Compressive deformation behavior and strain rate sensitivity of Al-cenosphere hybrid foam with mono-modal, bi-modal and tri-modal cenosphere size distribution

Materials Characterization 144 (2018) 563–574

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Materials Characterization journal homepage: www.elsevier.com/locate/matchar

Compressive deformation behavior and strain rate sensitivity of Alcenosphere hybrid foam with mono-modal, bi-modal and tri-modal cenosphere size distribution

T

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Ashutosh Pandeya, Shyam Birlaa,b, D.P. Mondala,b, , S. Dasa,b, Venkat A.N. Cha a b

CSIR-Advanced Materials and Processes Research Institute, Bhopal 462026, India Academy of Scientific and Innovative Research (AcSIR), India

A R T I C LE I N FO

A B S T R A C T

Keywords: Cenosphere size distribution Bi-modal and tri-modal distribution Hybrid aluminium foam Strain rate sensitivity Energy absorption

AlSi12Cu1Mg1 aluminium alloy-cenosphere closed cell hybrid foams with different kinds of cenosphere size distribution (mono-modal, bi-modal and tri-modal) are used to see the effect of cenosphere size distribution on their deformation behavior under quasi static compressive loading conditions at different strain rates. The stress strain curves are almost similar type irrespective of the cenosphere size distribution and strain rate. However, the plateau stress and energy absorption increased significantly when one used bi-modal and or tri-modal cenosphere size distribution instead of mono-modal cenosphere size distribution. These plateau stresses and energy absorption also increased marginally with strain rate. The densification strain remained almost invariant with strain rate and cenosphere size distribution. The strain rate sensitivity and strain rate sensitivity parameter is relatively lower in case of bi-modal and tri-modal cenosphere size distribution particularly at higher relative density.

1. Introduction With the development of new technology and design criteria, requirement of new material with improved properties is required. In today's world safety standards are very high and to achieve those standards there is a continuous force on design and research to improve property of the material. Aluminium foam is a class of light weight material having very low density (0.2 to 0.8 g/cm) [1]. It offers different unique combination of properties like high specific strength and stiffness, sound absorption capability [2], electromagnetic shielding [3], excellent energy absorption [4], thermal insulation [5] and vibration damping [1]. These properties make aluminium foam an important candidate material for use in light weight structure, crash worthiness, vibration and mechanical damping. Closed cell aluminium foam is a material which possesses incomparable properties like energy absorption and impermeability to fluids [6]. It is very effective where there is a requirement of high energy absorption keeping the plateau stress at lower values [7]. Hou et al. [8] investigated the effect of impact velocity, cell thickness and relative density of aluminium foam on energy absorption capacity through compressive deformation. It is reported by these investigators that under dynamic loading aluminium foam exhibits higher plateau stress as compared to that when loaded

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under quasi-static condition. In recent years, many researcher have studied the effect of strain rate on plateau stresses [9,10] especially under quasi-static condition. Closed cell aluminium foam is mainly produced through liquid metallurgy route using foaming agent [11–13]. Researchers have used different foaming agents to prepare aluminium foam. Cambranero et al. [14] used calcium carbonate (CaCo3) as foaming agent in Al-Mg-Si alloy foam. They investigated the effect of different characteristics of calcium carbonate powder (i.e. particle size and chemical composition) on micro-architectural and deformation behavior of aluminium foam and they found that the foam made using natural carbonate powder shows better uniaxial compressive properties as compared to that made using synthetic calcium carbonate. Wu et al. [15] used zirconium hydride (ZrH2) [15] as a foaming agent in an amount of 0.6%–1.4% (mass fraction) and they found that ZrH2 is mainly suitable for making small cell size with aluminium foams (average diameter 1 mm). TiH2 [16] and CaH2 [17] are generally used as a foaming agent. The foam made using foaming agent provides macro-pores (Cell), which is generated due to entrapments of gas bubbles formed due to dissociation of the foaming agents. In other kind of foam, where micro-balloons are introduced in metallic matrix, are called syntactic foams. The aluminium syntactic foam also exhibits very high strength and energy absorption

Corresponding author at: CSIR-Advanced Materials and Processes Research Institute, Bhopal 462026, India. E-mail address: [email protected] (D.P. Mondal).

https://doi.org/10.1016/j.matchar.2018.08.011 Received 3 July 2018; Received in revised form 5 August 2018; Accepted 6 August 2018 Available online 07 August 2018 1044-5803/ © 2018 Published by Elsevier Inc.

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distribution on the compressive deformation of Aluminium cenosphere foam. Present work deals with the preparation of hybrid foam using mono-modal bi-modal and tri-modal combination of cenosphere particle. Here in bi-modal conditions, combination of two particle size range (i.e. < 100 and > 212 μm) is added to aluminium matrix. Whereas in tri-modal combination, three particle size range (i.e. < 100 μm, 150–212 μm and > 212 μm) were added. Hybrid aluminium foam having bi-modal and tri-modal cenosphere particle size were compared with the one having mono-modal cenosphere particle size range with respect to their plateau stress, densification strain and energy absorption capacity. In addition the strain rate sensitivity and stain rate sensitivity parameter as a function of relative density and particle size distribution in aluminium hybrid foams have also been examined.

capacity under dynamic as well as quasi-static condition [18–22]. Based on this concept researcher have also used the micro-sphere in aluminium foam [23,24] and zinc foam [25] to improve compressive deformation response. These are called as hybrid foam [23]. So in order to reduce the use of foaming agent, reduce macro porosity as well as to increase the plateau stress and energy absorption of aluminium foam, some micro-sphere were incorporated in to melt prior to foaming. Doaud [26] made attempt to make Zn-Al alloy-cenosphere hybrid foam using 15% and 30% vol% of Cenosphere. They observed that the plateau stress of the Zn-Al alloy foam increases when Cenosphere are used for getting hybrid pores. It was noted by the investigator that plateau stress or yield stress of the alloy foam increase by few folds at fixed relative density. Xia et al. [27] investigated the compressive strength of aluminium foam having different content of micro-sphere and also found improved plateau stress and energy absorption over the conventional aluminium foam. Birla et al. [28] studied the effect of microsphere particle size on the compression deformation. They also investigated the variation of plateau stress with respect to size of microsphere. During the experiment they considered three different particle sizes and found that as the size of cenosphere particle decreases the values of plateau stress and energy absorption get increased. Synthetic, metallic and/or ceramic micro-sphere [27] are costly and adding these micro-spheres in foam increases the cost of aluminium foam. So, in order to increase the compressive strength without increasing the cost of aluminium foam, cenosphere (waste from power plant) was used as a microsphere [27]. Sanders et al. [29] showed the deformation mechanism of syntactic foam with hollow micro-sphere, in comparison to the existing closed cell metallic foam. According to these investigators with an increase of relative density of 10%, foam made using microsphere showed 3 times greater modulus and strength than that of conventional foam. Xia et al. [27] analyzed the effect of ceramic micro sphere content on yield strength, mean plateau stress and average densification strain under compression loading analysis of aluminium syntactic foam. They observed that the plateau stress of syntactic foam does not follow any specific trend with cenosphere content. The shells of cenosphere help in increasing the strength of matrix (cell wall). Birla et al. [28] also examined that the plateau stress of aluminium hybrid foam increases with increase in cenosphere up to 30%. They reported that this is due to decrease in macro-porosity and also increase in cenosphere shell. Adding cenosphere in closed cell aluminium foam gives two types of porosity, one is macro-porosity which is caused due to entrapment of gas and other is micro-porosity due to hollow cenosphere particle. In syntactic foam, some of the researchers have used the mixture of different microsphere size to enhance the property of material [30,31]. Tao et al. [30] uses the bimodal ceramic micro-sphere in aluminium matrix syntactic foam. They considered two range of micro-sphere particle size (i.e. fine particle (75–125 μm) and coarse particle (250–500 μm)). They found that the micro-sphere particle density in syntactic foam with bi-modal size distribution is 10% higher than that in the one with mono-modal size distribution. This led to 8% improvement in the plateau stress and the densification strain. Therefore, there is a need to develop cenosphere reinforced lightweight high strength Al-cenosphere hybrid foams. Ceramic microsphere reinforced Al-hybrid foam is expected to be more brittle than that of Alalloy foams or Al-composite foams. This is expected that after deformation the cell wall will be crushed in to finer particles. As strength and energy absorption are reported to be higher, the use of these hybrid foams could be extended for blast resistance panels, antimine boots, multicore integrated armour, crashworthiness components and storage and packaging of explosive. Ones it gets exploded, it will not generate any big heavy secondary debris which would cause further damage to the surrounding. That's why, these materials will be highly useful for crashworthiness, blast resistance and armour application. To the best of our knowledge, no research has been carried out to investigate the effect of combination of different particle size

2. Experimental 2.1. Raw Materials The aluminium alloy (AlSi12Cu1Mg1) nominally contains Cu: 0.7 wt%, Mg: 1.0 wt%, Si: 11.8 wt%, Fe: 1.0 wt%, Mn: 0.5 wt%, Ni: 1.5 wt%, Zn: 0.5 wt%, Pb: 0.05 wt%, Ti: 0.06 wt%, Al: balance. Cenospheres of three different size ranges (< 100 μm, 150–212 μm and > 212 μm) were 30 vol% are used and they are coded as CP1, CP2 and CP3. The size distribution of these cenospheres is shown in Fig. 1. The chemical composition and X-ray diffraction pattern of these cenospheres are reported elsewhere [32]. According to these reports the cenospheres used in the present studies primarily contain alumininosilicate phases like mullite and selliminite. In addition to these, minor amounts of ferro-silicate, quartz and carbon presents in these cenosphere. 2.2. Hybrid Aluminium Foams and Microstructures Closed cell aluminium-cenosphere hybrid foams (CAHF) were made using the stir-casting technique [28]. (i) Firstly the alloy was placed in the crucible and melt at a temperature of 730–750 °C in an electrical resistance furnace. Then, (ii) preheated (900 °C for 2–3 h) cenosphere particle were added manually in the melt through mechanical stirring at a speed 800 rpm. After mixing of cenosphere in the melt, stirring was continued for 4 – 5 min to ensure complete homogeneous mixing of cenospheres particles. After that, (iii) dry and preheated CaH2 powder (0.6 wt%) of average size: 18 ± 2 μm, was added manually in the melt again through mechanical stirring. While adding CaH2 powder, the melt temperature was maintained between 660 and 700 °C in order to get varying relative densities in hybrid foams. After completion of foaming agent addition, (iv) the melt is allowed to foam and within 20 to 30 s, the melt get completely foamed. This is ensured when the foaming head stop moving upward in the crucible. Finally, (v) the crucible with liquid foam is taken out of the furnace and force cooled by steam spraying to get HFs. The cross-sectional views of hybrid foam are shown in Fig. 2(a) and (b) respectively. These shows uniform distribution of cell size throughout the cross section in lateral and longitudinal direction. For making CAHF with different kinds of cenosphere size distribution, cenospheres with mono-modal, bi-modal and tri-modal size distributions are used. In case of mono-modal, three types of cenosphere (CP1, CP2 and CP3) are used separately for making CAHF and these CAHF with CP1, CP2 and CP3 cenosphere are referred as HFM1, HFM2, and HFM3 respectively. Similarly, for making CAHFs with bi-modal cenosphere distribution, two types of cenospheres: CP1 and CP3 are used together in equal proportion and these CAHFs are referred as HFBM. Similarly, CAHFs made with Tri-modal cenosphere distribution used mixture of CP1, CP2 and CP3, where each category is used in equal proportion; and these CAHFs are referred as HFTM. In our proceeding sections, these codes will be used for cenospheres and the hybrid foams for further discussion. 564

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Fig. 1. Cenosphere particle size distribution.

2.3. Compression Tests

The density of foams was determined using the Archimedes principle. For this, the foam samples were coated with thin plastic prior to measurement of its density. For metallographic examination, foams samples were cut from the foam ingots and then mounted with cold mounting materials to avoid fracturing of cell walls during subsequent grinding and polishing operation. After grinding and polishing of the mounted foam samples, the samples were gold sputtered and used for scanning electron microscopic observation using a Scanning Electron Microscope (JEOL: Model: 5600). Number of samples were prepared metallographically and used for measurement of cell size and cell wall thickness. For measurement of cell size and cell wall thickness, at least 200 cells and cell walls are selected from SEM micrograph and measured. Average of these cell wall thickness and cell sizes were reported.

Samples of sizes 20 mm × 20 mm × 30 mm were used for compression tests. The tests under same category and parameters are repeated thrice. The average of three test results was used for discussion. The compression tests were carried out at three different strain rates (i.e. 0.01, 0.1 and 1.0/s). During testing the opposite side of the test samples were polished and smoothen. MoS2 was used between the sample surface and the anvil (ram) to avoid friction between these two surfaces. The recoded data were used for making stress-strain diagram. The plateau stress, densification strain and energy absorptions are measured from these stress strain diagram using the methodology as stated elsewhere [33]. The average stress in the plateau region is considered as plateau stress and the densification strain is considered to be the strain corresponding to the intersection of tangent drawn on the densification and line corresponding to average plateau stress. The

(a)

(b)

Fig. 2. Cross sectional view of hybrid foam (a) Lateral and (b) Longitudinal direction. 565

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figure clearly showed the uniform distribution of coarser and finer cenospheres in the cell wall. Similarly (Fig. 4(c)) showed uniform distribution of coarser, medium and finer size cenosphere in the cell wall when one used tri-modal cenosphere size in HFTM. At lower magnification, it can be noted that a large extent of cenosphere is accommodated in the cell wall, when one use bi-or tri-modal cenosphere size for making CAHFs (Fig. 4(d)) and at higher magnification micrograph of HFTM clearly showed cenosphere of wider size range within the cell wall and the bonding between cenosphere shell and matrix is very sharp and strong (Fig. 4(e)). This led to the possibility of more micro-porosity in the cell wall of HFBM and HFTM. For same relative density, if microporosity increases, the extent of macro-porosity reduces. This finally led to higher strength and energy absorption in the HFBM and HFTM. The bonding between cenosphere shells and matrix in HFBM is noted to be quiet sharp and strong (Fig. 4(f)). The cell size, cell wall thickness, macro-porosity in different CAHFs as a function of relative density is reported in Table 1. It may be noted that the cell size increases and the cell wall thickness decreases with reduction in relative density of CAHFs. But, the cell size and cell wall thickness remained almost unchanged in case of HFM1 and HFM2. The cell size become coarser and cell wall become thinner in case of HFM3. This is due to coarser size of cenosphere which are least accommodated in the cell wall and make the liquid material less viscous during foaming. But, in case of HFBM and HFTM, it is noted that cell size decreased and the cell wall thickness increased. The average cell size of HFBM at relative density (ρrd) 0.17 is 4.1 ± 0.14 mm (Fig. 5(a)), whereas for HFTM at relative density 0.17 is 3.5 ± 0.24 mm (Fig. 5(b)). This is due to accommodation of more number of cenosphere with in the cell wall and greater viscosity of liquid melt during foaming. As more cenosphere get accommodated with in cell wall, it is expected that micro-porosity in the HFBM or HFTM will be higher than that in HFMs. The macro-porosity Vmp can be calculated using the equation as reported elsewhere [28]. The Vmp is a function of Vc (the cenosphere volume fraction). As Vc increases, value of Vmp decreases. The similar trend is observed in HFBM and HFTM. In Eq. (2), ‘t’ is the cenosphere shell thickness and r is cenosphere radius, one can express the relation among Vc, Vmp and ρrd of HFs through the following relation [28]:

energy absorption of foam is calculated as the area under the stressstrain curves up to densification strain. The energy absorption (Eab) of foam is defined as follows [33]: εd

Eab =

∫ σ∗dε 0

(1)

where σ is the flow stress, 0 and εd are strain at zero strain and densification strain respectively. Eab was calculated by gridding the stress–strain curves up to densification strain (εd) with very fine grids and then its area was calculated from the area of individual grids and the number of grids in the curves. For each category, the tests were repeated thrice and their average was used for analysis. 3. Results and Discussion 3.1. Cenospheres Size Distributions The cenosphere sizes were determine from its micrographs taken using scanning electron microscope. For each category, at least 200 randomly selected cenospheres were measured from the micrographs. Their distribution is plotted in Fig. 1. Fig. 1 also showed the micrographs of cenospheres of each category. It is noted that the average cenosphere size for CP1, CP2 and CP3 are 91.2 ± 5.2 μm, 165.1 ± 6.8, and 282.3 ± 10 μm respectively. When one used CP1, CP2 or CP3 separately for making foam, their size distributions are in narrow scatter band. When these are used together, the scatter band increases. This means, cenospheres of wider size range exist. This helps in accommodating more cenosphere in the cell wall. In case of tri-modal distribution, thus largest extent of cenospheres could be accommodated. These may be examined in the micrograph of CAHFs. 3.2. Microstructures and Relative Density The cellular structures of CAHFs with mono-modal cenosphere size distribution (HFMs) are shown in Fig. 3. Fig. 3(a) represents the circular structure of HFM1. It may be noted that cell wall contains cenosphere of narrow size range. Similar kinds of observations are noted in case of HFM2 (Fig. 3(b)). At higher magnification, it may be noted that a large number of cenospheres are pushed towards the side of cell walls (Fig. 3(c)). This may be due to the fact that solidification of liquid metal in foam cell wall starts from the center as the metal is more conducting than the gas entrapped in the cell. When the micrographs of cell wall examined at very high magnification, it is noted that the interface between cenosphere shell and matrix is sharp and strong. It is interestingly noted that the eutectic silicon are surrounding the cenosphere shell. This confirms push out of cenosphere by the dendritic fronts. A higher extent of eutectic silicon surrounding the cenosphere shell is observed, which might be due to dissolution of silicon from the cenosphere shell [33]. The cellular structures of CAHFs with HFBM or HFTM cenosphere size are found to be similar to those observed in case of HFMs. Here, the only difference is that the different sizes of cenospheres are present in the cell wall. During solidification, cenosphere are pushed towards the interface of cell wall or the cell boundary (Fig. 3(a)). The tendency of cenosphere pulling towards cell boundary is less in case of HFBM and HFTM in CAHFs (Fig. 4(a)). This figure indicates that large amount of cenosphere may be accommodated in the cell wall of CAHFs. It may also be noted that the cell wall is thicker as compared to that obtained in case of HFMs. Because of relatively more uniform cenosphere size, accommodation of larger extent of cenosphere in the cell wall is limited in HFMs. When a cenosphere size varies in wider range, finer cenospheres can be accommodated in between the spaces of coarser cenospheres. As a result, a larger extent of cenosphere is accommodated in cell wall and less is pushed towards the cell boundary. In case of HFBM the distribution of cenospheres in cell wall is shown in (Fig. 4(b)). This

1 − Vmp =

ρrd

(

⎡1 − 1 − ⎣

t 3 ∗Vc ⎤ r ⎦

)

(2)

3.3. Compressive Deformation The compressive stress strain curves of CAHFs (ρrd = 0.15) made with mono-modal (HFM1, HFM2 and HFM3), bi-modal (HFBM) and trimodal (HFTM) cenosphere size distribution at a strain rate of 0.01/s are shown in (Fig. 6(a)). It is evident from this figure that flow stress (plastic collapse stress, average plateau stress) increases with decrease in cenosphere size. But, whatever the average cenosphere sizes, the flow stress of HFBM and HFTM are higher than that obtained in HFM1, HFM2 and HFM3. Similar kinds of observations are also noted when the stress-strain curve of CAHFs of (ρrd = 0.19) at a strain rate of 0.01 are compared (Fig. 6(b)). After gathering this type of observation the tests are repeated to CAHFs with varying relative densities at different strain rates. Similar types of observations were made irrespective of strain rates and relative density. In general, following observations were noted: (i) Stress (flow stress, average plateau stress, plastic collapse stress) increases with decrease in cenosphere size, (ii) the average cenosphere size may be higher or lower in case of HFBM and HFTM as compared to that in HFMS, but the flow stress of CAHFs made with HFBM and HFTM are greater than that of HFMs. (iii) similar trend persists in case of energy absorption also. (iv) densification strain varies marginally with cenosphere size distribution; it is lower in case of HFBM and HFTM. (v) The 566

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200 µm

200 µm

100 µm

100 µm Fig. 3. Micrographs of HFMs.

cenosphere is higher as compared to that in case of HFMs (Fig. 4). This also makes the cells more stable and cause wider cell wall, in case of HFBM and HFTM. In case of HFTM, the cenosphere packing density as well as cell wall thickness is the highest. This causes more micro-porosity and thus less macro-porosity for a given ρrd in case of CAHFs with bi or tri-modal cenosphere size distribution. The inter cenosphere spacing is also reduced. As a result the strength of HFBM and HFTM is higher than that of HFMs. Because of the similar reason, HFTM exhibits the highest plateau stress.

trend is invariant to relative density and strain rate.

3.4. Effect of Relative Density and Strain Rate 3.4.1. Plateau Stress The plateau stress (σpl) as a function of relative density (ρrd) for different CAHFs when tested at a strain rate of 0.01/s, are compared in Fig. 7(a). It is evident from this figure that the σpl increases with increase in ρrd and with decrease in average cenosphere size in case of HFMs. But, in case HFBM and HFTM the σpl are much higher than those of HFMs even though, the average cenosphere size in HFBM and HFTM is higher than those in HFMs. However, it may be noted, in general, that σpl follows power law relationship with relative density. The exponent and coefficient are also varying with the cenosphere size. Both the exponent and coefficient are higher for HFBM and HFTM. Similar kinds of trends are noted when CAHFs are tested at strain rate of 0.1/s and 1/s as shown in Fig. 7(b) and (c) respectively. Comparison of Fig. 7(a), (b) and (c) states that the coefficient as well as exponent of power law relationship increases with increase in strain rates. This, indirectly states that the σpl is influenced with the strain rate also. In order to understand the effect of strain rate on σpl, the σpl values recorded in each condition and are reported in Table 2. The increase in plateau stress due to reduction in cenosphere size, in case of HFMs, has been explained elsewhere [28]. Here a significant amount of cenospheres pushed towards the cell boundary and thus extent of cenosphere packing density in cell wall is less, than that one expect (Fig. 3). In case of HFBM and HFTM the packing density of

3.4.2. Densification Strain The densification strain of CAHFs with mono-modal, bi-modal and tri-modal, cenosphere sizes when tested at strain rate of 0.01/s, 0.1/s and 1/s as function of relative density are shown in Fig. 8(a), (b) and (c) respectively. These figures in general, states that (i) the densification strain decreases with increase in relative density irrespective of cenosphere size distribution. (ii) The densification strain decreases with decrease in cenosphere size (in case of mono-modal). (iii) The densification strain reduced in case of HFBM and HFTM, (iv) The HFTM exhibits lower densification strain as compared to that in case of HFBM. It is further noted that εd follows linear relationship with relative density as was observed in case of other foams [28,34,35]. The εd of closed cell foam is expressed with the following relation [36].

εd = C (1 − ∝1 × ρrd )

(3)

where ‘C’ is a constant that varies from 0.9 to 1, ∝1 varies from 1.4 to 2 567

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Fig. 4. (a) The micrographs of CAHFs with (a) HFBM and HFTM (b) HFBM (c) HFTM (d) lower magnification (e) higher magnification (f) bonding between cenosphere shell and matrix.

and 1.0 respectively using Eq. (3). If ρrd is considered to be 1.0, the εd comes to be around 0.2 to 0.3. This could be considered to be the compressive εd of syntactic foams (cell walls) without any macro-porosity [21]. If ρrd is considered to be zero, the εd comes to be around 0.73 to 0.84. This may be due to the fact, that the existence of microspheres in the cell wall influencing these constants in the linear equation. The linear equations obtained in these studies are practically meaningful. It was already examined earlier that the packing density of cenosphere in the cell wall of CAHF increase when one use bi-modal or tri-modal cenosphere size distribution, which finally increases cell wall thickness and reduces the macro-porosity (Table 1). Because of reduction in macro-porosity, the εd in HFBM and HFTM are lower. In similar manner, it can be explained, the εd in HFTM is greater than that in HFBM one.

and ρrd is relative density of foam. The εd calculated using Eq. (3) considering C between 0.9 and 1 for different CAHFs, are in close agreement with the εd measured experimentally. The experimentally determined εd is very close to the value which is calculated using (C = 0.9) within the present domain. In the present study the value of intercept is between 0.73 and 0.84. The slope is also lower than that reported in Eq. (3). In fact, (i) when ρf = 1, the εd = 0.36 to 0.4. (ii) But, when, ρrd = 0, εd = 0.9 to 1.0 according to Eq. (3). The second case is practically meaningful, but the first case is not when one considers Eq. (3) for determining εd. If one considers, that the densification strain is primarily controlled by the macro-porosity, then the linear relationship obtained in the present study is practically meaningful. For example, for a relative density of 0.13, the Vmp is between 0.77 and 0.80. Thus, the maximum εd can be achieved between around 0.72 to 0.85 for C = 0.9 568

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Table 1 The cell size, cell wall thickness, relative densities, macroporosity and plateau stress (exp. and practical) as a function of foaming temperature. CAHFs

ρrd

HFM1

0.19 0.17 0.15 0.13 0.19 0.17 0.15 0.13 0.19 0.17 0.15 0.13 0.19 0.17 0.15 0.13 0.19 0.17 0.15 0.13

HFM2

HFM3

HFBM

HFTM

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.024 0.019 0.014 0.009 0.024 0.019 0.014 0.009 0.024 0.019 0.014 0.009 0.024 0.019 0.014 0.009 0.024 0.019 0.014 0.009

Cell size (mm)

Cell wall thickness (μm)

Vmp from Eq. (2)

Vmp exp.

3.4 4.4 5.3 5.6 3.2 3.7 4.6 5.4 3.5 3.9 4.7 5.2 2.8 4.1 5.1 5.4 2.9 3.5 5.2 5.5

624 527 415 322 634 529 433 345 640 532 430 325 656 569 478 450 675 618 521 476

0.76 0.78 0.81 0.83 0.76 0.78 0.81 0.83 0.76 0.78 0.81 0.83 0.76 0.78 0.81 0.83 0.76 0.78 0.81 0.83

0.74 0.76 0.79 0.81 0.75 0.76 0.78 0.80 0.75 0.76 0.79 0.81 0.72 0.75 0.78 0.80 0.71 0.74 0.77 0.79

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.22 0.31 0.51 0.36 0.23 0.35 0.38 0.32 0.21 0.27 0.39 0.48 0.18 0.14 0.37 0.39 0.18 0.24 0.37 0.49

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

41.10 36.97 29.11 24.21 42.10 32.41 34.52 29.74 44.80 37.24 30.11 17.12 43.10 36.41 32.52 23.84 42.10 35.41 28.52 18.84

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.041 0.045 0.049 0.057 0.031 0.035 0.045 0.052 0.032 0.035 0.042 0.054 0.039 0.042 0.044 0.052 0.041 0.045 0.049 0.057

Fig. 6. The compressive stress strain curves of HFM1, HFM2, HFM3, HFBM and HFTM at a strain rate of 0.01/s (a) for ρrd = 0.15 (b) ρrd = 0.19.

3.4.3. Energy Absorption The energy absorption (Eab) as a function of relative density (ρrd) for HFMs, HFBM and HFTM when tested at a strain rate of 0.01/s are compared in Fig. 9(a). It is evident from this figure that the Eab of HFMs increases with increase in ρrd and with decrease in average cenosphere size, when one uses mono-modal cenosphere distribution. But, in case of HFBM and HFTM, the Eab are much higher than those of HFMs, even though, the average cenosphere size in HFBM and HFTM is higher than those in HFM1. However, it may be noted, in general, that Eab follows power law relationship with relative density irrespective of cenosphere size distribution. The exponent and coefficient are varying with the cenosphere size. Both the exponent and coefficient are higher for HFBM and HFTM. Similar kinds of trends are noted when CAHFs are tested at strain rate of 0.1/s and 1/s as shown in Fig. 9(b) and (c) respectively. Comparison of Fig. 9(a), (b) and (c) states that the coefficient as well as exponent of power law relationship are varying with strain rates, but do not follow any specific trend. This, indirectly states that the Eab is influenced with the strain rates also. In order to understand the effect of strain rate on Eab, the Eab values recorded in each condition and reported in Table 2. The increase in Eab with strain rate is primarily due to increase in plateau stress with strain rate. But the strain varies marginally with strain rate. Here Eab is calculated considering strain up to 0.6. In the plateau region the oscillation of stress changes. Additionally in some cases, the onset of densification strain starts. As a result, the coefficient and exponent may not be following any specific trend with strain rate and cenosphere size distribution.

Fig. 5. The average cell size distribution for different CAHFs of different relative densities (a) HFBM (b) HFTM.

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Table 2 Effect of particle size distribution on σpl, ɛd, and Eab as a function of strain rate and relative density. Strain rate HFM1 0.01/s

0.1/s

1/s

HFM2 0.01/s

0.1/s

1/s

HFM3 0.01/s

0.1/s

1/s

HFBM 0.01/s

0.1/s

1/s

HFTM 0.01/s

0.1/s

Fig. 7. The plateau stress of CAHFs as a function of relative density (a) for 0.01/ s (b) 0.1/s (c) 1/s. 1/s

The plateau stress, energy absorption of these foams was compared with the reported values of other investigators in Table 3. It may be noted that the plateau stress or energy absorption of investigated hybrid Al-foams are comparable to others or even better. Xia et al. [27] used 20% cenosphere of size 300 μm and made foam with 0.225 relative density. But the plateau stress and energy absorption of their foam are only 4 MPa and 2.3 MJ/m3 respectively. In the contrast, the minimum plateau stress and energy absorption were noted to be 3.23 MPa and 2.32 MJ/m3 respectively when cenosphere contain is 30% and relative

ρ (g/cm)

ρrd

σpl (MPa)

ɛd

Eab (MJ/m3)

0.35 0.41 0.46 0.51 0.35 0.41 0.46 0.51 0.35 0.41 0.46 0.51

0.13 0.15 0.17 0.19 0.13 0.15 0.17 0.19 0.13 0.15 0.17 0.19

3.28 3.84 4.59 5.12 3.70 4.62 5.35 6.78 4.60 5.50 7.26 8.38

± ± ± ± ± ± ± ± ± ± ± ±

0.16 0.23 0.22 0.3 0.18 0.23 0.26 0.47 0.27 0.27 0.36 0.50

0.75 ± 0.04 0.743 ± 0.05 0.732 ± 0.04 0.711 ± 0.04 0.70 ± 0.05 0.69 ± 0.03 0.68 ± 0.03 0.675 ± 0.03 0.678 ± 0.03 0.67 ± 0.04 0.66 ± 0.03 0.646 ± 0.03

2.03 2.36 2.90 3.72 2.48 2.82 3.50 4.26 2.74 3.32 4.45 5.40

± ± ± ± ± ± ± ± ± ± ± ±

0.10 0.14 0.20 0.18 0.12 0.16 0.24 0.21 0.16 0.16 0.35 0.37

0.35 0.41 0.46 0.51 0.35 0.41 0.46 0.51 0.35 0.41 0.46 0.51

0.13 0.15 0.17 0.19 0.13 0.15 0.17 0.19 0.13 0.15 0.17 0.19

2.90 3.47 3.99 4.38 3.24 4.08 4.95 5.72 4.17 5.04 5.94 7.82

± ± ± ± ± ± ± ± ± ± ± ±

0.14 0.24 0.19 0.26 0.16 0.24 0.29 0.28 0.25 0.25 0.41 0.39

0.759 ± 0.05 0.748 ± 0.04 0.740 ± 0.04 0.72 ± 0.05 0.71 ± 0.04 0.7 ± 0.03 0.686 ± 0.03 0.679 ± 0.04 0.681 ± 0.03 0.676 ± 0.04 0.667 ± 0.03 0.653 ± 0.03

1.75 2.09 2.72 3.23 2.04 2.51 2.98 3.74 2.43 3.06 3.69 4.21

± ± ± ± ± ± ± ± ± ± ± ±

0.08 0.12 0.21 0.19 0.12 0.17 0.14 0.26 0.12 0.18 0.18 0.29

0.35 0.41 0.46 0.51 0.35 0.41 0.46 0.51 0.35 0.41 0.46 0.51

0.13 0.15 0.17 0.19 0.13 0.15 0.17 0.19 0.13 0.15 0.17 0.19

2.51 2.65 3.23 3.43 2.64 2.90 3.60 4.60 3.46 4.20 5.47 6.57

± ± ± ± ± ± ± ± ± ± ± ±

0.12 0.13 0.19 0.20 0.13 0.2 0.18 0.27 0.17 0.21 0.32 0.39

0.768 ± 0.04 0.753 ± 0.4 0.745 ± 005 0.732 ± 0.04 0.72 ± 0.04 0.707 ± 0.05 0.690 ± 0.03 0.683 ± 0.03 0.685 ± 0.03 0.68 ± 0.04 0.673 ± 0.04 0.664 ± 0.03

1.56 1.69 2.32 2.63 1.85 2.26 2.74 3.43 2.23 2.79 3.41 3.81

± ± ± ± ± ± ± ± ± ± ± ±

0.12 0.11 0.13 0.13 0.09 0.13 0.19 0.20 0.17 0.13 0.20 0.19

0.35 0.41 0.46 0.51 0.35 0.41 0.46 0.51 0.35 0.41 0.46 0.51

0.13 0.15 0.17 0.19 0.13 0.15 0.17 0.19 0.13 0.15 0.17 0.19

3.60 4.27 5.36 6.83 3.93 4.90 6.05 8.23 4.84 6.11 7.64 9.71

± ± ± ± ± ± ± ± ± ± ± ±

0.18 0.25 0.26 0.4 0.19 0.29 0.30 0.41 0.24 0.42 0.38 0.58

0.743 ± 0.03 0.736 ± 0.04 0.724 ± 0.05 0.716 ± 0.04 0.694 ± 0.03 0.685 ± 0.04 0.676 ± 0.03 0.670 ± 0.03 0.671 ± 0.05 0.66 ± 0.03 0.651 ± 0.03 0.638 ± 0.03

2.25 2.55 3.38 4.63 2.72 3.26 3.81 5.29 2.95 3.73 4.88 5.73

± ± ± ± ± ± ± ± ± ± ± ±

0.18 0.17 0.16 0.32 0.16 0.16 0.26 0.42 0.14 0.26 0.29 0.28

0.35 0.41 0.46 0.51 0.35 0.41 0.46 0.51 0.35 0.41 0.46 0.51

0.13 0.15 0.17 0.19 0.13 0.15 0.17 0.19 0.13 0.15 0.17 0.19

4.31 ± 0.21 5.43 ± 0.32 5.98 ± 0.29 7.38 ± 0.44 4.56 ± 0.22 5.93 ± 0.35 6.84 ± 0.34 9.28 ± 0.64 5.27 ± 0.26 6.51 ± 0.39 8.80 ± 0.44 10.30 ± 0.72

0.74 ± 0.04 0.731 ± 0.03 0.720 ± 0.05 0.710 ± 0.03 0.690 ± 0.04 0.682 ± 0.03 0.672 ± 0.04 0.665 ± 0.03 0.666 ± 0.03 0.656 ± 0.03 0.643 ± 0.04 0.632 ± 0.03

2.53 3.13 3.86 5.06 2.92 3.68 4.42 5.58 3.40 4.28 5.17 6.26

± ± ± ± ± ± ± ± ± ± ± ±

0.12 0.18 0.27 0.40 0.17 0.25 0.26 0.33 0.28 0.21 0.31 0.43

density is 0.17. When the relative density increased to 0.19, the minimum plateau stress and energy absorption of investigated foams comes to be 5.12 MPa and 3.72 MJ/m3 respectively (Table 2). The same things improve significantly when one use bimodal or tri-modal 570

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Fig. 9. The energy absorption of CAHFs as a function of relative density (a) for 0.01/s (b) 0.1/s (c) 1/s.

Fig. 8. The densification strain of CAHFs as a function of relative density (a) for 0.01/s (b) 0.1/s (c) 1/s.

where σpl is the plateau strength of foam, ε ̇ is the stain rate, m is the strain rate sensitivity, and Kf is the strengthening coefficient. At ε=̇ 1/s , the σpl = Kf or if m = 0, then σpl = Kf. In order to calculate ‘m’ and ‘Kf’, the ln(σpl) of different CAFMs as a function of ln(ἑ) is plotted in Fig. 10(a), (b) and (c) for ρrd = 0.13, 0.17, 0.19 respectively. The plots are best fitted linearly in order to get ‘m’ from the slop and Kf from the antilog of the intercept. It may be noted, in general, that the stress increases slowly with

cenosphere distribution. It may thus suggest that use of bi or tri modal cenosphere distribution to be used for making hybrid foam. 3.4.4. Effect of Strain Rate The strength of foam as a function of strain rate can be expressed with following relation [35]

̇ σpl = Kf × ε m

(4) 571

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A. Pandey et al.

Table 3 Comparison between compression properties of present work and other hybrid foam. Foam

R.D

LM13-30% vol% Cenosphere Al-QK150-20% vol% Cenosphere Al-QK300-20% vol% Cenosphere HFM1 HFM2 HFM3 HFBM HFTM

0.16

Strain rate (S−1) −3

1 × 10

−3

Plateau stress (σpl) MPa

Energy absorption (Eab) MJ/m3

References

3

2.22

Mondal et al. [13]

0.295

4 × 10

7

4.4

Xia et al. [27]

0.225

4 × 10−3

4

2.3

Xia et al. [27]

0.17 0.17 0.17 0.17 0.17

1 × 10−2 1 × 10−2 1 × 10−2 1 × 10−2 1 × 10−2

4.59 3.99 3.23 5.36 5.98

2.9 2.72 2.32 3.38 3.86

Present Present Present Present Present

than those of HFBM and HFTM, (ii) Ʃ of HFMs decreases with decrease in cenosphere size, (iii) Ʃ of HFBM is greater than that of HFTM, (iv) Ʃ generally increases with increase in relativity density, (v) Ʃ remains almost invariant to the strain rate. In general it is noted that Ʃ ≤ 0.1. This signifies that HFs is marginally influenced with strain rate. It is also reported by a group of investigators in other aluminium foams that under quasi static condition the aluminium composite foam is almost invariant to the strain rate [39–41]. But, at higher strain rate, especially when approaching to dynamic stage, the foams become sensitive to strain rate [42,43]. In the present study, it is noted that CAHFs are marginally influenced with strain rate. This may be due to the fact, that CAHF is tested at higher range of quasi-static strain rate (0.1 and 1/s). Here, the cell wall deforms at faster rate and dislocations or share bands which are generated get intersected relatively at faster rate, which led to relatively higher rate of cell wall strengthening, leading to marginal influence of strain rate on plateau stress. As the relative density increases, the cell wall thickness increases and cell size reduces very marginally (Table 1). As a result the cell wall is subjected to more deformation causing more shear band and dislocation interaction, which led to more strengthening at higher strain rate. Because of this fact, Ʃ increases with relative density. The average Ʃ is noted to be 0.063, 0.065, 0.072 and 0.089 for ρrd of 0.13, 0.15, 0.17 and 0.19 respectively. When cenosphere size reduces, there is a possibility of more number of cenosphere at the cell wall of CAHFs (Fig. 3(c)). As a result the interface (mechanically bonded region) between cenosphere and matrix alloy increases and inter cenosphere distance decreases. Higher extent of interface area acts as dislocation annihilation point. More cenosphere in cell wall causing reduction in micro-shear band interaction. As a result, extent of strengthening due to reduction in cenosphere size under the influence of higher strain rate is relatively less. This led to lower Ʃ value at finer cenosphere size. Similarly, when bi-modal or tri-modal cenosphere size are used, there is a possibility of more cenosphere accumulation at cell wall, which causes higher interface area and reduction in inter cenosphere spacing. These facts are more dominating in case of tri-modal cenosphere size as compared to that in bi-modal cenosphere size distribution. As a result, because of the similar reason as stated above (i) HFBM and HFTM exhibited low Ʃ value as compared to that obtained in case of HFMs, and (ii) HFTM exhibits lower Ʃ as compared to that in HFBM. In addition to the above facts, the stress distribution within the cell wall changes with the change in cenosphere size distribution.

increase in strain rate. A two order increase in strain rate led too only 25 to 30% increase in strength. In quasi-static condition in case of dense aluminium matrix composite, it was also noted that the yield stress is almost invariant to the strain rate [35]. This might be due to annihilation of dislocation at the mechanical interface between reinforcement and matrix. In case of Al-SiC composite, the value of ‘m’ is very much low (0.02 to 0.03) [37]. Similar range of ‘m’ value was also reported for Al-fly ash composite foam [26,35]. The CAHFs, in this study, exhibited relatively higher ‘m’ value (0.08–0.15). This signifies that the CAHFs are more strain rate sensitive as compared to the dense composite. It is further noted that the ‘m’ and ‘Kf’ increases with increase in relative density except in very few cases. It is further noted from Fig. 10 that at same relative density, the HFMs exhibit marginally higher ‘m’ value as compared to that obtained in HFBM and HFTM. It may further be noted that the value of ‘m’ reduced with reduction in average cenosphere size in case of a HFMs. Careful observation reveals that the HFTM exhibited less ‘m’ value as compared to that in HFBM. This may be due to the fact that the average cenosphere size in HFTM is less than that of HFBM. But, the average size may not be the only factor. The packing of cenosphere in the cell wall changes with cenosphere size distributions which also influence the value of ‘m’. The value of ‘kf’ on the other hand follows the reverse trend as that was observed in case of ‘m’. The value of ‘kf’ increases with decrease in cenosphere size and also noted to be higher in case of HFBM and HFTM. In case of HFTM ‘kf’ is the maximum. These results indicate that the influence of strain rate on deformation behavior of CAHF is strongly dictated by the cenosphere distribution. The higher amount of cenosphere matrix interfaces and also reduction in inter cenosphere spacing causes greater plastic constraint of cell wall and higher extent of dislocation annihilation. However, detailed TEM studying may be required for better understanding. 3.5. Strain Rate Sensitivity Parameter

∑=

σd − σq σ∗

1 ln

() εd εq

work work work work work

(5)

where, σd and σq are the flow stress at dynamic and quasi-static condition respectively, σ* is flow stress at given strain (i.e. 0.02) under a reference strain rate of 0.01/s, εd and εq are strain rate at dynamic and quasi-static test condition (0.01/s) respectively. The strain rate sensitivity parameter (Ʃ) can be calculated using the recorded data from stress strain curves following the relation as reported in Eq. (5) [38]. Here quasi-static strain rate is considered to be 0.01/s. The σ⁎ value is considered at 2% strain [38]. The values of Ʃ as a function of cenosphere size, relative density, and strain rate and cenosphere size distribution are recorded in Table 4. It is noted that the maximum value of Ʃ is 0.17 for HFM3 at a strain rate of 1/s. In majority of cases, the Ʃ is found to be < 0.1. It may be noted that Ʃ varies marginally with strain rate, relative density and cenosphere size distribution. In majority of cases, the following observations are made. (i) Ʃ of HFMs are higher

4. Conclusions The following conclusion can be drawn from the present chapter: 1. The compressive deformation responses of CAHFs are strongly influence with the cenosphere size distribution and marginally influenced with the strain rate. 2. The σpl, and Eab increases with decrease in cenosphere size, while 572

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Table 4 Strain rate sensitivity parameter (Ʃ) as a function of cenosphere size, relative density, and strain rate and cenosphere size distribution.

Fig. 10. ln(σpl) of different CAHFs as a function of ln(ε̇) (a) for ρrd = 0.13, (b) ρrd = 0.17 and (c) ρrd = 0.19.

RD

CAHFs

Strain rate

σq

σd

σ*

Ʃ

0.13

HFM3

0.13

HFM2

0.13

HFM1

0.13

HFBM

0.13

HFTM

0.15

HFM3

0.15

HFM2

0.15

HFM1

0.15

HFBM

0.15

HFTM

0.17

HFM3

0.17

HFM2

0.17

HFM1

0.17

HFBM

0.17

HFTM

0.19

HFM3

0.19

HFM2

0.19

HFM1

0.19

HFBM

0.19

HFTM

0.01 0.1 1 0.01 0.1 1 0.01 0.1 1 0.01 0.1 1 0.01 0.1 1 0.01 0.1 1 0.01 0.1 1 0.01 0.1 1 0.01 0.1 1 0.01 0.1 1 0.01 0.1 1 0.01 0.1 1 0.01 0.1 1 0.01 0.1 1 0.01 0.1 1 0.01 0.1 1 0.01 0.1 1 0.01 0.1 1 0.01 0.1 1 0.01 0.1 1

2.147 2.147 2.147 3.20 3.20 3.20 3.35 3.35 3.35 3.69 3.69 3.69 4.39 4.39 4.39 2.71 2.71 2.71 3.51 3.51 3.51 3.91 3.91 3.91 4.31 4.31 4.31 5.51 5.51 5.51 3.32 3.32 3.32 4.12 4.12 4.12 4.65 4.65 4.65 5.45 5.45 5.45 5.98 5.98 5.98 3.51 3.51 3.51 4.49 4.49 4.49 5.23 5.23 5.23 6.87 6.87 6.87 7.48 7.48 7.48

2.147 3.057 3.57 3.2 3.36 4.47 3.35 3.79 4.71 3.69 3.98 4.96 4.39 4.63 5.36 2.71 3.12 4.27 3.51 4.15 5.16 3.91 4.69 5.57 4.31 4.99 6.11 5.51 5.98 6.57 3.32 3.69 5.58 4.12 5.09 6.12 4.65 5.47 7.35 5.45 6.12 7.77 5.98 6.97 8.92 3.51 4.71 6.68 4.49 5.79 7.89 5.23 6.86 8.49 6.87 8.31 9.83 7.48 9.35 10.47

1.76 2.87 1.732 2.98 3.04 3.04 3.1 3.26 4.45 3.32 3.67 4.48 4.13 4.38 5.12 2.64 2.95 4.09 3.44 4.03 4.85 3.84 4.55 5.31 3.98 4.56 5.88 5.26 5.63 6.39 3.14 3.58 5.49 3.93 4.96 5.96 4.42 5.39 5.28 5.38 6.03 7.68 5.83 6.86 8.82 3.45 4.62 6.57 4.35 5.73 7.78 5.14 6.79 8.37 6.81 8.24 9.72 7.39 9.26 10.38

0 0.137703 0.178407 0 0.022858 0.090716 0 0.058616 0.066364 0 0.034318 0.061557 0 0.023797 0.041139 0 0.06036 0.082824 0 0.06897 0.073875 0 0.07445 0.067884 0 0.064763 0.066474 0 0.036255 0.036021 0 0.044885 0.08939 0 0.084933 0.072868 0 0.066071 0.111041 0 0.048255 0.065597 0 0.062675 0.072382 0 0.112804 0.104773 0 0.098531 0.094897 0 0.104256 0.084576 0 0.075896 0.066127 0 0.087703 0.06255

decrease in cenosphere size. The ‘m’ and ‘Ʃ’ are lower in case of HFBM and HFTM and are minimum in case of HFTM. These ‘m’ and ‘Ʃ’ decrease with increase in relative density. 6. For getting CAHFs improved σpl and Eab, it is better to use HFBM and HFTM or with very wide size distribution.

the reverse trend is true for εd in case of HF with HFMs. 3. The HFBM and HFTM exhibited higher σpl and Eab and lower εd as compared to those HFMs. The HFTM exhibited the maximum σpl and Eab. 4. The σpl, Eab and εd are also influenced by the strain rate. The strain rate sensitivity as well as strain rate sensitivity parameter in CAHFs is relatively higher as compared to those reported for Al-flyash or AlSiC composite foam. 5. The ‘m’ and ‘Ʃ’ are higher for HFMs. These values decrease with

Conflict of Interest The authors declare that they have no conflict of interest. 573

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