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Effect of relative density on the dynamic compressive behavior of carbon nanotube reinforced aluminum foam
Materials Science & Engineering A 689 (2017) 17–24
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Effect of relative density on the dynamic compressive behavior of carbon nanotube reinforced aluminum foam Abdelhakim Aldoshan, Sanjeev Khanna
MARK
⁎
Mechanical and Aerospace Engineering Department, University of Missouri, Columbia, MO 65211, USA
A R T I C L E I N F O
A BS T RAC T
Keywords: CNT reinforced Aluminum foam Liquid metallurgy Quasi-static and dynamic compression Plateau stress Energy absorption Relative density
Closed-cell aluminum foams represent a unique class of solid cellular light metals that are made by deliberately introducing voids or pores during fabrication. This lightweight material is able to undergo large deformation at a nearly constant stress known as Plateau Stress because of which aluminum foams are good energy absorbers under dynamic loads such as an impact. In this investigation, carbon nanotubes (CNT) reinforced closed-cell aluminum foams were fabricated using the liquid metallurgy route through the dissociation of a foaming agent within the liquid metal. Four different relative densities of CNT reinforced Al-foam were used: 0.16, 0.20, 0.26 and 0.30, to study the effect of strain rate on the mechanical properties. The compressive mechanical behavior of CNT reinforced Al-foam has been studied under quasi-static and dynamic loading conditions. The high strain rate compressive response was investigated using a Split Hopkinson Pressure Bar (SHPB) over a range of strain rates up to 2750 s−1. Mechanical properties such as peak stress, plateau stress and energy absorption increased with the increase in relative density; however, the densification strain decreased with the increase in relative density. Dynamic compressive properties improved as the strain rate increased indicating that this material is strain rate dependent. Among all the foams, the 0.30 relative density exhibited the highest mechanical properties whereas the 0.20 relative density foam displayed the highest strain rate sensitivity.
1. Introduction Aluminum foams are becoming a potential material for lightweight multifunctional applications due to the excellent physical and mechanical properties [1]. Because of the cellular structure, closed cell aluminum foams exhibit excellent damping capacity, sound and noise isolation, and energy absorption [2,3]. For example, in structural applications there is potential use of closed-cell aluminum foams as the core in sandwich panels, foam filled tubes, among others [4]. Also, these materials are good replacement for existing polymeric foams used in automobiles and trains, etc [5,6]. Metal foams have been found to contain porosity ranging from 70% to 95%. Because of this, metal foams display a unique mechanical behavior under compressive loading. The material can undergo large deformation under relatively constant strength. Fig. 1 presents the typical stress-strain response of closed cell aluminum foam under compression [7]. It can be seen that the foam exhibits linear elastic behavior up to a peak stress at low strain ( < 3%). This is followed by a plateau region, in which stress remains relatively constant up to nearly 60–70% strain. After that, material reaches densification stage in which stress increases significantly with strain. Among various mechanical properties, energy absorption capacity appears to be an important
⁎
property imparted by the aluminum foam. Therefore, the energy absorption per unit volume (Wv) is given as the area under stressstrain curve up to the onset of densification (shaded region in Fig. 1). Among different metallic foams, majority of the work has been done on aluminum foams. Many researchers have investigated the mechanical properties of closed cell aluminum foams under high strain rate impact loading, but there exist contradictory opinions. Compressive strength of closed cell aluminum foams is strain rate dependent over varying strain rates [8–11]. Also, Raj et al. [12] reported the effect of strain rate on mechanical properties under quasi-static (0.001 s−1) and dynamic compressive loadings (750 s−1) over a wide range of relative density (0.062–0.373). Plateau stress exhibited relative density and strain rate dependence, and the strain rate sensitively is apparently significant for relative density > 0.15. On the other hand, other researchers showed that the compressive strength of aluminum foams is apparently insensitive to strain rate (0.001–5000 s−1) [13–15]. This arises mainly because of their different foam structure (cell shape and size), relative density, homogeneity of cell walls and defects in the cell walls, and fabrication method of foam (liquid metallurgy vs powder metallurgy route). It's interesting to note that homogeneity of foam structure such as pore size and cell walls thickness is directly influenced by the viscosity of the liquid melt. The presence of defective cell
Corresponding author.
http://dx.doi.org/10.1016/j.msea.2017.01.100 Received 10 November 2016; Received in revised form 23 January 2017; Accepted 28 January 2017 Available online 31 January 2017 0921-5093/ © 2017 Elsevier B.V. All rights reserved.
Materials Science & Engineering A 689 (2017) 17–24
A. Aldoshan, S. Khanna
2. Experimental procedures 2.1. Materials Closed cell CNTs aluminum alloy composite foam was produced by melt route using a process being developed by CSIR-AMPRI Bhopal [18]. In particular, aluminum alloy 5083 (AA 5083) was used as the base metal. At the first instance, Al alloy-SiC particle (size: 10–30 µm) composite was prepared by melt stirring process. The steps used for synthesizing the Al alloy-composite closed cell foam were (i) melting of Al alloy in a graphite crucible (ii) stirring the melt with the help of a mechanical stirrer at a stirring speed of 700 RPM (iii) addition of SiC particles (8 wt%) to the melt during stirring (melt temperature: 800 °C) (iii) once the Al-SiC composite was ready, multi-walled carbon nanotubes (CNT powder was compressed in the form of solid tablet and added in the melt) was added into the melt. In this process, SiC particle was added in the melt as thickening agent (iv) after complete addition of CNT, calcium hydride was added in the melt as foaming agent. After completion of foaming, the metallic die with foam, was taken out from the furnace and cooled with compressed air. The foaming temperature was kept constant. The mold was of a relatively large size and was not thermally controlled during foaming. Thus there were temperature gradients with faster cooling near the mold walls resulting in smaller pores (or higher relative density), while the central region of the mold resulted in larger pores (or lower relative density). Thus, samples from different regions provided the relative density variation. The average cell size of RD=0.20 was 1.3 ± 0.3 mm and the cell wall thickness was 230 µm ± 50 µm, whereas the average cell size and cell wall thickness of RD=0.30 were 0.8 ± 0.2 mm and 170 µm ± 30 µm, respectively. The foam block prepared by this way was removed from the die and then cut into pieces conforming to the exact size for testing. The foam block prepared by this way was removed from the die and then cut into pieces conforming to the exact size for testing. Fig. 2 shows a cross-sectional view of closed-cell 2 wt% CNTs Alfoam sample obtained using scanning electron microscope (SEM, magnification 28-100x and voltage 10 kV). The cell size of the foam was measured along different sides of the specimen using the ASTM E112-10 [21] method for measuring diameter of grains in polycrystalline materials (at least 100 measurements were carried out using ImagJ software). The average cell size in the respective foams of different relative density varies in the range of 1.0–1.7 mm. Following the work of Muaki et al. [8,22], Raj et al. [12], and Hamada et al. [23], cubical specimens with 7.5 mm side length were used for high strain rate compression testing, which is ~80% of the SHPB bar diameter of 12.7 mm. Specimens for quasi-static compression were cut into rectangular prisms of 10 mm×10 mm×15 mm. All foam specimens were cut using a low speed diamond wafering cutter. To determine the
Fig. 1. A schematic of the compression stress-strain behavior of Al foam (Adapted from [7]).
structure leads to stress concentration points along the weakest struts, and drastically decreases the strength of the closed cell foam. It has been shown that using carbon based reinforcements (e.g. SiC, fly ash etc.) helps to increase the viscosity and, hence produce favorable uniform microstructure [16]. Moreover, using nanomaterials such as carbon nanotubes (CNTs) to reinforce the Al-foam matrix has been shown to enhance the strength of the foam composite [17–19]. The effect of relative density (density of foam divided by density of solid aluminum alloy) on the mechanical behavior of closed cell aluminum foams has been studied by few researchers. Mondal et al. [20] studied the compressive response of closed cell aluminum-fly ash foam over a range of relative densities (0.08–0.13) and quasi-static compression loading (0.01–10 s−1). Their investigation revealed that plateau stress increased with an increase in relative density, but plateau stress is insensitive to strain rate. Limited work was found on the effect of relative density on the dynamic mechanical behavior of closed cell reinforced aluminum foams. Therefore, further investigations are needed to examine the combined effect of strain rate and relative density on the mechanical properties of aluminum foams, i.e. strength and energy absorption capacity. In this current investigation, 2 wt% CNTs Al composite foam (AA 5083) produced through liquid melt route is studied under dynamic compression loading. The 2 wt% CNTs concentration has been chosen for this investigation based on the results obtained in an earlier study [18,19] on the effect of CNTs concentration in Al-foam on the dynamic compressive response. It was determined that 2 wt% concentration produces the highest peak stress, plateau stress and energy absorption among 1–3 wt% CNT reinforced Al-foams. In this study, Split Hopkinson Pressure Bar (SHPB) apparatus was used to study the dynamic stress-strain response over a varying range of strain rates (1300 s−1 to 2750 s−1) and relative densities (0.16–0.30). For comparison, quasi-static compression tests were carried out over the same range of relative densities.
Fig. 2. Closed cell CNT reinforced Al-foam composite for RD=0.20.
18
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A. Aldoshan, S. Khanna
Fig. 3. A schematic description of the in-house SHPB.
was developed by Kolsky in 1949 to determine the high strain rate properties of materials (up to 10,000 s−1) [24]. Fig. 3 shows a typical SHPB system, which consists of three bars: a striker, an incident bar and a transmitter bar. SHPB was utilized to investigate the dynamic mechanical properties of 2 wt% CNTs Al foams at high strain rate (up to 2750 s−1). SHPB is made of 7075 aluminum bars of 12.7 mm diameter. The lengths of striker, incident, and transmitted bars are 457.2 mm, 1820 mm and 1370 mm, respectively. To assure validity of the recorded signals from strain gages, calibration of incident and transmitted bars was carried out [25]. The specimen is sandwiched between the end of incident bar and front of transmitted bar. To minimize friction, a very thin layer of molybdenum grease was applied on both specimen-bar interfaces. After that, the striker bar is launched using pressurized nitrogen gas through the gas barrel. When the striker bar impacts the front end of incident bar, a compressive wave travels in the incident bar until it reaches the interface between back end of incident bar and the specimen, when part of that wave reflects back as a tensile wave and a part is transmitted through the specimen as a compressive wave and into the transmitted bar. Strain gages record three waves: incident (I), reflected (R) and transmitted (T). The recorded strain gage signals are used to determine the incident strain (εI), reflected strain (εR) and transmitted strain (εT). The theory behind SHPB is based on one dimensional elastic wave propagation theory. The expressions for average strain rate, engineering stress and strain in specimen are given in Eqs. (1), (2) and (3) respectively [25,26].
Fig. 4. Stress equilibrium in SHPB.
εṡ =
Fig. 5. Stress-strain response of 2 wt% CNT Al-foams with different relative densities under quasi-static compression (0.001 s−1).
2COB εR Hs0
(1)
⎛A E ⎞ σs (t )=⎜ B B ⎟ εT (t ) ⎝ As0 ⎠
(2)
⎛ 2C ⎞ εs (t )=⎜ OB ⎟ ⎝ Hs0 ⎠
(3)
∫
t
εR (t ) dt
where CoB, AB and EB are the wave speed, cross-sectional area and elastic Young's modulus of SHPB bars, respectively. HS0 and AS0 are the length, and the cross-sectional area of the specimen, respectively. The forces in incident and transmitted bars are given by Eqs. (4) and (5), respectively. To satisfy the 1-D assumption in SHPB, specimen must be under dynamic stress equilibrium and deform under constant strain rate [25,26]. Stress equilibrium is achieved when the forces on front (F1) and rear (F2) surfaces of specimen are nearly equal, which results in expression (6). This assumption is satisfied when long bars (incident and transmitted) have uniform elastic, homogeneous, isotropic characteristics across its cross-section and along its length; such
density of the foam, the dimensions of the specimen were accurately measured and weighed using a digital caliper and digital balance. Relative density was estimated as density of foam/density of base aluminum alloy.
2.2. Mechanical characterization The conventional split Hopkinson pressure bar (SHPB) apparatus 19
Materials Science & Engineering A 689 (2017) 17–24
A. Aldoshan, S. Khanna
Fig. 6. Compressive stress-strain response of 2 wt% CNT Al-foams with different relative densities at a strain rate of (a) 1300 s−1, (b) 1800 s−1, (c) 2300 s−1 and (d) 2750 s−1. Table 1 Peak stress (σPeak), plateau stress (σPl) and densification strain (εD) as a function of strain rate and relative density. Relative Density
0.16 0.20 0.26 0.30
Strain Rate (s−1) 0.001
Strain Rate (s−1) 1300
Strain Rate (s−1) 1800
Strain Rate (s−1) 2300
Strain Rate (s−1) 2750
σPeak (MPa)
σPl (MPa)
εD
σPeak (MPa)
σPl (MPa)
σPeak (MPa)
σPl (MPa)
σPeak (MPa)
σPl (MPa)
σPeak (MPa)
σPl (MPa)
3.51 8.15 12.03 18.06
4.23 7.52 10.54 16.60
0.71 0.59 0.55 0.46
6.21 7.53 11.12 17.57
4.22 6.71 11.54 17.14
6.53 9.15 11.85 18.66
5.54 8.52 12.11 18.13
7.13 12.04 14.33 20.54
4.82 12.24 13.56 21.14
7.5 13.1 15.2 21
5.76 13.67 15.8 21.4
Fig. 7. Dynamic compressive stress-strain response of 2 wt% CNT Al-foams of RD=0.20 as a function of strain rate.
Fig. 8. Dynamic compressive stress-strain response of 2 wt% CNT Al-foams of RD=0.30 as a function of strain rate.
as EB, AB and COB.
is achieved in the specimen. The stress equilibrium in the specimen takes less than 40 μs to be achieved. In every test we ensured that a fairly constant strain rate was achieved over the duration of the test. Quasi-static compression testing was carried out at strain rate of 1×10−3 s−1 using ADMET material testing machine.
F1=AB EB (εI +εR )
(4)
F2=AB EB εT
(5)
εI +εR=εT
(6)
To assure the 1-D wave theory assumption of SHPB holds, the specimen aspect ratio (length/width) is selected to be 1, and a copper (C14500) pulse shaper was used for this work, which helped to achieve stress equilibrium in the specimens [27]. The detailed process for selecting specimen aspect ratio and pulse shaper are reported elsewhere [18]. Fig. 4 shows that the stress equilibrium condition of Eq. (6)
3. Results and discussion The stress-strain response of 2 wt% CNT reinforced foam under quasi-static compression is shown in Fig. 5, which is similar in nature to a typical compression behavior shown in Fig. 1. Peak stress is reported as the maximum stress value attained just before the start of 20
Materials Science & Engineering A 689 (2017) 17–24
A. Aldoshan, S. Khanna
Fig. 12. Peak stress against strain rate at different relative densities.
Fig. 9. Peak stress as a function of relative density at different strain rates.
Fig. 13. Plateau stress against strain rate at different relative densities. Fig. 10. Plateau stress as a function of relative density at different strain rates. Table 3 Variation of “m” with relative density.
Table 2 Variation of “A” and “b” with strain rate. #
1 2 3 4
Strain Rate (s−1)
1300 1800 2300 2750
Peak Stress
#
Relative Density
mPeak
mPlateau
1 2 3 4
0.16 0.20 0.26 0.30
0.24 0.65 0.45 0.26
0.40 0.69 0.45 0.37
Plateau Stress
A
b
A
b
104.80 133.02 135.50 131.10
1.58 1.61 1.55 1.53
208.8 216.2 261.8 284.6
2.13 2.04 2.12 2.07
density varies from 0.16 to 0.30. Fig. 6a-d show engineering stress-strain plots under dynamic compression at different strain rates and relative densities. At 1300 s−1, it is found that compressive stress significantly increases as the relative density increases. Hence, the highest peak stress and plateau stress of 17.5 MPa and 17.0 MPa, respectively, are observed for the relative density of 0.30. For RD=0.16 foam, the peak stress and plateau stress increase up to a strain rate of 1800 s−1 and no further increase with strain rate is observed. The higher relative density foams (0.20, 0.26 and 0.30) exhibit an increase in peak and plateau stresses with strain rate up to 2300 s−1 with nearly no gain beyond this strain rate. It should be noted that higher relative density foam is stiffer due to the effect of having thicker cell walls, which in turn increases the stress levels. To better visualize the combined effect of strain rate and relative density, a summary of the compressive stresses of this investigation is presented in Table 1. It is observed that compressive stresses at any fixed relative density increase with strain rate. In a broad prospective, higher increase in plateau stress is observed for higher relative densities as the strain rate increases. This shows an agreement with the reported results of Raj et al. [12] that higher density foam, RD > 0.15, exhibits significant increase in compressive stress under dynamic compression. The compressive stress–strain curves of foam at various strain rates for relative density of 0.20 and 0.30 are shown in Fig. 7 and Fig. 8,
Fig. 11. Ln‘Apl’ vs. Ln'Strain Rate’.
plateau region. Plateau stress is reported as the average stress throughout the plateau region (see Fig. 1). It is observed that stressstrain curves show small oscillations in the plateau region. This is attributed to the localized cell deformation and sequential compaction of layers throughout the plateau region [9,12]. It should be noted that peak stress and plateau stress significantly increase as the relative 21
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A. Aldoshan, S. Khanna
Fig. 14. Cross-sectional view of closed cell Al-foam composite with different relative densities (a) 0.15, (b) 0.20, (c) 0.26, and (d) 0.30.
Fig. 15. Variations of densification strain as a function of relative density at strain rate of 0.001 s−1.
Fig. 16. Energy absorption as a function of strain rate and relative density.
respectively. For the relative density of 0.20, peak and plateau stresses displayed significant increases as the strain rate increased, whereas those with relative density of 0.30 exhibited smaller increase with the increase in strain rate. Hence, this indicates that foam with relative density of 0.20 is more sensitive to strain rate. In this study, peak stress (σPeak) also termed as the elastic collapse stress (σel) is shown in Fig. 1. Generally, the variation of peak stress (σPeak) and plateau stress (σPl) with relative density follow a power law relationship presented in Eqs. (7) and (8) [1].
⎛ ρ ⎞bP σPeak =AP ⎜ f ⎟ ⎝ ρs ⎠
Table 4 Energy absorption (WV) as a function of strain rate and relative density.
(7)
22
Relative Density
Strain Rate (s−1) 0.001 WV (MJ/ m3)
Strain Rate (s−1) 1300 WV (MJ/ m3)
Strain Rate (s−1) 1800 WV (MJ/ m3)
Strain Rate (s−1) 2300 WV (MJ/ m3)
Strain Rate (s−1) 2750 WV (MJ/ m3)
0.16 0.20 0.26 0.30
0.52 2.34 3.02 4.87
1.26 2.42 3.32 5.24
1.37 2.54 3.66 5.78
1.41 3.39 4.28 6.35
1.62 3.64 4.39 6.27
Materials Science & Engineering A 689 (2017) 17–24
A. Aldoshan, S. Khanna
Fig. 17. Deformation of closed cell Al-foam (RD=0.20) at different strain (a) 0%, (b) 5%, (c) 10%, and (d) 20%.
⎛ ρ ⎞bPl σPl =APl ⎜ f ⎟ ⎝ ρs ⎠
sensitivity observed in 0.20 relative density foam. For foam with RD=0.26, more small size pores appeared leading to less uniform cell size. As the relative density increased to 0.30, cell size becomes smaller with an average cell size of 0.8 ± 0.2 mm and the foam has more solid areas. Fig. 15 shows the variations of densification strain as a function of relative density of specimens tested under quasi-static compression (strain rate of 0.001 s−1). The densification strain is considered as the strain corresponding to the intersection of tangents drawn on the densified and the plateau regions. It is noted that densification strain decreases as the relative density increase. The curve fit line follows the equation of a linear line, y=mx+b in which m equals −1.5 and b equals 0.94. The constants of this straight-line equation are within ± 6% of the constants in Eq. (9) provided by Gibson et al. [1]. It may be noted that as the relative density varies from 0.16 to 0.30 the corresponding densification strain varies from 0.71 to 0.46. For RD less than 0.16, we hypothesize that the densification strain would be invariant to the change in relative density, following the study by Mondal et al. [3] even though their foam system had a different reinforcement, namely flyash. The densification strain cannot be determined for dynamic tests as the impact pulse duration is not long enough to produce sufficient densification.
(8)
where ‘Ap’ and ‘Apl’ are the respective strengthening coefficient, ρf is the density of foam, ρs is the density of solid metal and ‘bp’ and ‘bpl’ are the respective exponent to relative density. Fig. 9 shows the variation of peak stress as a function of relative density at different strain rates. The variation of plateau stress as a function of relative density at different strain rates is shown in Fig. 10. The data for peak stress and plateau stress as a function of relative density were curve fitted using a power low relationship y=Axb. The values of ‘A’ and ‘b’ are presented in Table 2. The value of ‘b’ in this present study shows a good agreement with the reported values (1.5–3.0) for aluminum foams [1]. Fig. 11 presents a the variation of Ln‘Apl’ with Ln'Strain Rate’. Peak stress and plateau stress are plotted against strain rate for different relative densities on a log-log plot (see Figs. 12 and 13) to estimate the strain rate sensitivity. The strain rate sensitivity ‘m’ is calculated as the slope of each line (in Figs. 12 and 13) for each relative density presented in Table 3. It is noted that peak stress for relative densities 0.2 and 0.26 show stronger strain rate sensitivity as compared to others. For plateau stress, the strain rate sensitivity of relative densities 0.16, 0.26 and 0.30 varies in the range 0.37–0.45, while a relative density of 0.20 displays the highest strain rate sensitivity of 0.69. Fig. 14a-d show the cross-sectional view of closed cell Al-foam composite with different relative densities 0.16, 0.20, 0.26, and 0.30, respectively. Foam with RD=0.16 has irregular cell size and shape whereas foam with RD=0.20 has more uniform cell size, cell wall thickness and cell distribution an average cell size of 1.3 ± 0.3 mm. Therefore, this might be the plausible reason for the higher strain rate
⎛ρ ⎞ εD=1 − 1.4 ⎜ f ⎟ ⎝ ρs ⎠
(9)
The energy needed under compression to deform any foam specimen up to particular strain is defined as the energy absorption capacity. Under uniaxial compressive loading, energy absorption, WV, per unit volume is given as the area under stress-strain curve up to a specific 23
Materials Science & Engineering A 689 (2017) 17–24
A. Aldoshan, S. Khanna
strain εo, and evaluated using the following expression:
WV=
∫0
εo
σ(ε)dε
Acknowledgement The authors wish to thank Dr. D.P. Mondal and Dr. S. Das of the Advance Materials and Processes Research Institute (AMPRI), CSIR, Bhopal, India for providing foam samples. Abdelhakim Aldoshan would like to acknowledge King Abdulaziz City for Science and Technology (KACST), Riyadh, for the scholarship.
(10)
The energy absorption of 2 wt% CNTs foams has been evaluated for different strain rates and relative density. Fig. 16 shows the energy absorption up to 30% strain of 2 wt% CNTs foams plotted against strain rate in the range 0.001 s−1–2750 s−1 for different relative densities. It can be seen that the energy absorption is strongly influenced by strain rate. The increase in energy absorption with strain rate is nearly the same for all foams of relative density of 0.20, 0.26 and 0.30, though the total energy absorption is higher for higher relative density due to the higher associated plateau stress. To visualize the combined effect of high strain rate as well as relative density, Table 4 summaries the energy absorption of 2 wt% CNTs foam. To study the deformation mechanisms in the CNT reinforced closed-cell Al-foam under quasi-static loading, images were captured for RD=0.20 at different strain 0%, 5%, 10% and 20%, as shown in Fig. 17a-d. In the undeformed image (Fig. 17a), eight cells were selected and then labeled with upper case letters ‘A’ to ‘H’. The labeled cells were then evaluated at higher strains based on the change in their shape and size. At 5% strain (Fig. 17b), cell ‘A’ showed plastic bending. The upper cell wall of ‘B’ experienced bending whereas the lower cell wall displayed plastic buckling. Cell C was mostly crushed (Closed). Also, the upper cell wall of ‘D’ exhibited plastic buckling whereas left cell wall remained undeformed. Moreover, the presence of defects in the cell wall such as uneven wall thickness could further lead to fracture, as shown in the right side cell wall of ‘H’. Also, a rapture in the cell membrane of ‘H’ was observed and a white arrow points at the location of the burst. This may be attributed to the release of the compressed gas inside the cell. It should be noted that other cells remain undeformed (such as E, G and F). At higher strain of 10% (Fig. 17c), plastic deformation progresses around the area of cells A, B, C and D while cells E, F and G maintained their original shape and size. As the strain increased to 20% (Fig. 17d), plastic collapse spreads further to the adjacent cells.
References [1] L.J. Gibson, M.F. Ashby, Cellular Solids: Structure and Properties, 2nd ed, UK Cambridge University Press, Cambridge, 1997. [2] T.J. Lu, A. Hess, M.F. Ashby, Sound absorption in metallic foams, J. Appl. Phys. 85 (11) (1999) 7528–7539. [3] D.P. Mondal, M.D. Goel, S. Das, Compressive deformation and energy absorption characteristics of closed cell aluminum-fly ash particle composite foam, Mater. Sci. Eng. A 507 (1–2) (2009) 102–109. [4] J. Banhart, H.W. Seeliger, Aluminium foam sandwich panels: manufacture, metallurgy and applications, Adv. Eng. Mater. 10 (9) (2008) 793–802. [5] G. Srinath, A. Vadiraj, G. Balachandran, S.N. Sahu, A.A. Gokhale, Characteristics of aluminium metal foam for automotive applications, Trans. Indian Inst. Met. 63 (5) (2010) 765–772. [6] GDA, A high-speed train made of aluminium foam [Online]. Available: 〈http:// www.aluinfo.de/index.php/gda-news-en/items/a-high-speed-train-made-ofaluminium-foam.html〉, 2014. [7] L.J. Gibson, Mechanical behavior of metallic foams, Annu. Rev. Mater. Sci. 30 (1) (2000) 191–227. [8] T. Mukai, H. Kanahashi, T. Miyoshi, M. Mabuchi, T.G. Nieh, K. Higashi, Experimental study of energy absorption in a close-celled aluminum foam under dynamic loading, Scr. Mater. 40 (8) (1999) 921–927. [9] K.A. Dannemann, J. Lankford, High strain rate compression of closed-cell aluminium foams, Mater. Sci. Eng. A 293 (1–2) (2000) 157–164. [10] H. Zhao, I. Elnasri, S. Abdennadher, An experimental study on the behaviour under impact loading of metallic cellular materials, Int. J. Mech. Sci. 47 (2005) 757–774. [11] P. Wang, S. Xu, Z. Li, J. Yang, H. Zheng, S. Hu, Temperature effects on the mechanical behavior of aluminum foam under dynamic loading, Mater. Sci. Eng. A 599 (2014) 174–179. [12] R. Edwin Raj, V. Parameswaran, B.S.S. Daniel, Comparison of quasi-static and dynamic compression behavior of closed-cell aluminum foam, Mater. Sci. Eng. A 526 (1–2) (2009) 11–15. [13] L. Kenny, Aluminium alloys - ICAA5, Mater. Sci. Forum 222 (1996) 1883–1890. [14] V.S. Deshpande, N.A. Fleck, High strain rate compressive behaviour of aluminium alloy foams, Int. J. Impact Eng. 24 (3) (2000) 277–298. [15] D. Ruan, G. Lu, F.L. Chen, E. Siores, Compressive behaviour of aluminium foams at low and medium strain rates, Compos. Struct. 57 (1–4) (2002) 331–336. [16] D.P. Mondal, S. Das, Effect of thickening agent and foaming agent on the microarchitecture and deformation response of closed cell aluminum foam, Materwiss Werksttech. 41 (5) (2010) 276–282. [17] I. Duarte, E. Ventura, S. Olhero, J.M. Ferreira, A novel approach to prepare aluminium-alloy foams reinforced by carbon-nanotubes, Mater. Lett. 160 (2015) 162–166. [18] A. Aldoshan, S.K. Khanna, Unpublished Results, High strain rate behavior of carbon nanotubes reinforced aluminum foams, J. Eng. Mater. Technol., In preperation. [19] A. Aldoshan, S. Khanna, Dynamic high temperature compression of carbon nanotubes reinforced aluminum foams, J. Dyn. Behav. Mater. (2016) 1–11. [20] D.P. Mondal, M.D. Goel, S. Das, Effect of strain rate and relative density on compressive deformation behaviour of closed cell aluminum-fly ash composite foam, Mater. Des. 30 (4) (2009) 1268–1274. [21] ASTM, Standard test methods for determining average grain size, ASTMP, E11210, p. Pennsylvania, 2011. [22] T. Mukai, T. Miyoshi, S. Nakano, H. Somekawa, K. Higashi, Compressive response of a closed-cell aluminum foam at high strain rate, Scr. Mater. 54 (2006) 533–537. [23] T. Hamada, H. Kanahashi, T. Miyoshi, N. Kanetake, Effects of the strain rate and alloying on the compression characteristics of closed cell aluminum foams, Mater. Trans. 50 (6) (2009) 1418–1425. [24] H. Kolsky, An investigation of the mechanical properties of materials at very high rates of loading, Proc. Phys. Soc.: Sect. B,1949, pp. 676–700. [25] B.A. Gama, S.L. Lopatnikov, J.W. Gillespie, Hopkinson bar experimental technique: A critical review, Appl. Mech. Rev. 57 (4) (2004) 223–250. [26] W.W. Chen, B. Song, Spilt Hopkinson (Kolsky)Bar: Design, Testing and Applications, Springer, New York, 2011. [27] K.S. Vecchio, F. Jiang, Improved pulse shaping to achieve constant strain rate and stress equilibrium in split-hopkinson pressure bar testing, Metall. Mater. Trans. A 38 (11) (2007) 2655–2665.
4. Conclusions Compressive mechanical properties of closed-cell CNT reinforced Al-foams have been investigated under quasi-static and dynamic loading with different relative densities of 0.16, 0.20, 0.26 and 0.30. Split Hopkinson pressure bar was used for studying the dynamic compression behavior. The salient observations of this work are listed below.
• • • •
At all applied strain rates, mechanical properties significantly increase as the relative density increases in terms of peak stress, plateau stress and energy absorption. For similar strain rates, plateau stress is approximately 230–300% higher for relative density of 0.30 compared to the low relative density foam (RD=0.16). Energy absorption in the foam of RD=0.30 is also 240–270% higher than low relative density foam RD=0.16. For all relative densities, compressive stresses and energy absorption displayed a strain rate dependence. The CNT foam of RD=0.20 exhibits the highest strain rate sensitivity among all the foams studied. It is postulated that this behavior relates to the more uniform cell structure in the 0.20 relative density foam.
24
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Effect of relative density on the dynamic compressive behavior of carbon nanotube reinforced aluminum foam Abdelhakim Aldoshan, Sanjeev Khanna
MARK
⁎
Mechanical and Aerospace Engineering Department, University of Missouri, Columbia, MO 65211, USA
A R T I C L E I N F O
A BS T RAC T
Keywords: CNT reinforced Aluminum foam Liquid metallurgy Quasi-static and dynamic compression Plateau stress Energy absorption Relative density
Closed-cell aluminum foams represent a unique class of solid cellular light metals that are made by deliberately introducing voids or pores during fabrication. This lightweight material is able to undergo large deformation at a nearly constant stress known as Plateau Stress because of which aluminum foams are good energy absorbers under dynamic loads such as an impact. In this investigation, carbon nanotubes (CNT) reinforced closed-cell aluminum foams were fabricated using the liquid metallurgy route through the dissociation of a foaming agent within the liquid metal. Four different relative densities of CNT reinforced Al-foam were used: 0.16, 0.20, 0.26 and 0.30, to study the effect of strain rate on the mechanical properties. The compressive mechanical behavior of CNT reinforced Al-foam has been studied under quasi-static and dynamic loading conditions. The high strain rate compressive response was investigated using a Split Hopkinson Pressure Bar (SHPB) over a range of strain rates up to 2750 s−1. Mechanical properties such as peak stress, plateau stress and energy absorption increased with the increase in relative density; however, the densification strain decreased with the increase in relative density. Dynamic compressive properties improved as the strain rate increased indicating that this material is strain rate dependent. Among all the foams, the 0.30 relative density exhibited the highest mechanical properties whereas the 0.20 relative density foam displayed the highest strain rate sensitivity.
1. Introduction Aluminum foams are becoming a potential material for lightweight multifunctional applications due to the excellent physical and mechanical properties [1]. Because of the cellular structure, closed cell aluminum foams exhibit excellent damping capacity, sound and noise isolation, and energy absorption [2,3]. For example, in structural applications there is potential use of closed-cell aluminum foams as the core in sandwich panels, foam filled tubes, among others [4]. Also, these materials are good replacement for existing polymeric foams used in automobiles and trains, etc [5,6]. Metal foams have been found to contain porosity ranging from 70% to 95%. Because of this, metal foams display a unique mechanical behavior under compressive loading. The material can undergo large deformation under relatively constant strength. Fig. 1 presents the typical stress-strain response of closed cell aluminum foam under compression [7]. It can be seen that the foam exhibits linear elastic behavior up to a peak stress at low strain ( < 3%). This is followed by a plateau region, in which stress remains relatively constant up to nearly 60–70% strain. After that, material reaches densification stage in which stress increases significantly with strain. Among various mechanical properties, energy absorption capacity appears to be an important
⁎
property imparted by the aluminum foam. Therefore, the energy absorption per unit volume (Wv) is given as the area under stressstrain curve up to the onset of densification (shaded region in Fig. 1). Among different metallic foams, majority of the work has been done on aluminum foams. Many researchers have investigated the mechanical properties of closed cell aluminum foams under high strain rate impact loading, but there exist contradictory opinions. Compressive strength of closed cell aluminum foams is strain rate dependent over varying strain rates [8–11]. Also, Raj et al. [12] reported the effect of strain rate on mechanical properties under quasi-static (0.001 s−1) and dynamic compressive loadings (750 s−1) over a wide range of relative density (0.062–0.373). Plateau stress exhibited relative density and strain rate dependence, and the strain rate sensitively is apparently significant for relative density > 0.15. On the other hand, other researchers showed that the compressive strength of aluminum foams is apparently insensitive to strain rate (0.001–5000 s−1) [13–15]. This arises mainly because of their different foam structure (cell shape and size), relative density, homogeneity of cell walls and defects in the cell walls, and fabrication method of foam (liquid metallurgy vs powder metallurgy route). It's interesting to note that homogeneity of foam structure such as pore size and cell walls thickness is directly influenced by the viscosity of the liquid melt. The presence of defective cell
Corresponding author.
http://dx.doi.org/10.1016/j.msea.2017.01.100 Received 10 November 2016; Received in revised form 23 January 2017; Accepted 28 January 2017 Available online 31 January 2017 0921-5093/ © 2017 Elsevier B.V. All rights reserved.
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2. Experimental procedures 2.1. Materials Closed cell CNTs aluminum alloy composite foam was produced by melt route using a process being developed by CSIR-AMPRI Bhopal [18]. In particular, aluminum alloy 5083 (AA 5083) was used as the base metal. At the first instance, Al alloy-SiC particle (size: 10–30 µm) composite was prepared by melt stirring process. The steps used for synthesizing the Al alloy-composite closed cell foam were (i) melting of Al alloy in a graphite crucible (ii) stirring the melt with the help of a mechanical stirrer at a stirring speed of 700 RPM (iii) addition of SiC particles (8 wt%) to the melt during stirring (melt temperature: 800 °C) (iii) once the Al-SiC composite was ready, multi-walled carbon nanotubes (CNT powder was compressed in the form of solid tablet and added in the melt) was added into the melt. In this process, SiC particle was added in the melt as thickening agent (iv) after complete addition of CNT, calcium hydride was added in the melt as foaming agent. After completion of foaming, the metallic die with foam, was taken out from the furnace and cooled with compressed air. The foaming temperature was kept constant. The mold was of a relatively large size and was not thermally controlled during foaming. Thus there were temperature gradients with faster cooling near the mold walls resulting in smaller pores (or higher relative density), while the central region of the mold resulted in larger pores (or lower relative density). Thus, samples from different regions provided the relative density variation. The average cell size of RD=0.20 was 1.3 ± 0.3 mm and the cell wall thickness was 230 µm ± 50 µm, whereas the average cell size and cell wall thickness of RD=0.30 were 0.8 ± 0.2 mm and 170 µm ± 30 µm, respectively. The foam block prepared by this way was removed from the die and then cut into pieces conforming to the exact size for testing. The foam block prepared by this way was removed from the die and then cut into pieces conforming to the exact size for testing. Fig. 2 shows a cross-sectional view of closed-cell 2 wt% CNTs Alfoam sample obtained using scanning electron microscope (SEM, magnification 28-100x and voltage 10 kV). The cell size of the foam was measured along different sides of the specimen using the ASTM E112-10 [21] method for measuring diameter of grains in polycrystalline materials (at least 100 measurements were carried out using ImagJ software). The average cell size in the respective foams of different relative density varies in the range of 1.0–1.7 mm. Following the work of Muaki et al. [8,22], Raj et al. [12], and Hamada et al. [23], cubical specimens with 7.5 mm side length were used for high strain rate compression testing, which is ~80% of the SHPB bar diameter of 12.7 mm. Specimens for quasi-static compression were cut into rectangular prisms of 10 mm×10 mm×15 mm. All foam specimens were cut using a low speed diamond wafering cutter. To determine the
Fig. 1. A schematic of the compression stress-strain behavior of Al foam (Adapted from [7]).
structure leads to stress concentration points along the weakest struts, and drastically decreases the strength of the closed cell foam. It has been shown that using carbon based reinforcements (e.g. SiC, fly ash etc.) helps to increase the viscosity and, hence produce favorable uniform microstructure [16]. Moreover, using nanomaterials such as carbon nanotubes (CNTs) to reinforce the Al-foam matrix has been shown to enhance the strength of the foam composite [17–19]. The effect of relative density (density of foam divided by density of solid aluminum alloy) on the mechanical behavior of closed cell aluminum foams has been studied by few researchers. Mondal et al. [20] studied the compressive response of closed cell aluminum-fly ash foam over a range of relative densities (0.08–0.13) and quasi-static compression loading (0.01–10 s−1). Their investigation revealed that plateau stress increased with an increase in relative density, but plateau stress is insensitive to strain rate. Limited work was found on the effect of relative density on the dynamic mechanical behavior of closed cell reinforced aluminum foams. Therefore, further investigations are needed to examine the combined effect of strain rate and relative density on the mechanical properties of aluminum foams, i.e. strength and energy absorption capacity. In this current investigation, 2 wt% CNTs Al composite foam (AA 5083) produced through liquid melt route is studied under dynamic compression loading. The 2 wt% CNTs concentration has been chosen for this investigation based on the results obtained in an earlier study [18,19] on the effect of CNTs concentration in Al-foam on the dynamic compressive response. It was determined that 2 wt% concentration produces the highest peak stress, plateau stress and energy absorption among 1–3 wt% CNT reinforced Al-foams. In this study, Split Hopkinson Pressure Bar (SHPB) apparatus was used to study the dynamic stress-strain response over a varying range of strain rates (1300 s−1 to 2750 s−1) and relative densities (0.16–0.30). For comparison, quasi-static compression tests were carried out over the same range of relative densities.
Fig. 2. Closed cell CNT reinforced Al-foam composite for RD=0.20.
18
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Fig. 3. A schematic description of the in-house SHPB.
was developed by Kolsky in 1949 to determine the high strain rate properties of materials (up to 10,000 s−1) [24]. Fig. 3 shows a typical SHPB system, which consists of three bars: a striker, an incident bar and a transmitter bar. SHPB was utilized to investigate the dynamic mechanical properties of 2 wt% CNTs Al foams at high strain rate (up to 2750 s−1). SHPB is made of 7075 aluminum bars of 12.7 mm diameter. The lengths of striker, incident, and transmitted bars are 457.2 mm, 1820 mm and 1370 mm, respectively. To assure validity of the recorded signals from strain gages, calibration of incident and transmitted bars was carried out [25]. The specimen is sandwiched between the end of incident bar and front of transmitted bar. To minimize friction, a very thin layer of molybdenum grease was applied on both specimen-bar interfaces. After that, the striker bar is launched using pressurized nitrogen gas through the gas barrel. When the striker bar impacts the front end of incident bar, a compressive wave travels in the incident bar until it reaches the interface between back end of incident bar and the specimen, when part of that wave reflects back as a tensile wave and a part is transmitted through the specimen as a compressive wave and into the transmitted bar. Strain gages record three waves: incident (I), reflected (R) and transmitted (T). The recorded strain gage signals are used to determine the incident strain (εI), reflected strain (εR) and transmitted strain (εT). The theory behind SHPB is based on one dimensional elastic wave propagation theory. The expressions for average strain rate, engineering stress and strain in specimen are given in Eqs. (1), (2) and (3) respectively [25,26].
Fig. 4. Stress equilibrium in SHPB.
εṡ =
Fig. 5. Stress-strain response of 2 wt% CNT Al-foams with different relative densities under quasi-static compression (0.001 s−1).
2COB εR Hs0
(1)
⎛A E ⎞ σs (t )=⎜ B B ⎟ εT (t ) ⎝ As0 ⎠
(2)
⎛ 2C ⎞ εs (t )=⎜ OB ⎟ ⎝ Hs0 ⎠
(3)
∫
t
εR (t ) dt
where CoB, AB and EB are the wave speed, cross-sectional area and elastic Young's modulus of SHPB bars, respectively. HS0 and AS0 are the length, and the cross-sectional area of the specimen, respectively. The forces in incident and transmitted bars are given by Eqs. (4) and (5), respectively. To satisfy the 1-D assumption in SHPB, specimen must be under dynamic stress equilibrium and deform under constant strain rate [25,26]. Stress equilibrium is achieved when the forces on front (F1) and rear (F2) surfaces of specimen are nearly equal, which results in expression (6). This assumption is satisfied when long bars (incident and transmitted) have uniform elastic, homogeneous, isotropic characteristics across its cross-section and along its length; such
density of the foam, the dimensions of the specimen were accurately measured and weighed using a digital caliper and digital balance. Relative density was estimated as density of foam/density of base aluminum alloy.
2.2. Mechanical characterization The conventional split Hopkinson pressure bar (SHPB) apparatus 19
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Fig. 6. Compressive stress-strain response of 2 wt% CNT Al-foams with different relative densities at a strain rate of (a) 1300 s−1, (b) 1800 s−1, (c) 2300 s−1 and (d) 2750 s−1. Table 1 Peak stress (σPeak), plateau stress (σPl) and densification strain (εD) as a function of strain rate and relative density. Relative Density
0.16 0.20 0.26 0.30
Strain Rate (s−1) 0.001
Strain Rate (s−1) 1300
Strain Rate (s−1) 1800
Strain Rate (s−1) 2300
Strain Rate (s−1) 2750
σPeak (MPa)
σPl (MPa)
εD
σPeak (MPa)
σPl (MPa)
σPeak (MPa)
σPl (MPa)
σPeak (MPa)
σPl (MPa)
σPeak (MPa)
σPl (MPa)
3.51 8.15 12.03 18.06
4.23 7.52 10.54 16.60
0.71 0.59 0.55 0.46
6.21 7.53 11.12 17.57
4.22 6.71 11.54 17.14
6.53 9.15 11.85 18.66
5.54 8.52 12.11 18.13
7.13 12.04 14.33 20.54
4.82 12.24 13.56 21.14
7.5 13.1 15.2 21
5.76 13.67 15.8 21.4
Fig. 7. Dynamic compressive stress-strain response of 2 wt% CNT Al-foams of RD=0.20 as a function of strain rate.
Fig. 8. Dynamic compressive stress-strain response of 2 wt% CNT Al-foams of RD=0.30 as a function of strain rate.
as EB, AB and COB.
is achieved in the specimen. The stress equilibrium in the specimen takes less than 40 μs to be achieved. In every test we ensured that a fairly constant strain rate was achieved over the duration of the test. Quasi-static compression testing was carried out at strain rate of 1×10−3 s−1 using ADMET material testing machine.
F1=AB EB (εI +εR )
(4)
F2=AB EB εT
(5)
εI +εR=εT
(6)
To assure the 1-D wave theory assumption of SHPB holds, the specimen aspect ratio (length/width) is selected to be 1, and a copper (C14500) pulse shaper was used for this work, which helped to achieve stress equilibrium in the specimens [27]. The detailed process for selecting specimen aspect ratio and pulse shaper are reported elsewhere [18]. Fig. 4 shows that the stress equilibrium condition of Eq. (6)
3. Results and discussion The stress-strain response of 2 wt% CNT reinforced foam under quasi-static compression is shown in Fig. 5, which is similar in nature to a typical compression behavior shown in Fig. 1. Peak stress is reported as the maximum stress value attained just before the start of 20
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Fig. 12. Peak stress against strain rate at different relative densities.
Fig. 9. Peak stress as a function of relative density at different strain rates.
Fig. 13. Plateau stress against strain rate at different relative densities. Fig. 10. Plateau stress as a function of relative density at different strain rates. Table 3 Variation of “m” with relative density.
Table 2 Variation of “A” and “b” with strain rate. #
1 2 3 4
Strain Rate (s−1)
1300 1800 2300 2750
Peak Stress
#
Relative Density
mPeak
mPlateau
1 2 3 4
0.16 0.20 0.26 0.30
0.24 0.65 0.45 0.26
0.40 0.69 0.45 0.37
Plateau Stress
A
b
A
b
104.80 133.02 135.50 131.10
1.58 1.61 1.55 1.53
208.8 216.2 261.8 284.6
2.13 2.04 2.12 2.07
density varies from 0.16 to 0.30. Fig. 6a-d show engineering stress-strain plots under dynamic compression at different strain rates and relative densities. At 1300 s−1, it is found that compressive stress significantly increases as the relative density increases. Hence, the highest peak stress and plateau stress of 17.5 MPa and 17.0 MPa, respectively, are observed for the relative density of 0.30. For RD=0.16 foam, the peak stress and plateau stress increase up to a strain rate of 1800 s−1 and no further increase with strain rate is observed. The higher relative density foams (0.20, 0.26 and 0.30) exhibit an increase in peak and plateau stresses with strain rate up to 2300 s−1 with nearly no gain beyond this strain rate. It should be noted that higher relative density foam is stiffer due to the effect of having thicker cell walls, which in turn increases the stress levels. To better visualize the combined effect of strain rate and relative density, a summary of the compressive stresses of this investigation is presented in Table 1. It is observed that compressive stresses at any fixed relative density increase with strain rate. In a broad prospective, higher increase in plateau stress is observed for higher relative densities as the strain rate increases. This shows an agreement with the reported results of Raj et al. [12] that higher density foam, RD > 0.15, exhibits significant increase in compressive stress under dynamic compression. The compressive stress–strain curves of foam at various strain rates for relative density of 0.20 and 0.30 are shown in Fig. 7 and Fig. 8,
Fig. 11. Ln‘Apl’ vs. Ln'Strain Rate’.
plateau region. Plateau stress is reported as the average stress throughout the plateau region (see Fig. 1). It is observed that stressstrain curves show small oscillations in the plateau region. This is attributed to the localized cell deformation and sequential compaction of layers throughout the plateau region [9,12]. It should be noted that peak stress and plateau stress significantly increase as the relative 21
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Fig. 14. Cross-sectional view of closed cell Al-foam composite with different relative densities (a) 0.15, (b) 0.20, (c) 0.26, and (d) 0.30.
Fig. 15. Variations of densification strain as a function of relative density at strain rate of 0.001 s−1.
Fig. 16. Energy absorption as a function of strain rate and relative density.
respectively. For the relative density of 0.20, peak and plateau stresses displayed significant increases as the strain rate increased, whereas those with relative density of 0.30 exhibited smaller increase with the increase in strain rate. Hence, this indicates that foam with relative density of 0.20 is more sensitive to strain rate. In this study, peak stress (σPeak) also termed as the elastic collapse stress (σel) is shown in Fig. 1. Generally, the variation of peak stress (σPeak) and plateau stress (σPl) with relative density follow a power law relationship presented in Eqs. (7) and (8) [1].
⎛ ρ ⎞bP σPeak =AP ⎜ f ⎟ ⎝ ρs ⎠
Table 4 Energy absorption (WV) as a function of strain rate and relative density.
(7)
22
Relative Density
Strain Rate (s−1) 0.001 WV (MJ/ m3)
Strain Rate (s−1) 1300 WV (MJ/ m3)
Strain Rate (s−1) 1800 WV (MJ/ m3)
Strain Rate (s−1) 2300 WV (MJ/ m3)
Strain Rate (s−1) 2750 WV (MJ/ m3)
0.16 0.20 0.26 0.30
0.52 2.34 3.02 4.87
1.26 2.42 3.32 5.24
1.37 2.54 3.66 5.78
1.41 3.39 4.28 6.35
1.62 3.64 4.39 6.27
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Fig. 17. Deformation of closed cell Al-foam (RD=0.20) at different strain (a) 0%, (b) 5%, (c) 10%, and (d) 20%.
⎛ ρ ⎞bPl σPl =APl ⎜ f ⎟ ⎝ ρs ⎠
sensitivity observed in 0.20 relative density foam. For foam with RD=0.26, more small size pores appeared leading to less uniform cell size. As the relative density increased to 0.30, cell size becomes smaller with an average cell size of 0.8 ± 0.2 mm and the foam has more solid areas. Fig. 15 shows the variations of densification strain as a function of relative density of specimens tested under quasi-static compression (strain rate of 0.001 s−1). The densification strain is considered as the strain corresponding to the intersection of tangents drawn on the densified and the plateau regions. It is noted that densification strain decreases as the relative density increase. The curve fit line follows the equation of a linear line, y=mx+b in which m equals −1.5 and b equals 0.94. The constants of this straight-line equation are within ± 6% of the constants in Eq. (9) provided by Gibson et al. [1]. It may be noted that as the relative density varies from 0.16 to 0.30 the corresponding densification strain varies from 0.71 to 0.46. For RD less than 0.16, we hypothesize that the densification strain would be invariant to the change in relative density, following the study by Mondal et al. [3] even though their foam system had a different reinforcement, namely flyash. The densification strain cannot be determined for dynamic tests as the impact pulse duration is not long enough to produce sufficient densification.
(8)
where ‘Ap’ and ‘Apl’ are the respective strengthening coefficient, ρf is the density of foam, ρs is the density of solid metal and ‘bp’ and ‘bpl’ are the respective exponent to relative density. Fig. 9 shows the variation of peak stress as a function of relative density at different strain rates. The variation of plateau stress as a function of relative density at different strain rates is shown in Fig. 10. The data for peak stress and plateau stress as a function of relative density were curve fitted using a power low relationship y=Axb. The values of ‘A’ and ‘b’ are presented in Table 2. The value of ‘b’ in this present study shows a good agreement with the reported values (1.5–3.0) for aluminum foams [1]. Fig. 11 presents a the variation of Ln‘Apl’ with Ln'Strain Rate’. Peak stress and plateau stress are plotted against strain rate for different relative densities on a log-log plot (see Figs. 12 and 13) to estimate the strain rate sensitivity. The strain rate sensitivity ‘m’ is calculated as the slope of each line (in Figs. 12 and 13) for each relative density presented in Table 3. It is noted that peak stress for relative densities 0.2 and 0.26 show stronger strain rate sensitivity as compared to others. For plateau stress, the strain rate sensitivity of relative densities 0.16, 0.26 and 0.30 varies in the range 0.37–0.45, while a relative density of 0.20 displays the highest strain rate sensitivity of 0.69. Fig. 14a-d show the cross-sectional view of closed cell Al-foam composite with different relative densities 0.16, 0.20, 0.26, and 0.30, respectively. Foam with RD=0.16 has irregular cell size and shape whereas foam with RD=0.20 has more uniform cell size, cell wall thickness and cell distribution an average cell size of 1.3 ± 0.3 mm. Therefore, this might be the plausible reason for the higher strain rate
⎛ρ ⎞ εD=1 − 1.4 ⎜ f ⎟ ⎝ ρs ⎠
(9)
The energy needed under compression to deform any foam specimen up to particular strain is defined as the energy absorption capacity. Under uniaxial compressive loading, energy absorption, WV, per unit volume is given as the area under stress-strain curve up to a specific 23
Materials Science & Engineering A 689 (2017) 17–24
A. Aldoshan, S. Khanna
strain εo, and evaluated using the following expression:
WV=
∫0
εo
σ(ε)dε
Acknowledgement The authors wish to thank Dr. D.P. Mondal and Dr. S. Das of the Advance Materials and Processes Research Institute (AMPRI), CSIR, Bhopal, India for providing foam samples. Abdelhakim Aldoshan would like to acknowledge King Abdulaziz City for Science and Technology (KACST), Riyadh, for the scholarship.
(10)
The energy absorption of 2 wt% CNTs foams has been evaluated for different strain rates and relative density. Fig. 16 shows the energy absorption up to 30% strain of 2 wt% CNTs foams plotted against strain rate in the range 0.001 s−1–2750 s−1 for different relative densities. It can be seen that the energy absorption is strongly influenced by strain rate. The increase in energy absorption with strain rate is nearly the same for all foams of relative density of 0.20, 0.26 and 0.30, though the total energy absorption is higher for higher relative density due to the higher associated plateau stress. To visualize the combined effect of high strain rate as well as relative density, Table 4 summaries the energy absorption of 2 wt% CNTs foam. To study the deformation mechanisms in the CNT reinforced closed-cell Al-foam under quasi-static loading, images were captured for RD=0.20 at different strain 0%, 5%, 10% and 20%, as shown in Fig. 17a-d. In the undeformed image (Fig. 17a), eight cells were selected and then labeled with upper case letters ‘A’ to ‘H’. The labeled cells were then evaluated at higher strains based on the change in their shape and size. At 5% strain (Fig. 17b), cell ‘A’ showed plastic bending. The upper cell wall of ‘B’ experienced bending whereas the lower cell wall displayed plastic buckling. Cell C was mostly crushed (Closed). Also, the upper cell wall of ‘D’ exhibited plastic buckling whereas left cell wall remained undeformed. Moreover, the presence of defects in the cell wall such as uneven wall thickness could further lead to fracture, as shown in the right side cell wall of ‘H’. Also, a rapture in the cell membrane of ‘H’ was observed and a white arrow points at the location of the burst. This may be attributed to the release of the compressed gas inside the cell. It should be noted that other cells remain undeformed (such as E, G and F). At higher strain of 10% (Fig. 17c), plastic deformation progresses around the area of cells A, B, C and D while cells E, F and G maintained their original shape and size. As the strain increased to 20% (Fig. 17d), plastic collapse spreads further to the adjacent cells.
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4. Conclusions Compressive mechanical properties of closed-cell CNT reinforced Al-foams have been investigated under quasi-static and dynamic loading with different relative densities of 0.16, 0.20, 0.26 and 0.30. Split Hopkinson pressure bar was used for studying the dynamic compression behavior. The salient observations of this work are listed below.
• • • •
At all applied strain rates, mechanical properties significantly increase as the relative density increases in terms of peak stress, plateau stress and energy absorption. For similar strain rates, plateau stress is approximately 230–300% higher for relative density of 0.30 compared to the low relative density foam (RD=0.16). Energy absorption in the foam of RD=0.30 is also 240–270% higher than low relative density foam RD=0.16. For all relative densities, compressive stresses and energy absorption displayed a strain rate dependence. The CNT foam of RD=0.20 exhibits the highest strain rate sensitivity among all the foams studied. It is postulated that this behavior relates to the more uniform cell structure in the 0.20 relative density foam.
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