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Experimental study of water tank under impulsive loading
ACME-263; No. of Pages 11 archives of civil and mechanical engineering xxx (2014) xxx–xxx
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Original Research Article
Experimental study of water tank under impulsive loading Y. Wang *, S.C. Lee Department of Civil and Environmental Engineering, National University of Singapore, Singapore
article info
abstract
Article history:
The performance of stainless steel water tank subjected to impulsive loading was experi-
Received 24 May 2014
mentally studied in this paper. The gas gun was utilized to activate the projectile with high
Accepted 18 September 2014
impact velocity. The activated projectile then impinged the impact transfer plate which
Available online xxx
pressed the airbag behind it. The inflated airbag between the impact transfer plate and water tank was adopted to transfer the impulsive loading from impact transfer plate to the water
Keywords:
tank. The ultra-thin pressure sensors were placed between the airbag and water tank to
High velocity impact
record the pressure imposed onto the water tank and the potentiometers were attached at
Water tank
the back of water tank to record the displacement histories. The water tanks with two
Impulsive loading
different front and rear plate thicknesses were investigated. In addition, the same water tank with and without filled water was compared to study the water effects on the response of
Gas gun
water tank under impulsive loading. Besides the experimental studies, the FE method was adopted to reproduce the experiment and improve the current test method. Finally, the experimentally verified FE models were further used to study the water effects in reducing the deformation of water tank under blast loading. # 2014 Politechnika Wrocławska. Published by Elsevier Sp. z o.o. All rights reserved.
1.
Introduction
The probability of bomb attack on structure has seen an increasing trend in recent years. Consequently, many critical buildings were designed for blast resistance either in the before-built design stage or by means of retrofitting with additional protective layers. Since the probability of the occurrence of blast threat is usually very low, the benefits of adopting a blast-mitigating or blast-enhanced design could be maximized by considering other aspects of the buildings operations such as sustainability and energy efficiency. The
water tank system was proposed to harvest solar energy and meanwhile reduce the thermal heat penetration into buildings in hot climate region. Its energy saving performance has been studied by numerical method [1]. Since the current water tank has potential blast resistant function, this work aims to study the performance of water tank under blast loading to extend the multi-uses of current water tank system and evaluate the workability of utilizing inflated airbag to generate blast loading. Water effects on blast wave mitigation have been studied by experimental and numerical methods for decades [2–8]. Both experimental and numerical results showed that water
* Corresponding author. Tel.: +65 94654835. E-mail addresses: [email protected], [email protected] (Y. Wang). http://dx.doi.org/10.1016/j.acme.2014.09.006 1644-9665/# 2014 Politechnika Wrocławska. Published by Elsevier Sp. z o.o. All rights reserved.
Please cite this article in press as: Y. Wang, S.C. Lee, Experimental study of water tank under impulsive loading, Archives of Civil and Mechanical Engineering (2015), http://dx.doi.org/10.1016/j.acme.2014.09.006
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had significant effects on mitigating blast wave, especially for the case that water was stored close to the explosive. The principle of water in mitigating blast wave is that the high pressure shock wave produced by detonation aerosolizes the water placed close to the explosive and causes both a phase change of water and the redistribution of internal and kinetic energy over the detonation gases, blast wave and barrier material [8]. The aforementioned research on water mitigation effects on blast wave was based on the scenario that water directly interacts with blast wave. However, the research on confined water effects on water tank's response has so far been little. Since confined water does not interact with blast wave, it cannot reduce the blast loading. In addition, the energy dissipation by confined water under blast loading is usually little due to the high bulk modulus and extremely small viscosity of water. However, confined water still can reduce the water tank's response by increasing the overall mass and ensuring the front and rear plate deforming together to absorb the blast energy. The blast loading is an impulsive loading which has extremely high pressure and short duration. The field explosive detonation is a conventional method to generate the blast loading [9–14]. However, the disadvantages of this method are that it is generally quite expensive and a long planning time is also needed. Due to the limitation of the field blast test, many other methods have been proposed to generate the impulsive loading. Shock tube is one of these methods. It is generally less expensive than field blast test and the loads are more reproducible. However, the specimen size is limited by the size of shock tube and the loading duration is relatively longer compared with field blast test [15]. Hence, it is more suitable for simulating far range blast loading. Whisler and Kim have developed a non-explosive test method for generating dynamic blast-type pressure pulse loading [16]. However, only impulse can be recorded in the test, while the pressure –time history is difficult to record. The pressure – time history is necessary for analyzing the specimen if the response of the specimen enters into dynamic or quasi-static response regime. A simple blast load simulation system has been proposed by Mostaghel [17]. As shown in Fig. 1, the invention comprises a test panel and a membrane mounted
within a frame system. The membrane in conjunction with the panel forms an airtight chamber. The airtight chamber is inflated with air before testing. The plate is dropped onto the membrane at various heights to achieve the required impulse magnitude and duration. This method is simple and can be easily conducted in the laboratory. Chen and Hao adopted this method and utilized the inflated airbag as the airtight chamber to investigate the multi-arch double-layered panel under impulsive loading [18]. Remennikov et al. also extended this method to simulating the column under impulsive loading [19]. In this study, this method was also adopted to generate impulsive loading since it is cheaper and easier to conduct in the laboratory compared with other methods. The limitation of this test is similar to the shock tube test, i.e. the loading duration is relatively long. This is due to the fact that the velocity of projectile is quite low due to the drop height limitation of the test equipment. In this study, the gas gun was adopted to activate the projectile with velocity up to 478.4 m/s. This paper starts with a description on the experimental studies on the water tanks under impulsive loading, following by the FE analysis. The solution to overcome the deficiencies of current test method has been presented and the water effects in reducing the deformation of water tank have been discussed.
2.
Description of specimens
The dimension of stainless steel water tank is shown in Fig. 2. Two stiffeners with cut-out holes for water flow were fully welded to the front and rear plate to increase the out-of-plate stiffness. The front and rear plates were extended out and five holes were drilled on the extension to connect the tank to the support system. There were totally three specimens being fabricated, i.e. S1.5, S2 and W2. The stainless steel 316 was adopted for the outer skin and stiffener of water tank, since it has better performance on corrosion resistance than mild steel. The specification of these specimens is given in Table 1. For all the specimens, the thickness of top plate, bottom plate, side plate and stiffener was 2 mm. The front and rear plate thickness was different, as given in Table 1. S1.5 and S2 were designed to study the effects of front and rear plate thickness on the response of water tank. S2 and W2 were designed to study the effects of water on the response of water tank.
Table 1 – Specification of all specimens. Specimens
Fig. 1 – Blast loading simulation system [17].
S1.5 S2 W2
Stainless steel 316
fy (MPa)
E (GPa)
308.6
198.3
Front/rear plate thickness (mm)
Water infilled
1.5 2 2
No No Yes
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ACME-263; No. of Pages 11 archives of civil and mechanical engineering xxx (2014) xxx–xxx
3
Fig. 2 – Dimension of water tank.
3.
Test setup
The gas gun system used in this test consists of compressed gas tank, gas gun, pipe and rigid box, as shown in Fig. 3. The compressed gas tank was utilized to supply high gas pressure to the gas gun. The regulator in the compressed gas tank was utilized to control the output gas pressure and the digital
pressure gauge was connected to the gas gun to measure the gas pressure inside the gas gun. After charging gas, the initial gas pressure inside the gas gun was significantly higher than the ambient pressure. When the trigger was on, the compressed gas would push the projectile from gas gun to the pipe and activate the projectile with high velocity. Then the projectile would move along the pipe and impact the specimens inside the rigid box. The rigid
Fig. 3 – Gas gun system. Please cite this article in press as: Y. Wang, S.C. Lee, Experimental study of water tank under impulsive loading, Archives of Civil and Mechanical Engineering (2015), http://dx.doi.org/10.1016/j.acme.2014.09.006
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Fig. 4 – Schematic diagram of test setup.
box was designed to prevent the projectile from hitting people. The schematic diagram of test setup is given in Fig. 4 and the main procedures of setting up the specimen are shown in Fig. 5. The specimen was connected to the two beams on the support through five bolts on each beam, as shown in Fig. 5(a) and the details of bolt connection is given in Fig. 4(b). The beam
was connected to the support plate through bolt connection. As shown in Fig. 4(c), a connection bolt is screwed into the beam in the one end and goes through the hole on the support plate in the other end. Hence, the beam was restrained in translational movement and only the rotation was allowed, which provided an axially restrained boundary condition for the specimen. The water tank can develop tensile membrane
Fig. 5 – The procedures of setting up specimen. Please cite this article in press as: Y. Wang, S.C. Lee, Experimental study of water tank under impulsive loading, Archives of Civil and Mechanical Engineering (2015), http://dx.doi.org/10.1016/j.acme.2014.09.006
ACME-263; No. of Pages 11 archives of civil and mechanical engineering xxx (2014) xxx–xxx
Fig. 6 – Projectile and impact transfer plate after impact.
force with this boundary condition and its resistance and ductility can be significantly improved compared with simply supported boundary condition. The whole support system was fixed to the rigid base plate through bolt connection. After setting up the specimen, the airbag (250 mm 250 mm 40 mm) was placed in the front of the specimen, as shown in Fig. 5(b). The initial pressure inside the airbag was equal to the ambient air pressure. The impact transfer plate was placed at the front of the airbag and four bolts were utilized to ensure the impact transfer plate at the right position before impact, as shown in Fig. 5(c). The top plate was also positioned on the top of airbag. The top plate, bottom plate and support plate were utilized to form a confining space for the airbag, as shown in Fig. 5(c). The impact transfer plate consists of two steel plates which were glued together. The dimensions of these two steel plates are 100 mm 100 mm 20 mm and 250 mm 250 mm 4 mm. The purpose of attaching a 20 mm thick steel plate in front was to avoid the perforation of projectile. The cylinder projectile was adopted in this test with dimension of 19.5 mm 26.5 mm (diameter length). In this test, the ultra-thin pressure sensors were placed between the airbag and specimen, as shown in Fig. 5(a) to record the pressure imposed onto the specimen. The velocity of projectile before impact was measured utilizing the laser system. The time interval of the projectile going through the
5
two laser points was recorded and the velocity of projectile was obtained by dividing the distance between the two laser points by the time interval. The potentiometers were utilized to record the displacement–time histories of the specimens and support, as shown in Fig. 5(d). It was found in the test that the displacements of the support and specimen were comparable. Hence, one potentiometer was attached to the support at the mid-span to record the displacement–time history of the support. The actual displacement of the specimen at mid-span can thus be obtained by subtracting the support displacement from the measured displacement of specimen. The signals from pressure sensors were captured by ELF data acquisition system from Tekscan, Inc. The signals from laser and potentiometers were captured by DL 1200A digital oscilloscope and DL 7500 digital oscilloscope, respectively.
4.
Test results and discussion
For all the three specimens, the projectiles were activated by the gas gun with initial pressure of 18 MPa and the velocity of activated projectile before impact varied from 442.4 to 478.4 m/ s. Fig. 6 shows the projectile and impact transfer plate after impact test. It can be observed that the indentation is evident on the impact area of impact transfer plate and the projectile is shortened due to the dramatically high impact pressure. The recorded pressure–time histories of pressure sensors for S1.5 are given in Fig. 7. Since the highest sampling rate of ELF data acquisition system is 5.7 kHz which is not high enough to capture the variation of the pressure, the recorded pressure–time histories may not accurately represent the pressure imposed onto the specimen. Although the ELF data acquisition system failed to provide the exact pressure–time history imposed onto the specimen. It still reflected some characteristics of the contact pressure between the airbag and specimens. It can be seen from Fig. 7 that the duration of the contact pressure is shorter compared with the low velocity impact test using airbag in Refs. [18,19], which is proven that increasing the projectile velocity is a way to shorten load duration. Besides, the peak contact pressure at center is higher than the other two points. This non-uniform pressure
Fig. 7 – Pressure–time histories of pressure sensors. Please cite this article in press as: Y. Wang, S.C. Lee, Experimental study of water tank under impulsive loading, Archives of Civil and Mechanical Engineering (2015), http://dx.doi.org/10.1016/j.acme.2014.09.006
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distribution may be due to the fact that the severe deformation of the impact transfer plate caused by the local impact of high velocity projectile provides a non-uniform pressing on the airbag. This non-uniform pressing can cause the shock wave propagation starting from center, which may give higher pressure at center and lower pressure at periphery, as shown in Fig. 8. By analyzing the test results in this paper and in Refs. [18,19], it is found that the utilizing of inflated airbag to simulate blast loading still has some deficiencies. If the low velocity projectile is adopted, the contact pressure is almost uniform and the contact pressure equals to the air pressure inside the airbag [18,19]. The measurement of pressure inside the airbag is much easier than measuring the contact pressure. However, the duration of contact pressure by using low velocity projectile is very long (usually more than 0.1 s), which may be different from real blast load. Hence, the behaviors of the specimen may also be different when it subjects to real blast load and simulated pressure load using low velocity projectile impact. For instance, the specimens in reference 19 were all within quasi-static response regime, while the structure is usually within impulsive and dynamic response regime under blast load. It is widely accepted that the behaviors of structure are different in different response regimes, such as failure mode and deflection shape. Taking the simple supported Reinforced Concrete (RC) beam for instance, the shear failure mode is more likely to occur in the impulsive response regime and flexure failure mode is more likely to occur in the quasi-static response regime. If the high velocity
3.5 Midpoint displacement(mm)
6
S1.5 S2 W2
3 2.5 2 1.5 1 0.5 0
0
0.005
0.01
0.015
Time(s)
Fig. 9 – Midpoint displacement–time histories of specimens.
projectile impact test using airbag is adopted, the contact pressure duration is short. However, the contact pressure is not uniformly distributed. Therefore, this method must be improved to better simulate the blast load. Based on above analysis, one possible solution is to use a rigid impact transfer plate to provide a uniform pressing on the airbag and the workability of this method will be investigated using FE method in the next section. Since some of the kinetic energy of the projectile was absorbed by the plastic deformation of projectile and impact transfer plate during the impact procedure, all the three specimens underwent elastic deformation. The displacement –time histories of specimens are given in Fig. 9 and the information on projectile velocity and maximum midpoint displacement is listed in Table 2. It is observed from Fig. 9 that all the displacements of specimens continuously increase to their maximum values after impact. The maximum displacements of specimens are listed in Table 2. By comparing the maximum midpoint displacements of S1.5 and S2, it is found that the displacement of S2 is slightly larger than that of S1.5. The possible reason is that the projectile velocity of S2 is higher than that of S1.5. It is believed that the specimen S2 with thicker front and rear steel plate will have smaller displacement if the projectile velocity is identical. By comparing the maximum midpoint displacements of S2 and W2, it is noted that the displacement of W2 is reduced compared with S2 under the similar projectile velocity impacting. Hence, the water effects in reducing the deformation of water tank was demonstrated through experimental study and FE analysis will be carried out to further study these effects.
Table 2 – Impact information on specimens. Specimens S1.5 S2 W2
Fig. 8 – Shock wave propagation inside the airbag during impact.
V (m/s)
Dmax (mm)
442.4 478.4 476.1
2.79 3.02 2.37
Note: V – velocity of projectile before impact; Dmax – maximum midpoint displacement of specimen.
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1200
Numerical investigation
The explicit code in LS-DYNA [20] was adopted to simulate the behaviors of water tanks under impulsive loading in order to verify the test method and investigate the water effects in reducing the deformation of water tank under blast loading.
5.1.
1000
True stress (MPa)
5.
800 600 400 200
FE model
0
The whole process of the high velocity impact test was captured by the FE model, which includes the water tank, water, support, airbag, air, impact transfer plates and projectile. Fig. 10 gives the FE model of W2 and only quarter FE model was built due to symmetry. The shell element was adopted for water tank, stiffener, airbag, 4 mm thick impact transfer plate and confined plate, as it can capture the performance of thin plate components and reduce the computing time compared with fine solid element. While the eight-node solid element was adopted for water, air, 20 mm thick impact plate, beam, bolt and support. The Eulerian formulation, which is ideal for modeling fluid problems, was applied for water and air in the FE model. It should be mentioned that the mesh surrounding water and air, which allowed the materials to flow, was built in the FE model but not shown in Fig. 10 to avoid blocking other components. The Lagrange formation, which is generally suitable for elements without severe element distortion, was applied for the other elements. The penalty fluid–structure coupling method in LS-DYNA was used to model the interactions between the water tank and water, and the airbag and air. While the penalty-based surface to surface contact option was used to model the contacts between the elements with Lagrange formulation.
0
0.1
0.2
0.3
0.4
0.5
0.6
Effecve Plasc Strain
Fig. 11 – True stress-effective plastic strain curve of stainless steel 316.
5.2.
Material models
The piecewise linear plasticity material model was adopted for stainless steel 316. For this material model, an arbitrary stress versus strain curve and arbitrary strain rate dependency can be defined and the failure based on a plastic strain can also be defined. The material properties of stainless steel were obtained from the tensile coupon test and the input true stress-effective plastic strain curve is shown in Fig. 11. In this material model, the Cowper–Symonds model is adopted to scales the yield stress as 2 !1=P 3 p e_ eff p p p 4 5 (1) s y ðeeff ; e_ eff Þ ¼ s y ðeeff Þ 1 þ C p
where s y ðeeff Þ is the yielding stress without considering strain p rate effects, e_ eff is the effective plastic strain rate, C and P are the strain rate parameters. In this study, the strain rate parameters C and P were 240 and 4.74 for stainless steel 316 [21]. The elastic plastic material model was adopted for mild steels and the material properties are given in Table 3. The Cowper– Symonds model is also adopted in this material model to capture the strain rate effects and the strain rate parameters C and P were 40.4 and 5 for mild steel [22]. The elastic material model was applied for airbag, since there was no plastic deformation of airbag after test. The airbag is made of polyvinyl chloride (PVC) material and the Young's modulus is 3.38 GPa [23]. The null material model was used to describe the deviatoric response of air and water. The linear polynomial equation of
Table 3 – Material properties of mild steels. Material S355
Fig. 10 – FE model of W2.
AISI 1045
Component
fy (MPa)
E (GPa)
Impact transfer plate, confined plate, bolt, support and beam Projectile
355
200
375
200
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3.5
r0 (kg/m3) 1.290
E (MPa) 0.253
C0 (MPa)
C1–C3
0.1
0
C4
C5
0.4
0.4
C6 0
state was used to simulate the volumetric response of air, which is written as P ¼ C0 þ C1 m þ C2 m2 þ C3 m3 þ ðC4 þ C5 m þ C6 m2 ÞE
(2)
where m ¼ r=r0 1, r is the current density, r0 is the initial density, E is the initial internal energy per unit reference volume, and C0–C6 are parameters of the equation of state. The material properties of air are given in Table 4. The Gruneisen equation of state with cubic shock velocity–particle velocity (Vs–Ps), which was used to simulate the volumetric response of water, is given by P¼
r0 C2 m½1 þ ð1 g 0 =2Þm a=2m2 2
½1 ðS1 1Þm S2 ðm2 =ðm þ 1ÞÞ S3 ðm3 =ðm þ 1Þ2 Þ
þ ðg 0 þ amÞE
(3)
for compressed material and is given by Eq. (4) for expanded material P ¼ r0 C2 m þ ðg 0 þ amÞE
(4)
where C is the intercept of the Vs–Ps curve, S1, S2 and S3 are the coefficients of the slop of the Vs–Ps curve, g 0 is the Gruneisen gamma, a is the first order volume correction to g 0 . The material properties of water are given in Table 5 [24].
5.3.
Results and discussion
The midpoint displacement–time histories of the water tanks from FE analyses are compared with test results in Fig. 12 and reasonable agreement between the two can be seen from the comparison. The differences between the test results and FE analyses in terms of maximum midpoint displacement are 1.03%, 26.85% and 7.53% for S1.5, S2 and W2, respectively. All the FE predicted maximum midpoint displacements are smaller than the test results and the disparity between FE analysis and test for S2 may be introduced by the measurement errors in the test. Based on above comparison, the established FE model is reasonable and can be used to further investigate the test method and performance of water tank under blast loading. As discussed in Section 4, the non-uniform pressure on the water tanks is caused by the local impact of projectile, which results in the shock wave propagation starting from the center. This can be demonstrated by the plotting the contours of air
Table 5 – Material parameters of water [24]. r0 (kg/m3) 998.2
E
C (m/s)
S1
S2
S3
g0
a
0.0
1647
1.921
0.096
0
0.35
0
Midpoint displacement (mm)
Table 4 – Material parameters of air.
S1.5(Test) S2(Test) W2(Test) S1.5 (FE) S2(FE) W2(FE)
3 2.5 2 1.5 1 0.5 0
0
0.001
0.002
0.003
0.004
0.005
0.006
Time(s)
Fig. 12 – Comparison of FE predicted displacement–time histories with test results.
pressure in Fig. 13(a). It was also mentioned in Section 4 that the rigid impact transfer plate could be used to provide a uniform pressing on the airbag and therefore could provide uniform pressure on the water tank. Hence, the FE analysis was carried out to study the shock wave propagation with rigid impact transfer plate, which is shown in Fig. 13(b). The uniform pressure acting on the water tank can be observed and the air pressure is generally uniform in 0.35 ms after impact. The air pressure–time histories of different locations with rigid impact transfer plate are given Fig. 14. It can be seen that the air pressures of selected locations are very similar during the impact except for location E near the corner. This may be caused by the folded airbag at corner under compression. Since the air pressure on the water tank is almost uniform except for the corner, it is possible to measure the applied pressure on the water tank by recording the air pressure–time history. There are several types of pressure sensors with response time less than 5 ms available in the market, which makes it easier to obtain the accurate air pressure–time history. Therefore, this test method can be more reliable to generate blast loading if the rigid impact transfer plate is adopted. The experimentally verified FE models were further used to investigate the water effects in reducing the response of water tank under blast loading. In this analysis, the support was removed from the FE model and the axially restrained boundary condition was specified by restraining the displacements of the nodes along the two edges of front and rear plates in vertical and axial directions. The blast pressure–time history was applied onto the whole front plate. In this analysis, the triangle pressure profile with zero rise time, which is usually adopted in the blast resistant design [25,26], was adopted as the profile of blast loading. Fig. 15 compares the displacement–time histories of S2 and W2 under the same blast loading with peak pressure and load duration of 8 MPa and 0.5 ms, respectively. It is noted that the front and rear plate midpoint displacements of W2 with infilled water are reduced by 6.4% and 27.7% as compared to S2. This proves that water can reduce the deformation of water tank under blast loading. By comparing the front and rear plate displacement of S2 and W2, the front plate displacement is higher than the rear plate
Please cite this article in press as: Y. Wang, S.C. Lee, Experimental study of water tank under impulsive loading, Archives of Civil and Mechanical Engineering (2015), http://dx.doi.org/10.1016/j.acme.2014.09.006
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Fig. 13 – Shock wave propagation with different impact transfer plates.
for S2, which means that the blast loading is mainly taken by the front plate for S2. However, the rear plate deforms more than the front plate for W2, which indicates that water helps to transfer the blast loading from the front plate to the rear plate
and ensure them deforming together to absorb the blast energy. Based on above comparison, the principle of water effects in reducing the deformation of water tank is that the addition of water increases the overall mass and ensures the
Please cite this article in press as: Y. Wang, S.C. Lee, Experimental study of water tank under impulsive loading, Archives of Civil and Mechanical Engineering (2015), http://dx.doi.org/10.1016/j.acme.2014.09.006
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A B C D E
0.45
Air pressure (MPa)
0.40 0.35 0.30 0.25 0.20 0.15
applied pressure on the water tank was uniform when adopting the rigid impact transfer plate and could be measured by recording the air pressure–time history. The principle of water effects in reducing the deformation of water tank is that the addition of water increases the overall mass and ensures the front and rear plate deforming together to absorb the blast energy.
0.10 0.05 0.00
references 0
0.001
0.002
0.003
0.004
0.005
Time (s)
Fig. 14 – The air pressure–time histories with rigid impact transfer plate.
Midpoint displacement (mm)
25 20 15 10
S2-front plate S2-rear plate W2-front plate W2-rear plate
5 0
0
0.0005
0.001
0.0015
0.002
Time (s)
Fig. 15 – Displacement–time histories of S2 and W2 under blast loading.
front and rear plate deforming together to absorb the blast energy. Both of them can reduce the front plate displacement (as shown in Fig. 15) and therefore can reduce the external work done by the blast loading. It is noted in the FE analysis that the external work of W2 is reduced by 45.1% compared with S2. Since the external work will transfer to the internal energy of water tank at final stage, the less external work will result in less deformation or damage to the water tank.
6.
Conclusions
The performance of stainless steel water tank subjected to impulsive loading was experimentally studied in this paper. The adopted test method for generating blast loading still has some deficiencies. The low velocity projectile impact test can provide a uniform pressure but the load duration is very long compared with field blast test. However, the high velocity projectile impact test adopted in this paper can provide an impulsive loading with shorter duration but the pressure is non-uniform. Hence, this method should be improved to better simulate the blast load. The possible solution has been provided and its workability has also been studied by using FE method. It was demonstrated by FE investigation that the
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[18] W. Chen, H. Hao, Experimental investigations and numerical simulations of multi-arch double-layered panels under uniform impulsive loadings, International Journal of Impact Engineering 63 (2014) 140–157. [19] A.M. Remennikov, J.Y.R. Liew, S.Y. Kong, K.W. Kang, Simulation of impulsive loading on columns using an inflatable airbag technique, in: Proceedings of the 8th International Conference on Shock & Impact Loads on Structures, 2009. [20] J.O. Hollquist, LS-DYNA Keyword User's Manual, Livermore Software Technology Corporation, California, 2012. [21] J.W. Boh, L.A. Louca, Y.S. Choo, Strain rate effects on the response of stainless steel corrugated firewalls subjected to hydrocarbon explosions, Journal of Constructional Steel Research 60 (2004) 1–29.
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[22] N. Jones, Structural Impact, second ed., Cambridge University Press, New York, 2012. [23] W.V. Titow, PVC Technology, fourth ed., Elsevier Applied Science, London, 1984. [24] E.S. Hertel, The CTH Data Interface for Equation-of-State and Constitutive Model Parameters, Sandia Report SAND92-1297, 1992. [25] U.S. Army Corps of Engineers, UFC 3-340-02: Structural to Resist the Effects of Accidental Explosions, Washington, 2008. [26] ASCE, Blast Protection of Buildings, American Society of Civil Engineers, Virginia, 2011.
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Original Research Article
Experimental study of water tank under impulsive loading Y. Wang *, S.C. Lee Department of Civil and Environmental Engineering, National University of Singapore, Singapore
article info
abstract
Article history:
The performance of stainless steel water tank subjected to impulsive loading was experi-
Received 24 May 2014
mentally studied in this paper. The gas gun was utilized to activate the projectile with high
Accepted 18 September 2014
impact velocity. The activated projectile then impinged the impact transfer plate which
Available online xxx
pressed the airbag behind it. The inflated airbag between the impact transfer plate and water tank was adopted to transfer the impulsive loading from impact transfer plate to the water
Keywords:
tank. The ultra-thin pressure sensors were placed between the airbag and water tank to
High velocity impact
record the pressure imposed onto the water tank and the potentiometers were attached at
Water tank
the back of water tank to record the displacement histories. The water tanks with two
Impulsive loading
different front and rear plate thicknesses were investigated. In addition, the same water tank with and without filled water was compared to study the water effects on the response of
Gas gun
water tank under impulsive loading. Besides the experimental studies, the FE method was adopted to reproduce the experiment and improve the current test method. Finally, the experimentally verified FE models were further used to study the water effects in reducing the deformation of water tank under blast loading. # 2014 Politechnika Wrocławska. Published by Elsevier Sp. z o.o. All rights reserved.
1.
Introduction
The probability of bomb attack on structure has seen an increasing trend in recent years. Consequently, many critical buildings were designed for blast resistance either in the before-built design stage or by means of retrofitting with additional protective layers. Since the probability of the occurrence of blast threat is usually very low, the benefits of adopting a blast-mitigating or blast-enhanced design could be maximized by considering other aspects of the buildings operations such as sustainability and energy efficiency. The
water tank system was proposed to harvest solar energy and meanwhile reduce the thermal heat penetration into buildings in hot climate region. Its energy saving performance has been studied by numerical method [1]. Since the current water tank has potential blast resistant function, this work aims to study the performance of water tank under blast loading to extend the multi-uses of current water tank system and evaluate the workability of utilizing inflated airbag to generate blast loading. Water effects on blast wave mitigation have been studied by experimental and numerical methods for decades [2–8]. Both experimental and numerical results showed that water
* Corresponding author. Tel.: +65 94654835. E-mail addresses: [email protected], [email protected] (Y. Wang). http://dx.doi.org/10.1016/j.acme.2014.09.006 1644-9665/# 2014 Politechnika Wrocławska. Published by Elsevier Sp. z o.o. All rights reserved.
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had significant effects on mitigating blast wave, especially for the case that water was stored close to the explosive. The principle of water in mitigating blast wave is that the high pressure shock wave produced by detonation aerosolizes the water placed close to the explosive and causes both a phase change of water and the redistribution of internal and kinetic energy over the detonation gases, blast wave and barrier material [8]. The aforementioned research on water mitigation effects on blast wave was based on the scenario that water directly interacts with blast wave. However, the research on confined water effects on water tank's response has so far been little. Since confined water does not interact with blast wave, it cannot reduce the blast loading. In addition, the energy dissipation by confined water under blast loading is usually little due to the high bulk modulus and extremely small viscosity of water. However, confined water still can reduce the water tank's response by increasing the overall mass and ensuring the front and rear plate deforming together to absorb the blast energy. The blast loading is an impulsive loading which has extremely high pressure and short duration. The field explosive detonation is a conventional method to generate the blast loading [9–14]. However, the disadvantages of this method are that it is generally quite expensive and a long planning time is also needed. Due to the limitation of the field blast test, many other methods have been proposed to generate the impulsive loading. Shock tube is one of these methods. It is generally less expensive than field blast test and the loads are more reproducible. However, the specimen size is limited by the size of shock tube and the loading duration is relatively longer compared with field blast test [15]. Hence, it is more suitable for simulating far range blast loading. Whisler and Kim have developed a non-explosive test method for generating dynamic blast-type pressure pulse loading [16]. However, only impulse can be recorded in the test, while the pressure –time history is difficult to record. The pressure – time history is necessary for analyzing the specimen if the response of the specimen enters into dynamic or quasi-static response regime. A simple blast load simulation system has been proposed by Mostaghel [17]. As shown in Fig. 1, the invention comprises a test panel and a membrane mounted
within a frame system. The membrane in conjunction with the panel forms an airtight chamber. The airtight chamber is inflated with air before testing. The plate is dropped onto the membrane at various heights to achieve the required impulse magnitude and duration. This method is simple and can be easily conducted in the laboratory. Chen and Hao adopted this method and utilized the inflated airbag as the airtight chamber to investigate the multi-arch double-layered panel under impulsive loading [18]. Remennikov et al. also extended this method to simulating the column under impulsive loading [19]. In this study, this method was also adopted to generate impulsive loading since it is cheaper and easier to conduct in the laboratory compared with other methods. The limitation of this test is similar to the shock tube test, i.e. the loading duration is relatively long. This is due to the fact that the velocity of projectile is quite low due to the drop height limitation of the test equipment. In this study, the gas gun was adopted to activate the projectile with velocity up to 478.4 m/s. This paper starts with a description on the experimental studies on the water tanks under impulsive loading, following by the FE analysis. The solution to overcome the deficiencies of current test method has been presented and the water effects in reducing the deformation of water tank have been discussed.
2.
Description of specimens
The dimension of stainless steel water tank is shown in Fig. 2. Two stiffeners with cut-out holes for water flow were fully welded to the front and rear plate to increase the out-of-plate stiffness. The front and rear plates were extended out and five holes were drilled on the extension to connect the tank to the support system. There were totally three specimens being fabricated, i.e. S1.5, S2 and W2. The stainless steel 316 was adopted for the outer skin and stiffener of water tank, since it has better performance on corrosion resistance than mild steel. The specification of these specimens is given in Table 1. For all the specimens, the thickness of top plate, bottom plate, side plate and stiffener was 2 mm. The front and rear plate thickness was different, as given in Table 1. S1.5 and S2 were designed to study the effects of front and rear plate thickness on the response of water tank. S2 and W2 were designed to study the effects of water on the response of water tank.
Table 1 – Specification of all specimens. Specimens
Fig. 1 – Blast loading simulation system [17].
S1.5 S2 W2
Stainless steel 316
fy (MPa)
E (GPa)
308.6
198.3
Front/rear plate thickness (mm)
Water infilled
1.5 2 2
No No Yes
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3
Fig. 2 – Dimension of water tank.
3.
Test setup
The gas gun system used in this test consists of compressed gas tank, gas gun, pipe and rigid box, as shown in Fig. 3. The compressed gas tank was utilized to supply high gas pressure to the gas gun. The regulator in the compressed gas tank was utilized to control the output gas pressure and the digital
pressure gauge was connected to the gas gun to measure the gas pressure inside the gas gun. After charging gas, the initial gas pressure inside the gas gun was significantly higher than the ambient pressure. When the trigger was on, the compressed gas would push the projectile from gas gun to the pipe and activate the projectile with high velocity. Then the projectile would move along the pipe and impact the specimens inside the rigid box. The rigid
Fig. 3 – Gas gun system. Please cite this article in press as: Y. Wang, S.C. Lee, Experimental study of water tank under impulsive loading, Archives of Civil and Mechanical Engineering (2015), http://dx.doi.org/10.1016/j.acme.2014.09.006
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Fig. 4 – Schematic diagram of test setup.
box was designed to prevent the projectile from hitting people. The schematic diagram of test setup is given in Fig. 4 and the main procedures of setting up the specimen are shown in Fig. 5. The specimen was connected to the two beams on the support through five bolts on each beam, as shown in Fig. 5(a) and the details of bolt connection is given in Fig. 4(b). The beam
was connected to the support plate through bolt connection. As shown in Fig. 4(c), a connection bolt is screwed into the beam in the one end and goes through the hole on the support plate in the other end. Hence, the beam was restrained in translational movement and only the rotation was allowed, which provided an axially restrained boundary condition for the specimen. The water tank can develop tensile membrane
Fig. 5 – The procedures of setting up specimen. Please cite this article in press as: Y. Wang, S.C. Lee, Experimental study of water tank under impulsive loading, Archives of Civil and Mechanical Engineering (2015), http://dx.doi.org/10.1016/j.acme.2014.09.006
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Fig. 6 – Projectile and impact transfer plate after impact.
force with this boundary condition and its resistance and ductility can be significantly improved compared with simply supported boundary condition. The whole support system was fixed to the rigid base plate through bolt connection. After setting up the specimen, the airbag (250 mm 250 mm 40 mm) was placed in the front of the specimen, as shown in Fig. 5(b). The initial pressure inside the airbag was equal to the ambient air pressure. The impact transfer plate was placed at the front of the airbag and four bolts were utilized to ensure the impact transfer plate at the right position before impact, as shown in Fig. 5(c). The top plate was also positioned on the top of airbag. The top plate, bottom plate and support plate were utilized to form a confining space for the airbag, as shown in Fig. 5(c). The impact transfer plate consists of two steel plates which were glued together. The dimensions of these two steel plates are 100 mm 100 mm 20 mm and 250 mm 250 mm 4 mm. The purpose of attaching a 20 mm thick steel plate in front was to avoid the perforation of projectile. The cylinder projectile was adopted in this test with dimension of 19.5 mm 26.5 mm (diameter length). In this test, the ultra-thin pressure sensors were placed between the airbag and specimen, as shown in Fig. 5(a) to record the pressure imposed onto the specimen. The velocity of projectile before impact was measured utilizing the laser system. The time interval of the projectile going through the
5
two laser points was recorded and the velocity of projectile was obtained by dividing the distance between the two laser points by the time interval. The potentiometers were utilized to record the displacement–time histories of the specimens and support, as shown in Fig. 5(d). It was found in the test that the displacements of the support and specimen were comparable. Hence, one potentiometer was attached to the support at the mid-span to record the displacement–time history of the support. The actual displacement of the specimen at mid-span can thus be obtained by subtracting the support displacement from the measured displacement of specimen. The signals from pressure sensors were captured by ELF data acquisition system from Tekscan, Inc. The signals from laser and potentiometers were captured by DL 1200A digital oscilloscope and DL 7500 digital oscilloscope, respectively.
4.
Test results and discussion
For all the three specimens, the projectiles were activated by the gas gun with initial pressure of 18 MPa and the velocity of activated projectile before impact varied from 442.4 to 478.4 m/ s. Fig. 6 shows the projectile and impact transfer plate after impact test. It can be observed that the indentation is evident on the impact area of impact transfer plate and the projectile is shortened due to the dramatically high impact pressure. The recorded pressure–time histories of pressure sensors for S1.5 are given in Fig. 7. Since the highest sampling rate of ELF data acquisition system is 5.7 kHz which is not high enough to capture the variation of the pressure, the recorded pressure–time histories may not accurately represent the pressure imposed onto the specimen. Although the ELF data acquisition system failed to provide the exact pressure–time history imposed onto the specimen. It still reflected some characteristics of the contact pressure between the airbag and specimens. It can be seen from Fig. 7 that the duration of the contact pressure is shorter compared with the low velocity impact test using airbag in Refs. [18,19], which is proven that increasing the projectile velocity is a way to shorten load duration. Besides, the peak contact pressure at center is higher than the other two points. This non-uniform pressure
Fig. 7 – Pressure–time histories of pressure sensors. Please cite this article in press as: Y. Wang, S.C. Lee, Experimental study of water tank under impulsive loading, Archives of Civil and Mechanical Engineering (2015), http://dx.doi.org/10.1016/j.acme.2014.09.006
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distribution may be due to the fact that the severe deformation of the impact transfer plate caused by the local impact of high velocity projectile provides a non-uniform pressing on the airbag. This non-uniform pressing can cause the shock wave propagation starting from center, which may give higher pressure at center and lower pressure at periphery, as shown in Fig. 8. By analyzing the test results in this paper and in Refs. [18,19], it is found that the utilizing of inflated airbag to simulate blast loading still has some deficiencies. If the low velocity projectile is adopted, the contact pressure is almost uniform and the contact pressure equals to the air pressure inside the airbag [18,19]. The measurement of pressure inside the airbag is much easier than measuring the contact pressure. However, the duration of contact pressure by using low velocity projectile is very long (usually more than 0.1 s), which may be different from real blast load. Hence, the behaviors of the specimen may also be different when it subjects to real blast load and simulated pressure load using low velocity projectile impact. For instance, the specimens in reference 19 were all within quasi-static response regime, while the structure is usually within impulsive and dynamic response regime under blast load. It is widely accepted that the behaviors of structure are different in different response regimes, such as failure mode and deflection shape. Taking the simple supported Reinforced Concrete (RC) beam for instance, the shear failure mode is more likely to occur in the impulsive response regime and flexure failure mode is more likely to occur in the quasi-static response regime. If the high velocity
3.5 Midpoint displacement(mm)
6
S1.5 S2 W2
3 2.5 2 1.5 1 0.5 0
0
0.005
0.01
0.015
Time(s)
Fig. 9 – Midpoint displacement–time histories of specimens.
projectile impact test using airbag is adopted, the contact pressure duration is short. However, the contact pressure is not uniformly distributed. Therefore, this method must be improved to better simulate the blast load. Based on above analysis, one possible solution is to use a rigid impact transfer plate to provide a uniform pressing on the airbag and the workability of this method will be investigated using FE method in the next section. Since some of the kinetic energy of the projectile was absorbed by the plastic deformation of projectile and impact transfer plate during the impact procedure, all the three specimens underwent elastic deformation. The displacement –time histories of specimens are given in Fig. 9 and the information on projectile velocity and maximum midpoint displacement is listed in Table 2. It is observed from Fig. 9 that all the displacements of specimens continuously increase to their maximum values after impact. The maximum displacements of specimens are listed in Table 2. By comparing the maximum midpoint displacements of S1.5 and S2, it is found that the displacement of S2 is slightly larger than that of S1.5. The possible reason is that the projectile velocity of S2 is higher than that of S1.5. It is believed that the specimen S2 with thicker front and rear steel plate will have smaller displacement if the projectile velocity is identical. By comparing the maximum midpoint displacements of S2 and W2, it is noted that the displacement of W2 is reduced compared with S2 under the similar projectile velocity impacting. Hence, the water effects in reducing the deformation of water tank was demonstrated through experimental study and FE analysis will be carried out to further study these effects.
Table 2 – Impact information on specimens. Specimens S1.5 S2 W2
Fig. 8 – Shock wave propagation inside the airbag during impact.
V (m/s)
Dmax (mm)
442.4 478.4 476.1
2.79 3.02 2.37
Note: V – velocity of projectile before impact; Dmax – maximum midpoint displacement of specimen.
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1200
Numerical investigation
The explicit code in LS-DYNA [20] was adopted to simulate the behaviors of water tanks under impulsive loading in order to verify the test method and investigate the water effects in reducing the deformation of water tank under blast loading.
5.1.
1000
True stress (MPa)
5.
800 600 400 200
FE model
0
The whole process of the high velocity impact test was captured by the FE model, which includes the water tank, water, support, airbag, air, impact transfer plates and projectile. Fig. 10 gives the FE model of W2 and only quarter FE model was built due to symmetry. The shell element was adopted for water tank, stiffener, airbag, 4 mm thick impact transfer plate and confined plate, as it can capture the performance of thin plate components and reduce the computing time compared with fine solid element. While the eight-node solid element was adopted for water, air, 20 mm thick impact plate, beam, bolt and support. The Eulerian formulation, which is ideal for modeling fluid problems, was applied for water and air in the FE model. It should be mentioned that the mesh surrounding water and air, which allowed the materials to flow, was built in the FE model but not shown in Fig. 10 to avoid blocking other components. The Lagrange formation, which is generally suitable for elements without severe element distortion, was applied for the other elements. The penalty fluid–structure coupling method in LS-DYNA was used to model the interactions between the water tank and water, and the airbag and air. While the penalty-based surface to surface contact option was used to model the contacts between the elements with Lagrange formulation.
0
0.1
0.2
0.3
0.4
0.5
0.6
Effecve Plasc Strain
Fig. 11 – True stress-effective plastic strain curve of stainless steel 316.
5.2.
Material models
The piecewise linear plasticity material model was adopted for stainless steel 316. For this material model, an arbitrary stress versus strain curve and arbitrary strain rate dependency can be defined and the failure based on a plastic strain can also be defined. The material properties of stainless steel were obtained from the tensile coupon test and the input true stress-effective plastic strain curve is shown in Fig. 11. In this material model, the Cowper–Symonds model is adopted to scales the yield stress as 2 !1=P 3 p e_ eff p p p 4 5 (1) s y ðeeff ; e_ eff Þ ¼ s y ðeeff Þ 1 þ C p
where s y ðeeff Þ is the yielding stress without considering strain p rate effects, e_ eff is the effective plastic strain rate, C and P are the strain rate parameters. In this study, the strain rate parameters C and P were 240 and 4.74 for stainless steel 316 [21]. The elastic plastic material model was adopted for mild steels and the material properties are given in Table 3. The Cowper– Symonds model is also adopted in this material model to capture the strain rate effects and the strain rate parameters C and P were 40.4 and 5 for mild steel [22]. The elastic material model was applied for airbag, since there was no plastic deformation of airbag after test. The airbag is made of polyvinyl chloride (PVC) material and the Young's modulus is 3.38 GPa [23]. The null material model was used to describe the deviatoric response of air and water. The linear polynomial equation of
Table 3 – Material properties of mild steels. Material S355
Fig. 10 – FE model of W2.
AISI 1045
Component
fy (MPa)
E (GPa)
Impact transfer plate, confined plate, bolt, support and beam Projectile
355
200
375
200
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3.5
r0 (kg/m3) 1.290
E (MPa) 0.253
C0 (MPa)
C1–C3
0.1
0
C4
C5
0.4
0.4
C6 0
state was used to simulate the volumetric response of air, which is written as P ¼ C0 þ C1 m þ C2 m2 þ C3 m3 þ ðC4 þ C5 m þ C6 m2 ÞE
(2)
where m ¼ r=r0 1, r is the current density, r0 is the initial density, E is the initial internal energy per unit reference volume, and C0–C6 are parameters of the equation of state. The material properties of air are given in Table 4. The Gruneisen equation of state with cubic shock velocity–particle velocity (Vs–Ps), which was used to simulate the volumetric response of water, is given by P¼
r0 C2 m½1 þ ð1 g 0 =2Þm a=2m2 2
½1 ðS1 1Þm S2 ðm2 =ðm þ 1ÞÞ S3 ðm3 =ðm þ 1Þ2 Þ
þ ðg 0 þ amÞE
(3)
for compressed material and is given by Eq. (4) for expanded material P ¼ r0 C2 m þ ðg 0 þ amÞE
(4)
where C is the intercept of the Vs–Ps curve, S1, S2 and S3 are the coefficients of the slop of the Vs–Ps curve, g 0 is the Gruneisen gamma, a is the first order volume correction to g 0 . The material properties of water are given in Table 5 [24].
5.3.
Results and discussion
The midpoint displacement–time histories of the water tanks from FE analyses are compared with test results in Fig. 12 and reasonable agreement between the two can be seen from the comparison. The differences between the test results and FE analyses in terms of maximum midpoint displacement are 1.03%, 26.85% and 7.53% for S1.5, S2 and W2, respectively. All the FE predicted maximum midpoint displacements are smaller than the test results and the disparity between FE analysis and test for S2 may be introduced by the measurement errors in the test. Based on above comparison, the established FE model is reasonable and can be used to further investigate the test method and performance of water tank under blast loading. As discussed in Section 4, the non-uniform pressure on the water tanks is caused by the local impact of projectile, which results in the shock wave propagation starting from the center. This can be demonstrated by the plotting the contours of air
Table 5 – Material parameters of water [24]. r0 (kg/m3) 998.2
E
C (m/s)
S1
S2
S3
g0
a
0.0
1647
1.921
0.096
0
0.35
0
Midpoint displacement (mm)
Table 4 – Material parameters of air.
S1.5(Test) S2(Test) W2(Test) S1.5 (FE) S2(FE) W2(FE)
3 2.5 2 1.5 1 0.5 0
0
0.001
0.002
0.003
0.004
0.005
0.006
Time(s)
Fig. 12 – Comparison of FE predicted displacement–time histories with test results.
pressure in Fig. 13(a). It was also mentioned in Section 4 that the rigid impact transfer plate could be used to provide a uniform pressing on the airbag and therefore could provide uniform pressure on the water tank. Hence, the FE analysis was carried out to study the shock wave propagation with rigid impact transfer plate, which is shown in Fig. 13(b). The uniform pressure acting on the water tank can be observed and the air pressure is generally uniform in 0.35 ms after impact. The air pressure–time histories of different locations with rigid impact transfer plate are given Fig. 14. It can be seen that the air pressures of selected locations are very similar during the impact except for location E near the corner. This may be caused by the folded airbag at corner under compression. Since the air pressure on the water tank is almost uniform except for the corner, it is possible to measure the applied pressure on the water tank by recording the air pressure–time history. There are several types of pressure sensors with response time less than 5 ms available in the market, which makes it easier to obtain the accurate air pressure–time history. Therefore, this test method can be more reliable to generate blast loading if the rigid impact transfer plate is adopted. The experimentally verified FE models were further used to investigate the water effects in reducing the response of water tank under blast loading. In this analysis, the support was removed from the FE model and the axially restrained boundary condition was specified by restraining the displacements of the nodes along the two edges of front and rear plates in vertical and axial directions. The blast pressure–time history was applied onto the whole front plate. In this analysis, the triangle pressure profile with zero rise time, which is usually adopted in the blast resistant design [25,26], was adopted as the profile of blast loading. Fig. 15 compares the displacement–time histories of S2 and W2 under the same blast loading with peak pressure and load duration of 8 MPa and 0.5 ms, respectively. It is noted that the front and rear plate midpoint displacements of W2 with infilled water are reduced by 6.4% and 27.7% as compared to S2. This proves that water can reduce the deformation of water tank under blast loading. By comparing the front and rear plate displacement of S2 and W2, the front plate displacement is higher than the rear plate
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Fig. 13 – Shock wave propagation with different impact transfer plates.
for S2, which means that the blast loading is mainly taken by the front plate for S2. However, the rear plate deforms more than the front plate for W2, which indicates that water helps to transfer the blast loading from the front plate to the rear plate
and ensure them deforming together to absorb the blast energy. Based on above comparison, the principle of water effects in reducing the deformation of water tank is that the addition of water increases the overall mass and ensures the
Please cite this article in press as: Y. Wang, S.C. Lee, Experimental study of water tank under impulsive loading, Archives of Civil and Mechanical Engineering (2015), http://dx.doi.org/10.1016/j.acme.2014.09.006
ACME-263; No. of Pages 11
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A B C D E
0.45
Air pressure (MPa)
0.40 0.35 0.30 0.25 0.20 0.15
applied pressure on the water tank was uniform when adopting the rigid impact transfer plate and could be measured by recording the air pressure–time history. The principle of water effects in reducing the deformation of water tank is that the addition of water increases the overall mass and ensures the front and rear plate deforming together to absorb the blast energy.
0.10 0.05 0.00
references 0
0.001
0.002
0.003
0.004
0.005
Time (s)
Fig. 14 – The air pressure–time histories with rigid impact transfer plate.
Midpoint displacement (mm)
25 20 15 10
S2-front plate S2-rear plate W2-front plate W2-rear plate
5 0
0
0.0005
0.001
0.0015
0.002
Time (s)
Fig. 15 – Displacement–time histories of S2 and W2 under blast loading.
front and rear plate deforming together to absorb the blast energy. Both of them can reduce the front plate displacement (as shown in Fig. 15) and therefore can reduce the external work done by the blast loading. It is noted in the FE analysis that the external work of W2 is reduced by 45.1% compared with S2. Since the external work will transfer to the internal energy of water tank at final stage, the less external work will result in less deformation or damage to the water tank.
6.
Conclusions
The performance of stainless steel water tank subjected to impulsive loading was experimentally studied in this paper. The adopted test method for generating blast loading still has some deficiencies. The low velocity projectile impact test can provide a uniform pressure but the load duration is very long compared with field blast test. However, the high velocity projectile impact test adopted in this paper can provide an impulsive loading with shorter duration but the pressure is non-uniform. Hence, this method should be improved to better simulate the blast load. The possible solution has been provided and its workability has also been studied by using FE method. It was demonstrated by FE investigation that the
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