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Dynamic compression behavior of cenosphere aluminum alloy syntactic foam
Materials and Design 42 (2012) 418–423
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Technical Report
Dynamic compression behavior of cenosphere aluminum alloy syntactic foam Manmohan Dass Goel a,⇑, Marco Peroni b, George Solomos b, Dehi Pada Mondal a, Vasant A. Matsagar c, Anil K. Gupta a, Martin Larcher d, Steffen Marburg e a
CSIR-Advanced Materials and Processes Research Institute (AMPRI), Council of Scientific and Industrial Research (CSIR), Bhopal 462 064, India European Commission Joint Research Centre (JRC), Institute for the Protection and Security of the Citizen, European Laboratory for Structural Assessment (ELSA), 21027 Ispra, Italy c Department of Civil Engineering, Indian Institute of Technology (IIT) Delhi, New Delhi 110 016, India d Institute of Mechanics and Statics, University of German Armed Forces, Neubiberg 85577, Munich, Germany e Department of Aerospace Engineering, University of German Armed Forces, Neubiberg 85577, Munich, Germany b
a r t i c l e
i n f o
Article history: Received 21 April 2012 Accepted 8 June 2012 Available online 27 June 2012
a b s t r a c t The compression behavior of aluminum cenosphere syntactic foam has been studied and full stress– strain diagrams have been obtained for strain rates ranging from quasi-static to 1400/s. The foam exhibits peak stress at a strain of about 5%, especially during quasi-static compression, and the maximum value of stress around this strain is used to examine strain rate sensitivity and to determine an appropriate sensitivity parameter. The compressive strength and energy absorption of these foams attain a maximum at strain rates of approximately 750/s and then they decrease with further increase in the strain rate. The foam with coarser cenosphere appears to be more sensitive to strain rate. An empirical relation is developed for predicting the dynamic compressive strength of aluminum cenosphere syntactic foams. Explanation of the observed mechanical behavior in terms of the material failure mechanisms is provided. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Syntactic foams are composite materials synthesized by filling a metal, polymer or ceramic matrix with the hollow particles known as micro-balloons. These foams exhibit excellent combination of physical and mechanical properties. They have high damage tolerance through high energy absorbing capabilities, high specific stiffness, improved strength, and high acoustic and mechanical damping capacities. These properties make syntactic foams an attractive choice for various applications such as, core in sandwich structures, for packaging/fire proof, crash safety, damping panels, and underwater buoyant structures [1–4]. The ceramic particle filled syntactic foams exhibit excellent thermal insulation and low thermal expansion coefficient due to a significant volume fraction of ceramic phase in the matrix. Although, syntactic foams containing hollow ceramic spheres, i.e. cenosphere have higher densities than conventional aluminum foams (produced either by gas entrapment in the melt or infiltration of salt preforms), they have the advantages of higher strengths, isotropic mechanical properties, and excellent energy absorbing capacities due to extensive strain accumulation at relatively high stresses [5–10]. In order to use syntactic foams in the advanced applications such as crash or impact, blast resistance, aeronautical, and space struc⇑ Corresponding author. Tel.: +91 755 2457244. E-mail address: [email protected] (M.D. Goel). 0261-3069/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.matdes.2012.06.013
tures, it is crucial to understand their behavior under high rate of loading. Quasi-static compression behavior of syntactic foams has been studied in the past by a few researchers for assessing their energy absorption capacity [3–5,11–14]. Wu et al. examined high strain rate deformation behavior on commercially pure aluminum cenosphere syntactic foam [12]. However, for engineering and other applications aluminum alloys are preferred as they provide improved strength and toughness. In the literature, high strain rate response of aluminum syntactic foam is scarce. In aluminum alloy foams strain rate sensitivity is dependent on matrix materials [14], whereas in case of metal matrix composites (MMCs), the particles govern the strain rate sensitivity instead of matrix [15,16]. Syntactic foam exhibits a structure combination of both metal foam and MMCs and hence their deformation behavior under varying strain rate is highly complex and is not consistent in nature. In quasi-static condition, the strain rate sensitivity is reported to be very low [13]. The present investigation is aimed at characterizing the dynamic compressive behavior of syntactic foams as compared to that in quasi-static compression condition.
2. Material and experiments Aluminum alloy (Al-2014) cenosphere syntactic foam is prepared using cenosphere of two different size ranges. The average size of cenosphere is noted to be 90 lm and 200 lm. The size distribution of cenospheres of 90 lm and 200 lm is shown in Fig. 1a. It is to be noted that cenosphere size in both cases varies
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90 μm
% Frequency
20
15 10
5
100 µm 0
110-120
210-220
90 µm
Size Range (micron) 25
200 μm
% Frequency
20 15 10 5
100 µm 0 120-130
220-230
320-330
200 µm
Size Range (micron)
(b)
(a)
Fig. 1. (a) Size distribution of cenosphere. (b) Microstructure of Al-cenosphere syntactic foam.
in wide range. The average size of cenosphere is measured from the dimension of at least 200 individual cenosphere separately from the micrograph of as received cenospheres used for developing the syntactic foam. The cenospheres are dispersed on a glass slide which is then transferred to a double sided tape attached on metallic stud. The cenospheres get attached to the tape and then these are gold sputtered prior to scanning electron microscope (SEM). The micrographs are used for measuring the size of individual cenosphere. The size distribution of cenosphere is reported in the form of histogram. The cenospheres are selected randomly in the micrographs to avoid the subjective judgment. Similarly, the shell thickness of these cenospheres is measured from the micrographs of syntactic foam and their average values are reported. The foam is prepared by stir-casting technique, the details of the process are reported elsewhere [17]. The alloy and cenosphere are used in the ratio of 92:8 to attain volume fraction of cenosphere to be about 35%. Table 1 shows density and porosity fraction of aluminum cenosphere syntactic foam used in the present investigation. The porosity fraction of syntactic foam is about 8–10% less than the volume fraction of cenospheres used. This is attributed to the presence of cenosphere shell and it is about 20–30% of the cenosphere [13]. The porosity fraction (fp) in cenosphere aluminum alloy syntactic foam is determined using the following relation [12],
3 t fp ¼ fc 1 : R
ð1Þ
Here, t is the thickness of the cenosphere shell; R is the radius of the cenospheres and fc is the volume fraction of cenospheres. In parallel, the porosity fraction is measured experimentally following the point counting technique considering 25 randomly selected field at a magnification of 50 [18]. Quasi-static compression tests are performed at ambient temperature using BiSS Universal Testing Machine (Model Bi-00–002, 50 kN Load Cell) at Advanced Materials and Processes Research Institute (AMPRI), Council of Scientific and Industrial Research (CSIR), Bhopal, India at a strain rate of 0.001/s [19]. Cylindrical samples of 10 mm diameter and 15 mm length are used for quasi-static compression test. For each set three samples are tested. The average values of plateau stress, the densification strain and energy absorption are calculated from the all the samples tested for each set. The same machine and similar samples are also used for compression testing of syntactic foam at strain rate up to 10/s. The surfaces of the specimens are polished mechanically prior to testing and are lubricated with thin molybdenum sulfide coating in order to reduce the friction between the specimen surface and the compression test platens. The load–displacement data is recorded during the testing and converted to stress–strain curves using standard methodology. The high strain rate tests are conducted using a modified split Hopkinson pressure bar (SHPB) at the European Commission Joint Research Centre (JRC), Institute for the Protection and Security of the Citizen, European Laboratory for Structural Assessment (ELSA), Ispra Italy. A standard SHPB
Table 1 Physical parameters of the Al-2014 cenosphere syntactic foam.
a b c
Foam
Density (g/cm3)
Shell thickness (lm)
fca (%)
fpb (%)
fpc (%)
90 lm Al-2014 cenosphere foam 200 lm Al-2014 cenosphere foam
2.05 1.95
5 ± 0.2 8 ± 0.2
34.2 35.1
26.2 ± 1.8 27.4 ± 1.3
24.01 27.33
fc – Cenosphere fraction. fp – Porosity fraction, experimental. fp – Porosity fraction, computed.
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consists of a striker, an incident (input) bar and a transmitter (output) bar, with the specimen sandwiched between the incident and transmitter bars [20]. These bars, which remain always elastic, are made of maraging steel alloy. For the current tests, the input bar has a diameter of 10 mm and a length of 2.2 m. The output bar is 2 m long and 10 mm in diameter [21–22]. The role of the striker is played by a 1 m long bar which is the solid continuation of the input bar. This bar is stretched and suddenly released in order to generate the necessary compressive pulse, which propagates down the input bar towards the specimen. Semiconductor strain-gauges (Kyowa Model KSN-6–350-E4–11), strain gauge amplifier (EFS Model SGA02HF) and acquisition board gauge (Octopus CompuScope 84XX) are used for recording signals during the testing with a sampling rate of 10 MSamples/s. A cubical shape syntactic foam specimen with 6 mm size is used for this testing to achieve the required strain rates by the present SHPB setup. After the tests, the specimens are cut for the examination of the microstructure of the deformed samples. 3. Results and discussion Fig. 2a and b show the compressive stress–strain curves of aluminum cenosphere syntactic foam with 90 lm and 200 lm cenosphere, respectively under quasi-static and high strain rate compressive loading condition. It can be observed that the curve under quasi-static loading follows a zigzag pattern whereas under high strain rate it shows relatively smoother transition from elastic to plastic range. At lower strain rate, the peak stress (hump) is observed just after yielding at a strain of about 5%. The peak stress, termed here as compressive strength, is used for measuring the strain rate sensitivity parameter. It is observed that peak stress of syntactic foam increased from 183 MPa at 0.001/s to 223 MPa at 750/s for 90 lm. However, when the strain rate increased to 1400/s, the peak stress reduces to 204 MPa. In case of aluminum syntactic foam with 200 lm cenosphere, the peak stress increases from 160 MPa at 0.001/s to 206 MPa at 750/s. Aluminum syntactic foam with 200 lm cenosphere also exhibits peak stress of 197 MPa when strain rate further increased to 1400/s. The sensitivity parameter () is computed by using the following equation [3],
rd rq 1 _ _ ðed =eq Þ : ln r
ð2Þ
Here, r is the compressive strength, r⁄ is the quasi-static flow stress at 5% strain, e_ is the strain rate, wherein, subscripts ‘d’ and ‘q’ define
rd ¼ r0 ½Cð1 þ ðe_ =e_ 0 Þm Þ:
Here, rd is the dynamic compressive strength (=rd computed), r0 is the quasi-static compressive strength (i.e. compressive strength at strain rate of 0.001), C is a constant (strengthening coefficient), e_ is the strain rate, e_ 0 is a reference strain rate and m is the strain rate sensitivity [15]. The value of m is calculated from the slope of ln (compressive strength) vs. ln (strain rate) curve assuming a linear variation. The average value of m is found to be about 0.015. Considering m = 0.015 and adjusting the value of C, the value of rd was calculated at different strain rates. The values C, m, rd computed and rd experimental are also reported in Table 2. It can be observed that C value increases marginally with increase in the cenosphere size. It is attributed to the fact that the inter-cenosphere distance increases with increase in cenosphere size (as in both the cases same amount of cenosphere is used) and wider matrix space (in between cenosphere), could accommodate more dislocations during matrix deformation and leads to greater extent of matrix strengthening. Balch et al. [3] also stated that the deformation of aluminum syntactic foam under varying strain rate is controlled by the matrix deformation. The parameter C is considered to be strengthening parameter and the value of C increases with increase in e_ up to 750/s. This is also attributed to the fact that the flow stress of alloy increases with increase in strain rate. However, at strain rate > 750/ s the value of C starts reducing. This is attributed to the greater possibility of cenosphere crushing at this strain rate. At strain rate > 750/s, the deformation of these foams is primarily controlled 400
400
200 μm
90 μm 350
350
900/s
1/s
1400/s
300
750/s
Stress, σ (MPa)
750/s 250
10/s
200 150
420/s 0.001/s
1/s
50
Compressive Strength (MPa)
Stress, σ (MPa)
300
100
ð3Þ
250 200 150
200
10/s 250
150 100
100
0.001/s
50 0
0.001 1
10
50
420 750 900 1400
1400/s
250
Compressive Strength (MPa)
R¼
dynamic and quasi-static conditions, respectively. The various parameters of Eq. (2) are computed and reported in Table 2. It is observed that the dynamic compressive strength at strain rate > 750/s of the present syntactic foams is about 10–30% higher than that of quasi-static compressive strength and the sensitivity parameter is in the range of 0.005–0.021, which is close to that of the aluminum matrix as reported by Balch et al. [3]. This is confirming the presence of rate sensitivity in the present syntactic foam. The sensitivity parameter is, however, noted to be marginally lower than that reported by Dou et al. [4]. It is attributed to the fact that they used different size of cenosphere and fabrication method for making the syntactic foam. The source and nature of cenosphere are also different. These observations thus demonstrate that deformation behavior of aluminum cenosphere foam strongly depends on the nature, volume fraction, and size of cenosphere. Dou et al. [4] proposed the following relation for computing the dynamic strength,
200 150 100
Strain Rate (/s)
0 0.0
0.1
0.2
0.3
0.4
0.5
50 0
0.001
1
10
750
1400
Strain Rate (/s)
0.6
0 0.0
0.1
0.2
0.3
Strain, ε
Strain, ε
(a)
(b)
0.4
0.5
0.6
Fig. 2. Compressive stress–strain curves of Al-cenosphere syntactic foam under quasi-static and high strain rate loading: (a) 90 lm, (b) 200 lm.
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M.D. Goel et al. / Materials and Design 42 (2012) 418–423 Table 2 High strain rate compressive properties of the Al-2014 cenosphere syntactic foam. P Cenosphere size (lm) rq (MPa) r⁄ (MPa)
m
C
e_
rd experimental (MPa)
rd computed (MPa)
90 lm Al-2014 cenosphere foam
183.5
183
0.005 0.007 0.006 0.016 0.011 0.008
0.015 0.015 0.015 0.015 0.015 0.015
0.49 0.495 0.485 0.545 0.515 0.495
1 10 420 750 900 1400
190 ± 3.8 195 ± 2.8 197 ± 3.0 223 ± 4.0 210 ± 4.5 204 ± 3.5
189.65 195.12 197.07 222.51 210.58 203.14
200 lm Al-2014 cenosphere foam
161
160
0.005 0.018 0.021 0.016
0.015 0.015 0.015 0.015
0.49 0.54 0.575 0.545
1 10 750 1400
167 ± 2.0 187 ± 3.5 206 ± 5.0 197 ± 4.0
166.39 186.76 205.97 196.24
by deformation of cenospheres shell. At dynamic strain rate, the deformation is so fast that hump could not be captured clearly. However, at lower strain rate, the load is applied for longer duration and cenosphere shell (which is very brittle in nature) accommodates more stress and leads to gradual fracture of cenosphere shell which in due course leads to decrease in modulus. The discussion on the occurrence of peak stress at slower strain rate has been reported elsewhere [13]. Bao and Lin [15] reported that the mechanisms of plastic deformation at low and high strain rates are different; a constant value of m may not capture the rate dependence of the material over a large range of applied strain rates. Mondal et al. [13] also observed different but very low m values depending on strain rate. However, a constant average m value is taken in this study due to its simplicity for empirical prediction of dynamic strength. Using Eq. (3) the dynamic strength is predicted (rd computed) and the same is compared with experimental (rd experimental) as reported in Table 2. Because of the change in the deformation mechanism, the value of C changes with strain rate. However, it is interestingly noted that C increases marginally up to strain rate of 10/s and then increases drastically when the strain rate increased to 750/s. It is further noted that the value of C starts decreasing with further increase in strain rate beyond 750/s. This is due to the variation in deformation mechanism with strain rate. The relation for predicting the dynamic strength as proposed by Dou et al. [4] considering constant pair of m and C values is not valid for the entire strain rates because of the change in deformation mechanism at a critical strain rate. The critical strain rate would be different for different matrix alloy and nature of cenosphere. Prior to use of syntactic foam with different types of cenosphere and matrix alloy its deformation behavior should be examined in detail. In the present investigation, the critical strain rate is observed to be 750/s. In the present study, an attempt has been made to predict empirically the dynamic strength of the investigated syntactic foam considering the effect of strain rate on strengthening parameter, C, and by considering constant strain rate sensitivity, m. The strengthening parameter varies with strain rate and has different set of values depending on cenosphere size (Table 2). In order to establish the relation between strengthening parameter and strain rate, best fit equation for the curve of C vs. ln ðe_ Þ is developed for both sizes of cenosphere used in the present investigation. The equation for two different cenosphere sizes is averaged (as C does not vary significantly with cenosphere size) and a final equation is developed (Eq. (4)),
rd ¼ r0 0:49 0:0151e_ þ 0:016e_ 2 0:00185e_ 3 1 þ ðe_ =e_ 0 Þm :
ð4Þ
Here, r0 is the compressive strength of syntactic foam at quasistatic strain rate (at 5% strain) and it varies with the cenosphere volume fraction as follows [17],
r0 ¼ C rm ð1 fc Þn þ C rmu ½ð1 fv sh Þð1 fcv Þn :
ð5Þ
Here, rm and rmu are compressive strengths of matrix and mullite, respectively; fc is the cenosphere volume fraction; fvsh is the porosity fraction in the cenosphere cell; fcv is the void fraction in cenosphere; C⁄ and n are the empirical constants depending on the cenosphere volume fractions and the type of cenosphere and their values vary from 0.1 to 1 and 1.5 to 2.5, respectively. The value of fvsh is considered to be 0.1 in the present investigation [17]. The fcv is expressed as, fcv = (1 t/R)3; here, t is the shell wall thickness and R is outer radius of cenosphere. Thus, combining the Eqs. (4) and (5), the dynamic strength of syntactic foam can be computed as a function of cenosphere size and the strain rate. Considering the value of C⁄ = 0.95, n = 1.89, rm = 250 MPa, rmu = 1000 MPa, [17]; and t as 5 mm and 8 mm for 90 lm and 200 lm respectively. The value of r0 is computed to be 189 MPa and 155 MPa for 90 and 200 lm size cenosphere, respectively. These values are in good agreement with experimentally observed values of r⁄ as reported in Table 2. Thus, dynamic strength can be predicted using the Eqs. (4) and (5) quite accurately. The dynamic compressive strength is then computed using Eq. (4) and the results are compared with the experimental values obtained using SHPB test (Table 3). It can be observed that the predicted values are within ± 6% of the experimental values. Hence, this empirical equation, (Eq. (4)), can be used to compute the dynamic strength of present syntactic foams under the used domain of strain rate, cenosphere size, and its nature. The similar methodology could be used for predicting dynamic strength of syntactic foam with different cenosphere sizes and nature. The rd of this foam varies with cenosphere size due to variation of r0 (i.e. quasi-static compressive strength) with cenosphere size under fixed strain rate. The value r0 is noted to be decreasing with increase in cenosphere size. This may be attributed to the fact that the stress concentration on the cenosphere cell increases with increase in cenosphere size, which results in earlier failure of cenospheres vis-à-vis reduction in strength of the foam material. Energy absorption (Eabs) of the present syntactic foam is computed by calculating the area under stress–strain curve up to densification strain (30%) and the same is reported in Table 2. It can be observed that the energy absorption of aluminum syntactic foam with 90 lm cenosphere is higher than that of aluminum syntactic foam with 200 lm cenosphere which is due to higher compressive and plateau strength of this foam. Moreover, energy absorption increases by up to 55% for the strain rates under dynamic loading. Higher energy absorption under dynamic condition is due to relatively higher yield stress or flow stress as compared to that in quasi-static condition and smooth transition between yielding and plastic region. Further, energy absorption efficiency (g) is computed using following relation [23–24],
R 0:3
g¼
rde : rmax e
0
ð6Þ
Here, rmax is the maximum stress in the stress strain curve up to a strain level of 0.3. The efficiency (g) of the present foam is varying in
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M.D. Goel et al. / Materials and Design 42 (2012) 418–423
Table 3 Comparison of dynamic strength computed using developed equation with experimental values and energy efficiency of aluminum cenosphere syntactic foam.
rd computed (MPa)
rd experimental (MPa)
Da (%)
Eabs (MJ/m3)
g (%)
90 lm Al-2014 Cenosphere Foam 1 0.49 10 0.52 750 0.55 900 0.55 1400 0.52
189.65 203.98 226.40 222.98 212.16
190 ± 3.8 195 ± 2.8 223 ± 4.0 210 ± 4.5 204 ± 3.5
0.19 4.61 1.52 6.18 4.00
45.74 ± 0.92 50.05 ± 0.72 69.69 ± 1.25 63.76 ± 1.36 59.99 ± 1.03
75.5 84.7 81.1 80.8 86.2
200 lm Al-2014 Cenosphere Foam 1 0.49 10 0.52 750 0.55 1400 0.52
166.39 178.97 198.64 186.15
167 ± 2.0 187 ± 3.5 206 ± 5.0 197 ± 4.0
0.36 4.29 3.57 5.51
51.33 ± 0.62 49.73 ± 0.93 62.46 ± 1.52 57.99 ± 1.78
82.7 81.7 82.3 86.3
e_ (/s)
a
D¼
Ccomputed
rdexperimental rdcomputed 100. rdexperimental
a narrow range (0.75–0.86) and the same is reported in Table 3. The energy absorption efficiency of aluminum cenosphere syntactic foam is noted to be about 80% or more indicating that the energy absorption efficiency of this foam is reasonably better than the conventional metal foams. This is primarily attributed to the relatively smoother plateau region in the syntactic foams because of finer and uniform porosity. Fig. 3 shows a microstructure of deformed foam samples (90 lm cenosphere) at 750/s and 1400/s strain rates. It can be observed that under the abovementioned strain rates the foam is fully densified and all the cenosphere are crushed and compacted indicating matrix got deformed without any major crack formation. The deformed matrix encapsulates the crush and compacted cenosphere particles. At strain rate up to 750/s the cenosphere shell gets gradually fractured (Fig. 3b) due to accommodation of stress on the cenosphere matrix interface during deformation. Relatively more gradual deformation of the matrix causes matrix strengthening with increase in strain rate while the strain rate is 6750/s. At higher strain rate, because of greater degree of impact, the cenospheres get fully crushed and densified immediately after loading (Fig. 3d). It signifies that deformation of aluminum syntactic foam at strain rate P750/s is controlled by the deformation of cenosphere shell. As a result, the dynamic compressive strength vis-à-vis strengthening coefficient is found to be reduced when strain rate increase P750/s irrespective of cenosphere size. The
deformation mechanism at different strain levels under varying quasi-static strain rates are discussed in details elsewhere [13]. 4. Conclusions The present syntactic foam has about 10–30% higher dynamic compressive strength than that of quasi-static condition. The compressive strength of these foams reaches to the maximum at a critical strain rate of 750/s. When the strain rate exceeds this critical value it reduces further with the increase in strain rate. The energy absorption capacity also follows the same trend with strain rate and it increases by up to 55% under critical dynamic loading. The quasi-static and dynamic compressive strength could effectively be predicted using following newly developed empirical relation,
rd ¼ r0 0:49 0:0151e_ þ 0:016e_ 2 0:00185e_ 3 1 þ ðe_ =e_ 0 Þm : Here,
r0 ¼ C rm ð1 fc Þn þ C rmu ½ð1 fv sh Þð1 fcv Þn
The strength and energy absorption is also a strong function of cenosphere size. These parameters decrease with increase in cenosphere size. The energy absorption efficiency of aluminum cenosphere syntactic foam is noted to be about 80% or more. Acknowledgement
750/s
The doctoral scholarship received to the lead author from German Academic Exchange Service, i.e. DAAD (Deutscher Akademischer Austausch Dienst) in completing the reported investigation is gratefully acknowledged.
750/s
References
(a)
100 µm
20 µm
1400/s
1400/s
(c)
(b)
100 µm
(d)
10 µm
Fig. 3. Microstructure of deformed foam samples (90 lm cenosphere) at 750/s and 1400/s strain rates.
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Technical Report
Dynamic compression behavior of cenosphere aluminum alloy syntactic foam Manmohan Dass Goel a,⇑, Marco Peroni b, George Solomos b, Dehi Pada Mondal a, Vasant A. Matsagar c, Anil K. Gupta a, Martin Larcher d, Steffen Marburg e a
CSIR-Advanced Materials and Processes Research Institute (AMPRI), Council of Scientific and Industrial Research (CSIR), Bhopal 462 064, India European Commission Joint Research Centre (JRC), Institute for the Protection and Security of the Citizen, European Laboratory for Structural Assessment (ELSA), 21027 Ispra, Italy c Department of Civil Engineering, Indian Institute of Technology (IIT) Delhi, New Delhi 110 016, India d Institute of Mechanics and Statics, University of German Armed Forces, Neubiberg 85577, Munich, Germany e Department of Aerospace Engineering, University of German Armed Forces, Neubiberg 85577, Munich, Germany b
a r t i c l e
i n f o
Article history: Received 21 April 2012 Accepted 8 June 2012 Available online 27 June 2012
a b s t r a c t The compression behavior of aluminum cenosphere syntactic foam has been studied and full stress– strain diagrams have been obtained for strain rates ranging from quasi-static to 1400/s. The foam exhibits peak stress at a strain of about 5%, especially during quasi-static compression, and the maximum value of stress around this strain is used to examine strain rate sensitivity and to determine an appropriate sensitivity parameter. The compressive strength and energy absorption of these foams attain a maximum at strain rates of approximately 750/s and then they decrease with further increase in the strain rate. The foam with coarser cenosphere appears to be more sensitive to strain rate. An empirical relation is developed for predicting the dynamic compressive strength of aluminum cenosphere syntactic foams. Explanation of the observed mechanical behavior in terms of the material failure mechanisms is provided. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Syntactic foams are composite materials synthesized by filling a metal, polymer or ceramic matrix with the hollow particles known as micro-balloons. These foams exhibit excellent combination of physical and mechanical properties. They have high damage tolerance through high energy absorbing capabilities, high specific stiffness, improved strength, and high acoustic and mechanical damping capacities. These properties make syntactic foams an attractive choice for various applications such as, core in sandwich structures, for packaging/fire proof, crash safety, damping panels, and underwater buoyant structures [1–4]. The ceramic particle filled syntactic foams exhibit excellent thermal insulation and low thermal expansion coefficient due to a significant volume fraction of ceramic phase in the matrix. Although, syntactic foams containing hollow ceramic spheres, i.e. cenosphere have higher densities than conventional aluminum foams (produced either by gas entrapment in the melt or infiltration of salt preforms), they have the advantages of higher strengths, isotropic mechanical properties, and excellent energy absorbing capacities due to extensive strain accumulation at relatively high stresses [5–10]. In order to use syntactic foams in the advanced applications such as crash or impact, blast resistance, aeronautical, and space struc⇑ Corresponding author. Tel.: +91 755 2457244. E-mail address: [email protected] (M.D. Goel). 0261-3069/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.matdes.2012.06.013
tures, it is crucial to understand their behavior under high rate of loading. Quasi-static compression behavior of syntactic foams has been studied in the past by a few researchers for assessing their energy absorption capacity [3–5,11–14]. Wu et al. examined high strain rate deformation behavior on commercially pure aluminum cenosphere syntactic foam [12]. However, for engineering and other applications aluminum alloys are preferred as they provide improved strength and toughness. In the literature, high strain rate response of aluminum syntactic foam is scarce. In aluminum alloy foams strain rate sensitivity is dependent on matrix materials [14], whereas in case of metal matrix composites (MMCs), the particles govern the strain rate sensitivity instead of matrix [15,16]. Syntactic foam exhibits a structure combination of both metal foam and MMCs and hence their deformation behavior under varying strain rate is highly complex and is not consistent in nature. In quasi-static condition, the strain rate sensitivity is reported to be very low [13]. The present investigation is aimed at characterizing the dynamic compressive behavior of syntactic foams as compared to that in quasi-static compression condition.
2. Material and experiments Aluminum alloy (Al-2014) cenosphere syntactic foam is prepared using cenosphere of two different size ranges. The average size of cenosphere is noted to be 90 lm and 200 lm. The size distribution of cenospheres of 90 lm and 200 lm is shown in Fig. 1a. It is to be noted that cenosphere size in both cases varies
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90 μm
% Frequency
20
15 10
5
100 µm 0
110-120
210-220
90 µm
Size Range (micron) 25
200 μm
% Frequency
20 15 10 5
100 µm 0 120-130
220-230
320-330
200 µm
Size Range (micron)
(b)
(a)
Fig. 1. (a) Size distribution of cenosphere. (b) Microstructure of Al-cenosphere syntactic foam.
in wide range. The average size of cenosphere is measured from the dimension of at least 200 individual cenosphere separately from the micrograph of as received cenospheres used for developing the syntactic foam. The cenospheres are dispersed on a glass slide which is then transferred to a double sided tape attached on metallic stud. The cenospheres get attached to the tape and then these are gold sputtered prior to scanning electron microscope (SEM). The micrographs are used for measuring the size of individual cenosphere. The size distribution of cenosphere is reported in the form of histogram. The cenospheres are selected randomly in the micrographs to avoid the subjective judgment. Similarly, the shell thickness of these cenospheres is measured from the micrographs of syntactic foam and their average values are reported. The foam is prepared by stir-casting technique, the details of the process are reported elsewhere [17]. The alloy and cenosphere are used in the ratio of 92:8 to attain volume fraction of cenosphere to be about 35%. Table 1 shows density and porosity fraction of aluminum cenosphere syntactic foam used in the present investigation. The porosity fraction of syntactic foam is about 8–10% less than the volume fraction of cenospheres used. This is attributed to the presence of cenosphere shell and it is about 20–30% of the cenosphere [13]. The porosity fraction (fp) in cenosphere aluminum alloy syntactic foam is determined using the following relation [12],
3 t fp ¼ fc 1 : R
ð1Þ
Here, t is the thickness of the cenosphere shell; R is the radius of the cenospheres and fc is the volume fraction of cenospheres. In parallel, the porosity fraction is measured experimentally following the point counting technique considering 25 randomly selected field at a magnification of 50 [18]. Quasi-static compression tests are performed at ambient temperature using BiSS Universal Testing Machine (Model Bi-00–002, 50 kN Load Cell) at Advanced Materials and Processes Research Institute (AMPRI), Council of Scientific and Industrial Research (CSIR), Bhopal, India at a strain rate of 0.001/s [19]. Cylindrical samples of 10 mm diameter and 15 mm length are used for quasi-static compression test. For each set three samples are tested. The average values of plateau stress, the densification strain and energy absorption are calculated from the all the samples tested for each set. The same machine and similar samples are also used for compression testing of syntactic foam at strain rate up to 10/s. The surfaces of the specimens are polished mechanically prior to testing and are lubricated with thin molybdenum sulfide coating in order to reduce the friction between the specimen surface and the compression test platens. The load–displacement data is recorded during the testing and converted to stress–strain curves using standard methodology. The high strain rate tests are conducted using a modified split Hopkinson pressure bar (SHPB) at the European Commission Joint Research Centre (JRC), Institute for the Protection and Security of the Citizen, European Laboratory for Structural Assessment (ELSA), Ispra Italy. A standard SHPB
Table 1 Physical parameters of the Al-2014 cenosphere syntactic foam.
a b c
Foam
Density (g/cm3)
Shell thickness (lm)
fca (%)
fpb (%)
fpc (%)
90 lm Al-2014 cenosphere foam 200 lm Al-2014 cenosphere foam
2.05 1.95
5 ± 0.2 8 ± 0.2
34.2 35.1
26.2 ± 1.8 27.4 ± 1.3
24.01 27.33
fc – Cenosphere fraction. fp – Porosity fraction, experimental. fp – Porosity fraction, computed.
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consists of a striker, an incident (input) bar and a transmitter (output) bar, with the specimen sandwiched between the incident and transmitter bars [20]. These bars, which remain always elastic, are made of maraging steel alloy. For the current tests, the input bar has a diameter of 10 mm and a length of 2.2 m. The output bar is 2 m long and 10 mm in diameter [21–22]. The role of the striker is played by a 1 m long bar which is the solid continuation of the input bar. This bar is stretched and suddenly released in order to generate the necessary compressive pulse, which propagates down the input bar towards the specimen. Semiconductor strain-gauges (Kyowa Model KSN-6–350-E4–11), strain gauge amplifier (EFS Model SGA02HF) and acquisition board gauge (Octopus CompuScope 84XX) are used for recording signals during the testing with a sampling rate of 10 MSamples/s. A cubical shape syntactic foam specimen with 6 mm size is used for this testing to achieve the required strain rates by the present SHPB setup. After the tests, the specimens are cut for the examination of the microstructure of the deformed samples. 3. Results and discussion Fig. 2a and b show the compressive stress–strain curves of aluminum cenosphere syntactic foam with 90 lm and 200 lm cenosphere, respectively under quasi-static and high strain rate compressive loading condition. It can be observed that the curve under quasi-static loading follows a zigzag pattern whereas under high strain rate it shows relatively smoother transition from elastic to plastic range. At lower strain rate, the peak stress (hump) is observed just after yielding at a strain of about 5%. The peak stress, termed here as compressive strength, is used for measuring the strain rate sensitivity parameter. It is observed that peak stress of syntactic foam increased from 183 MPa at 0.001/s to 223 MPa at 750/s for 90 lm. However, when the strain rate increased to 1400/s, the peak stress reduces to 204 MPa. In case of aluminum syntactic foam with 200 lm cenosphere, the peak stress increases from 160 MPa at 0.001/s to 206 MPa at 750/s. Aluminum syntactic foam with 200 lm cenosphere also exhibits peak stress of 197 MPa when strain rate further increased to 1400/s. The sensitivity parameter () is computed by using the following equation [3],
rd rq 1 _ _ ðed =eq Þ : ln r
ð2Þ
Here, r is the compressive strength, r⁄ is the quasi-static flow stress at 5% strain, e_ is the strain rate, wherein, subscripts ‘d’ and ‘q’ define
rd ¼ r0 ½Cð1 þ ðe_ =e_ 0 Þm Þ:
Here, rd is the dynamic compressive strength (=rd computed), r0 is the quasi-static compressive strength (i.e. compressive strength at strain rate of 0.001), C is a constant (strengthening coefficient), e_ is the strain rate, e_ 0 is a reference strain rate and m is the strain rate sensitivity [15]. The value of m is calculated from the slope of ln (compressive strength) vs. ln (strain rate) curve assuming a linear variation. The average value of m is found to be about 0.015. Considering m = 0.015 and adjusting the value of C, the value of rd was calculated at different strain rates. The values C, m, rd computed and rd experimental are also reported in Table 2. It can be observed that C value increases marginally with increase in the cenosphere size. It is attributed to the fact that the inter-cenosphere distance increases with increase in cenosphere size (as in both the cases same amount of cenosphere is used) and wider matrix space (in between cenosphere), could accommodate more dislocations during matrix deformation and leads to greater extent of matrix strengthening. Balch et al. [3] also stated that the deformation of aluminum syntactic foam under varying strain rate is controlled by the matrix deformation. The parameter C is considered to be strengthening parameter and the value of C increases with increase in e_ up to 750/s. This is also attributed to the fact that the flow stress of alloy increases with increase in strain rate. However, at strain rate > 750/ s the value of C starts reducing. This is attributed to the greater possibility of cenosphere crushing at this strain rate. At strain rate > 750/s, the deformation of these foams is primarily controlled 400
400
200 μm
90 μm 350
350
900/s
1/s
1400/s
300
750/s
Stress, σ (MPa)
750/s 250
10/s
200 150
420/s 0.001/s
1/s
50
Compressive Strength (MPa)
Stress, σ (MPa)
300
100
ð3Þ
250 200 150
200
10/s 250
150 100
100
0.001/s
50 0
0.001 1
10
50
420 750 900 1400
1400/s
250
Compressive Strength (MPa)
R¼
dynamic and quasi-static conditions, respectively. The various parameters of Eq. (2) are computed and reported in Table 2. It is observed that the dynamic compressive strength at strain rate > 750/s of the present syntactic foams is about 10–30% higher than that of quasi-static compressive strength and the sensitivity parameter is in the range of 0.005–0.021, which is close to that of the aluminum matrix as reported by Balch et al. [3]. This is confirming the presence of rate sensitivity in the present syntactic foam. The sensitivity parameter is, however, noted to be marginally lower than that reported by Dou et al. [4]. It is attributed to the fact that they used different size of cenosphere and fabrication method for making the syntactic foam. The source and nature of cenosphere are also different. These observations thus demonstrate that deformation behavior of aluminum cenosphere foam strongly depends on the nature, volume fraction, and size of cenosphere. Dou et al. [4] proposed the following relation for computing the dynamic strength,
200 150 100
Strain Rate (/s)
0 0.0
0.1
0.2
0.3
0.4
0.5
50 0
0.001
1
10
750
1400
Strain Rate (/s)
0.6
0 0.0
0.1
0.2
0.3
Strain, ε
Strain, ε
(a)
(b)
0.4
0.5
0.6
Fig. 2. Compressive stress–strain curves of Al-cenosphere syntactic foam under quasi-static and high strain rate loading: (a) 90 lm, (b) 200 lm.
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M.D. Goel et al. / Materials and Design 42 (2012) 418–423 Table 2 High strain rate compressive properties of the Al-2014 cenosphere syntactic foam. P Cenosphere size (lm) rq (MPa) r⁄ (MPa)
m
C
e_
rd experimental (MPa)
rd computed (MPa)
90 lm Al-2014 cenosphere foam
183.5
183
0.005 0.007 0.006 0.016 0.011 0.008
0.015 0.015 0.015 0.015 0.015 0.015
0.49 0.495 0.485 0.545 0.515 0.495
1 10 420 750 900 1400
190 ± 3.8 195 ± 2.8 197 ± 3.0 223 ± 4.0 210 ± 4.5 204 ± 3.5
189.65 195.12 197.07 222.51 210.58 203.14
200 lm Al-2014 cenosphere foam
161
160
0.005 0.018 0.021 0.016
0.015 0.015 0.015 0.015
0.49 0.54 0.575 0.545
1 10 750 1400
167 ± 2.0 187 ± 3.5 206 ± 5.0 197 ± 4.0
166.39 186.76 205.97 196.24
by deformation of cenospheres shell. At dynamic strain rate, the deformation is so fast that hump could not be captured clearly. However, at lower strain rate, the load is applied for longer duration and cenosphere shell (which is very brittle in nature) accommodates more stress and leads to gradual fracture of cenosphere shell which in due course leads to decrease in modulus. The discussion on the occurrence of peak stress at slower strain rate has been reported elsewhere [13]. Bao and Lin [15] reported that the mechanisms of plastic deformation at low and high strain rates are different; a constant value of m may not capture the rate dependence of the material over a large range of applied strain rates. Mondal et al. [13] also observed different but very low m values depending on strain rate. However, a constant average m value is taken in this study due to its simplicity for empirical prediction of dynamic strength. Using Eq. (3) the dynamic strength is predicted (rd computed) and the same is compared with experimental (rd experimental) as reported in Table 2. Because of the change in the deformation mechanism, the value of C changes with strain rate. However, it is interestingly noted that C increases marginally up to strain rate of 10/s and then increases drastically when the strain rate increased to 750/s. It is further noted that the value of C starts decreasing with further increase in strain rate beyond 750/s. This is due to the variation in deformation mechanism with strain rate. The relation for predicting the dynamic strength as proposed by Dou et al. [4] considering constant pair of m and C values is not valid for the entire strain rates because of the change in deformation mechanism at a critical strain rate. The critical strain rate would be different for different matrix alloy and nature of cenosphere. Prior to use of syntactic foam with different types of cenosphere and matrix alloy its deformation behavior should be examined in detail. In the present investigation, the critical strain rate is observed to be 750/s. In the present study, an attempt has been made to predict empirically the dynamic strength of the investigated syntactic foam considering the effect of strain rate on strengthening parameter, C, and by considering constant strain rate sensitivity, m. The strengthening parameter varies with strain rate and has different set of values depending on cenosphere size (Table 2). In order to establish the relation between strengthening parameter and strain rate, best fit equation for the curve of C vs. ln ðe_ Þ is developed for both sizes of cenosphere used in the present investigation. The equation for two different cenosphere sizes is averaged (as C does not vary significantly with cenosphere size) and a final equation is developed (Eq. (4)),
rd ¼ r0 0:49 0:0151e_ þ 0:016e_ 2 0:00185e_ 3 1 þ ðe_ =e_ 0 Þm :
ð4Þ
Here, r0 is the compressive strength of syntactic foam at quasistatic strain rate (at 5% strain) and it varies with the cenosphere volume fraction as follows [17],
r0 ¼ C rm ð1 fc Þn þ C rmu ½ð1 fv sh Þð1 fcv Þn :
ð5Þ
Here, rm and rmu are compressive strengths of matrix and mullite, respectively; fc is the cenosphere volume fraction; fvsh is the porosity fraction in the cenosphere cell; fcv is the void fraction in cenosphere; C⁄ and n are the empirical constants depending on the cenosphere volume fractions and the type of cenosphere and their values vary from 0.1 to 1 and 1.5 to 2.5, respectively. The value of fvsh is considered to be 0.1 in the present investigation [17]. The fcv is expressed as, fcv = (1 t/R)3; here, t is the shell wall thickness and R is outer radius of cenosphere. Thus, combining the Eqs. (4) and (5), the dynamic strength of syntactic foam can be computed as a function of cenosphere size and the strain rate. Considering the value of C⁄ = 0.95, n = 1.89, rm = 250 MPa, rmu = 1000 MPa, [17]; and t as 5 mm and 8 mm for 90 lm and 200 lm respectively. The value of r0 is computed to be 189 MPa and 155 MPa for 90 and 200 lm size cenosphere, respectively. These values are in good agreement with experimentally observed values of r⁄ as reported in Table 2. Thus, dynamic strength can be predicted using the Eqs. (4) and (5) quite accurately. The dynamic compressive strength is then computed using Eq. (4) and the results are compared with the experimental values obtained using SHPB test (Table 3). It can be observed that the predicted values are within ± 6% of the experimental values. Hence, this empirical equation, (Eq. (4)), can be used to compute the dynamic strength of present syntactic foams under the used domain of strain rate, cenosphere size, and its nature. The similar methodology could be used for predicting dynamic strength of syntactic foam with different cenosphere sizes and nature. The rd of this foam varies with cenosphere size due to variation of r0 (i.e. quasi-static compressive strength) with cenosphere size under fixed strain rate. The value r0 is noted to be decreasing with increase in cenosphere size. This may be attributed to the fact that the stress concentration on the cenosphere cell increases with increase in cenosphere size, which results in earlier failure of cenospheres vis-à-vis reduction in strength of the foam material. Energy absorption (Eabs) of the present syntactic foam is computed by calculating the area under stress–strain curve up to densification strain (30%) and the same is reported in Table 2. It can be observed that the energy absorption of aluminum syntactic foam with 90 lm cenosphere is higher than that of aluminum syntactic foam with 200 lm cenosphere which is due to higher compressive and plateau strength of this foam. Moreover, energy absorption increases by up to 55% for the strain rates under dynamic loading. Higher energy absorption under dynamic condition is due to relatively higher yield stress or flow stress as compared to that in quasi-static condition and smooth transition between yielding and plastic region. Further, energy absorption efficiency (g) is computed using following relation [23–24],
R 0:3
g¼
rde : rmax e
0
ð6Þ
Here, rmax is the maximum stress in the stress strain curve up to a strain level of 0.3. The efficiency (g) of the present foam is varying in
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Table 3 Comparison of dynamic strength computed using developed equation with experimental values and energy efficiency of aluminum cenosphere syntactic foam.
rd computed (MPa)
rd experimental (MPa)
Da (%)
Eabs (MJ/m3)
g (%)
90 lm Al-2014 Cenosphere Foam 1 0.49 10 0.52 750 0.55 900 0.55 1400 0.52
189.65 203.98 226.40 222.98 212.16
190 ± 3.8 195 ± 2.8 223 ± 4.0 210 ± 4.5 204 ± 3.5
0.19 4.61 1.52 6.18 4.00
45.74 ± 0.92 50.05 ± 0.72 69.69 ± 1.25 63.76 ± 1.36 59.99 ± 1.03
75.5 84.7 81.1 80.8 86.2
200 lm Al-2014 Cenosphere Foam 1 0.49 10 0.52 750 0.55 1400 0.52
166.39 178.97 198.64 186.15
167 ± 2.0 187 ± 3.5 206 ± 5.0 197 ± 4.0
0.36 4.29 3.57 5.51
51.33 ± 0.62 49.73 ± 0.93 62.46 ± 1.52 57.99 ± 1.78
82.7 81.7 82.3 86.3
e_ (/s)
a
D¼
Ccomputed
rdexperimental rdcomputed 100. rdexperimental
a narrow range (0.75–0.86) and the same is reported in Table 3. The energy absorption efficiency of aluminum cenosphere syntactic foam is noted to be about 80% or more indicating that the energy absorption efficiency of this foam is reasonably better than the conventional metal foams. This is primarily attributed to the relatively smoother plateau region in the syntactic foams because of finer and uniform porosity. Fig. 3 shows a microstructure of deformed foam samples (90 lm cenosphere) at 750/s and 1400/s strain rates. It can be observed that under the abovementioned strain rates the foam is fully densified and all the cenosphere are crushed and compacted indicating matrix got deformed without any major crack formation. The deformed matrix encapsulates the crush and compacted cenosphere particles. At strain rate up to 750/s the cenosphere shell gets gradually fractured (Fig. 3b) due to accommodation of stress on the cenosphere matrix interface during deformation. Relatively more gradual deformation of the matrix causes matrix strengthening with increase in strain rate while the strain rate is 6750/s. At higher strain rate, because of greater degree of impact, the cenospheres get fully crushed and densified immediately after loading (Fig. 3d). It signifies that deformation of aluminum syntactic foam at strain rate P750/s is controlled by the deformation of cenosphere shell. As a result, the dynamic compressive strength vis-à-vis strengthening coefficient is found to be reduced when strain rate increase P750/s irrespective of cenosphere size. The
deformation mechanism at different strain levels under varying quasi-static strain rates are discussed in details elsewhere [13]. 4. Conclusions The present syntactic foam has about 10–30% higher dynamic compressive strength than that of quasi-static condition. The compressive strength of these foams reaches to the maximum at a critical strain rate of 750/s. When the strain rate exceeds this critical value it reduces further with the increase in strain rate. The energy absorption capacity also follows the same trend with strain rate and it increases by up to 55% under critical dynamic loading. The quasi-static and dynamic compressive strength could effectively be predicted using following newly developed empirical relation,
rd ¼ r0 0:49 0:0151e_ þ 0:016e_ 2 0:00185e_ 3 1 þ ðe_ =e_ 0 Þm : Here,
r0 ¼ C rm ð1 fc Þn þ C rmu ½ð1 fv sh Þð1 fcv Þn
The strength and energy absorption is also a strong function of cenosphere size. These parameters decrease with increase in cenosphere size. The energy absorption efficiency of aluminum cenosphere syntactic foam is noted to be about 80% or more. Acknowledgement
750/s
The doctoral scholarship received to the lead author from German Academic Exchange Service, i.e. DAAD (Deutscher Akademischer Austausch Dienst) in completing the reported investigation is gratefully acknowledged.
750/s
References
(a)
100 µm
20 µm
1400/s
1400/s
(c)
(b)
100 µm
(d)
10 µm
Fig. 3. Microstructure of deformed foam samples (90 lm cenosphere) at 750/s and 1400/s strain rates.
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