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Compressive deformation and energy absorption characteristics of closed cell aluminum-fly ash particle composite foam
Materials Science and Engineering A 507 (2009) 102–109
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Compressive deformation and energy absorption characteristics of closed cell aluminum-fly ash particle composite foam D.P. Mondal ∗ , M.D. Goel, S. Das Advanced Materials and Processes Research Institute (CSIR), Bhopal 462 064, India
a r t i c l e
i n f o
Article history: Received 2 July 2008 Received in revised form 24 November 2008 Accepted 7 January 2009 Keywords: Aluminum foam Plateau stress Energy absorption Relative density Closed cell
a b s t r a c t Deformation response and energy absorption characteristics of closed cell aluminum-fly ash particle composite foam have been assessed under compressive loading at different strain rates (10−2 to 101 s−1 ). The investigated foams were made by melt route using CaH2 as foaming agent. The influence of strain rate on the deformation responses is found to be very marginal; within the domain considered in the present study, and the strain rate sensitivity was measured to be very low and varying in the range of 0.02–0.04 when the foam relative density is greater than 0.1. The plateau stress, and energy absorption increase significantly following power law relationship with relative density; whereas the densification strain is almost invariant to the relative density. The strain rate sensitivity of the investigated material was found to be negative when the foam relative density is less than 0.1. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Metal foams especially the ones based on lightweight metals have interesting combinations of properties such as high specific stiffness, strength combined with good energy absorption characteristics. These make metallic foams to be potential material for absorbing impact energy during the crashing of a vehicle either against another vehicle or a pedestrian. Potential applications of these foams also exist in shipbuilding, aerospace industry and civil engineering [1]. In order to absorb the impact energy more effectively, a material is required to exhibit an extended plateau stress region and high densification strain, and this is the most attractive feature of the metal foams [1]. Thus, these foams found wide application in energy absorption. Furthermore, such applications require indepth knowledge on deformation response especially compressive deformation response of metal foams, at various impact velocities vis-à-vis strain rates. The deformation behaviour of metal foams has been investigated recently by a group of investigators [2–7]. Unique combination of properties such as low density, high stiffness, strength, and energy absorption in metal foam can be tailored through design of its microstructure. Strain rate effects on polymeric foams have been studied in past to a large extent, whereas only a few data, sometimes contradict-
∗ Corresponding author. Tel.: +91 7552417652; fax: +91 7552587042. E-mail address: [email protected] (D.P. Mondal). 0921-5093/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2009.01.019
ing, can be found in literature on the deformation behaviour of Al metal foams. Kenny [2], Lankford and Dannemann [3] reported that the specific energy absorption of aluminum foam and plateau stress was independent of strain rate. Deshpande and Fleck [4] also studied the compressive deformation behaviour of Alulight closed-cell foam and Duocel open-cell foam under varying strain rates and concluded that the plateau stress was almost insensitive to strain rate, for strain rates ε´ up to 5000 s−1 . Similar observations were made by Ruan et al. [5]. On the other hand, Mukai et al. [6] reported that the compressive behaviour of closed cell aluminum foam under high strain rate is associated with an apparent strain hardening. They further observed that strain rate sensitivity of plateau stress increases with decreasing relative density. According to their investigations, this is attributed to gas pressure in the closed cell. Recently, Montanini [8] studied three types of foam including both open cell and closed cell and observed that plateau stress is independent of strain rate for CYMAT and MPORE foam while the dependency of plateau stress with strain rate is quite remarkable for SHUNK foams. It was also observed that specific energy dissipation of similar density foam could be quite different depending on strain rate. Thus, there exists an ambiguous opinion about strain rate sensitivity of metals foams. Most of the above studies have been conferred to Al foam or Al–SiC composite foam. The understanding of deformation response and energy absorption characteristics as a function of strain rate and relative density has yet not been crystallized. The present paper aims at studying the compressive deformation response of Al-fly ash composite foam and then to assess their energy absorption
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characteristics as a function of strain rate and relative density. This aspect comes into mind from the available literature where fly ash particles have found application for synthesis of Al-fly ash composite [9–11]. It is thus understood that fly ash particles are stable in liquid Al melt and it could also be used as thickening agent like that of SiC particles. Additionally, the fly ash are waste generated in coal based thermal power plant and thus very much cheaper than SiC particles, which would lead to reduction in cost of Al composite foam. Furthermore, a waste can be used for generation of value added product. An attempt has also been made to examine the strain rate sensitivity of Al-fly ash composite foam of varying relative density. In this paper attention has been focused on the effect of strain rate and relative density on the plateau stress, densification strain and energy absorption characteristics of closed cell aluminum-fly ash composite foam. 2. Experimental Closed cell aluminum-fly ash composite foams of relative densities ranging from 0.08 to 0.13 were prepared using fine fly ash particle as thickening agent and calcium hydride (CaH2 ) as foaming agent through liquid metallurgy route. The matrix alloy (AA2014Al-alloy) normally contains 4.6 wt% Cu, 1.9 wt% Mg, 0.5 wt% Mn, 0.4 wt% Si, 0.5 wt% Fe, 0.1 wt% Ti, 0.1 wt% Cr and balance Al. The details of the process have been reported elsewhere [12]. Fly ash particles in the size range of 2–10 m of about 5% by weight were used as thickening agent. CaH2 powder of 0.60% by weight in the size range of 20–50 m was used as foaming agent. The size distribution of CaH2 and fly ash particles are shown in Fig. 1(a) and (b), respectively. One typical bulk aluminum foam sample is shown in Fig. 2. Microstructural characterization of foam is made using Scanning Electron Microscope (SEM). The methodology applied for microstructural examination of Al-fly ash foam has been explained in the other paper [13–16]. The diameter of the cell of the synthesized foam was measured according to the method prescribed by ASTM for the measurement of grain diameter in polycrystalline materials [17]. The cell size of the synthesized foam varies in the range of 1.0–3.0 mm. The cell sizes of foams changed with their densities. The cell size increases with decreases in relative density. For compression test, specimens were cut from the fabricated foam with average dimensions of 4.5 cm × 4.5 cm in cross-section and 5.5 cm in height. Specimen size is so chosen to avoid size effect on mechanical properties of the foam. Compression test at strain rate of 10−2 to 101 s−1 were performed using BISS universal testing machine. Samples were placed on the bottom ram of the machine and load was applied to the samples when the top ram moved downward. Before testing, contact surfaces between samples and two loading head were coated with a spray of MoS3 to reduce friction. A computer attached to the machine recorded the load and the displacement data automatically, which is used to obtain the stress–strain relation diagram. A few set of samples were tested to the strain level of 0.005, 0.02 and 0.05 in order to understand the densification mechanism. These samples after testing were cut carefully and examined in SEM. 3. Results and discussions
Fig. 1. (a) Size distribution of CaH2 and (b) fly ash particles.
the cell size in the foams made at 690 ◦ C is bigger than that made at 670 ◦ C. The cell wall thickness, cell sizes and relative density of the investigated foam samples as a function of foaming temperature is shown in Table 1. This table clearly indicates that the cell wall thickness increases and cell size decreases with decreases in foaming temperature. Thinner cell wall and coarser cell size at higher foaming temperature lead to lower relative density. Variation is also expected due to decrease in viscosity and surface tension of melt with increase in temperature [18,19]. From the reported relation, it could be noted that surface tension of 2014 Al-alloy at a temperature of 670 ◦ C and 690 ◦ C would be ∼750 Nm/m and 720 Nm/m, respectively. In addition, the gas volume increases with increase in
Table 1 Cell size, cell wall thickness and relative densities of Al-fly ash composite foams.
3.1. Microstructural characterization
Sr. no.
Foaming temperature (◦ C)
Cell size (mm)
Cell wall thickness (m)
Relative density
The overall cellular structure of typical Al-fly ash composite foams made at a foaming temperature of 670 and 690 ◦ C is shown in Fig. 3(a) and (b), respectively. It may be noted that the foams structure are not so uniform, which contains random cell sizes. In both the cases a few cells are relatively bigger in size. As a whole,
1. 2. 3. 4. 5.
675 680 685 690 695
1.70 1.81 2.29 2.88 3.21
193 183 156 130 112
0.130 0.110 0.100 0.090 0.080
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temperature and this leads to higher gas pressure within the cell. This, in turn, facilitates growth of the cell until the pressure inside the cell equals to that its surrounding pressure, which is a function of surface tension and viscosity. Because of lower surface tension and viscosity, greater surface area required to make the cell in equilibrium. Thus the cell grows to bigger size at higher temperature. Fly ash particles through the control of melt viscosity decreases melt flowability in all direction and helps in giving a stable shape to the cell. 3.2. Compressive stress–strain curves
Fig. 2. One typical bulk aluminum foam sample.
Stress and nominal strain are deduced from the recorded load and displacement data using standard methodology. The stress–strain curves for all the tested foam samples are found to be similar kind, in which, they all have an initial linear elastic region (stage-I), an yield point (stage-II), a plateau region where the stress increases slowly with strain as the cells deform plastically (stageIII), and a region of rapidly increasing load (densification region), (stage-IV). Fig. 4 shows a typical stress–strain curve of closed cell aluminum-fly ash particle composite foam having relative density 0.11 and tested at a strain rate 0.01 s−1 . It may further be noted that at plateau region the stress varied in zig-zag fashion with strain. Hence, Plateau stress is considered, here, as the average stress in the plateau region and the densification strain is considered to be the strain corresponding to the intersection of tangents drawn on the densified and the plateau regions as schematically shown in Fig. 4. The energy absorption (Eab ) is considered to be the area under the curves up to the densification strain (εd ) as marked in Fig. 4. This can be expressed as follows:
Eab =
εd
dε
(1)
0
For each relative density and strain rate a set of five samples was tested. Only typical plot for one sample from each set has been reported. However, average plateau stress, densification strain and energy absorption were concluded by considering all the plots for each set. In fact, here for each set, the relative density reported is the average relative density within accuracy of 0.005. The relative density of foam samples varies by varying the process parameter like foaming temperature. For testing, foam samples from the centre of the block were taken to avoid the effect of foaming direction on the deformation behaviour.
Fig. 3. Cellular structure of Al-fly ash composite foams at foaming temperature of (a) 670 ◦ C and (b) 690 ◦ C.
Fig. 4. Stress–strain curve (RD = 0.11and strain rate = 0.01).
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Fig. 7. Variation of plateau stress with relative density at varying strain rate. Fig. 5. Compressive stress–strain curves of Al-fly ash composite foam for various relative densities at fixed strain rate of 0.10.
3.3. Effect of strain rate and relative density The compressive stress–strain curves of Al-fly ash composite foam for various relative densities at fixed strain rate of 0.10/s is shown in Fig. 5. It is evident from this figure that at fixed strain, stress increases with increase in relative density. Also, variation of compressive stress–strain curves at different strain rates is shown in Fig. 6 for a fixed relative density of 0.107. This figure indicates that the plateau stress lies in a narrow range even with the variation of strain rate at wider range (0.01–10). It may further be noted that at higher strain rate plateau stress is marginally less (for strain rate 0.01–1.0). But at higher strain rate (10/s) the plateau stress is noted to be marginally higher than that of at strain rate of 1/s. This demonstrates that the plateau stress does not follow any specific relationship with strain rate; it varies in a narrow region randomly with strain rate. Fig. 7 represents the variation of plateau stress with relative density at different strain rate. It is noted that the plateau stress follow power law relationships with relative density irrespective of strain rate. It may further be noted
Fig. 6. Variation of compressive stress–strain curves at different strain rates.
that the overall variation of plateau stress at fixed relative density for the entire range of strain rate is around 0.5 MPa. Additionally, the plateau stress at higher strain rate is noted to be marginally less than that at lower strain rate. This figure, in fact, indicates that the plateau stress does not follow any specific trend with strain rate. The variation of densification strain at different strain rate with relative density is shown in Fig. 8. It may be noted that the densification strain is varying in a very narrow range (0.68–0.73) and it seems to be almost invariant to the relative density and strain rate. The plateau stress at different relative densities as a function of strain rate in the ln-scale is plotted in Fig. 9. It is evident from this figure that the slope of the line is negative for relative density less than or equal to 0.10, at higher relative density, the slope is positive. This signifies that at higher relative density, the plateau stress increases with strain rate where as at lower relative density, the plateau stress decreases with strain rate. However, the absolute magnitude of the slope is very marginal (0.022–0.047). This signifies that the value of strain rate sensitivity is considerably less and the effect of strain rate on plateau stress is insignificant.
Fig. 8. Variation of densification strain at different strain rate with relative density.
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Fig. 9. Plateau stress at different relative density as a function of strain rate. Fig. 11. Coefficient m as function of relative density.
3.4. Strain rate sensitivity The effect of strain rate on plateau stress could be expressed in the following form: pl = Kf ε˙ m
(2)
where pl is the plateau stress, Kf is the strengthening coefficient,
ε´ is the strain rate and m is the strain rate sensitivity. Thus, the slope of ln ( f ) vs ln (ε´ ) plot gives the value of m and antilog of intercept gives the value of Kf , the strengthening coefficient. The value of Kf and m is plotted as function of relative density in Figs. 10 and 11, respectively. It is noted from Fig. 10 that Kf decreases with relative density when relative density changes from 0.08 to 0.089. With further increase in relative density, Kf increases with relative density very sharply. This demonstrates that the strengthening coefficient, which is primarily controlled by deformation response of the cell walls, is noted to be minimum at a relative density between 0.09 and 0.010. Below and above this relative density the strengthening coefficient is higher. At higher relative density, because of wider cell wall thickness, the cell wall material could withstand higher stress value prior to deformation, bending and crushing. At lower relative density, the cell walls are very thin and thus they have greater tendency of bending rather
than crushing. In addition, more gas pressure (hydrostatic in nature) on the coarser cell causes delay in cell fracture [20–22], which may lead to greater Kf value. At intermediate relative density the tendency of cell wall crushing is reasonably higher and the effect of gas pressure is relatively lower, which may lead to less strengthening coefficient. Fig. 11 shows the variation of m with relative density. It is evident from this figure that the m is negative when the relative density is less than 0.10. At higher relative density, the m is positive. This signifies that the plateau stress increases with strain rate marginally, when the relative density is greater than 0.10. The plateau stress decreases with strain rate when relative density is less than 0.10. But the value of m is very low 0.02–0.04, which signifies that the variation of stress with strain rate is very marginal. This may be attributed to the fact, that the deformation and compaction behaviour of foam is primarily controlled by the cell wall bending, stretching and crushing. It rarely may be controlled by the slip and dislocation controlled deformation mechanism in the plateau region especially when the cell walls are very thin. It primarily depends on the stress–strain distribution on the cell walls. At higher relative density, (i.e. relative density >0.10), cell walls are relatively thicker and the shear type of deformation of cell wall material could be observed prior to fracture or crushing. However, in the present study, the relative density is estimated to 0.13 and thus the cell walls are noted to be very thin irrespective of relative density. This may be another cause for marginal variation in m values which is also very low. 3.5. Plateau stress and relative density correlation The plateau stress and energy absorption found to be almost invariant to strain rate. The strain rate sensitivity calculated in these materials in the used domain of strain rate was noted to be very low. But, these properties are strongly influenced by the relative density. According to Gibson and Ashby model [22], the plateau stress of foam follows following relation with relative density: pl ys
Fig. 10. Kf as function of relative density.
3/2 f
≈ 0.3 ϕ
s
+ (1 − j)
f s
+
p0 − pat ys
(3)
where pl is the plateau stress of foam, ys and s are the yield stress and density of the dense material that the foam cell wall is made of, f is the density of foam, ϕ is the fraction of solid in the cell edges of foam, p0 is the initial fluid pressure in the cell of foam and pat is atmospheric pressure. In manmade foams p0 is usually equal to pat which means that the gas has little effect on the plateau stress. So
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the third term in the above formula is very insignificant. It has been found that the second term of the above formula also has little contribution to plateau stress [13], which may be attributed to the fact that ϕ is very close to 1 as most of the materials in foam is occupied in the edges and the plateau region. Thin layer of the material, separating the cells is significantly less than that present in the cell wall and the plateau region. Thus, only the first term of the above formula is adequate to describe the plateau stress even for closed-cell foams. Moreover, it has also been observed by other researchers [2,20–22] that many properties of foam including plateau stress obey a power law: A() = A0 n
(4)
where A is the property of foam, is the density of foam, A0 is a factor, which reflects the properties of the solid cell wall material, and n is an exponent. In the present case, the plateau stress follows the power law of variation: pl =
ys
n f
s
=K
s f
n
(5)
where ys is the yield strength of the solid material with which the foam is made off. pl is the plateau stress of the foam and n is the exponent. The value of n varies in the range of 2.034–2.205 depending on the strain rate. This is in good agreement with the reported values. Similarly, the value of coefficient is varying in the range of 227 MPa to 294 MPa which is the measure of the product of yield strength of the solid material ( ys ) of the foam and the fractional coefficient in Eq. (5). The yield strength of 2014 Al–5 wt% fly ash composite at a strain rate of 1/s measured to be 298 MPa. It is observed by the present authors that the strength of 2014 Al–SiC Composite is almost invariant to the strain rate [12,13]. This also supports the strain rate independent of plateau stress of the Al-fly ash composite foam. Considering the yield strength of 298 MPa of the Al-fly ash composite in the present foam, the coefficient could be calculated using the following relation: =
K ys
(6)
The value of comes to be in 0.76–0.98 depending on the relative density. Present authors in their recent publication [15,23] also found that the coefficient is around 0.70 while the modulus of closed cell foam is expressed following Gibson and Ashy relation [17]. The value of in the range of 0.76–0.98 is also reported by other investigators [5–7,12–14,21,24–41]. The differences in the coefficient may be due to influence of strain rate or the differences in the actual materials property of the cell walls of the investigated foam as a whole at various relative densities. This fact has been observed from the microhardness measurement in the plateau region of the investigated foam samples as a function of relative density as shown in Table 2. It is evident from this table that at higher relative density the microhardness values are higher. However, the value of calculated on the basis of yield stress of the dense materials. The difference in the average microhardness values from the overall average is noted to be ±10%. This is within the acceptable range of variation in microhardness measurement.
Thus, it could be considered that overall microhardness variation in matrix is very marginal with relative density. If we average out the constant, the value becomes 0.88 and the lower and upper limit comes between 15% of accuracy. The present investigation notes that the plateau stress follows a power law variation with relative density and it varies marginally with strain rate. At lower strain rate, the plateau stress is higher than that at higher strain rates. 3.6. Energy absorption The study further states that the densification strain is almost invariant to the relative density and strain rate. Hence, the variation of energy absorption with relative density and strain rate is also noted to be of the similar trend to that of plateau stress with relative density. The energy absorption by unit volume of the investigated foam samples was plotted as a function of relative density in Fig. 12 when the foam samples are loaded at different strain rate. It is evident from this figure that the energy absorption by the Al-fly ash foam also follows a power law variation with relative density irrespective of the strain rate. It is further noted that the Al-fly ash foam exhibits lower energy absorption while tested at higher strain rate (>1.0/s). At lower strain rate the foam samples exhibits relatively higher energy absorption characteristics. This is attributed to the fact that the cell wall material of foam having very low relative density behaves differently under varying strain rate. As expressed earlier, that the relative density of the investigated foam is very low (max. 0.13), the cell walls are also very thin. At higher strain rate, because of dynamic nature of force, the cell wall might be fractured/crushed more easily and thus leading to lower plateau stress as well as energy absorption characteristics. Whereas at lower strain rate gradual bending followed by crushing of the cell wall may be the dominating mechanism. Thus, the foam exhibits higher stress vis-à-vis energy absorption at lower strain rate. Thus, the energy absorption of Al-fly ash composite foam could be expressed as follows: Eab = K
n2 f
s
Relative density
Microhardness (kgf/mm2 )
1. 2. 3. 4. 5.
0.130 0.110 0.100 0.090 0.080
118 115 110 107 105
± ± ± ± ±
6 5 5 4 5
(7)
The value of n2 is expected to be almost same as that of n in Eq. (4) as the energy absorption primarily dependent on pl . This is exactly observed in the present study. The value of n2 comes to be in the range of 1.84–2.5, which is comparable to the value of n (2.0–2.25). The energy absorption value of the Al-fly ash foam varies in a narrow range. Overall magnitude of differ-
Table 2 Microhardness of aluminum-fly ash composite foam as a function of relative densities. Sr. no.
107
Fig. 12. Variation of energy absorption with relative density.
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Fig. 13. Micrograph of deformed closed cell Al-fly ash composite foam at strain rate of 0.001/s: (a) 0.5%, (b) 2%, (c) 5%, (d) 5% (higher magnification).
Fig. 14. Micrograph of deformed closed cell Al-fly ash composite foam at strain rate of 1/s: (a) 0.5%, (b) 2%, (c) 5%, (d) 5% (higher magnification).
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ences: (0.25 MJ/m3 to 0.30 MJ/m3 ) at fixed relative density for wide range of variation in strain rate. This signifies only marginal effect of strain rate on energy absorption of the Al-fly ash composite foam. 3.7. Deformation mechanism During compressive loading, the cell wall may behave differently under different strain rate. In order to confer these fact, Al-fly ash composite foam samples having relative density of 0.089 were tested respectively up to strain levels of i.e. 0.5%, 2% and 5% under two strain rates i.e. 0.001/s and 1.0/s. Fig. 13(a) shows the cell structure of Al-fly ash composite foam after 0.5% deformation at strain rate of 0.001/s. It is evident from this figure that the cell walls gets slightly bulged and bent (arrow mark). When the same sample is deformed up to 2%, it is noted that the cell walls get bent significantly (arrow mark) and also subjected to crack inside (as marked C) as shown in Fig. 13(b). Further increase in strain level (5%) leads to further bending (arrow mark) and greater degree of cell wall cracking (marked C) as shown in Fig. 13(c). The cracked cell wall in due coarse get sheared and crushed. Fig. 13(d) shows clearly the through cracking of cell wall even in plateau region (marked C). Fig. 14(a) depicts the cell structure of Al-fly ash composite foam having density of 0.089 after 0.5% deformation at a strain rate of 1/s. This figure shows the slight bending of the cell wall (arrow marked) along with its shearing of cell wall (marked S). When the strain increases to 2%, the cell walls (which are relatively thin) start shearing (arrow marked) and in due course get crushed as shown in Fig. 14(b). When the cell walls are relatively thicker the start of shearing of cell wall (marked ‘arrow’) could be more clearly examined in Fig. 14(c). Shearing of cell wall and its crushing followed by tendency of compaction could be shown in Fig. 14(d), when the Al-fly ash foam is tested up to strain rate of 1/s up to 5% strain. These figures indicate that the cell wall has the tendency of bending followed by shearing and crushing during compressive loading at lower strain rate. This bendiness is more for thin cell walls. As the cell walls are thinner at lower relative density, it is also expected that greater extent of cell wall bending would took place in the case of deformation of foam with lower relative density. However, at higher strain rate, the cell wall primarily gets sheared prior to crushing and hardly subjected to bending. As stated by other investigators, the deformation progresses layer by layer with increase in strain level. Because of the variation in deformation mechanism of cell wall with cell wall thickness i.e. relative density and strain rate, the m and K are noted to be varying (in a narrow range) with these parameters. At lower relative density, greater extent of bending and relatively less shearing leads to relatively higher K value. At intermediate relative density both bending and shearing are equally responsible for cell crushing and leading to lower K value. At higher relative density, shearing deformation is dominating and extent of bending is less, which leads to increase in K value. The deformation, in the metal foam, particularly in plateau region is primarily controlled by bending, shearing, crushing and compaction of cell walls vis-à-vis cell, which also influenced by strain rate. Similarly, the value of m is also varying with relative density. However, the value of m varies within a very narrow range ±0.04, which demonstrates that the compressive deformation of low density Al-foam is almost insensitive to strain rate.
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4. Conclusions Compressive tests at strain rates 10−2 to 101 s−1 have been conducted on closed cell aluminum-fly ash composite foam. The stress versus nominal strain curve for all the tested foam samples is similar. They all have four characteristics: an initial linear elastic region, a yield point, a plateau region and densification. The densification strain is almost invariant to the relative density and the strain rate; and the plateau stress depends highly upon the relative density and marginally upon the strain rate. Plateau stress is not sensitive to strain rate in present domain of study. This signifies that the strain rate effect on the compressive deformation response for the very light aluminum foam is insignificant. However, the deformation response is strongly influenced by the relative density. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41]
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Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Compressive deformation and energy absorption characteristics of closed cell aluminum-fly ash particle composite foam D.P. Mondal ∗ , M.D. Goel, S. Das Advanced Materials and Processes Research Institute (CSIR), Bhopal 462 064, India
a r t i c l e
i n f o
Article history: Received 2 July 2008 Received in revised form 24 November 2008 Accepted 7 January 2009 Keywords: Aluminum foam Plateau stress Energy absorption Relative density Closed cell
a b s t r a c t Deformation response and energy absorption characteristics of closed cell aluminum-fly ash particle composite foam have been assessed under compressive loading at different strain rates (10−2 to 101 s−1 ). The investigated foams were made by melt route using CaH2 as foaming agent. The influence of strain rate on the deformation responses is found to be very marginal; within the domain considered in the present study, and the strain rate sensitivity was measured to be very low and varying in the range of 0.02–0.04 when the foam relative density is greater than 0.1. The plateau stress, and energy absorption increase significantly following power law relationship with relative density; whereas the densification strain is almost invariant to the relative density. The strain rate sensitivity of the investigated material was found to be negative when the foam relative density is less than 0.1. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Metal foams especially the ones based on lightweight metals have interesting combinations of properties such as high specific stiffness, strength combined with good energy absorption characteristics. These make metallic foams to be potential material for absorbing impact energy during the crashing of a vehicle either against another vehicle or a pedestrian. Potential applications of these foams also exist in shipbuilding, aerospace industry and civil engineering [1]. In order to absorb the impact energy more effectively, a material is required to exhibit an extended plateau stress region and high densification strain, and this is the most attractive feature of the metal foams [1]. Thus, these foams found wide application in energy absorption. Furthermore, such applications require indepth knowledge on deformation response especially compressive deformation response of metal foams, at various impact velocities vis-à-vis strain rates. The deformation behaviour of metal foams has been investigated recently by a group of investigators [2–7]. Unique combination of properties such as low density, high stiffness, strength, and energy absorption in metal foam can be tailored through design of its microstructure. Strain rate effects on polymeric foams have been studied in past to a large extent, whereas only a few data, sometimes contradict-
∗ Corresponding author. Tel.: +91 7552417652; fax: +91 7552587042. E-mail address: [email protected] (D.P. Mondal). 0921-5093/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2009.01.019
ing, can be found in literature on the deformation behaviour of Al metal foams. Kenny [2], Lankford and Dannemann [3] reported that the specific energy absorption of aluminum foam and plateau stress was independent of strain rate. Deshpande and Fleck [4] also studied the compressive deformation behaviour of Alulight closed-cell foam and Duocel open-cell foam under varying strain rates and concluded that the plateau stress was almost insensitive to strain rate, for strain rates ε´ up to 5000 s−1 . Similar observations were made by Ruan et al. [5]. On the other hand, Mukai et al. [6] reported that the compressive behaviour of closed cell aluminum foam under high strain rate is associated with an apparent strain hardening. They further observed that strain rate sensitivity of plateau stress increases with decreasing relative density. According to their investigations, this is attributed to gas pressure in the closed cell. Recently, Montanini [8] studied three types of foam including both open cell and closed cell and observed that plateau stress is independent of strain rate for CYMAT and MPORE foam while the dependency of plateau stress with strain rate is quite remarkable for SHUNK foams. It was also observed that specific energy dissipation of similar density foam could be quite different depending on strain rate. Thus, there exists an ambiguous opinion about strain rate sensitivity of metals foams. Most of the above studies have been conferred to Al foam or Al–SiC composite foam. The understanding of deformation response and energy absorption characteristics as a function of strain rate and relative density has yet not been crystallized. The present paper aims at studying the compressive deformation response of Al-fly ash composite foam and then to assess their energy absorption
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characteristics as a function of strain rate and relative density. This aspect comes into mind from the available literature where fly ash particles have found application for synthesis of Al-fly ash composite [9–11]. It is thus understood that fly ash particles are stable in liquid Al melt and it could also be used as thickening agent like that of SiC particles. Additionally, the fly ash are waste generated in coal based thermal power plant and thus very much cheaper than SiC particles, which would lead to reduction in cost of Al composite foam. Furthermore, a waste can be used for generation of value added product. An attempt has also been made to examine the strain rate sensitivity of Al-fly ash composite foam of varying relative density. In this paper attention has been focused on the effect of strain rate and relative density on the plateau stress, densification strain and energy absorption characteristics of closed cell aluminum-fly ash composite foam. 2. Experimental Closed cell aluminum-fly ash composite foams of relative densities ranging from 0.08 to 0.13 were prepared using fine fly ash particle as thickening agent and calcium hydride (CaH2 ) as foaming agent through liquid metallurgy route. The matrix alloy (AA2014Al-alloy) normally contains 4.6 wt% Cu, 1.9 wt% Mg, 0.5 wt% Mn, 0.4 wt% Si, 0.5 wt% Fe, 0.1 wt% Ti, 0.1 wt% Cr and balance Al. The details of the process have been reported elsewhere [12]. Fly ash particles in the size range of 2–10 m of about 5% by weight were used as thickening agent. CaH2 powder of 0.60% by weight in the size range of 20–50 m was used as foaming agent. The size distribution of CaH2 and fly ash particles are shown in Fig. 1(a) and (b), respectively. One typical bulk aluminum foam sample is shown in Fig. 2. Microstructural characterization of foam is made using Scanning Electron Microscope (SEM). The methodology applied for microstructural examination of Al-fly ash foam has been explained in the other paper [13–16]. The diameter of the cell of the synthesized foam was measured according to the method prescribed by ASTM for the measurement of grain diameter in polycrystalline materials [17]. The cell size of the synthesized foam varies in the range of 1.0–3.0 mm. The cell sizes of foams changed with their densities. The cell size increases with decreases in relative density. For compression test, specimens were cut from the fabricated foam with average dimensions of 4.5 cm × 4.5 cm in cross-section and 5.5 cm in height. Specimen size is so chosen to avoid size effect on mechanical properties of the foam. Compression test at strain rate of 10−2 to 101 s−1 were performed using BISS universal testing machine. Samples were placed on the bottom ram of the machine and load was applied to the samples when the top ram moved downward. Before testing, contact surfaces between samples and two loading head were coated with a spray of MoS3 to reduce friction. A computer attached to the machine recorded the load and the displacement data automatically, which is used to obtain the stress–strain relation diagram. A few set of samples were tested to the strain level of 0.005, 0.02 and 0.05 in order to understand the densification mechanism. These samples after testing were cut carefully and examined in SEM. 3. Results and discussions
Fig. 1. (a) Size distribution of CaH2 and (b) fly ash particles.
the cell size in the foams made at 690 ◦ C is bigger than that made at 670 ◦ C. The cell wall thickness, cell sizes and relative density of the investigated foam samples as a function of foaming temperature is shown in Table 1. This table clearly indicates that the cell wall thickness increases and cell size decreases with decreases in foaming temperature. Thinner cell wall and coarser cell size at higher foaming temperature lead to lower relative density. Variation is also expected due to decrease in viscosity and surface tension of melt with increase in temperature [18,19]. From the reported relation, it could be noted that surface tension of 2014 Al-alloy at a temperature of 670 ◦ C and 690 ◦ C would be ∼750 Nm/m and 720 Nm/m, respectively. In addition, the gas volume increases with increase in
Table 1 Cell size, cell wall thickness and relative densities of Al-fly ash composite foams.
3.1. Microstructural characterization
Sr. no.
Foaming temperature (◦ C)
Cell size (mm)
Cell wall thickness (m)
Relative density
The overall cellular structure of typical Al-fly ash composite foams made at a foaming temperature of 670 and 690 ◦ C is shown in Fig. 3(a) and (b), respectively. It may be noted that the foams structure are not so uniform, which contains random cell sizes. In both the cases a few cells are relatively bigger in size. As a whole,
1. 2. 3. 4. 5.
675 680 685 690 695
1.70 1.81 2.29 2.88 3.21
193 183 156 130 112
0.130 0.110 0.100 0.090 0.080
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temperature and this leads to higher gas pressure within the cell. This, in turn, facilitates growth of the cell until the pressure inside the cell equals to that its surrounding pressure, which is a function of surface tension and viscosity. Because of lower surface tension and viscosity, greater surface area required to make the cell in equilibrium. Thus the cell grows to bigger size at higher temperature. Fly ash particles through the control of melt viscosity decreases melt flowability in all direction and helps in giving a stable shape to the cell. 3.2. Compressive stress–strain curves
Fig. 2. One typical bulk aluminum foam sample.
Stress and nominal strain are deduced from the recorded load and displacement data using standard methodology. The stress–strain curves for all the tested foam samples are found to be similar kind, in which, they all have an initial linear elastic region (stage-I), an yield point (stage-II), a plateau region where the stress increases slowly with strain as the cells deform plastically (stageIII), and a region of rapidly increasing load (densification region), (stage-IV). Fig. 4 shows a typical stress–strain curve of closed cell aluminum-fly ash particle composite foam having relative density 0.11 and tested at a strain rate 0.01 s−1 . It may further be noted that at plateau region the stress varied in zig-zag fashion with strain. Hence, Plateau stress is considered, here, as the average stress in the plateau region and the densification strain is considered to be the strain corresponding to the intersection of tangents drawn on the densified and the plateau regions as schematically shown in Fig. 4. The energy absorption (Eab ) is considered to be the area under the curves up to the densification strain (εd ) as marked in Fig. 4. This can be expressed as follows:
Eab =
εd
dε
(1)
0
For each relative density and strain rate a set of five samples was tested. Only typical plot for one sample from each set has been reported. However, average plateau stress, densification strain and energy absorption were concluded by considering all the plots for each set. In fact, here for each set, the relative density reported is the average relative density within accuracy of 0.005. The relative density of foam samples varies by varying the process parameter like foaming temperature. For testing, foam samples from the centre of the block were taken to avoid the effect of foaming direction on the deformation behaviour.
Fig. 3. Cellular structure of Al-fly ash composite foams at foaming temperature of (a) 670 ◦ C and (b) 690 ◦ C.
Fig. 4. Stress–strain curve (RD = 0.11and strain rate = 0.01).
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Fig. 7. Variation of plateau stress with relative density at varying strain rate. Fig. 5. Compressive stress–strain curves of Al-fly ash composite foam for various relative densities at fixed strain rate of 0.10.
3.3. Effect of strain rate and relative density The compressive stress–strain curves of Al-fly ash composite foam for various relative densities at fixed strain rate of 0.10/s is shown in Fig. 5. It is evident from this figure that at fixed strain, stress increases with increase in relative density. Also, variation of compressive stress–strain curves at different strain rates is shown in Fig. 6 for a fixed relative density of 0.107. This figure indicates that the plateau stress lies in a narrow range even with the variation of strain rate at wider range (0.01–10). It may further be noted that at higher strain rate plateau stress is marginally less (for strain rate 0.01–1.0). But at higher strain rate (10/s) the plateau stress is noted to be marginally higher than that of at strain rate of 1/s. This demonstrates that the plateau stress does not follow any specific relationship with strain rate; it varies in a narrow region randomly with strain rate. Fig. 7 represents the variation of plateau stress with relative density at different strain rate. It is noted that the plateau stress follow power law relationships with relative density irrespective of strain rate. It may further be noted
Fig. 6. Variation of compressive stress–strain curves at different strain rates.
that the overall variation of plateau stress at fixed relative density for the entire range of strain rate is around 0.5 MPa. Additionally, the plateau stress at higher strain rate is noted to be marginally less than that at lower strain rate. This figure, in fact, indicates that the plateau stress does not follow any specific trend with strain rate. The variation of densification strain at different strain rate with relative density is shown in Fig. 8. It may be noted that the densification strain is varying in a very narrow range (0.68–0.73) and it seems to be almost invariant to the relative density and strain rate. The plateau stress at different relative densities as a function of strain rate in the ln-scale is plotted in Fig. 9. It is evident from this figure that the slope of the line is negative for relative density less than or equal to 0.10, at higher relative density, the slope is positive. This signifies that at higher relative density, the plateau stress increases with strain rate where as at lower relative density, the plateau stress decreases with strain rate. However, the absolute magnitude of the slope is very marginal (0.022–0.047). This signifies that the value of strain rate sensitivity is considerably less and the effect of strain rate on plateau stress is insignificant.
Fig. 8. Variation of densification strain at different strain rate with relative density.
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Fig. 9. Plateau stress at different relative density as a function of strain rate. Fig. 11. Coefficient m as function of relative density.
3.4. Strain rate sensitivity The effect of strain rate on plateau stress could be expressed in the following form: pl = Kf ε˙ m
(2)
where pl is the plateau stress, Kf is the strengthening coefficient,
ε´ is the strain rate and m is the strain rate sensitivity. Thus, the slope of ln ( f ) vs ln (ε´ ) plot gives the value of m and antilog of intercept gives the value of Kf , the strengthening coefficient. The value of Kf and m is plotted as function of relative density in Figs. 10 and 11, respectively. It is noted from Fig. 10 that Kf decreases with relative density when relative density changes from 0.08 to 0.089. With further increase in relative density, Kf increases with relative density very sharply. This demonstrates that the strengthening coefficient, which is primarily controlled by deformation response of the cell walls, is noted to be minimum at a relative density between 0.09 and 0.010. Below and above this relative density the strengthening coefficient is higher. At higher relative density, because of wider cell wall thickness, the cell wall material could withstand higher stress value prior to deformation, bending and crushing. At lower relative density, the cell walls are very thin and thus they have greater tendency of bending rather
than crushing. In addition, more gas pressure (hydrostatic in nature) on the coarser cell causes delay in cell fracture [20–22], which may lead to greater Kf value. At intermediate relative density the tendency of cell wall crushing is reasonably higher and the effect of gas pressure is relatively lower, which may lead to less strengthening coefficient. Fig. 11 shows the variation of m with relative density. It is evident from this figure that the m is negative when the relative density is less than 0.10. At higher relative density, the m is positive. This signifies that the plateau stress increases with strain rate marginally, when the relative density is greater than 0.10. The plateau stress decreases with strain rate when relative density is less than 0.10. But the value of m is very low 0.02–0.04, which signifies that the variation of stress with strain rate is very marginal. This may be attributed to the fact, that the deformation and compaction behaviour of foam is primarily controlled by the cell wall bending, stretching and crushing. It rarely may be controlled by the slip and dislocation controlled deformation mechanism in the plateau region especially when the cell walls are very thin. It primarily depends on the stress–strain distribution on the cell walls. At higher relative density, (i.e. relative density >0.10), cell walls are relatively thicker and the shear type of deformation of cell wall material could be observed prior to fracture or crushing. However, in the present study, the relative density is estimated to 0.13 and thus the cell walls are noted to be very thin irrespective of relative density. This may be another cause for marginal variation in m values which is also very low. 3.5. Plateau stress and relative density correlation The plateau stress and energy absorption found to be almost invariant to strain rate. The strain rate sensitivity calculated in these materials in the used domain of strain rate was noted to be very low. But, these properties are strongly influenced by the relative density. According to Gibson and Ashby model [22], the plateau stress of foam follows following relation with relative density: pl ys
Fig. 10. Kf as function of relative density.
3/2 f
≈ 0.3 ϕ
s
+ (1 − j)
f s
+
p0 − pat ys
(3)
where pl is the plateau stress of foam, ys and s are the yield stress and density of the dense material that the foam cell wall is made of, f is the density of foam, ϕ is the fraction of solid in the cell edges of foam, p0 is the initial fluid pressure in the cell of foam and pat is atmospheric pressure. In manmade foams p0 is usually equal to pat which means that the gas has little effect on the plateau stress. So
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the third term in the above formula is very insignificant. It has been found that the second term of the above formula also has little contribution to plateau stress [13], which may be attributed to the fact that ϕ is very close to 1 as most of the materials in foam is occupied in the edges and the plateau region. Thin layer of the material, separating the cells is significantly less than that present in the cell wall and the plateau region. Thus, only the first term of the above formula is adequate to describe the plateau stress even for closed-cell foams. Moreover, it has also been observed by other researchers [2,20–22] that many properties of foam including plateau stress obey a power law: A() = A0 n
(4)
where A is the property of foam, is the density of foam, A0 is a factor, which reflects the properties of the solid cell wall material, and n is an exponent. In the present case, the plateau stress follows the power law of variation: pl =
ys
n f
s
=K
s f
n
(5)
where ys is the yield strength of the solid material with which the foam is made off. pl is the plateau stress of the foam and n is the exponent. The value of n varies in the range of 2.034–2.205 depending on the strain rate. This is in good agreement with the reported values. Similarly, the value of coefficient is varying in the range of 227 MPa to 294 MPa which is the measure of the product of yield strength of the solid material ( ys ) of the foam and the fractional coefficient in Eq. (5). The yield strength of 2014 Al–5 wt% fly ash composite at a strain rate of 1/s measured to be 298 MPa. It is observed by the present authors that the strength of 2014 Al–SiC Composite is almost invariant to the strain rate [12,13]. This also supports the strain rate independent of plateau stress of the Al-fly ash composite foam. Considering the yield strength of 298 MPa of the Al-fly ash composite in the present foam, the coefficient could be calculated using the following relation: =
K ys
(6)
The value of comes to be in 0.76–0.98 depending on the relative density. Present authors in their recent publication [15,23] also found that the coefficient is around 0.70 while the modulus of closed cell foam is expressed following Gibson and Ashy relation [17]. The value of in the range of 0.76–0.98 is also reported by other investigators [5–7,12–14,21,24–41]. The differences in the coefficient may be due to influence of strain rate or the differences in the actual materials property of the cell walls of the investigated foam as a whole at various relative densities. This fact has been observed from the microhardness measurement in the plateau region of the investigated foam samples as a function of relative density as shown in Table 2. It is evident from this table that at higher relative density the microhardness values are higher. However, the value of calculated on the basis of yield stress of the dense materials. The difference in the average microhardness values from the overall average is noted to be ±10%. This is within the acceptable range of variation in microhardness measurement.
Thus, it could be considered that overall microhardness variation in matrix is very marginal with relative density. If we average out the constant, the value becomes 0.88 and the lower and upper limit comes between 15% of accuracy. The present investigation notes that the plateau stress follows a power law variation with relative density and it varies marginally with strain rate. At lower strain rate, the plateau stress is higher than that at higher strain rates. 3.6. Energy absorption The study further states that the densification strain is almost invariant to the relative density and strain rate. Hence, the variation of energy absorption with relative density and strain rate is also noted to be of the similar trend to that of plateau stress with relative density. The energy absorption by unit volume of the investigated foam samples was plotted as a function of relative density in Fig. 12 when the foam samples are loaded at different strain rate. It is evident from this figure that the energy absorption by the Al-fly ash foam also follows a power law variation with relative density irrespective of the strain rate. It is further noted that the Al-fly ash foam exhibits lower energy absorption while tested at higher strain rate (>1.0/s). At lower strain rate the foam samples exhibits relatively higher energy absorption characteristics. This is attributed to the fact that the cell wall material of foam having very low relative density behaves differently under varying strain rate. As expressed earlier, that the relative density of the investigated foam is very low (max. 0.13), the cell walls are also very thin. At higher strain rate, because of dynamic nature of force, the cell wall might be fractured/crushed more easily and thus leading to lower plateau stress as well as energy absorption characteristics. Whereas at lower strain rate gradual bending followed by crushing of the cell wall may be the dominating mechanism. Thus, the foam exhibits higher stress vis-à-vis energy absorption at lower strain rate. Thus, the energy absorption of Al-fly ash composite foam could be expressed as follows: Eab = K
n2 f
s
Relative density
Microhardness (kgf/mm2 )
1. 2. 3. 4. 5.
0.130 0.110 0.100 0.090 0.080
118 115 110 107 105
± ± ± ± ±
6 5 5 4 5
(7)
The value of n2 is expected to be almost same as that of n in Eq. (4) as the energy absorption primarily dependent on pl . This is exactly observed in the present study. The value of n2 comes to be in the range of 1.84–2.5, which is comparable to the value of n (2.0–2.25). The energy absorption value of the Al-fly ash foam varies in a narrow range. Overall magnitude of differ-
Table 2 Microhardness of aluminum-fly ash composite foam as a function of relative densities. Sr. no.
107
Fig. 12. Variation of energy absorption with relative density.
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Fig. 13. Micrograph of deformed closed cell Al-fly ash composite foam at strain rate of 0.001/s: (a) 0.5%, (b) 2%, (c) 5%, (d) 5% (higher magnification).
Fig. 14. Micrograph of deformed closed cell Al-fly ash composite foam at strain rate of 1/s: (a) 0.5%, (b) 2%, (c) 5%, (d) 5% (higher magnification).
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ences: (0.25 MJ/m3 to 0.30 MJ/m3 ) at fixed relative density for wide range of variation in strain rate. This signifies only marginal effect of strain rate on energy absorption of the Al-fly ash composite foam. 3.7. Deformation mechanism During compressive loading, the cell wall may behave differently under different strain rate. In order to confer these fact, Al-fly ash composite foam samples having relative density of 0.089 were tested respectively up to strain levels of i.e. 0.5%, 2% and 5% under two strain rates i.e. 0.001/s and 1.0/s. Fig. 13(a) shows the cell structure of Al-fly ash composite foam after 0.5% deformation at strain rate of 0.001/s. It is evident from this figure that the cell walls gets slightly bulged and bent (arrow mark). When the same sample is deformed up to 2%, it is noted that the cell walls get bent significantly (arrow mark) and also subjected to crack inside (as marked C) as shown in Fig. 13(b). Further increase in strain level (5%) leads to further bending (arrow mark) and greater degree of cell wall cracking (marked C) as shown in Fig. 13(c). The cracked cell wall in due coarse get sheared and crushed. Fig. 13(d) shows clearly the through cracking of cell wall even in plateau region (marked C). Fig. 14(a) depicts the cell structure of Al-fly ash composite foam having density of 0.089 after 0.5% deformation at a strain rate of 1/s. This figure shows the slight bending of the cell wall (arrow marked) along with its shearing of cell wall (marked S). When the strain increases to 2%, the cell walls (which are relatively thin) start shearing (arrow marked) and in due course get crushed as shown in Fig. 14(b). When the cell walls are relatively thicker the start of shearing of cell wall (marked ‘arrow’) could be more clearly examined in Fig. 14(c). Shearing of cell wall and its crushing followed by tendency of compaction could be shown in Fig. 14(d), when the Al-fly ash foam is tested up to strain rate of 1/s up to 5% strain. These figures indicate that the cell wall has the tendency of bending followed by shearing and crushing during compressive loading at lower strain rate. This bendiness is more for thin cell walls. As the cell walls are thinner at lower relative density, it is also expected that greater extent of cell wall bending would took place in the case of deformation of foam with lower relative density. However, at higher strain rate, the cell wall primarily gets sheared prior to crushing and hardly subjected to bending. As stated by other investigators, the deformation progresses layer by layer with increase in strain level. Because of the variation in deformation mechanism of cell wall with cell wall thickness i.e. relative density and strain rate, the m and K are noted to be varying (in a narrow range) with these parameters. At lower relative density, greater extent of bending and relatively less shearing leads to relatively higher K value. At intermediate relative density both bending and shearing are equally responsible for cell crushing and leading to lower K value. At higher relative density, shearing deformation is dominating and extent of bending is less, which leads to increase in K value. The deformation, in the metal foam, particularly in plateau region is primarily controlled by bending, shearing, crushing and compaction of cell walls vis-à-vis cell, which also influenced by strain rate. Similarly, the value of m is also varying with relative density. However, the value of m varies within a very narrow range ±0.04, which demonstrates that the compressive deformation of low density Al-foam is almost insensitive to strain rate.
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4. Conclusions Compressive tests at strain rates 10−2 to 101 s−1 have been conducted on closed cell aluminum-fly ash composite foam. The stress versus nominal strain curve for all the tested foam samples is similar. They all have four characteristics: an initial linear elastic region, a yield point, a plateau region and densification. The densification strain is almost invariant to the relative density and the strain rate; and the plateau stress depends highly upon the relative density and marginally upon the strain rate. Plateau stress is not sensitive to strain rate in present domain of study. This signifies that the strain rate effect on the compressive deformation response for the very light aluminum foam is insignificant. However, the deformation response is strongly influenced by the relative density. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41]
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