperature respectively, A, B, C, n and m are the model parameters. The research of Børvik [30] indicated that the failure criterion of metal material, which was based on plastic work per unit volume proposed by Cockcroft and Latham [31] can effectively capture the fracture behavior for metal plate under blunt projectile impact. Recently, the simple failure criterion verified can accurately predict the damage of aluminum plate exposed to hydrodynamic ram [32] and is expressed as: D=
W 1 = Wc Wc
∫0
εeq
⟨σ1 ⟩dεeq
(2)
where Wc is the failure parameter of material, and it can be calculated by uniaxial tension test, in which the major principal stress integrated along the entire equivalent plastic strain path until the plastic strain reach at failure strain εf. And ⟨σ1 ⟩ denotes the first principal stress. The failure of aluminum alloy occur when D equals 1. The parameters of 5A06 aluminum were listed in Table 1. The diameter and length of the cylindrical blunt projectiles used in the tests were 15.9 mm and 32 mm, respectively, as shown in Fig. 3. The material of 45# steel with full annealing were used to ensure that the projectile strength was enough to penetrate the water-filled container with non-plastic deformation. The mechanical properties of 45# steel are also listed in Table 1. The initial velocities of projectile ranging from
2.2. Target panels and projectiles The target plates were fixed to the front and rear sides of the container frame by using sixteen equal spaced blots and steel fixtures. The assemble method of the target panels can be defined as the clamped boundary conditions. The sealing strips were employed to ensure the seal of the container. The size of front and rear panels used in the tests was 298 mm × 290 mm × 1.5 mm, and the effective loading region of panels was 180 mm × 250 mm, as shown in Fig. 2. The target plates of the container were made from 5A06 aluminum Table 1 Mechanical parameters of target plate and projectile. Material
ρ (kg/m3)
E (GPa)
A (MPa)
B (MPa)
C
m
n
Wc(MPa)
45#Steel 5A06 Al PMMA
7850 2780 1180
210 74 3
710 167.0 –
510 458.7 –
0.014 0.44 –
1.03 2.3 –
0.26 0.02 –
75.3 –
3
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Fig. 4. The Details of simulation mode for the analysis. Table 3 Materials parameters of water and air parameters used in simulation. Material
ρ0(kg/m3)
vd (Pa s)
cw (m/s)
S1
S2
S3
γ0
a
C4
C5
E0(J/m3)
Water Air
1000 1.22
0.89 × 10−3 1.77 × 10−5
1448 –
1.979 –
0 –
0 –
0.11 –
3.0 –
– 0.4
– 0.4
– 2.53 × 105
parameters of PMMA and projectile were shown in Table 1 [21]. The front and rear plates of the water-filled container were modeled with Belytschko-Tsay shell element. The mesh-size of plates used in the numerical approach was determined by performing a convergence study. The square mesh with length of side 0.5 mm can minimize the effect of the orientation of mesh on the failure of impact site of plates [22,32]. Meanwhile, for improving computation efficiency, a progressive and coarser mesh growing with the distance to the impact point was employed for the plates. In order to ensure the water flow freely during the impact process, the Euler element was used for the fluid and air. The Mie-Gruneisen Equation and a linear polynomial equation are selected to describe the water and air, respectively [23,29]. The parameters for water and air used in the simulation are listed in Table 3.
100 m/s to 300 m/s were accurately measured by the laser-velocity gate. 2.3. Experimental results A series of experiments were carried out and the summary of experimental results was shown in Table 2, including the projectile mass mp, the initial impact velocity of projectile vi, Ff and Fr denoting the failure modes of the front and rear plates, respectively. From Table 2, it can be observed that the plugging failure and outward deformation of the front and rear plates were the dominated failure modes in the tests. A slight crack without penetration was found on the rear plate when the initial velocity of projectile was below 134.32 m/s. Then, the projectile penetrated the container and the plug of rear plate was formed when the projectile velocity reached to 142.75 m/s.
3.2. Validation of numerical simulation
3. Numerical simulation study
The effectiveness of the numerical simulation had been verified by the comparation with the corresponding test results, as shown in Figs. 5–8. It can be observed that the test and simulation results presented a good agreement. The numerical models can capture the projectile motion and the deformation of the water-filled container. Fig. 5 shows the comparison of the cavity evolution behind projectile in test and simulation at the initial velocity of projectile 178.61 m/s. The initial time was defined as the time when the projectile impacted the front wall of the water-filled container. The cavity was formed when the projectile penetrated into water. And the diameter of cavity at the fixed position in the container increased with the increasing of the penetration depth of the projectile. It also can be found that the sizes of the cavities predicted by the simulation were similar to those in the test results obtained by high-speed camera at different moments. Moreover,
3.1. Simulation model The simulations were conducted to give insight into the failure mechanism of water-filled containers subjected to high speed projectile. According to the research of Hassan [33], the Arbitrary Lagrange-Euler (ALE) technique of LS-DYNA can effectively describe the hydrodynamic ram. As shown in Fig. 2, the water-filled container used in the tests was a symmetric structure. Hence, the quarter model was established to shorten the computation time, as shown in Fig. 4. The sizes of the models were same as those in the experiments. The Lagrange mesh with 8-node solid elements was adopted for the container frame, projectile and PMMA window. The material 4
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Fig. 5. Comparison of cavity evolution between experimental (left) and numerical (right) results, vi = 178.61 m/s.
The initial time was that the projectile impacted the front wall of the container. And the average velocities of projectile at different positions can be calculated according to two frames. It can be seen that the velocity of projectile rapidly decreased after the projectile penetrating the
the stability of projectile trajectory performed well because of a uniform distribution of drag force on the flat nose of projectile [24]. Fig. 6 shows the velocity decay of the projectiles in water at the initial velocity of projectile 178.61 m/s and 241.67 m/s, respectively.
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well with the test results. The comparison of the numerical prediction and experiments in typical failure modes of front and rear plates of water-filled containers are shown in Fig. 7, when the velocities of projectile were 134.32 m/s and 178.61 m/s, respectively. It can be found that plugging and outward deformation were the main failure modes of front plates. The projectile could not penetrate the rear plate when the initial velocity of projectile was 134.32 m/s. The rear plate just presented outward deformation with crack around the impact site. It means the initial velocity of projectile was closed to the ballistic limit velocity of the waterfilled tank. Meanwhile, the water resistance caused the slight lateral deviation of projectile when the projectile reached the rear plate. This also resulted in a slight asymmetric deformation of rear wall, as shown in Fig. 7(a). With the velocity increasing, the rear plate was penetrated and the plug was formed, similar to the prediction in the numerical simulation. Additionally, the slight asymmetric deformation of rear plate was not obtained in simulation because of a quarter model of the container used. The permanent deformation of front and rear plates obtained from post-test were illustrated in Fig. 8. In order to compare the discrepancy between experiments and simulations, the horizontal and vertical directions were defined as x axis and y axis, respectively. The maximum deflection of front and rear plates caused by HRAM effects was predicted well by the numerical simulation. The ideal boundary condition used in the simulation resulted in the larger deformation of the plates than that in experiments. Meanwhile, the deviation of impact site of rear plates in the tests also affected the symmetry of deformation of rear plates, especially at the initial velocity of projectile 134.32 m/s. It also resulted in the deviated location of the bullet hole of rear plate from the y axis, as shown in Fig. 8(f). Additionally, the global deflection of rear plates was larger than that of front plates for all tests, due to the initial shock wave mainly loading on the rear plate [16,21]. The deflections of front and rear plates increased with the increasing of the velocity projectile. Comprehensively, the simulation model used in the study could effectively predict the failure of the water-filled container subjected to impact of flat projectile.
Fig. 6. The velocity attenuation of flat projectile in water obtained from tests and simulations.
4. Discussion 4.1. Pressure history Fig. 9 shows the prediction results of typical propagation of initial shock wave in water-filled container. The cambered shock wave was formed after the projectile impacted the front wall of container. Then, the shock wave propagated along the horizontal line, and the intensity of shock wave decreased with the distance increasing, also observed in the previous experimental studies [16]. It is worth to mention that the reflection of shock wave began when the shock wave touched the rear wall of the container. And the intensity of reflected wave decreased closed to zero before the reflected wave colliding the cavitation [15,34]. For the further study on the propagation characteristic of the initial pressure, four positions were chosen to analyze the attenuation of the shock wave in the simulation, as shown in Fig. 4. Position 1 and position 2 located at the central line of the container, and the distances from front plate were 100 mm and 200 mm, respectively. Position 3 and position 4 were deployed along the same vertical line with position 1 and position 2, respectively. The vertical distance between two positions was 50 mm. The typical pressure histories of the four positions were obtained from the simulation at the initial velocity of projectile 178.61 m/s and shown in Fig. 10. The initial time was corresponding to the time when the projectile impacted on the front panel. The initial peak pressures at four different positions were observed after 0.07 ms. The pressure of initial shock waves showed exponential attenuation trend along the central line of the container. The peak pressure in position 2 was approximately equal to one third of that in position 4. The
Fig. 7. Comparison of failure modes of plates between experimental and simulation results, (a, b) vi = 134.32 m/s, (c, d) vi = 178.61 m/s.
front wall of container. Then, the velocity of projectile obtained from tests showed the exponential attenuation trend and that in the simulations prediction presented the similar trend with a faster deceleration of projectiles. Meanwhile, the projectile with the higher initial velocity suffered more drag resistance and lost more velocity within the same time [6,24]. In general, the simulation curves were correlated quite 6
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Fig. 8. Comparison of plates deformation between experimental and simulation results, (a, b) x and y axis, vi = 178.61 m/s, (c, d) x and y axis, vi = 241.67 m/s, (e, f) x and y axis, vi = 134.32 m/s.
Fig. 9. The propagation characteristics of initial shock wave caused by flat projectile, vi = 241.67 m/s.
positions along the vertical line were at different spherical surfaces, indicating that the distances from the initial impact point of the front plate to the two measurement positions were different and resulting in the time delay of pressures existing between position 1 and 2. The similar phenomenon was observed between position 3 and position 4. The second peak pressures of position 1 and position 2 were observed
peak pressures of two positions along the same vertical line exhibited little difference and the highest pressure was at the central line of the container because of the arc scattering of shock wave during the propagation in water, as shown in Fig. 9. The peak pressure along the vertical line decreased with the increasing of the distance from the projectile trajectory. According to Fig. 4, the two measurement 7
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Fig. 10. The pressure histories of different position, vi = 178.61 m/s.
Fig. 11. The pressure histories of position 3 at different velocities.
Fig. 12. The motion of projectile in water-filled tank, (a) velocity variable verse initial velocity, (b) penetration distance with time, (c) cavity diameter with time, (d) residual velocity verse initial velocity.
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Fig. 13. The deformation of plates impacted by flat projectile with different velocities, (a, b) front plate,(c, d) rear plate.
Fig. 14. The section-profile of target panels along longitudinal direction, (a, c) front plate, (b, d) rear plate.
after 0.6 ms. The pressures were caused by the squeezing of projectile in water, as shown in Fig. 5. The intensity of pressure around the projectile nose was even higher than that of the initial shock wave. When the projectile reached the measurement position on the central line, the pressure rapidly dropped down to zero due to the formation of cavitation. Fig. 11 depicts the pressure histories in position 3 at different projectile velocities. It can be concluded that the peak pressure increased with the projectile initial velocity increasing. And all the second peak pressures in simulations were obviously smaller than the first ones, meaning that the pressure caused by the projectile moving into water was mainly distributed in the front of the projectile, as shown in Fig. 10.
Fig. 15. Fitting curves between maximum deformation and initial velocity of projectiles.
increasing. More kinetic energy transferred to water when the projectile had the higher initial velocity. According to Fig. 6, the velocity of projectile presented the exponential decay in water due to the drag effect. It indicates that more energy was dissipated in the initial stage of projectile penetrating into water than that in other stages. Fig. 12(b) shows the relationship between the distances of projectile penetration and the time at three different initial velocities, respectively. The projectile with higher initial velocity could produce the deeper penetration during the identical time. With the penetration of projectile increasing, the cavitation was formed following the projectile in the water-filled container. The diameter evolution of cavitation at 40 mm far from front plate was shown in Fig. 12(c). The cavity diameter grew with the penetration depth increasing, but its growth rate gradually decreased. It
4.2. Velocity attenuation of projectile and cavitation Fig. 12(a) shows the projectile velocity variable, represented for the variation of projectile velocity moving in the water. It can be observed that the velocity variable increased with initial velocity of projectile 9
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Fig. 16. Failure prediction of the walls of fluid-filled tank impacted by flat projectile, (a) vi = 67.30 m/s, (b) vi = 270.15 m/s, (c) vi = 385.20 m/s.
4.3. Deformation and failure modes of the plates
also can be seen that the higher velocity of projectile could produce bigger cavity in water. After the cavity completely formed in water, the projectile exited the rear plate preloaded by initial shock and the motion of water. Based on the research of Recht and Ipson [35], the residual velocity of projectile can be fitted and shown in Fig. 12(d). The ballistic limited velocity of the water-filled container used in the study was regard as 137.3 m/s.
The deformation of the water-filled container was a significant factor to indicate the degree of destruction. Fig. 13(a) and (b) show the global deformation curves of front plates along x and y direction, respectively. It can be seen that the ultimate deformation of front plates along the two directions increased with the initial impact velocity of projectile increasing. The similar phenomenon was obtained from rear plates, as shown in Fig. 13(c) and (d). The typical section-profiles of front and rear plates are shown in Fig. 14. It is worth to mention that 10
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as shown in Fig. 16(a). With the velocity increasing, the projectile penetrated into the container and the plug of rear plate was formed. But the plug of rear plate was not detached until the velocity of projectile reached to 178.61 m/s, as shown in Fig. 7(c). According to the previous study [16], the formation of bullet hole of rear plate was attributed to the cooperation of tension and shear. The similar results were obtained from simulation, and the plug was completely detached from the rear plate because of the ideal boundary in the simulation, as shown in Fig. 7(d). The smooth edge of bullet hole shows that the hydrodynamic ram was insufficient to generate the initial crack around the hole and also indicates that the velocity of projectile was not enough to provide the sufficient kinetic energy for tearing failure of the plates. Fig. 16(b) shows the petaling failure of rear plate obtained from numerical simulation. The slight cracks appeared at the edge of the hole when the initial velocity of projectile increased to 270.15 m/s. And the length of cracks extended with the velocity of projectile increasing, as shown in Fig. 16(c). The failure mode maps of front and rear plates with a variety of initial velocities of projectile were summarized in Fig. 17. The solid and dashed lines represented the critical values of initial velocity of projectile obtained from experiments and simulations, respectively. The failure modes of front and rear plates impacted by flat projectile were classified into four categories. At a low initial velocity of projectile, the front plate of water-filled container was not penetrated and just experienced a slight plastic deformation around the impacting site, referred to as mode I. At a medium velocity of projectile, the front plate of the container was penetrated. And, the plugging following the global deformation of plate in the opposite direction was referred to as mode IIa. With the velocity of projectile increasing, the projectile penetrated the rear plate. The global deformation and plugging in the same direction was referred to as mode IIb. At a high velocity of projectile, the petaling with large plastic deformation of plate was referred to as mode III. It can be seen that the deformation and damage of front and rear plates became more serious with the initial velocity of projectile increasing. For rear plate, mode IIb and mode III failure appeared when the velocities of projectile reached to 134.32 m/s and 270.15 m/s, respectively. Meanwhile, the front plates only experienced mode I and mode IIa failure in this study. For the similar failure mode, more kinetic energy of flat projectile was needed for front plate than rear plate, because the initial shock wave of hydrodynamic ram mainly acted on rear plate. Moreover, the projectile motion squeezing the water also aggravated the damage of rear plate. The critical tearing failure of rear plate was observed when the projectile velocity was 270.15 m/s. But the tearing failure of front plate was not obtained in this research. In the previous researches [16,36], the experiments results about the deformation of the water-filled container with 0.5 mm and 2 mm thickness plates subjected to impact by flat projectile were obtained. Combined with the experimental results in this study, the relationship among the normalized deformation (δ/h0) of measurement point, the normalized velocity (vi/cw) of projectile and the normalized thickness
Fig. 17. Failure mode maps of front and rear plates with different projectile velocity.
the global deformation of rear plate was obviously larger than that of front plate, because the pre-loading of initial shock wave and water motion on rear plate caused slight outward deformation before the projectile penetration. It is illustrated that the rear plate was more sensitive to hydrodynamic ram than front plate [23,29]. Additionally, the deformation of front and rear plates along longitudinal direction was larger than that along horizontal direction, caused by the difference of the loading length of sides. The plugging with outward plastic deformation was the typical failure mode of front and rear plates after the flat projectile penetrated the water-filled container. The radius of bullet hole was approximately equal to the projectile. The point with 40 mm from the center of plate on vertical axis of symmetry was chosen to analyze the effect of initial velocity of projectile on the ultimate deformation of plates, as shown in Fig. 15. Where δ, vi, cw and h were the transverse deflection of measurement point, initial velocity of projectile, speed of sound in water and thickness of the plates, respectively. The fitting curves in Fig. 15 indicate that the linear relationship between the normalized deformation (δ/h) of plates and normalized velocity (vi/cw) could be established based on experimental and simulation results. The maximum local deflection of plates increased with the initial velocity of projectile increasing. The slope of the linear relationship showed that the increasing rate of deformation of rear plates was more sensitive than that of front plates. Based on the previous researches [15,22], the petaling with outward deformation of plates can be observed when the initial velocity of projectile increased to critical value. The plugging failure of plate was obtained from experimental results in this study. Hence, the numerical simulations with high speed velocity of projectile were conducted to study the petaling failure of the container walls. Figs. 7 and 15 show plugging and petaling failure obtained from experiments and simulations, respectively. It can be found that the front plate was not penetrated when the initial velocity of projectile was lower than 67.30 m/s,
Fig. 18. The effect of plate thickness on ultimate deformation of front and rear plates, (a) front plate, (b) rear plate. 11
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(h0/lh) of plate was shown in Fig. 18. Where lh was the height of loading area of the plate. It can be observed that the front and rear plates was deflected with similar trends under the hydrodynamic ram. Through the comparation and analysis of the deflection of three different thickness plates, it can be found that the plates with 2 mm thickness exhibited better resistance performance to damage. The normalized deformation of plates was more sensitive to the normalized thickness of plates than the velocity of projectile. The water-filled container with thinner plates were more susceptible to deform when impacted by projectile with higher initial velocity. The quantitative relationship obtained from the fitting curved surfaces was given by
= a⋅(vi/ c w )b⋅(h 0 / lh)c
J. Appl. Phys. 17 (1946) 541–555. [5] L.A. Swanson, A Detailed Examination of the Pressure Produced by a Hydrodynamic Ram Event, The University of Cincinnati, 2007. [6] W. Huang, W. Zhang, P. Ren, Z.T. Guo, N. Ye, D.C. Li, Y.B. Gao, An experimental investigation of water-filled tank subjected to horizontal high speed impact, Exp. Mech. 55 (2015) 1123–1138. [7] Minhyung Lee, Generation of Shock Waves by a Body during High-Speed Water Entry, The University of Texas at Austin, 1995. [8] N. Lecysyn, A. Dandrieux, F. Heymes, P. Slangen, L. Munier, E. Lapébie, C. LeGallic, G. Dusserre, Preliminary study of ballistic impact on an industrial tank: Projectile velocity decay, Int. J. Loss Prev. Process. Ind. 21 (2008) 627–634. [9] N. Lecysyn, A. Dandrieux, F. Heymes, L. Aprin, P. Slange, L. Munier, E. Lapébie, C.L. Gallic, G. Dusserre, Ballistic impact on an industrial tank: Study and modeling of consequences, J. Hazard Mater. 172 (2009) 587–594. [10] N. Lecysyn, A. Dandrieux, F. Heymes, L. Aprin, P. Slange, L. Munier, Lapébie, C.L. Gallic, G. Dusserre, Experimental study of hydraulic ram effects on a liquid storage: Analysis of overpressure and cavitation induced by a high-speed projectile, J. Hazard Mater. 178 (2010) 635–643. [11] H.H. Shi, M. Kume, An experimental research on the flow field of water entry by pressure measurements, Phys. Fluids 13 (2001) 347–349. [12] H.H. Shi, M. Kume, Optical observation of the supercavitation induced by highspeed water entry, J. Fluids Eng. 122 (2000) 806–810. [13] E. Deletombe, J. Fabis, J. Dupas, J.M. Mortier, Experimental analysis of 7.62mm hydrodynamic ram in containers, J. Fluids Struct. 37 (2) (2013) 1–21. [14] D. Townsend, N. Park, P.M. Devall, Failure of fluid filled structures due to high velocity fragment impact, Int. J. Impact Eng. 29 (2003) 723–733. [15] P.J. Disimile, J. Davis, N. Toy, Mitigation of shock waves within a liquid filled tank, Int. J. Impact Eng. 38 (2011) 61–72. [16] P. Ren, J.Q. Zhou, A.L. Tian, R.C. Ye, L. Shi, W. Zhang, Experimental investigation on dynamic failure of water-filled vessel subjected to projectile impact, Int. J. Impact Eng. 117 (2018) 153–163. [17] D. Varas, R. Zaera, J. López-Puente, Experimental study of CFRP fluid-filled tubes subjected to high-velocity impact, Compos. Struct. 36 (2009) 363–374. [18] A.L. Tian, R.C. Ye, Y.M. Chen, A new higher order analysis model for sandwich plates with flexible core, J. Compos. Mater. 50 (7) (2016) 949–961. [19] K.D. Kimsey, Numerical Simulation of Hydrodynamic Ram, Technical report, ARBRL-TR-02217 US Army Ballistic Research, 1980. [20] E.A. Lundstrom, Fluid/structure interaction in hydraulic ram, Proceedings of the Hydrodynamic Ram Seminar, May 1977, pp. 223–230. Technical report AFFDLTR77-32, JTCG/AS-77-D-002. [21] D. Varas, J. Lopez-Puente, R. Zaera, Experimental analysis of fluid filled aluminium tubes subjected to high velocity impact, Int. J. Impact Eng. 36 (2009) 81–91. [22] D. Varas, R. Zaera, J. López-Puente, Numerical modeling of the hydrodynamic ram phenomenon, Int. J. Impact Eng. 36 (2009) 363–374. [23] D. Varas, R. Zaera, J. López-Puente, Numerical modeling of partially filled aircraft fuel tanks submitted to Hydrodynamic Ram, Aero. Sci. Technol. 16 (2012) 19–28. [24] Z.T. Guo, W. Zhang, X.K. Xiao, G. Wei, P. Ren, An investigation into horizontal water enter behaviors of projectiles with different nose shapes, Int. J. Impact Eng. 49 (2012) 43–60. [25] D. Li, X. Zhu, H.L. Hou, Numerical analysis of protective efficacy of water-filled structure subjected to high velocity long-rod projectile penetration, J. Nav. Univ. Eng. 4 (21) (2015) 21–25. [26] D. Li, X. Zhu, H.L. Hou, Q. Zhong, Finite element analysis of load characteristic of liquid-filled structure subjected to high velocity long-rod projectile penetration, Explos. Shock Waves 01 (2016) 1–8. [27] J.A. Artero-Guerrero, J. Pernas-Sánchez, D. Varas, J. López-Puente, Numerical analysis of CFRP fluid-filled tubes subjected to high-velocity impact, Compos. Struct. 96 (2013) 286–297. [28] P. Ren, J.Q. Zhou, A.L. Tian, R.C. Ye, L. Shi, W. Zhang, W. Huang, Experimental investigation on dynamic failure of carbon/epoxy laminates under underwater impulsive loading, Mar. Struct. 59 (2018) 285–300. [29] W. Huang, B. Jia, W. Zhang, X.L. Huang, D.C. Li, P. Ren, Dynamic failure of clamped metallic circular plates subjected to underwater impulsive loads, Int. J. Impact Eng. 94 (2016) 96–108. [30] S. Dey, T. Børvik, O.S. Hopperstad, M. Langseth, On the influence of fracture criterion in projectile impact of steel plates, Comput. Mater. Sci. 38 (2006) 176–191. [31] M.G. Cockcroft, D.J. Latham, Ductility and the workability of metals, J. Inst. Met. 96 (1968) 33–39. [32] Vincent Faucher, Folcl Casadei, Georgios Valsamos, Martin Larcher, High resolution adaptive framework for fast transient fluid-structure interaction with interfaces and structural failure-Application to failing tanks under impact, Int. J. Impact Eng. 127 (2019) 62–85. [33] Mansoori Hassan, Hamidreza Zarei, FSI simulation of hydrodynamic ram event using LS-Dyna software, Thin-Walled Struct. 134 (2019) 310–318. [34] J. Zhang, X.H. Shi, C.G. Soares, Experimental study on the response of multi-layered protective structure subjected to underwater contact explosions, Int. J. Impact Eng. 100 (2017) 23–34. [35] R.F. Recht, T.W. Ipson, Ballistic perforation dynamics, Int. J. Appl. Mech. (Trans. ASME) 30 (1963) 384–390. [36] Y.X. Liu, P. Ren, L. Shi, Damage characteristics of liquid-filled tanks impacted by low speed projectiles, J. Vib. Shock 37 (15) (2018) 84–89.
(3)
where a, b, c in the equation were constants. For front plates, a, b and c were equal to 0.23, 1.10 and −1.04, respectively. And 0.03, 0.55, −1.29 were for rear plates. 5. Conclusions The present work addresses the analysis of the penetration process of water-filled container impacted to blunt projectile using experimental and numerical methods. The results in this study show that the projectile velocity in water-filled container presented exponential decay trends with the time increasing, and the peak pressure of initial shock wave and the diameter of cavitation both increased with the increase of the initial velocity of projectile. The higher velocity of projectile lead to more serious damage of the plates, and the petaling failure of rear plate was observed when the velocity of projectile was over 270.15 m/s. Additionally, the approximate linear relationships between the outward deformation of plates and the velocity of projectile were also established. In this study, four kinds of typical failure modes of target plates were concluded: plastic deformation (mode I), outward plastic deformation and plugging in opposite direction (mode IIa), outward deformation and plugging in the same direction (mode IIb), petaling failure with large plastic deformation (mode III). Finally, the quantitative relationship of plate thickness, velocity of projectile and transverse deformation of plates was assessed through the combination with the previous research results. The experimental and simulation results provide a general guideline to design high-performance water-filled container. Conflicts of interest The authors declared that they have no conflicts of interest to this work. Acknowledgements The authors are grateful to the National Natural Science Foundation of China (grant No. 51509115); Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX18_2309). References [1] N.A. Mouse, M.D. Whale, D.E. Groszmann, X.J. Zhang, The Potential for Fuel Tank Fire and Hydrodynamic Ram from Uncontained Aircraft Engine Debris, U.S. Department of Transportation, Federal Aviation Administration, 1997 DOT/FAA/ AR-96/95. [2] R.E. Ball, Aircraft Fuel Tank Vulnerability to Hydraulic Ram: Modification of the Northrop Finite Element, Computer Code BR-1 to Include Fluid–Structure Interaction: Theory and User’s Manual for BR-1HR, (July 1974) NPS-57B p.74071. [3] J.H. McMillen, Shock wave pressures in water produced by impact of small spheres, Phys. Rev. 68 (1945) 198–209. [4] J.H. McMillen, E.N. Harvey, A spark shadow graphic study of body waves in water,
12
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Full length article
A combined experimental and numerical investigation on projectiles penetrating into water-filled container
T
Peng Rena,*, Lu Shia, Renchuan Yea, Dongliang Chaia, Wei Zhaoa, Jie Wua, Wei Zhangb, Zhongcheng Muc a
School of Naval Architecture & Ocean Engineering, Jiangsu University of Science and Technology, Jiangsu, 212003, PR China High Velocity Impact Dynamics Lab, Harbin Institute of Technology, Harbin, 150080, PR China c School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai, 200240, PR China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Water-filled container Fluid-structure interaction Hydrodynamic ram Failure mode Finite element analysis
The experiments and numerical simulations of projectile penetrating into water-filled container with aluminum target plates were conducted. The motion of projectile and cavity evolution of hydrodynamic ram in water were assessed. The results show the propagation characteristics of initial shock wave of hydrodynamic ram in the container. The study presents that the plugging with outward deformation was the main failure mode of the target plates when the velocity of projectile was below 270 m/s. With the velocity of projectile increasing, the ultimate deformation of plates increased linearly and the petaling failure appeared on the rear plates. Four kinds of typical failure modes for plates of water-filled container were concluded through the combining results of experiment and simulation. In addition, the effect of plate thickness on the plastic deformation were discussed, and the quantitative relation among the deformation of target plates, velocity of projectile and plate thickness were established.
1. Introduction The serious damages of fluid-filled tank was generated when the structures were impacted by high-velocity projectiles and fragments [1]. Compared to the empty structure, the hydrodynamic ram (HRAM) in the fluid-filled tank played an important role in the damage of the container [2]. Hence, it is inevitable to investigate the failure mechanism of the tank under the coupling effect of impact and HRMA. The process of HRAM can be divided into four stages, including initial shock wave, drag, cavity and exit [3]. Firstly, the propagation of initial shock wave from the impacting of projectile caused the slight deformation of the container. Then, the projectile penetrated into water, the velocity decay of the projectile could be observed due to the drag force of fluid. The partial kinetic energy of the projectile transferred to fluid in this stage. Meanwhile, a cavity was formed behind the projectile. Finally, the projectile penetrated the rear wall and exited the fluid-filled container. In order to illustrate the mechanism of HRAM, the scholars have investigated the phenomenon of HRAM by experiments, numerical simulations and theoretical analysis over half of the century. The earlier experimental tests were performed by McMillen [4] on the propagation characteristic of initial shock. The negative correlation between the *
measured pressure and the angle along the arc of the shock wave away from the shot line was found. Based on the research, Swanson [5] conducted a series of experiments to measure the pressure of the initial shock wave by using the fixed transducers in the container, and the shock wave was also visualized through the shadowgraph technique. Using the similar experimental method, Huang [6] obtained the attenuation characteristic of shock wave from the experimental results, and concluded the effect of projectile shape on the peak pressure. According to Minhyung [7], the initial shock wave could be divided into ballistic wave and collapse wave. The ballistic wave was produced by the projectile penetrating into fluid and collapse waves generated from the cavity collapse. The analysis showed that the pressure of ballistic waves increased with the initial velocity of projectile increasing, while the collapse waves was irrelevant to the initial velocity of projectile. Then, Lecysyn [8–10] investigated the cavity stage of HRAM by utilizing the high-speed photography. The relationship among the velocity decay of projectile, the cavitation parameters (cavity radius, cavity wall velocity, cavity collapse time) and the initial velocity of projectile were analyzed. Meanwhile, Shi [11,12] found that the deflection of projectile trajectory in water depended on the distance of penetration, and the cavity behind the projectile was strongly chaotic. Deletombe [13] also observed the evolution of cavity and measured the cavity geometry
Corresponding author. E-mail address: [email protected] (P. Ren).
https://doi.org/10.1016/j.tws.2019.106230 Received 14 December 2018; Received in revised form 23 May 2019; Accepted 29 May 2019 Available online 08 June 2019 0263-8231/ © 2019 Elsevier Ltd. All rights reserved.
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Fig. 1. Sketch of the experimental device.
contributed great to the damage of fluid-filled container, and HRAM was affected by the shape and velocity of projectiles. Meanwhile, it can be found that the damage of fluid-filled tank was caused by the combination of penetration and HRAM loads, which is obviously different from the damage of metallic structures resulted from impulsive or impact loading. Although there are many studies on failure modes of the metallic structures, the research on the critical conditions for failure modes of water-filled container subjected to projectiles was still shortage. Additionally, the ballistic limit velocity for most empty aluminum tank was only approximate 200 m/s [23], however the velocity of projectile used in the mentioned researches almost above 600 m/s. Hence, the studies on the deformation and failure of water-filled tank subjected to projectile impact with initial velocity from 100 to 400 m/s was also shortage. The relevant results can provide supports for promoting the protective performance of the fluid-filled container effective. In the present work, a series of experiments were conducted to investigate the damage of the water-filled container impacted by flat projectiles with the different velocities from 100 to 300 m/s. The motion of projectile and cavity evolution in water were measured by using the high-speed photography. The deformation and failure modes of the water-filled container were assessed. Additionally, the numerical simulation was performed to analyze the dynamic response of the waterfilled container. The critical values among failure modes of the fluidfilled container were also identified, and the quantitative relations between the deformation of target plates, velocity of projectile and plate thickness were established. The future work will involve the structure optimization of the container to alleviate the damage of structures.
during the growth stage according to the images recording in tests. The fluid-filled container can be seriously damaged by the coupling action of HRAM and projectile impact. Based on the phenomenon, Townsend [14] investigated the failure of water-filled container impacted by projectiles, and designed a new kind of container with air baffles, which could effectively alleviate damage of container. At the same time, the research of Disimile [15] showed that triangular bars in the container could also weaken the damage of rear wall of the container because the triangular bars can effectively prevent the cavitation expanding. In order to study the failure mechanism of the container under the fluid-structure interaction, Ren [16] carried out experiments to analyze the failure modes of water-filled vessel subjected to projectile impact. The results show that the ogive-nose projectile can produce more severe failure of vessel walls. Recently, the composite materials were applied to enhance the impact resistance of fluid-filled container. Varas [17] analyzed the deformation of the water-filled carbon fiber reinforced plastics (CFRP) tube impacted by projectiles and found that the CFRP panels could improve the protective properties of the water tube, due to the delaminated of CFRP panels which can effectively absorption energy of projectile. Tian [18] presented that the sandwich plates with flexible core could be used as bulkhead of the water-filled container because of the good performance of energy absorption on the initial shock wave. Numerical simulation as a useful method was applied to reproduce all the stages of HARM. Firstly, the lagrangian method was used to simulate the hydrodynamic ram phenomenon and the results showed that the meshes might be distorted during the simulation [19]. Then, the Coupling Euler-Lagrange method was introduced to solve the problem, and good results were obtained [20]. Recent years, Varas [21–23] used two commercial finite element code ABAQUS and LS-DYNA to simulate the hydrodynamic ram events. The numerical results were compared with the experimental results to assess the accuracy of finite element technique in performing such a complex phenomenon of hydrodynamic ram. Guo [24] conducted the numerical simulation to descript the effect of different nose shapes of projectiles on drag phase and cavity phase of hydrodynamic ram. Three major parameters in the cavity model were determined both in the theoretical and experimental studies. Moreover, a drag coefficients model independent of the cavitation number was proposed based on the experimental and numerical results. The similar work was conducted by Li [25,26] that the effects of initial velocity, radius and length of long-rod projectiles on HARM were analyzed in the numerical study. Guerrero [27] carried out the numerical simulations to investigate the influence of the fluid filling level in container on the hydrodynamic ram phenomenon and found that the rear wall of the container presented the largest plastic deformation when the container was filled in fluid. Comprehensively, the researches showed that HRAM
2. Experimental study 2.1. Experimental device A one-stage light gas gun was employed to perform the experiments, and the sketch of the experimental device was shown in Fig. 1. The diameter of the launch tube of light gas gun was 16 mm. The lab-scaled water-filled container was designed to provide a variety of structure configurations. In order to achieve a perpendicular impact of the projectile, the water-filled container was fixed in the protective tank with fixture, which can keep the axis of launch tube perpendicular to front wall of the container. The distance between the muzzle of the launch tube and the container is 60 mm. Meanwhile, a 50 mm thickness wood block was fixed on the back wall of the protective tank to prevent the spring back of projectile after exiting from the water-filled container. Fig. 2(a) shows the geometry of the container frame, in which the length, width and height of the container were 300 mm, 298 mm and 2
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Fig. 3. Dimension of blunt projectiles (unit: mm). Table 2 The experimental results of flat projectiles. Test number
mp(g)
vi(m/s)
Ff
Fr
1 2 3 4 5 6 7 8 9 10
44.51 44.49 44.52 44.53 44.51 44.55 44.56 44.51 44.55 44.57
134.32 142.75 151.85 178.61 184.37 191.85 200.12 217.14 234.92 241.67
Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation
Crack+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation Plug+Deformation
alloy. The mechanics properties of 5A06 aluminum alloy at the strain rates from 10−3 s−1 to 2000 s−1 were obtained by experimental tests [29]. The constitutive model of 5A06 aluminum alloy is taken as Johnson-Cook model that accounts the equivalent stress σeq as a function of effective strain, strain rate and temperature, given as
Fig. 2. Geometry of the water-filled container, (a) The structure of container, (b, c) The sketch of the specimen.
n * )(1 − T *m) σeq = (A + Bεeq )(1 + C ln ε˙eq
290 mm, respectively. The container frame was made from high strength steel. For the direct observation of the projectile motion and cavity evolution during the whole test, two transparent PMMA windows with 20 mm thickness were installed on the laterals of the container by using bolts. The Photron SA-Z high-speed camera was employed to record the travelling process of the projectile in the container. Based on previous researches [6,24], the frame rate of the high-speed camera selected in the experiments was 30000 per second, and the resolution was 256 × 256 pixels. Meanwhile, two 1200 W lamps as backlighting were utilized to light the water-filled container for accurately capturing profile of the cavity shape. The settings exhibited an optimal trade-off between the available lighting and minimization of blur in the images. The measurement accuracy of camera used in the tests was within 3% [16,28].
(1)
* is the non-dimensionalized effective where εeq is the effective strain, ε˙eq plastic strain rate, T*=(T-Tr)/(Tm-Tr) is the non-dimensionalized temperature, Tr and Tm are the reference temperature and melt temperature respectively, A, B, C, n and m are the model parameters. The research of Børvik [30] indicated that the failure criterion of metal material, which was based on plastic work per unit volume proposed by Cockcroft and Latham [31] can effectively capture the fracture behavior for metal plate under blunt projectile impact. Recently, the simple failure criterion verified can accurately predict the damage of aluminum plate exposed to hydrodynamic ram [32] and is expressed as: D=
W 1 = Wc Wc
∫0
εeq
⟨σ1 ⟩dεeq
(2)
where Wc is the failure parameter of material, and it can be calculated by uniaxial tension test, in which the major principal stress integrated along the entire equivalent plastic strain path until the plastic strain reach at failure strain εf. And ⟨σ1 ⟩ denotes the first principal stress. The failure of aluminum alloy occur when D equals 1. The parameters of 5A06 aluminum were listed in Table 1. The diameter and length of the cylindrical blunt projectiles used in the tests were 15.9 mm and 32 mm, respectively, as shown in Fig. 3. The material of 45# steel with full annealing were used to ensure that the projectile strength was enough to penetrate the water-filled container with non-plastic deformation. The mechanical properties of 45# steel are also listed in Table 1. The initial velocities of projectile ranging from
2.2. Target panels and projectiles The target plates were fixed to the front and rear sides of the container frame by using sixteen equal spaced blots and steel fixtures. The assemble method of the target panels can be defined as the clamped boundary conditions. The sealing strips were employed to ensure the seal of the container. The size of front and rear panels used in the tests was 298 mm × 290 mm × 1.5 mm, and the effective loading region of panels was 180 mm × 250 mm, as shown in Fig. 2. The target plates of the container were made from 5A06 aluminum Table 1 Mechanical parameters of target plate and projectile. Material
ρ (kg/m3)
E (GPa)
A (MPa)
B (MPa)
C
m
n
Wc(MPa)
45#Steel 5A06 Al PMMA
7850 2780 1180
210 74 3
710 167.0 –
510 458.7 –
0.014 0.44 –
1.03 2.3 –
0.26 0.02 –
75.3 –
3
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Fig. 4. The Details of simulation mode for the analysis. Table 3 Materials parameters of water and air parameters used in simulation. Material
ρ0(kg/m3)
vd (Pa s)
cw (m/s)
S1
S2
S3
γ0
a
C4
C5
E0(J/m3)
Water Air
1000 1.22
0.89 × 10−3 1.77 × 10−5
1448 –
1.979 –
0 –
0 –
0.11 –
3.0 –
– 0.4
– 0.4
– 2.53 × 105
parameters of PMMA and projectile were shown in Table 1 [21]. The front and rear plates of the water-filled container were modeled with Belytschko-Tsay shell element. The mesh-size of plates used in the numerical approach was determined by performing a convergence study. The square mesh with length of side 0.5 mm can minimize the effect of the orientation of mesh on the failure of impact site of plates [22,32]. Meanwhile, for improving computation efficiency, a progressive and coarser mesh growing with the distance to the impact point was employed for the plates. In order to ensure the water flow freely during the impact process, the Euler element was used for the fluid and air. The Mie-Gruneisen Equation and a linear polynomial equation are selected to describe the water and air, respectively [23,29]. The parameters for water and air used in the simulation are listed in Table 3.
100 m/s to 300 m/s were accurately measured by the laser-velocity gate. 2.3. Experimental results A series of experiments were carried out and the summary of experimental results was shown in Table 2, including the projectile mass mp, the initial impact velocity of projectile vi, Ff and Fr denoting the failure modes of the front and rear plates, respectively. From Table 2, it can be observed that the plugging failure and outward deformation of the front and rear plates were the dominated failure modes in the tests. A slight crack without penetration was found on the rear plate when the initial velocity of projectile was below 134.32 m/s. Then, the projectile penetrated the container and the plug of rear plate was formed when the projectile velocity reached to 142.75 m/s.
3.2. Validation of numerical simulation
3. Numerical simulation study
The effectiveness of the numerical simulation had been verified by the comparation with the corresponding test results, as shown in Figs. 5–8. It can be observed that the test and simulation results presented a good agreement. The numerical models can capture the projectile motion and the deformation of the water-filled container. Fig. 5 shows the comparison of the cavity evolution behind projectile in test and simulation at the initial velocity of projectile 178.61 m/s. The initial time was defined as the time when the projectile impacted the front wall of the water-filled container. The cavity was formed when the projectile penetrated into water. And the diameter of cavity at the fixed position in the container increased with the increasing of the penetration depth of the projectile. It also can be found that the sizes of the cavities predicted by the simulation were similar to those in the test results obtained by high-speed camera at different moments. Moreover,
3.1. Simulation model The simulations were conducted to give insight into the failure mechanism of water-filled containers subjected to high speed projectile. According to the research of Hassan [33], the Arbitrary Lagrange-Euler (ALE) technique of LS-DYNA can effectively describe the hydrodynamic ram. As shown in Fig. 2, the water-filled container used in the tests was a symmetric structure. Hence, the quarter model was established to shorten the computation time, as shown in Fig. 4. The sizes of the models were same as those in the experiments. The Lagrange mesh with 8-node solid elements was adopted for the container frame, projectile and PMMA window. The material 4
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Fig. 5. Comparison of cavity evolution between experimental (left) and numerical (right) results, vi = 178.61 m/s.
The initial time was that the projectile impacted the front wall of the container. And the average velocities of projectile at different positions can be calculated according to two frames. It can be seen that the velocity of projectile rapidly decreased after the projectile penetrating the
the stability of projectile trajectory performed well because of a uniform distribution of drag force on the flat nose of projectile [24]. Fig. 6 shows the velocity decay of the projectiles in water at the initial velocity of projectile 178.61 m/s and 241.67 m/s, respectively.
5
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well with the test results. The comparison of the numerical prediction and experiments in typical failure modes of front and rear plates of water-filled containers are shown in Fig. 7, when the velocities of projectile were 134.32 m/s and 178.61 m/s, respectively. It can be found that plugging and outward deformation were the main failure modes of front plates. The projectile could not penetrate the rear plate when the initial velocity of projectile was 134.32 m/s. The rear plate just presented outward deformation with crack around the impact site. It means the initial velocity of projectile was closed to the ballistic limit velocity of the waterfilled tank. Meanwhile, the water resistance caused the slight lateral deviation of projectile when the projectile reached the rear plate. This also resulted in a slight asymmetric deformation of rear wall, as shown in Fig. 7(a). With the velocity increasing, the rear plate was penetrated and the plug was formed, similar to the prediction in the numerical simulation. Additionally, the slight asymmetric deformation of rear plate was not obtained in simulation because of a quarter model of the container used. The permanent deformation of front and rear plates obtained from post-test were illustrated in Fig. 8. In order to compare the discrepancy between experiments and simulations, the horizontal and vertical directions were defined as x axis and y axis, respectively. The maximum deflection of front and rear plates caused by HRAM effects was predicted well by the numerical simulation. The ideal boundary condition used in the simulation resulted in the larger deformation of the plates than that in experiments. Meanwhile, the deviation of impact site of rear plates in the tests also affected the symmetry of deformation of rear plates, especially at the initial velocity of projectile 134.32 m/s. It also resulted in the deviated location of the bullet hole of rear plate from the y axis, as shown in Fig. 8(f). Additionally, the global deflection of rear plates was larger than that of front plates for all tests, due to the initial shock wave mainly loading on the rear plate [16,21]. The deflections of front and rear plates increased with the increasing of the velocity projectile. Comprehensively, the simulation model used in the study could effectively predict the failure of the water-filled container subjected to impact of flat projectile.
Fig. 6. The velocity attenuation of flat projectile in water obtained from tests and simulations.
4. Discussion 4.1. Pressure history Fig. 9 shows the prediction results of typical propagation of initial shock wave in water-filled container. The cambered shock wave was formed after the projectile impacted the front wall of container. Then, the shock wave propagated along the horizontal line, and the intensity of shock wave decreased with the distance increasing, also observed in the previous experimental studies [16]. It is worth to mention that the reflection of shock wave began when the shock wave touched the rear wall of the container. And the intensity of reflected wave decreased closed to zero before the reflected wave colliding the cavitation [15,34]. For the further study on the propagation characteristic of the initial pressure, four positions were chosen to analyze the attenuation of the shock wave in the simulation, as shown in Fig. 4. Position 1 and position 2 located at the central line of the container, and the distances from front plate were 100 mm and 200 mm, respectively. Position 3 and position 4 were deployed along the same vertical line with position 1 and position 2, respectively. The vertical distance between two positions was 50 mm. The typical pressure histories of the four positions were obtained from the simulation at the initial velocity of projectile 178.61 m/s and shown in Fig. 10. The initial time was corresponding to the time when the projectile impacted on the front panel. The initial peak pressures at four different positions were observed after 0.07 ms. The pressure of initial shock waves showed exponential attenuation trend along the central line of the container. The peak pressure in position 2 was approximately equal to one third of that in position 4. The
Fig. 7. Comparison of failure modes of plates between experimental and simulation results, (a, b) vi = 134.32 m/s, (c, d) vi = 178.61 m/s.
front wall of container. Then, the velocity of projectile obtained from tests showed the exponential attenuation trend and that in the simulations prediction presented the similar trend with a faster deceleration of projectiles. Meanwhile, the projectile with the higher initial velocity suffered more drag resistance and lost more velocity within the same time [6,24]. In general, the simulation curves were correlated quite 6
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Fig. 8. Comparison of plates deformation between experimental and simulation results, (a, b) x and y axis, vi = 178.61 m/s, (c, d) x and y axis, vi = 241.67 m/s, (e, f) x and y axis, vi = 134.32 m/s.
Fig. 9. The propagation characteristics of initial shock wave caused by flat projectile, vi = 241.67 m/s.
positions along the vertical line were at different spherical surfaces, indicating that the distances from the initial impact point of the front plate to the two measurement positions were different and resulting in the time delay of pressures existing between position 1 and 2. The similar phenomenon was observed between position 3 and position 4. The second peak pressures of position 1 and position 2 were observed
peak pressures of two positions along the same vertical line exhibited little difference and the highest pressure was at the central line of the container because of the arc scattering of shock wave during the propagation in water, as shown in Fig. 9. The peak pressure along the vertical line decreased with the increasing of the distance from the projectile trajectory. According to Fig. 4, the two measurement 7
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Fig. 10. The pressure histories of different position, vi = 178.61 m/s.
Fig. 11. The pressure histories of position 3 at different velocities.
Fig. 12. The motion of projectile in water-filled tank, (a) velocity variable verse initial velocity, (b) penetration distance with time, (c) cavity diameter with time, (d) residual velocity verse initial velocity.
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Fig. 13. The deformation of plates impacted by flat projectile with different velocities, (a, b) front plate,(c, d) rear plate.
Fig. 14. The section-profile of target panels along longitudinal direction, (a, c) front plate, (b, d) rear plate.
after 0.6 ms. The pressures were caused by the squeezing of projectile in water, as shown in Fig. 5. The intensity of pressure around the projectile nose was even higher than that of the initial shock wave. When the projectile reached the measurement position on the central line, the pressure rapidly dropped down to zero due to the formation of cavitation. Fig. 11 depicts the pressure histories in position 3 at different projectile velocities. It can be concluded that the peak pressure increased with the projectile initial velocity increasing. And all the second peak pressures in simulations were obviously smaller than the first ones, meaning that the pressure caused by the projectile moving into water was mainly distributed in the front of the projectile, as shown in Fig. 10.
Fig. 15. Fitting curves between maximum deformation and initial velocity of projectiles.
increasing. More kinetic energy transferred to water when the projectile had the higher initial velocity. According to Fig. 6, the velocity of projectile presented the exponential decay in water due to the drag effect. It indicates that more energy was dissipated in the initial stage of projectile penetrating into water than that in other stages. Fig. 12(b) shows the relationship between the distances of projectile penetration and the time at three different initial velocities, respectively. The projectile with higher initial velocity could produce the deeper penetration during the identical time. With the penetration of projectile increasing, the cavitation was formed following the projectile in the water-filled container. The diameter evolution of cavitation at 40 mm far from front plate was shown in Fig. 12(c). The cavity diameter grew with the penetration depth increasing, but its growth rate gradually decreased. It
4.2. Velocity attenuation of projectile and cavitation Fig. 12(a) shows the projectile velocity variable, represented for the variation of projectile velocity moving in the water. It can be observed that the velocity variable increased with initial velocity of projectile 9
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Fig. 16. Failure prediction of the walls of fluid-filled tank impacted by flat projectile, (a) vi = 67.30 m/s, (b) vi = 270.15 m/s, (c) vi = 385.20 m/s.
4.3. Deformation and failure modes of the plates
also can be seen that the higher velocity of projectile could produce bigger cavity in water. After the cavity completely formed in water, the projectile exited the rear plate preloaded by initial shock and the motion of water. Based on the research of Recht and Ipson [35], the residual velocity of projectile can be fitted and shown in Fig. 12(d). The ballistic limited velocity of the water-filled container used in the study was regard as 137.3 m/s.
The deformation of the water-filled container was a significant factor to indicate the degree of destruction. Fig. 13(a) and (b) show the global deformation curves of front plates along x and y direction, respectively. It can be seen that the ultimate deformation of front plates along the two directions increased with the initial impact velocity of projectile increasing. The similar phenomenon was obtained from rear plates, as shown in Fig. 13(c) and (d). The typical section-profiles of front and rear plates are shown in Fig. 14. It is worth to mention that 10
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as shown in Fig. 16(a). With the velocity increasing, the projectile penetrated into the container and the plug of rear plate was formed. But the plug of rear plate was not detached until the velocity of projectile reached to 178.61 m/s, as shown in Fig. 7(c). According to the previous study [16], the formation of bullet hole of rear plate was attributed to the cooperation of tension and shear. The similar results were obtained from simulation, and the plug was completely detached from the rear plate because of the ideal boundary in the simulation, as shown in Fig. 7(d). The smooth edge of bullet hole shows that the hydrodynamic ram was insufficient to generate the initial crack around the hole and also indicates that the velocity of projectile was not enough to provide the sufficient kinetic energy for tearing failure of the plates. Fig. 16(b) shows the petaling failure of rear plate obtained from numerical simulation. The slight cracks appeared at the edge of the hole when the initial velocity of projectile increased to 270.15 m/s. And the length of cracks extended with the velocity of projectile increasing, as shown in Fig. 16(c). The failure mode maps of front and rear plates with a variety of initial velocities of projectile were summarized in Fig. 17. The solid and dashed lines represented the critical values of initial velocity of projectile obtained from experiments and simulations, respectively. The failure modes of front and rear plates impacted by flat projectile were classified into four categories. At a low initial velocity of projectile, the front plate of water-filled container was not penetrated and just experienced a slight plastic deformation around the impacting site, referred to as mode I. At a medium velocity of projectile, the front plate of the container was penetrated. And, the plugging following the global deformation of plate in the opposite direction was referred to as mode IIa. With the velocity of projectile increasing, the projectile penetrated the rear plate. The global deformation and plugging in the same direction was referred to as mode IIb. At a high velocity of projectile, the petaling with large plastic deformation of plate was referred to as mode III. It can be seen that the deformation and damage of front and rear plates became more serious with the initial velocity of projectile increasing. For rear plate, mode IIb and mode III failure appeared when the velocities of projectile reached to 134.32 m/s and 270.15 m/s, respectively. Meanwhile, the front plates only experienced mode I and mode IIa failure in this study. For the similar failure mode, more kinetic energy of flat projectile was needed for front plate than rear plate, because the initial shock wave of hydrodynamic ram mainly acted on rear plate. Moreover, the projectile motion squeezing the water also aggravated the damage of rear plate. The critical tearing failure of rear plate was observed when the projectile velocity was 270.15 m/s. But the tearing failure of front plate was not obtained in this research. In the previous researches [16,36], the experiments results about the deformation of the water-filled container with 0.5 mm and 2 mm thickness plates subjected to impact by flat projectile were obtained. Combined with the experimental results in this study, the relationship among the normalized deformation (δ/h0) of measurement point, the normalized velocity (vi/cw) of projectile and the normalized thickness
Fig. 17. Failure mode maps of front and rear plates with different projectile velocity.
the global deformation of rear plate was obviously larger than that of front plate, because the pre-loading of initial shock wave and water motion on rear plate caused slight outward deformation before the projectile penetration. It is illustrated that the rear plate was more sensitive to hydrodynamic ram than front plate [23,29]. Additionally, the deformation of front and rear plates along longitudinal direction was larger than that along horizontal direction, caused by the difference of the loading length of sides. The plugging with outward plastic deformation was the typical failure mode of front and rear plates after the flat projectile penetrated the water-filled container. The radius of bullet hole was approximately equal to the projectile. The point with 40 mm from the center of plate on vertical axis of symmetry was chosen to analyze the effect of initial velocity of projectile on the ultimate deformation of plates, as shown in Fig. 15. Where δ, vi, cw and h were the transverse deflection of measurement point, initial velocity of projectile, speed of sound in water and thickness of the plates, respectively. The fitting curves in Fig. 15 indicate that the linear relationship between the normalized deformation (δ/h) of plates and normalized velocity (vi/cw) could be established based on experimental and simulation results. The maximum local deflection of plates increased with the initial velocity of projectile increasing. The slope of the linear relationship showed that the increasing rate of deformation of rear plates was more sensitive than that of front plates. Based on the previous researches [15,22], the petaling with outward deformation of plates can be observed when the initial velocity of projectile increased to critical value. The plugging failure of plate was obtained from experimental results in this study. Hence, the numerical simulations with high speed velocity of projectile were conducted to study the petaling failure of the container walls. Figs. 7 and 15 show plugging and petaling failure obtained from experiments and simulations, respectively. It can be found that the front plate was not penetrated when the initial velocity of projectile was lower than 67.30 m/s,
Fig. 18. The effect of plate thickness on ultimate deformation of front and rear plates, (a) front plate, (b) rear plate. 11
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(h0/lh) of plate was shown in Fig. 18. Where lh was the height of loading area of the plate. It can be observed that the front and rear plates was deflected with similar trends under the hydrodynamic ram. Through the comparation and analysis of the deflection of three different thickness plates, it can be found that the plates with 2 mm thickness exhibited better resistance performance to damage. The normalized deformation of plates was more sensitive to the normalized thickness of plates than the velocity of projectile. The water-filled container with thinner plates were more susceptible to deform when impacted by projectile with higher initial velocity. The quantitative relationship obtained from the fitting curved surfaces was given by
= a⋅(vi/ c w )b⋅(h 0 / lh)c
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(3)
where a, b, c in the equation were constants. For front plates, a, b and c were equal to 0.23, 1.10 and −1.04, respectively. And 0.03, 0.55, −1.29 were for rear plates. 5. Conclusions The present work addresses the analysis of the penetration process of water-filled container impacted to blunt projectile using experimental and numerical methods. The results in this study show that the projectile velocity in water-filled container presented exponential decay trends with the time increasing, and the peak pressure of initial shock wave and the diameter of cavitation both increased with the increase of the initial velocity of projectile. The higher velocity of projectile lead to more serious damage of the plates, and the petaling failure of rear plate was observed when the velocity of projectile was over 270.15 m/s. Additionally, the approximate linear relationships between the outward deformation of plates and the velocity of projectile were also established. In this study, four kinds of typical failure modes of target plates were concluded: plastic deformation (mode I), outward plastic deformation and plugging in opposite direction (mode IIa), outward deformation and plugging in the same direction (mode IIb), petaling failure with large plastic deformation (mode III). Finally, the quantitative relationship of plate thickness, velocity of projectile and transverse deformation of plates was assessed through the combination with the previous research results. The experimental and simulation results provide a general guideline to design high-performance water-filled container. Conflicts of interest The authors declared that they have no conflicts of interest to this work. Acknowledgements The authors are grateful to the National Natural Science Foundation of China (grant No. 51509115); Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX18_2309). References [1] N.A. Mouse, M.D. Whale, D.E. Groszmann, X.J. Zhang, The Potential for Fuel Tank Fire and Hydrodynamic Ram from Uncontained Aircraft Engine Debris, U.S. Department of Transportation, Federal Aviation Administration, 1997 DOT/FAA/ AR-96/95. [2] R.E. Ball, Aircraft Fuel Tank Vulnerability to Hydraulic Ram: Modification of the Northrop Finite Element, Computer Code BR-1 to Include Fluid–Structure Interaction: Theory and User’s Manual for BR-1HR, (July 1974) NPS-57B p.74071. [3] J.H. McMillen, Shock wave pressures in water produced by impact of small spheres, Phys. Rev. 68 (1945) 198–209. [4] J.H. McMillen, E.N. Harvey, A spark shadow graphic study of body waves in water,
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