Energy Absorption under Quasi-static Compression and Impact in Cellular Al-Si12 with Different Pore Shape and SizeAbstract
Equiaxed and rounded pore cellular metals with five different size ranges based on an aluminium-silicon alloy were fabricated by a soluble particle infiltration technique, in order to evaluate and compare their energy absorption capacity under impact and quasi-static compression. Under compression, the equiaxed cellular metal with the smallest pore size (4-4.75 mm) recorded the highest energy absorption (4.9 MJ/m3). In addition, the equiaxed pore cellular metals exhibited an energy absorption capacity 68.2% higher than that of the rounded pore ones. Under impact, for a standard strain of 9.8%, the highest energy absorption capacity was presented in the equiaxed cellular metal with the largest pore size (9.5-11.2 mm). In turn, the energy absorption in equiaxed pore cellular metals was 53.1% higher than that of the rounded pore ones. Cellular metals of both pore shapes showed a higher energy absorption capacity under impact. Therefore, it is concluded that this property varies depending on the shape and size of the pore, but also with the deformation rate.
Keywords:
Cellular metals; infiltration process; quasi-static compression; impact; energy absorption; pore size; pore shape
1. Introduction
In order to expand the applications of metals and imitate the porous structures that form in nature, man has manufactured cellular metals1,2. A cellular metal is a three-dimensional artificial cellular solid, formed by a metal matrix and a set of small polyhedral compartments called cells or pores3,4. The properties of these materials depend on the metal of the matrix and the porous structure, and these, in turn, depend on the manufacturing technique used5-7.
These materials are characterized by their low density and high porosity, in addition to exhibiting novel physical, mechanical, thermal, electrical, and acoustic properties, including high strength-to-weight and stiffness-to-weight ratios, sound insulation, thermal energy dissipation, and above all, high energy absorption capacity when subjected to static and dynamic forces2,8. This novel combination of properties makes cellular metals suitable for use in various engineering sectors, such as automotive, structural, aerospace, defense, acoustic, railway, and biomedicine9-11.
Due to their ability to absorb mechanical energy, cellular metals are part of a group of materials called energy absorbers12,13, which are systems and/or materials that convert kinetic energy into another form of energy. The converted energy can be reversible, for example, elastic strain energy in solids, or it can be irreversible, for example, plastic strain energy12.
Historically, energy absorber designs have evolved from simple, monolithic structures that provided basic impact resistance to more sophisticated multicellular designs capable of distributing loads more efficiently14. The demand for lightweight structures with high energy absorption capacity is increasing for application in various fields of engineering. Consequently, various energy absorbers with different structures, such as columns, sandwich structures, plates, honeycombs, and foams, have been proposed in recent years. While the cited studies have demonstrated significant capacity for energy absorption, these structures have not yet been optimized13. Therefore, the development of advanced energy absorbers has become a critical area of research, driven by the need to improve safety and efficiency in various engineering applications, particularly in motor vehicle accidents. Drawing inspiration on natural structures such as animal bones, plant stems, and microstructural features, researchers have developed innovative designs that offer superior energy absorption, weight efficiency, and adaptability to complex loading conditions14. Because the energy generated, especially at high strain rates, is too high to be absorbed by bare foams, it has been found that filling thin-walled sections with foam can significantly improve energy absorption capacity. This increase is mainly attributed to the interaction between the foam filling and the tube wall12.
To determine the energy absorption capacity of cellular metals, samples are subjected to compression tests either quasi-static or dynamic, unit stress-strain curves are obtained from the test data, and the area under the curve between zero strain and densification strain is integrated15,16. The energy absorption behaviour in cellular metals under impact is very different compared to the behaviour under quasi-static compression, since the dynamic energy absorption properties of these are closely related to the propagation and reflection of shock waves plastic under impact loads17-19.
In the manufacture of cellular metals, a wide variety of processing techniques are currently used20-23. These techniques are usually classified based on different criteria, one of which is based on topology, that is techniques for manufacturing closed-pore cellular metals or metal foams, and techniques for manufacturing open-pore cellular metals or metal foams24. One of the techniques commonly used in the manufacture of open-pore cellular metals, from the matrix metal in a liquid state, is the infiltration of removable fillers or soluble particles20,23,24. The conventional technique is developed in five stages20,23,25 and, in two of them, the sintering of the preform and the fusion of the metal, is necessary to carry out two separate heating operations7, which imply greater energy consumption, a longer process time and probably higher cost. The novelty of this work lies in the use of a controlled atmosphere device in the process of obtaining the cellular metals, which is described in the methodology. In this device, a single heating operation simultaneously performs the sintering of the soluble particles, the melting of the aluminum alloy, and the infiltration of the metal into the soluble particles, thus reducing process time, energy consumption, the possibility of metal oxidation, and the potential waste of the main raw material26,27. This is not only an innovation but also an advantage over the conventional technique.
Numerous research work has been carried out to determine the effect of different parameters on the mechanical properties of cellular metals and, in particular, on their energy absorption capacity. This property has been evaluated by compression tests at different strain rates. Under quasi-static compression, it has been evaluated as a function of density28, porosity percentage29,30, relative density9,28, pore size and/or shape1,28,30-32, in addition to other parameters such as base metal type, compression pressure, infiltration pressure, and specimen size1,8,31,33. At higher strain rates, the energy absorption capacity by impact was evaluated as a function of density13,34,35, porosity percentage36, pore size37, and impactor velocity38. Through quasi-static compression and impact, the energy absorption capacity has been evaluated and compared as a function of pore size, relative density and strain rates10,39. However, in this review of background studies, no research work was found that evaluated and compared the absorption capacity of energy by quasi-static compression and impact by varying the shape and size of the pore.
This research, therefore, reports the manufacture of cellular metals making use of the soluble particle infiltration (SPI) technique, and using as base metal an aluminium alloy with 12% silicon (Al-Si12), and soluble NaCl particles of rounded shape (R) and equiaxed shape (E), with five different sizes. The manufactured cellular metals were subjected to quasi-static compression and impact tests to determine their energy absorption capacity and to evaluate their behaviour based on shape, pore size and strain rate.
2. Materials and Methods
2.1. Materials
An aluminium-silicon alloy for casting called Al-Si12 was used as a base metal or matrix. The alloy was supplied in the form of ingots by the Colombian company Propulsora S.A., which reported a chemical composition of 85.5% Al, 12% Si, 0.8% Fe and 2.2% of other elements such as Mg, Mn and Zn, melting point between 650 and 750°C and density of 2.66 g/cm3. High purity sea salt (99% NaCl), with a melting point of 801°C and density of 2.17 g/cm3, was used as soluble material to generate the pores. The salt was supplied by the company Aquasal Ltda., in 25 kg sacks, which was sieved to obtain equiaxed shape particles in five size ranges: T1 (4-4.75 mm); T2 (4.75 to 6.3 mm); T3 (6.3 to 8.0 mm); T4 (8.0 to 9.5 mm) and T5 (9.5 to 11.2 mm). This form of identification was also used to identify pore size.
2.2. Rounding of NaCl particles
As rounded NaCl particles with five size ranges were also used, particles of equiaxed shape were placed inside cylinders internally coated with sandpaper of different grain size in such a way that by friction and rotation the rounded shape was achieved as shown in Figure 1a.
Number 80 grit sandpaper was used to round particles of sizes T5 (9.5 to 11.2 mm) and T4 (8.0 to 9.5 mm), #150 grit sandpaper was used for size T3 (6.3 to 8.0 mm), and #180 grit sandpaper was used for sizes T2 (4.75 to 6.3 mm) and T1 (4.0 to 4.75 mm). The process consisted of loading the cylinders with salt particles of the size to be rounded, rotating them for 2 hours, after which they were removed to clean and renew sandpaper. This process was repeated approximately 6 times. The time for rounding the particles of each size was 12 hours on average.
The process was carried out in the equipment shown in Figure 2, which was designed and built by Hernández et al.40.
2.3. Manufacturing of cellular metals
Cellular metals with five ranges of pore size, equiaxed (E) and rounded (R), were manufactured using a soluble particle infiltration (SPI) technique. A controlled atmosphere device was used for this purpose, which can be observed in Figure 3, whose components and function can be found in Moreno and Baez41.
The first stage in the process for the manufacture of cellular metals based on this technique was to prepare the controlled atmosphere device. The operations performed were: filling the metal mold with NaCl particles, depositing the appropriate quantity of solid metal into a metal container with a hole at the bottom, assembling the mold and container with screws, and placing the mold-container system inside the vacuum chamber, securing it internally with a threaded ring. The second stage consisted of placing the controlled atmosphere device inside the electric resistance furnace, programming the furnace, and starting it up. This stage involved performing the following operations: placing the sealing cap, activating the cooling vacuuming to -25 psi, programming the heating ramp, and urning the furnace on. The furnace heating ramp was programmed at a rate of 10°C/minute. To heat the furnace from room temperature (approximately 20°C) to 100°C, took 8 minutes. Maintaining the temperature at 100°C took 30 minutes and heating the furnace temperature from 100°C to 660°C took 56 minutes. Once the temperature reached 660°C, the metal reached the liquid state. At this point, the temperature was maintained for another 5 minutes to achieve greater fluidity, and the infiltration stage of the liquid metal into the bed of salt particles began. At that time, the vacuum was suspended and the first argon injection was made at a pressure of 2.5 psi for three minutes. Vacuum was applied again for two minutes, the second argon injection was made for three minutes, a two-minute vacuum was made, and finally, a final argon injection was made. The furnace was then shut down and allowed to cool, during which time the pressure remained relatively constant. Once the process is finished, the device is removed from the furnace, the mold-container system is removed and disassembled, and a compact (alloy-salt) is extracted, which undergoes the stage of dissolving the salt to obtain the cellular metal.
2.4. Mechanical characterization
Cylindrical specimens of 42 mm in diameter and 34 mm in height were cut out for the purpose of carrying out the mechanical tests. The quasi-static compression test was carried out on a Humboldt Master Loader 5000 machine with a capacity of 50 kN, and a head speed of 2 mm/minute, which corresponds to a strain rate of 9.8x10-4 s-1. This speed was calculated by dividing the head speed by the specimen height. The impact test was carried out on a Drop Weight Instrumented (DWI) machine, dropping on each sample a mass of 16 kg from a height of 45 cm, which corresponds to an impact speed of 2.97 m/s. Dividing this speed by the specimen height results in a strain rate of 8.8 x 101 s1. Five samples of each pore size and shape were subjected to compression and impact. From the values of force, strain and the area and height of each specimen, values of stress in MPa and unit strain in % were obtained. Then, stress-strain curves were constructed and the energy absorption capacity was determined from the area under the stress-strain curve from 0 to the densification strain in the case of compression test and from 0 to a standard strain in the impact test.
3. Results and Discussion
3.1. Results of the quasi-static compression test
Figure 4 shows the stress-strain curves for Al-Si12-based cellular metals, with equiaxed pores identified by continuous lines and rounded pores identified by dashed lines.
Stress-strain curves of Al-Si12 with irregular pore and rounded pore under compression. Continuous lines correspond to cellular Al-Si12 with equiaxed pore and the dashed lines correspond to cellular Al-Si12 with rounded pore.
In the curves of Figure 4, three regions can be identified that are typical of cellular metals subjected to compression. A short initial elastic region in which the stress is directly proportional to the unit strain, a second plastic region characterized by a significant increase in strain while maintaining stress almost constant which is called the plateau region, and a third region in which stress increases without any significant increase in the unit strain, which corresponds to the densification region1,6,9,23,31,42.
According to the stress-strain curve shape, cellular metals with equiaxed pore sizes ranging from E1 to E5 can be considered as fragile cellular metals without significant disintegration, since they have curves in which there are no significant peaks and/or valleys and, in addition, they present a clear plateau region. Rounded pore cellular metals with sizes ranging from R1 to R5 can be considered very fragile cellular metals with disintegration, since the stress-strain curves are characterized by presenting a first peak of stress (maximum compressive stress), followed by a sharp drop in stress after the peak or after certain strain and, generally, do not show a defined plateau region, according to the classification proposed by Florek et al.43.
The energy absorption capacity for each specimen was determined by calculating the area under the stress-strain curve by integration between a strain of 0 and the densification strain (εd), which was obtained using the method proposed by Li et al.16. The maximum average energy absorption for equiaxed pore cellular metals was 4.9 MJ/m3 and for rounded pores was 3.19 MJ/m3, corresponding in both cases to the smallest pore size range (4-4.75 mm). On average, the energy absorption capacity of equiaxed pore cellular metals is 3.7 MJ/m3 and of rounded pores is 2.2 MJ/m3, which represents a difference between the former and the latter of 68.2%.
Figure 5 is a graph of the energy absorption capacity under quasi-static compression for cellular metals with equiaxed pores and rounded pores as a function of pore size. The figure shows that the energy absorption capacity per unit volume tends to decrease as the pore size increases, both for the equiaxed and rounded shapes, results that are consistent with those obtained by other researchers1,28,32. In cellular metals, the energy absorption capacity is directly related to the plateau stress and the densification strain44-46. In addition to the average values and standard deviation of the energy absorption capacity for the two pore shapes, Table 1 also presents the average values and standard deviation of the plateau stress obtained by applying the method proposed by ISO 13314 of 200147, and the densification strain.
Energy absorption capacity versus pore size of cell Al-Si12 with equiaxed pore and rounded pore under quasi-static compression.
Average values of plateau stress, densification strain and energy absorption capacity in cellular Al-Si12 with equiaxed pore and rounded pore.
As can be seen in Table 1, both the plateau stress and the densification strain of cellular metals with equiaxed and rounded pores tend to decrease as pore size increases. Therefore, this behavior explains the tendency of energy absorption capacity to decrease with increasing pore size.
When observing the standard deviations of the plateau stress of size T5, for the two pore shapes, and the densification strain for sizes T4 and T5 rounded pores, some outliers are observed. This is because, as the pore size increases, the pores become more heterogeneous, and therefore the stress-strain unit curves are characteristic of very brittle cellular metals and certainly do not show a defined plateau region, according to the classification formulated by Florek et al.43.
Figure 5 also shows that equiaxed pore cellular metals exhibit a higher energy absorption capacity in all sizes, compared to rounded pore. This result is contrary to that obtained by Bafti and Habibolahzadeh48. However, it is necessary to consider the significant differences between the two research projects, related to the technique of manufacturing cellular metal used, the material and shape of the soluble particles and the pore sizes evaluated. The difference in the energy absorption capacity between both pore shapes is attributable to the direct relationship between the plateau stress and the relative density49,50. Based on the above, it can be concluded that equiaxed pore cellular metals present a greater energy absorption capacity than those with rounded pores because in equiaxed pore metals the relative density is higher, as observed in Figure 6.
The tendency of the relative density of equiaxed pore cellular metals to increase as pore size increases can be explained from the analysis of quantities (masses) and volumes of raw materials used in the manufacturing process for each sample. During the preparation phase, it was shown that, for a constant volume of the mold, as the size of the NaCl particles increased, their mass decreased and, consequently, the mass of metal to be infiltrated increased. Of course, as the mass of metal increases, it is expected that after the dissolution of the salt, both the density and the relative density will increase.
3.2. Impact test results
Figure 7 shows the stress-strain curves for Al-Si12-based cellular metals, with equiaxed pores identified by continuous lines and rounded pores identified by dashed lines, resulting from the impact test. As can be seen, for the same speed and impact energy, strains were very variable, as was the energy absorption capacity.
The variability in deformations, for the same impact energy, may be due to three factors: the sensitivity of the matrix metal to the strain rate, the effects of lateral microinertia and the pressure of the gas trapped inside the cells or pores6. The first two factors are related to the base metal, and the third to the cellular structure. With regard to the effect of the sensitivity to the strain rate of the matrix metal (Al-Si12), it appears that it is negligible, considering the findings of Liu et al.51, who argue that pure aluminum is known to be sensitive to strain rate, while most of its alloys are insensitive. Microinertia is a factor that can cause effects on sensitivity to the strain rate of cellular metals. In open-pore cellular metals, the predominant mechanisms of deformation under compression are the plastic bending of the struts oriented perpendicularly to the direction of the applied load and the plastic buckling of struts oriented parallel to the direction of the load52. Lateral microinertia is likely to have an influence on the variability in strain. However, evaluating this behavior on the basis of this parameter is very complex due to the difficulties involved in obtaining a suitable sample for carrying out the respective tests.
Regarding gas trapped in the pores, Zhao et al.53, argue that it can come out without resistance under a quasi-static load. However, under an impact load, there is a great possibility that the gas will not have enough time to leave, increasing the resistance to plastic deformation of the cellular metal due to increased internal pressure. Consistent with the above, and taking into account that the cellular Al-Si12 samples of irregular pore used in the impact test had approximately the same dimensions (length, diameter), therefore, each sample contained a different number of pores depending on the size. In general, greater deformation was observed for larger pore sizes, implying that, the larger pore size, the smaller the number of pores and the greater the probability that trapped gas could escape more easily compared to smaller pores cellular metals. Due to this variability, a reference deformation of 9.8% was taken as the minimum value obtained for one of the impact test specimens in order to establish comparisons of energy absorption between the two pore shapes, the five sizes, and quasi-static compression test.
The energy absorption capacity for each specimen was determined by calculating the area under the stress-strain curve by integration in a strain range between 0 and 9.8%. For this reference strain, the highest average energy absorption capacity for equiaxed pore cellular metals was 1.24 MJ/m3 corresponding to the largest pore size (T5), and for rounded pores it was 0.80 MJ/m3 corresponding to size T2. The average energy absorption capacity of equiaxed pore cellular metals was 0.98 MJ/m3 and for rounded pores it was 0.64 MJ/m3, which means that equiaxed pore cellular metals have a higher energy absorption capacity by 53.1%.
Figure 8 is a graph of the energy absorption capacity under impact for equiaxed pore and rounded pore cellular metals as a function of pore size. The most significant result that can be derived from the observation of this figure is that, for a unit reference strain, the equiaxed pore cellular metals exhibit greater energy absorption capacity compared to rounded pore metals. This behaviour is due to the fact that cellular metals with equiaxed pores have less porosity (64.80 ± 0.79%), than those with rounded pores (71.36 ± 1.09%), as seen in Figure 9, an explanation that is consistent with that proposed by Parveez et al.36, who state that high porosity values can reduce the energy-absorbing capacity of cellular metals, in addition to the research published by Fang et al.38, in which the effect of porosity on the energy absorption capacity under impact of aluminium foams with four porosities was evaluated and they concluded that as porosity increases, the energy absorption capacity decreases.
Energy absorption capacity at 9.8% respect to the pore size of an Al-Si12 cell with equiaxed pore and rounded pore under impact.
3.3. Comparison of energy absorption between compression and impact
Figures 10 and 11 compare the energy absorption capacity obtained of impact and quasi-static compression tests for cellular metals with equiaxed pores and rounded pores, respectively, and a unit strain of 9.8%.
Comparison of energy absorption capacity at 9.8%, under impact and under quasi-static compression for equiaxed pore.
Comparison of energy absorption capacity at 9.8%, under impact and under quasi-static compression for rounded pore.
Looking at the graphs in the figures above, it can be seen that, in both cases, cellular metals absorb more energy under impact. This difference lies in the fact that in the impact test there is a densification front or plastic shock wave which propagates along the impact direction from the initial impact surface to the surface in contact with the support and then it reflects on this17,18,54; that is to say, two compressions of the cellular metal are generated, so that the impact energy is transformed into kinetic energy. The kinetic energy increases during the first compression and decreases during the second. However, all this kinetic energy is transferred to internal energy in the cellular metal to plastically strain it19. The other reason for this behaviour lies in the sensitivity of cellular metals to the strain rate. Experimental and simulation studies39,55,56 have concluded that, by increasing the strain rate to which the cellular metal is subjected, the energy absorption capacity increases. The strain rate to which the cellular Al-Si12 specimens were subjected in the impact test was of the order of 101 s-1, while in the quasi-static compression test it was of the order of 10-4 s-1, that is, a significant increase in the strain rate.
4. Conclusions
In conclusion, equiaxed pore and rounded pore cellular metals were successfully fabricated using the soluble particle infiltration (SPI) technique and employing a controlled atmosphere device. On the other hand, the energy absorption capacity of these materials, which was determined through quasi-static compression tests and impact tests, allows us to conclude that this property varies with the shape and size of the pores, as well as the strain rate. The energy absorption capacity obtained by quasi-static compression tests for the cellular metals with both pore shapes decrease as the pore size is increased. The cellular metal with the highest energy absorption corresponds to the smallest equiaxial pore size (4-4.75 mm and 4.9 MJ/m3). In addition, this cellular metal has the lowest relative density, which makes it a good candidate for use in energy absorber applications, e.g. tubes filled with this cell metal for use in passive safety. In general, the equiaxed pore cellular metals obtained showed a higher energy absorption capacity compared to those with the rounded pores. This property was 68.2% higher when the quasi-static compression tests was employed and 42.2% higher when the impact tests was employed. However, for the two morphologies and a standard strain at 9.8%, the cellular metals exhibit a higher energy absorption capacity when subjected to impact tests compared to the quasi-static compression test, this behavior is due to a higher strain rate in the impact test, in consequence, these materials are good candidates for use in crash applications, e.g. vehicles and aircrafts.
5. Acknowledgments
The authors would like to acknowledge Universidad Nacional de Colombia through the DNIL, VRI, FIA for the financial support through the HERMES project numbers 59166 and 57267. They would also like to thank the managers of the Department of Mechanical Engineering at Universidad de los Andes and the technical staff of the laboratories of both universities for their support in carrying out the mechanical tests.
6. Data Availability
Some data supporting the results of this study are included in the article. The data not included are available and can be requested from the corresponding author, Luis E. Moreno, upon justified request.
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Edited by
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Associate Editor:
Aloisio Klein.
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Editor-in-Chief:
Luiz Antonio Pessan.
