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c Pleiades Publishing, Ltd., 2015. ISSN 0010-5082, Combustion, Explosion, and Shock Waves, 2015, Vol. 51, No. 3, pp. 373–380. c M.D. Goel, Ph. Altenhofer, V.A. Matsagar, A.K. Gupta, Ch. Mundt, S. Marburg. Original Russian Text

Interaction of a Shock Wave with a Closed Cell Aluminum Metal Foam M. D. Goela , Ph. Altenhoferb , V. A. Matsagarc , A. K. Guptaa , Ch. Mundtb , and S. Marburgb

UDC 534.2

Published in Fizika Goreniya i Vzryva, Vol. 51, No. 3, pp. 98–105, May–June, 2015. Original article submitted November 1, 2013; revision submitted July 14, 2014.

Abstract: The present investigation examines the interaction of shock waves with closed cell aluminum foam samples in a conventional shock tube. The effect of the sample thickness on shock wave attenuation and/or enhancement and the use of the foam in the sandwich structure is studied. Results in terms of incident and reflected shock pressures are obtained, and the effectiveness of the samples with and without the foam is compared. It is demonstrated that the foam density and thickness, as well as the placement of cover plates of the same material in front of and behind the foam have the most significant effect on the reflected shock pressure. It is concluded that the closed cell aluminum metal foam can be effectively used as a sacrificial layer in blast protection of structures. Keywords: blast loading, metal foam, shock tube, shock wave, shock-foam interaction. DOI: 10.1134/S0010508215030144

INTRODUCTION Foams used in various engineering applications (especially in the field of blast and impact protection/mitigation) have shown significance due to their distinctive compressive stress–strain behavior. Two varieties of foams, namely, polymeric and metal foams, have diverse applications. For the protection of human lives, polymeric foams are used nowadays, especially due to their lighter weight. On the other hand, recent technical advances in metal foams have proven their usability in protecting industrial structures and allied services. This encouraged further research in the area of developing metal foams, which are more effective in protecting structures against blast events. a

CSIR-Advanced Materials and Processes Research Institute (AMPRI), Council of Scientific and Industrial Research (CSIR), 462064 Bhopal, India; [email protected]. b Institute of Thermodynamics, Department of Aerospace Engineering, University of German Armed Forces Munich, 85577 Neubiberg, Germany. c Department of Civil Engineering, Indian Institute of Technology (IIT) Delhi, 110016 New Delhi, India.

Generally, the stress–strain diagram of foam materials depicts three regimes: (i) a linear region at the initial elastic stage, (ii) a plateau region upon yielding, which is followed by (iii) a densification region due to compaction and plastic deformation. The plateau region is crucial in exploiting energy absorption because the strain in this region increases monotonically without a significant increase in stress. In the densification region, a higher stress is required to compress the foam material back into the solid material from which the foam was developed. Shock waves are generated by quick energy deposition, such as an explosion or rapid piston movement. Shock waves cause severe damage in enclosed spaces, rooms, near walls, and in trenches or bunkers where numerous reflections occur. In order to develop an effective protection/mitigation system against blasts, it is important to understand the mechanism of interaction of shock waves with materials used for this purpose. It is further essential to understand the propagation of a shock wave through materials in order to mitigate its devastating effect of the explosion [1]. It has been observed by many researchers that foams can amplify the

c 2015 by Pleiades Publishing, Ltd. 0010-5082/15/5103-0373

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374 shock wave pressure [2]. Gel’fand (see [3]) carried out experiments and showed the pressure amplification by a foam material for the first time. He concluded that the amplification might be a result of a transfer of the momentum acquired during the full compression of the foam. Monti [4] studied the normal reflection on deformable walls and observed the amplification of the wall pressure. Borisov et al. [5] showed that porous media can be used to protect the surrounding medium from the effects caused by shock waves. Gel’fand et al. [6] presented the influence of gas–foam and foam– gas interfaces on shock wave reflection, enhancement, and attenuation. Gvozdeva et al. [7] presented results on pressure reflection, transmission, and attenuation for a polyurethane foam and formed plastics. Yasuhara et al. [8] studied the interaction of a one-dimensional shock wave with rubber and low-porosity foam experimentally, analytically, and numerically, and reported the pressure amplification in terms of the dynamic load factor (DLF). Kitagawa et al. [9] studied the attenuation of shock waves propagating in polyurethane foams experimentally and numerically, and reported the impulse and attenuation factor in relation with the number of foam cells and the foam cell structure. Further, structures exposed to blast loading were analyzed experimentally under the influence of shock waves generated by explosives that detonated at some distance away from the structure and in shock tubes [10–15]. Skews [16] analyzed soft materials experimentally, and Baer [17] presented a theoretical analysis of such materials. Lagutov and Gvozdeva (see [3]) observed a complex amplifying response of an elastically loaded foam material. Henderson (see [3]) observed different regions of amplification and attenuation, and presented a concept of a region where the foam can attenuate the shock wave pressure depending upon weak and strong shocks. Ouellet et al. [18] studied the response of a polymeric foam to blast and shock loading, and presented a comparison of these two types of loading of the same material. Seitz and Skew [19] examined the effect of porous open cell compressible metal foam properties on pressure amplification under shock loading. Wang et al. [20] studied the blast resistance of sandwich composites made of E-glass vinyl ester composite face sheets and stepwise graded styrene foam cores using a shock tube and presented a method for calculating the incident, reflected, and deformation energy. Bouamoul [21] carried out a finite element study to predict the response of a polymeric foam to both shock tube and free-field loading, and discussed the comparison with experimentally observed results. Based on the study of past literature, it is observed that the earlier research was focused on the interac-

Goel et al. tion of shock waves with polymeric foams and the pressure attenuation and/or enhancement mechanism under shock loading. However, very few studies have been carried out on the interaction of metal foams (especially, closed cell aluminum metal foams) with shock waves in a shock tube. Furthermore, the mechanism responsible for the amplification or attenuation of the blast wave overpressure caused by the presence of the foam still requires confirmation. This indicates an immediate need for research on metal foams and their interaction with shock waves in a shock tube. Hence, the present investigation has been focused on studying the shock attenuation/enhancement capability of a low-density metal foam, in the form of a pure sample and as a sandwich structure, experimentally by exposing it to shock wave loading. The results will help in understanding the performance and the mechanisms of failure of the metal foam under shock loading, and provide a guideline for a better protective design of structures.

1. FOAM MATERIAL Aluminum foams used in the present investigation were developed through the liquid metallurgy route at the Advanced Materials and Processes Research Institute (AMPRI), Council of Scientific and Industrial Research (CSIR), Bhopal, India. The foam was developed by adopting the following steps: (i) melting of the alloy, followed by (ii) dispersion of calcium hydride (CaH2 ) particles in the melt, (iii) allowing short duration of the melt at the foaming temperature for completion of foaming, (iv) immediate cooling of the crucible in which the foaming was carried out through forced air, and (v) ejection of the foam from the crucible after cooling [22–24]. The foaming temperature was varied in the range of 675–695◦C with an interval of 5◦ C to achieve different relative densities of the foams. Figure 1 shows a bulk aluminum fly ash foam sample and its microstructure. The density of this foam was determined by weighing each foam sample, dividing its mass by its volume, and averaging the obtained values of all samples. Different lengths and combinations of foam samples were used for testing purposes. Further, the relative density (RD) of the foam was computed and expressed as the ratio of the density of the foam material to the density of the solid material from which the foam was developed. The relative density of the foam used in the present investigation varies as RD = 0.100– 0.114, and it is to be noted that the foam considered in the present investigation has a closed cell structure.

Interaction of a Shock Wave with a Closed Cell Aluminum Metal Foam

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Fig. 1. Representative closed cell aluminum foam.

2. SHOCK TUBE SETUP

Fig. 2. Quasi-static compressive stress–strain behavior of the closed cell aluminum foam.

Quasi-static compression tests on the developed foam were conducted at CSIR-AMPRI by using a BiSS Universal Testing Machine (Model Bi-00-002, 50 kN load cell) at a strain rate of 0.001 s−1 [22–24]. For compression testing, specimens were cut from the fabricated foam with average cross-sectional dimensions of 40×45 mm and 55 mm in height. The load-displacement data were recorded during the testing and converted to stress–strain curves by using a standard procedure. A typical compressive stress–strain curve of the closed cell aluminum fly ash foam is shown in Fig. 2, clearly indicating three regions as described earlier: (i) linear elastic region, (ii) plateau of the plastic collapse region, and (iii) densification region.

In the present investigation, all the experiments were carried out in a shock tube. Shock tube testing has an advantage of being less expensive than actual field blast tests. The shock tube allows many tests to be completed in a short time as compared to field blast tests. Moreover, the shock tube offers good repeatability of experimental data, as these experiments are performed in the laboratory under more controlled conditions than field blast tests. Due to its capability of producing uniaxial strain conditions, the pressure wave generated in the shock tube can be applied directly to material testing. A double-diaphragm shock tube with a constant circular cross section located at the Institute of Thermodynamics, University of German Armed Forces Munich, Germany was used in the present investigation [25]. The driver section of this shock tube is 1.53 m in length. A steel plate 200×200 mm in size and 45 mm in thickness covers the inlet end of the driver. The maximum driver pressure of the facility is 10 MPa. The samples are placed under simply-supported conditions in the cavity of the end section of the shock tube. The driver section is separated from the driven section by two diaphragms and a valve section. The driven section is 8.33 m long with flanges similar to those used on the driver section at both ends. The tube has an inner diameter of 100 mm with a wall thickness of 7.5 mm and is made of high-strength steel. The double-diaphragm section between the driver and driven sections has a length of 0.03 m. Earlier this shock tube was used for gas dynamic studies; consequently, the end section of this shock tube was modified to accommodate the foam material. For this purpose, a specially designed fixture was developed and used for holding and testing of the foam samples. Steel diaphragms of different burst pressures were used for varying the driver and driven pressures.

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Pressurized dry air used to load the driver section and rupture the diaphragm was provided by an industrial duty air compressor. A pressure gauge was mounted in the inlet line of the driver section to monitor the driving pressure until the diaphragms burst. All the tests were conducted with air as both the driver and driven gas. The shock tube was instrumented with two piezoelectric pressure sensors of the Kistler type 603B, which were utilized to obtain the shock wave profiles. The signals of the sensors were amplified by charge amplifiers (Kistler type 5011) and recorded with an oscilloscope (LeCroy 9304AM). The sampling rate in recording pressure was 100 MHz.

3. DYNAMIC LOAD FACTOR Yasuhara et al. [8] defined the dynamic load factor as DLF = ΔP5,layer /ΔP5 , where ΔP5 is the reflected pressure from a rigid wall recorded by a sensor placed at the end of the tube and ΔP5,layer is the maximum pressure recorded by a sensor also placed at the end of the tube, but under the layer of the test material. However, in the present shock tube setup, the sensors were placed in front of the foam specimen: sensor 2 was placed close to the front face of the foam sample and sensor 1 was placed at a distance of 5 cm from sensor 2. The DLF value was used for understanding the effect of the presence/absence of the metal foam.

4. EXPERIMENTAL RESULTS AND DISCUSSION The measured incident shock pressures were of the order of 0.35 MPa, with the initial shock wave velocities of 760 m/s. The initial pressures for the air/air experiments in the driver section and driven section were 97 bar and 900 mbar, respectively. The table shows the details of tests carried out in the present investigation. The diameter of the foam samples used in the present investigation was d = 85 mm, and the sample thickness was varied: L = 50, 45, and 40 mm. Sandwich samples (with a total thickness of 50 mm) were also used in the study (Fig. 3). The samples touched the end wall of the shock tube section and were held in this position by a sample holder designed for these experiments.

Details of foam samples and sandwich structures Sample

d, mm

Foam sample

Sandwich ∗ 40

85

structure∗

85

L, mm

RD

50

0.114, 0.107, 0.100

45

0.114

40

0.114

50

0.114, 0.100

mm foam + 5 mm aluminum cover plates on each face.

4.1. Calibration of Shock Tests First, an initial test was carried out without placing any foam sample with an aluminum rigid end wall to observe the incident and reflection pressure time traces at a theoretical Mach number of 2.39 (Fig. 4). However, it is to be noted that the measured Mach number is lower than the theoretical Mach number. This is attributed to the fact of associated losses during the shock wave travel in a long shock tube. Nevertheless, it can be observed from these figures that, in the case of a perfectly rigid surface, there are no vibrations after the shock wave is reflected from the rigid end. The ratio of the reflected pressure to the incident pressure is around 2.0, which is the case for the metal loaded in the linear stress–strain region [8, 26]. 4.2. Shock Tests of Foam Samples Figure 5 shows the DLF values for a 50-mm foam sample placed at the end section and subjected to the same level of Mach number loading as the reference test for RD = 0.100, 0.107, and 0.114. When the incident shock wave interacted with the front face of the foam material, it resulted in a reflected compression wave, which moved in the opposite direction to the foam sample and caused foam compression. The vibratory nature of the pressure time history depicts the fact that the foam was moving backward at this point of time. Further, it can be observed from Fig. 5 that there was a steep rise of pressure due to the shock wave; subsequently, after reaching a peak value, it turned to a dumping vibration mode due to the presence of the foam material. Moreover, it can be observed that the presence of the foam resulted in enhancement of the reflected pressure in comparison with the incident pressure; this, in turn resulted, in the DLF value of 2.92. This is attributed to the fact that the incident pressure was in the range of the elastic region of the foam, causing enhancement of the reflected pressure. A similar behavior was also observed by Ouellet et al. [18]


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Fig. 3. Representative foam samples for shock tube tests.

Fig. 4. Normalized profiles of the incident and reflected shock waves in the shock tube with an aluminum rigid end wall.

for polymeric foams if the pressure remained within the elastic region. The DLF for this case was calculated to be 2.92, indicating the rise of the pressure to a higher level in comparison to the case when only the rigid wall was present. The inspection of the foam sample after the test showed partial compression of the foam. This implies that the pressure applied had not been able to fully compress the foam material; it rather resulted in reflected pressure enhancement because the pressure was only up to a level in the elastic region of the foam material. Similar observations were made for foam samples with other densities; however, it is observed that the foam density affects the reflected pressure considerably. Based on the experimental tests conducted for RD = 0.114, the value DLF = 2.92 was observed, whereas the DLF value in the case with the relative density of the foam equal to 0.100 was 2.5 for all other experimental conditions being same.

4.3. Shock Tests on Sandwich Foam Samples Figure 6 shows the DLF values for two different densities of the foam samples in the sandwich structure (0.100 and 0.114) subjected to the same loading as the other samples. It can be observed that the change in density resulted in enhancement of pressure approximately to 3.4, but eventually resulted in faster dumping of vibrations returning almost to the original incident pressure. After the test, the inspection of the foam sample showed that the foam was compressed to a higher level as compared to the pure foam case. This is attributed to a higher momentum transferred to the foam sample because of the difference in densities of the front and core materials of the sandwich structure. Similar observations were made for another foam density in the sandwich foam sample. It is observed that, while using metal foams for blast applications, it is important to place and design the structure only for the loading

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Fig. 6. Normalized profiles of the incident and reflected shock waves in sandwich samples with foams of different relative densities.

Fig. 5. Normalized profiles of the incident and reflected shock waves in 50-mm thick aluminum foam samples with different RD values.

region near to the plateau stress region of the foam material because the foam behavior for different levels of blast loading is altogether different. It is observed that the pressure profiles (represented in terms of the DLF) of the incident shock wave recorded by sensor 1 differ in Figs. 5 and 6. This is attributed to the sensitivity of the pressure transducers to vibrations of the shock tube during the test. Several tests were carried out to confirm this factor, and similar results were observed. Further, the foam samples were placed under simply supported conditions in all the experiments. Due to the incident shock wave, the foam samples were compressed; at the same time, these samples loosened around their perimeter, which resulted in vibrations due to multiple reflections within and near the foam. This behavior of the foam samples resulted in the wave profiles recorded by the sensors. Moreover, it is observed that the pressure profiles measured by the sensor closest to the specimen differ considerably from the profiles measured by the distal sensor, which is attributed to the overload in sensitivity.

4.4 Shock Tests with Varying Thicknesses of Foam Samples Figure 7 shows the pressure time histories (represented in terms of the DLF) for foam samples 40 and 45 mm thick with a relative density RD = 0.114. It can be observed that the foam thickness affects the DLF considerably. In the present investigation, foams of three different relative densities were used. In the high-density foam, the incident shock was less penetrative, and the mobility of the gas inside the foam diminished. However, in the present investigation, the foam pores (closed pores) were crushed to the state in the densification region. This resulted in a dumping and diminishing type of the reflected shock response, as observed in the case of the sandwich type structure.

CONCLUSIONS The interaction between aluminum closed cell foams of different densities and lengths of samples with a shock wave is studied experimentally. Results from the shock tube study show that the foam density and


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deswehr Munchen, Germany) for their help and support in completing the reported experimental investigation. The doctoral scholarship received by the lead author from the German Academic Exchange Service, i.e., DAAD (Deutscher Akademischer Austausch Dienst), for completing the reported investigation is gratefully acknowledged.

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thickness, as well as the placement of cover plates in front of and behind the foam, have a considerable effect on the reflected pressure histories. Based on this study, it is observed that, while using metal foams for blast applications, it is important to place and design the structure only for the loading region where the blast loading is near the plateau stress region of the foam material because the foam behavior for different levels of blast loading is altogether different. The use of sandwich foam samples resulted in a faster rate of diminishing vibrations as compared to the foam only, indicating the effectiveness of the composite behavior. The dynamic load factor is found to increase from 2.0 for a perfectly rigid material to 2.92 for the foam with a relative density of 0.114 and to 3.4 for the sandwich structure, respectively. However, in the case of the sandwich structure, it resulted in a very fast decay of pressure, which is a desirable phenomenon in the development of a blast protection system in the form of a sacrificial layer. The lead author (M. D. Goel) expresses his gratitude to Prof. K. Hornung and W. Hallmannseder (Department of Aerospace Engineering, University of the German Armed Forces Munich (Universität der Bun-

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