Crashworthiness performance and microstructural characteristics of foam-filled thin-walled tubes under diverse strain rate

Journal of Alloys and Compounds 775 (2019) 675e689

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Crashworthiness performance and microstructural characteristics of foam-filled thin-walled tubes under diverse strain rate Dipen Kumar Rajak a, b, Nikhil N. Mahajan a, Emanoil Linul c, * a

Department of Mechanical Engineering, Sandip Institute of Technology and Research Centre, Nashik, 422213, MH, India Materials Science Lab, Sandip Institute of Technology and Research Centre, Nashik, 422213, MH, India c Department of Mechanics and Strength of Materials, Politehnica University of Timisoara, 1 Mihai Viteazu Avenue, 300 222, Timisoara, Romania b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 12 September 2018 Received in revised form 12 October 2018 Accepted 13 October 2018 Available online 15 October 2018

The implementation of Aluminum Alloy Foam (AAF) has made an impact in automobile and aerospace applications where crash energy absorption, vibration and sound damping and weight reduction is obligatory. The AAF is an emerging lightweight material providing high strength and stiffness at relatively low density. This research is carried out to quantify the energy absorption of mild steel reinforced AAF having empty mild steel and foam-filled tubes for different strain rates and geometry parameters. The AAF used in the current study is AlSi10Mg foam of densities 0.45, 0.65, 0.85 g/cm3, which is produced using melt route process. The circular, square and rectangular geometries were tested at strain rates of 0.1, 1, 10 mm/s. From the obtained compressive stress-strain curves Specific Energy Absorption (SEA), Total Energy Absorption (TEA), plateau stress of the empty and filled sections were determined, which were then evaluated. AAF was assessed by both light and electron microscopy. Field Emission Scanning Electron Microscope (FESEM) and Analysis of Variance (ANOVA) technique was employed to investigate the highest contributing factor in energy absorption. It was observed that foam filled tube can absorb more energy than empty tubes before reaching densification point. © 2018 Elsevier B.V. All rights reserved.

Keywords: Aluminum alloy foam Density Strain rate Energy absorption capability Microstructure ANOVA technique

1. Introduction Tubular structures are most commonly implemented and recognised energy-absorbing devices in the field of structural and automotive industries. With all current advancements in technologies, safety is an important aspect. To avoid fatal losses and harms during mishaps, there is an urge of energy absorbing devices. Energy absorbing devices are essential for the prevention of injuries and undesirable losses to crucial components of the system. Energy absorption can be defined as the capability of material or system to absorb the energy in various consequences of loading, which is achieved by conversion of kinetic energy into some another form of energy. The advantage of tubular structures are, they are lightweight, low cost and easy manufacturing processes. From the last two decades, these tubular structures are employed in automobiles to improve crashworthiness, which hand in hand increases the safety level of various vital components as well as occupants [1,2]. In automobile body in white (BIW), the crash box is widely used for

* Corresponding author. E-mail address: [email protected] (E. Linul). https://doi.org/10.1016/j.jallcom.2018.10.160 0925-8388/© 2018 Elsevier B.V. All rights reserved.

crash energy absorption. This crash box is merely a thin walled metal tube, usually made up of aluminium. These structures can be circular, rectangular, pentagonal or any polygonal shape. Also, these structures are useful in shipbuilding, aerospace, defence sector and many more [3e5]. Use of dense solid materials has been on downline in the last 20 years. Engineers have always searched for materials with lightweight, high strength, excellent vibration damping characteristics, especially high-energy absorption capabilities and recyclability [6]. The researchers have focused on developing class materials whose properties can be tailored as per the necessity of the application [7e9]. These materials include various alloys, metal and polymer composites, metal foams. Aluminium foams are most preferred present-day materials because of remarkable mechanical and physical properties. The improvement in production processes, foaming and thickening agents, these foams have gained popularity in numerous applications. Aluminium foams have boundless applications in structural as well as functional applications. They can be used for improvement in energy absorption with minimal increment in weight. Also, they have low density, high strength to weight ratio with sound and vibration suppressing properties. Due

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to the corrosion resistance property of parent metal aluminium, the property is improved into alloyed foam [10e14]. Due to excellent energy absorption capacity, much work has been carried out on the enhancement in energy absorption using aluminium foams. The aluminium foam handles plateau stress is in a direct relationship with the strain in the material and densification strain that depends upon the morphology of pores. The enhancement is done preferably using the hollow tubular structures and aluminium foam as the filler in the tubes. Investigations are done on varying the geometrical parameters of tubular structures for different loading and changing the pore size, wall thickness for aluminium foams. It was evident in studies that energy absorption capabilities vary according to change in pore morphology. The energy absorption capabilities are a function of buckling in cell-walls and collapse of cell-walls [15e17]. Rajak et al. [18] studied energy absorption capacities of empty tubes (ETs) and foam filled tubes (FFTs) at different strain rates. They showed that stress-strain graph obtained from compression test showed three distinct regions, while energy absorption capabilities increased by 33.45% in FFTs than ETs. Movahedi and co-workers [19e21] performed research on ETs and FFTs at elevated temperature; the result showed improvement in energy absorption. Zlamal et al. [22] studied comparison of Alporas aluminium alloy foam and polystyrene foam, found out aluminium foam was a better option for improved energy absorption characteristics. Goel [23] studied deformation behaviour for single, double and multi-walled tubes for circular and square geometries using Altair for simulation. Azarakhsh et al. [24] studied the crushing behaviour of bi-tubular brass cylindrical tubes using foam as filler materials. Ahmad and Thambiratnam [25] loaded tubular structures obliquely and studied the effect of leap angle, loading on the absorption results. Li et al. [26] studied for same oblique loading with aluminium foam as the inner matrix and concluded absorption is dependent upon tube geometry and foam density. Duarte et al. [27] studied dynamic and quasi-static bending FFTs for energy absorption capabilities. Guilliow [28] tested 70 specimens under compressive loading and results were distinguished on the basis of deformation zones and mechanisms. Various multi-objective design studies (MOD) are done for increasing energy absorption capabilities, by making various design changes. Along with physical experimentation, various studying is done using modelling the aluminium foam and simulating the compression for validating the results. The numerical modelling is found to be 25% accurate to the real-world experimentation. The quasi-static and dynamic studies are done on ETs and FFTs, and it is found that energy absorption is based upon peak load, strain rate, crushing force, foam density [29]. From the past 15 years, energy absorption behaviour of FFTs has covered vast and vivid research literature. Tubular structures are most preferred because of their regular axial folding pattern. Due to enhancement in recent times, the foam is used as filler material in tubes and produced in a variety

of ways. The interaction effect between the tube and porous foam structure is essential aspect in enhancement energy absorption [30e32]. Crushing force of FFTs is greater than the total crushing force of foam and ETs [33,34]. The current research is based on AlSi10Mg foam manufactured by melt route process. The mild steel tubes of circular, square and rectangular geometries are used as tubular structures. The foam density is varied between 0.45, 0.65 and 0.85 g/cm3 and average pore size between 2.55 and 5.56 mm. The specimens are subjected to strain rates 0.1, 1 and 10 mm/s and comparison is made based on energy absorption behaviour. Finally, the ANOVA technique is employed for finding percentage contribution of various factors (foam density, tube shape and strain rate) on specific energy absorption. 2. Materials and methods 2.1. Foam synthesis The closed-cell AlSi10Mg aluminium alloy (trade name of AlSi10Mg) foam was prepared by melt-route foaming process, depicted by Fig. 1. The AlSi10Mg alloy was stabilized with 10 wt% SiC particles using stir casting technique, in which SiC acts as a thickening agent and titanium hydride powder (TiH2) acts as foaming agent. The AlSi10Mg alloy with 10 wt% SiC (with average size 20 mm) as placed inside crucible and heated at a temperature around 670e680
C in an electric furnace. The melt is mechanically stirred for 2 min, with 900 rpm, to ensure proper mixing. Afterwards, 0.8 wt% of TiH2 is added in the molten slurry manually for foaming (the powder had an average size of 7 ± 1.2 mm). The melt was again mechanical stirred at about 1200 rpm. Temperatures were varied between 640 and 690
C for achieving various relative densities. After foaming agent addition, the temperature is maintained for 2 min. When the expansion of molten mixture is recognised (after complete foaming), the cooling is done with compressed nitrogen air [35e38]. Finally, the obtained foam material is cut into sheets of 40 mm thickness as shown in Fig. 2. The densities of 0.45, 0.65 and 0.85 g/cm3 were obtained from the given process. Determination of foam density will be presented in Section 3. The AlSi10Mg alloy chemical composition is shown in Table 1. 2.2. Macro- and micro-structure characterization The AAF samples were assessed both macro and microscopically. Pore size, pore distribution, cell wall thickness are essential characteristics in energy absorption as mentioned in the earlier section [37,39]. The macroscopic analysis was done by using the high-resolution camera and optical scanner. However, to investigate the details not possible within magnification of digital camera microscopic studies are employed. Electron microscopy was

Fig. 1. Melt route process for synthesising AlSi10Mg foam.

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Fig. 2. Synthesised AlSi10Mg foam sheets of various densities: 0.45 (a), 0.65 (b) and 0.85 (c) g/cm3.

Table 1 The chemical composition of the AlSi10Mg aluminium alloy. Element

Al

Si

Mg

Fe

Mn

Ti

Zn

Cu

wt.%

balance

9.5e10

00.35

0.15

0.01

0.004

0.002

0.001

performed on the foam samples. Metallography foam specimen is done before putting it to the actual test. Bakelite powder is used for hot mounting, in which the powder is heated up to 180
C and about 20 min are required until it gets cured. After the curing, the specimen is grinded with rough silicon carbide papers and then finished with fine polishing with a higher number of emery grit papers. The diamond paste was used as abrasive for final polishing and mirror finish is obtained on AlSi10Mg aluminium foam mounted specimens. The specimen is etched with Keller's reagent with gold sputtering before Field Emission Scanning Electron Microscope (FESEM). The specimens are then put into electron microscopy of microstructure characterization. The various measurement of pore size and cell wall thickness are done with monitoring system attached to FESEM with Mean Intercept Length Method (MILM) [39]. Nearly 50e60 readings were taken for measuring cell wall thickness, and the average value was calculated. To investigate the composition of fabricated AlSi10Mg foam. 2.3. Sample preparation In this research, the energy absorption capability of different empty tubes (ETs), foam filled tubes (FFTs) and aluminium alloys foams (AAFs) is experimentally investigated. Furthermore, three

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tube geometries are proposed for energy absorption performances, named circular tubes (CTs), rectangular tubes (RTs) and square tubes (STs). The geometrical parameters of the circular, square and rectangular samples are presents in Fig. 3 for investigated configurations (ETs, FFTs and AAFs). The Wire Electro Discharge Machining (WEDM) was chosen for the foam sample preparation. The pores play an essential role in energy absorption, and damages pores will affect it significantly. Hence, to avoid the stochastic effect of foam Wire WEDM was employed [19,40e42] because it gave precise and accurate control over dimensional accuracy (0.5 mm). Mild steel (MS) tubes of grade FE330 were used for tubular structures. MS is low carbon alloy steel, having less than 0.25 wt% carbon. MS tubes chosen for the current research were electrically resistance welded. These are martensitic steels containing about 19% Cr. They offer better corrosion resistance and have better mechanical properties [20,43,44]. The height and the thickness of MS tubes were chosen to be 40 mm and 1.2 mm, respectively. Due to the exact geometrical parameters of AAF, obtained by WEDM cut machining, all the FFTs have been filled very easily through press-fit technique. No epoxy resin was used in filling foam inside of tube, because it affects the inertia effect in energy absorption performances [18]. Figs. 7e9 shows the obtained circular, square and rectangular ET, FFT and AAF samples used for compression tests. 2.4. Quasi-static compression tests The quasi-static compression tests are carried out on a servohydraulic INSTRON-8800 Universal Testing Machine (UTM), at Indian Institute of Technology, Bombay-India. In order to evaluate energy absorption capability, the ET, FFT and AAF samples (Fig. 4) were loaded under different loading rates, i.e. 0.1, 1 and 10 mm/s. Considering the height of the samples, the proposed loading rates are converted into strain rates, i.e. 0.0025, 0.025, 0.25 s1. It can be referred that each strain rate and foam density have been tested for each geometry so that compression results can be appropriately evaluated. Al experimental tests were performed at room temperature, according to ISO13314 standard [45]. In order to obtain the reproducibility and reliability of the results, three samples were used for each test conditions. In the given test, the sample is placed on the base of UTM and crosshead is applied with variable speed as mentioned and axially loaded. For avoiding the friction between the sample and crosshead, molybdenum disulfide is used as a lubricant. If the compression test is restrained by frictional effect, then specimen would show different deformation pattern about loading point, and experimental results will be invalid [38,46e48]. The data is

Fig. 3. Geometrical parameters of the investigated CS (a), SS (b) and RS (c) samples.

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Fig. 5. Effect of foaming temperature on density of the AlSi10Mg foam.

Fig. 4. Circular, square, rectangular AAFs, ETs and FFTs samples.

monitored through an integrated Data Acquisition System (DAS). 2.5. Analysis of Variance (ANOVA) ANOVA method is utilised to analyse the influence of various factors on output parameters. This method is employed as a statistical tool for determination of the influence of various factors on the results of the process and gives the relation between factors by mean squares and errors at the individual level [49,50]. It considers input parameters (factors) and output parameters (response) respectively and builds a nest based upon it. Box-Cox transformation is applied for investigating the interrelation and finding the contribution of each factor on output. In this research, the shape of the specimen, strain rate, the density of the foam, pore sizes are taken as contributing factors and the SEA is taken as the response of all of these factors. 3. Result and discussions 3.1. Effect of temperature and time on AlSi10Mg foam Various foaming temperatures were used to obtain different densities of the AlSi10Mg foam. It is evident that pore size increases and cell-wall thickness of pore decrease with a decrease in the obtained density. The most affecting parameter causing this was found to be foaming temperature. The density decreases with increase in foaming temperature. This is caused because, as there is an increment in temperature, the molten slurry tends to become less viscous and surface tension also decreases. This, in turn, causes a gas bubble to grow bigger in size and cell wall thickness decreases [51,52]. Fig. 5 depicts the exact relation between foaming

temperature and density. Also, the stirring time and holding time influences microstructure of foam strongly. As seen from Fig. 6 a, with increasing time porosity decreases gradually. During the first 1.5 min, changes are negligible, but with increasing time, porosity tends to decrease faster. This is because stirring is done for mixing of TiH2 with the mixture uniformly. However, keeping it too long restricts bubble formation. Therefore, optimum stirring time should be decided for the fabrication of AlSi10Mg foam [38]. There is no linear relation found between stirring time and pore diameter. During the first 1.5 min, it decreases, and after that, there is a noticeable increase followed by slight changes. The other thing that affects the morphology of obtained foam is holding time. A large amount of hydrogen gas is generated while foaming through an oxidation process. When the flow rate of hydrogen gas in the mixture is high, the pore becomes circular. As gas is reduced in the melt, bounded pores tend to form. As per the Laplace theorem, maximum pressure developed in large bubbles is relatively small. In that case, surface tension is not strong enough to keep in pore orientation circular. The effect of holding time on porosity and pore diameter is as shown in Fig. 6b. Nevertheless, one thing should also be considered that, foaming temperature is significant factor that affects the pore growth. Ideally, the stirring time about 1.5 min should be considered optimum and holding time should be between 4 and 5 min for better quality foams. 3.2. Density and porosity calculation The density of the synthesised foam is calculated by mass and volume measurement from the AlSi10Mg sheet of different densities. Also, the porosity is an essential parameter in case of aluminium alloy foam as it affects the energy absorption. The strength of porous aluminium foam increases as the porosity of alloy metal decreases [53,54]. The porosity of AAFs is dependent upon the porosity of microspheres used in the synthesis. The porosity is measured by Eq. (1):

% Porosity ¼

Density of Parent Alloy  Density of Foamed Alloy Density of Parent Alloy  100 (1)

The density as one can refer is dependent upon foaming temperature and porosity is dependent upon stirring and holding time

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Fig. 6. Effect of stirring time (a) and effect of holding time (b) on AlSi10Mg foam morphology.

Fig. 7. Frequency vs. pore size plot for AlSi10Mg foam of 0.45 (a), 0.65 (b) and 0.85 (c) g/cm3 density.

Fig. 8. The AlSi10Mg foam of 0.45 (a), 0.65 (b) and 0.85 (c) g/cm3 density.

of mixture. The relative density of the foams is also calculated as shown in Table 2. Another aspect is the pore size calculation, which is done by the MILM method mentioned in the previous section. The pore size and frequency of pores varied with different densities. The plot between the frequency of occurrence of pore versus pore size for each density is shown by Fig. 7. The average pore size of 0.45 g/cm3 density sample is 5.56 mm as shown in Fig. 7a, the average pore size of 0.65 g/cm3 sample is 4.35 mm as shown in Fig. 7b and the average pore size of 0.85 g/cm3 sample is 2.55 mm as shown in Fig. 7c.

Fig. 8 shows the macrostructure for different foam densities. 3.3. Microstructure characterization and energy dispersive X-ray analysis (EDX) Pore size and cell-wall thickness are essential geometrical parameters to study the microstructure of metal foam. Microstructure evaluation for metal foam is complicated because of varying pore size and pore density. Macro and micro aspects are studied for a better understanding of AlSi10Mg structure. The macrostructure of various densities is analysed by optical scanner image, Fig. 9. It can

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Fig. 9. Optically scanned images of AlSi10Mg foam with 0.45 (a) 0.65 (b) and 0.85 (c) g/cm3 density.

Table 2 Density and porosity values of AlSi10Mg foams. Specimen

Dimensions (mm3)

Mass (g)

Volume (mm3)

Density (g/cm3)

Relative Density ()

Porosity (%)

Sheet 1 Sheet 2 Sheet 3

40  40  40 40  40  40 40  40  40

28.72 41.83 54.38

64000 64000 64000

0.4488 0.6535 0.8497

0.168 0.245 0.318

83.19 75.52 68.18

be easily inferred from the images, that each sample has different density. These images are used to determine pore distribution in the foam sample. However, from these images, some underlying details cannot be uncovered. The electron microscopy is used for investigating into the microstructure of AlSi10Mg foam. Hot mounted specimen prepared in the previous section is used for this study. Higher magnification and better facilities are required for the measurement of cell wall thickness. The principle of working of FESEM is similar to that optical microscope instead it uses electrons. The gold is sputtered over specimen before the test for better backscatter for forming images. The mounted specimen is treated with Keller's reagent for investigation. The typical FESEM micrograph is seen in Fig. 10. The given micrographs are for 0.65 g/cm3 foam density. The test is carried out at 15, 50, 100 and 500 magnifications for proper

investigation and measurement of cell wall thickness. Figs. 10a and b show typical microstructure of foam, while Fig. 10c and d show magnified pore and cell wall structure respectively. The cell wall thickness measured in the given sample was 140e170 mm. For AlSi10Mg foam with 0.45 g/cm3 density, the cell wall thickness was found to be 80e110 mm, and for 0.85 g/cm3, cell wall thickness was found to be 180e210 mm. The variation in cell wall thickness is found because of variation in flow from the cell wall to the plateau borders during the settling of foam [55e57]. The flow reduction during setting of foam results in an increase in cell wall thickness. 3.4. Quasi-static compression behaviour The geometrical parameters of the investigated ETs, FFTs and AAFs samples are presented in Table 3. The area and volume are

Fig. 10. FESEM images of foam with 0.65 g/cm3 density at 15 (a), 50 (b), 100 (c) and 500 (d).

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Table 3 Geometrical parameters of experimentally investigated ETs, FFTs and AAFs samples. Sample geometry Circular

Square

Rectangular

ET FFT AAF ET FFT AAF ET FFT AAF

Cross-section dimensions (mm)

Sample thickness/height (mm)

Area calculation formulae

Area (mm2)

Volume (mm3)

Radius r ¼ 12.77

t ¼ 1.2 h ¼ 40

p [r2-(r-t)2] pr2 pr2

91.71 512.05 512.05 116.83 652.29 652.29 138.24 800.00 800.00

3668.52 20481.96 20481.96 4673.28 26091.66 26091.66 5529.60 32000.00 32000.00

Side l ¼ 25.54

4  t  (l-t) l2 l2

Side l ¼ 20, b ¼ 40

l  b-[(l-2t)  (b-2t)] lb lb

presented for the further energy absorption calculations. From the experimental tests, with appropriate monitoring, at diverse strain rates, for each sample configuration, the distinct stress-strain graph is obtained. Compressive stress and strain data were measured during the test by using the standard method [45]. The various results obtained from tests are shown in the plot of stress-strain curves. Figs. 11e13 depict the stress-strain curves for ETs, FFTs and AAFs for different sample shapes, strain rates and densities. Regardless of strain rate (0.1, 1 and 10 mm/s), the shape of the tube section (CT, ST and RT), specimen configuration (ET, FFT and AAF) and foam density (0.45, 0.65 and 0.85 g/cm3), the stress-strain graphs highlight three different deformation regions: a narrow linear-elastic region, followed by a plateau region and ended with a densification region. These deformation regions have also been found in other works investigating the energy absorption performances of metal foams, empty tubes and tubes filled with metal foams [58e60].

The ETs and FFTs compressive stress-strain graphs reveal a yield point with a peak value at the end of the elastic region, while a smooth transition from linear-elastic to plateau region is observed in the case of AAFs [61,62]. The stress oscillations present in the plateau regions are consistent with the appearance of the folds on the ETs and FFTs test samples. These oscillations are found throughout the plateau region between the deformation corresponding to the yield point and densification strain. On the other hand, the AAFs does not show any kind of oscillation in the plateau region. This is due to a progressive and controlled deformation manner of the foam cell-walls (bending, buckling, fracture etc.) [63]. Plateau stress (spl), specific energy absorption (SEA) and total energy absorption (TEA) are essential parameters determined by quasi-static compression test. Strain rate, loading type, deformation mechanisms and inertia effects affect the energy absorption behaviour. Among all strain rate is an essential factor, depending upon which dynamic or quasi-static test is distinguished. The

Fig. 11. Stress-strain curves of circular (a), square (b) and rectangle (c) samples for a strain rate of 10 mm/s. Influence of density.

Fig. 12. Stress-strain curves of circular AAF (a), ET (b) and FFT (c) samples for a density of 0.85 g/cm3. Influence of strain rate.

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Fig. 13. Stress-strain curves of AAF (a), ET (b) and FFT (c) samples at 10 mm/s and for a density of 0.85 g/cm3. Influence of sample shape.

applied load is almost constant over given time, and inertia effects are negligible in case of quasi-static loading [64,65]. From stress-strain curve data, one can determine energy absorption and plateau stress. Plateau region in stress-strain graph shows approximately constant stress during compression. According to standard procedure [45], this region is approximately between 0.20 and 0.40 strains. The specimens are compressed 70% of their original dimensions. Specific energy absorption is a function of plateau stress [66e68]. The SEA per unit volume of ETs, FFTs and AAFs are given by Eq. (2): εð2

SEA ¼

spl dε

Table 4 Plateau stress for circular, square and rectangular shape. Specimen

ET

AAF0.45

AAF0.65

(2)

AAF0.85

Total energy absorption (TEA), for ETs, FFTs and AAFs of volume V, which comprises of numerous diminutive volume (dV) is given by formula (3):

FFT0.45

ε1

2 3 ð εð2 TEA ¼ 4 spl dε5dV

(3)

ε1

Table 4 lists the average (with standard deviation) of plateau stress values and Table 5 lists energy absorption (with respect to SEA and TEA) results of circular, square and rectangular sections (as three samples were used), depending on the strain rate sensitivity. The spl, SEA and TEA values are also presented for ETs, FFTs and AAFs depending on foam density. The subsequent energy absorption was calculated from the area under stress-strain curve up to onset strain of densification strain. The FFTs and AAFs index indicates the density of the used foam, i.e. FFT0.45 is a tube filled with aluminium foam with a density of 0.45 g/ cm3 etc. The maximum plateau stress and energy absorption capability of ETs, FFTs and AAFs samples are obtained at 10 mm/s, while the lowest values were obtained at a strain rate of 1 mm/s. So, the loading rate influences the main mechanical properties of all investigates sections and densities. Fig. 14 present the variation of spl, SEA and TEA results with foam density for AAF and FFT samples. From Fig. 14 and Table 4, it can easily be observed that the foam strength and energy absorption increase with the increase in foam density. Also, the foam density plays an essential role in the mechanical behaviour of foams and foam filled tubes. Regardless of the sample configuration (AAFs or FFTs), the plateau stress increase by up to 7%, and energy absorption capability (SEA and TEA) by up to 20%. On the other hand, circular samples show higher properties

FFT0.65

FFT0.85

Strain rate (mm/s)

0.1 1 10 0.1 1 10 0.1 1 10 0.1 1 10 0.1 1 10 0.1 1 10 0.1 1 10

Plateau Stress (MPa) CT

ST

RT

28.35 ± 0.18 26.26 ± 0.22 30.19 ± 0.27 15.37 ± 0.39 10.18 ± 0.48 19.64 ± 0.67 17.57 ± 0.25 11.97 ± 0.42 20.52 ± 0.54 18.26 ± 0.22 12.7 ± 0.38 21.27 ± 0.48 50.49 ± 1.59 43.25 ± 1.89 56.94 ± 2.12 51.55 ± 1.24 44.37 ± 1.45 58.66 ± 1.69 52.57 ± 0.93 45.36 ± 1.12 60.97 ± 1.46

12.37 ± 0.48 13.66 ± 0.65 14.32 ± 0.72 10.64 ± 0.57 7.45 ± 0.72 13.7 ± 0.89 11.78 ± 0.37 8.12 ± 0.49 15.12 ± 0.78 12.52 ± 0.27 8.97 ± 0.35 16.99 ± 0.43 23.55 ± 1.65 20.37 ± 1.98 30.66 ± 2.59 27.99 ± 1.31 23.25 ± 1.78 32.94 ± 1.95 30.07 ± 1.21 26.86 ± 1.26 34.97 ± 1.52

14.26 ± 0.32 13.7 ± 0.47 15.43 ± 0.61 12.37 ± 0.48 7.99 ± 0.63 16.14 ± 0.73 14.1 ± 0.32 8.98 ± 0.45 17.13 ± 0.61 15.23 ± 0.29 10.9 ± 0.42 18.43 ± 0.52 29.46 ± 1.62 24.32 ± 1.82 33.46 ± 2.36 30.87 ± 1.29 26.44 ± 1.65 34.35 ± 1.72 31.6 ± 1.16 27.57 ± 1.28 36.74 ± 1.59

compared to square and rectangular samples, for both AAFs and FFTs, i.e. about 30% for AAFs and 47% for FFTs. Therefore, in order to obtain higher strength properties and energy absorption capability, the circular cross-section samples present the optimal shape. However, it is observed that the highest stress values at the end of linear region (compressive yield strength) were obtained for this rectangular shape. The circular samples have simplest geometry and have no intersecting edges. During compression, this is advantageous as it results in efficient compression compared to other shapes. The square shape has intersecting edges and as it compresses, the edges resist given crushing force. This affects the energy absorption capabilities. Rectangular section is advantageous as compared to square section because the one side has greater length and crushing force is distributed over larger area. This is the reason; the energy absorption is highest in circular section, followed by rectangular and square section. Also, the higher the strain rate high is plateau stress value, which in turn enhances the energy absorption capabilities. Therefore, the highest energy absorption is observed with strain rate of 10 mm/s. For easier comparison of the results, Fig. 15 shows the spl, SEA and TEA results for ET, AAF and FFT samples at a strain rate of 10 mm/s.

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Table 5 Energy absorption for circular, square and rectangular shape. Specimen

ET

AAF0.45

AAF0.65

AAF0.85

FFT0.45

FFT0.65

FFT0.85

Strain rate (mm/s)

0.1 1 10 0.1 1 10 0.1 1 10 0.1 1 10 0.1 1 10 0.1 1 10 0.1 1 10

Specific Energy Absorption (MJ/m3)

Total Energy Absorption (J)

CT

ST

RT

CT

ST

RT

19.84 ± 0.14 18.38 ± 0.17 21.13 ± 0.21 10.76 ± 0.32 7.13 ± 0.43 13.75 ± 0.61 12.3 ± 0.18 8.38 ± 0.35 14.37 ± 0.46 12.78 ± 0.19 8.89 ± 0.32 14.89 ± 0.43 35.34 ± 1.26 30.27 ± 1.45 39.86 ± 1.76 36.08 ± 0.83 31.06 ± 1.02 41.06 ± 1.16 36.8 ± 0.78 31.75 ± 0.89 42.68 ± 1.12

8.66 ± 0.42 9.56 ± 0.59 10.03 ± 0.61 7.45 ± 0.52 5.21 ± 0.66 9.59 ± 0.78 8.25 ± 0.31 5.69 ± 0.43 10.58 ± 0.69 8.77 ± 0.24 6.28 ± 0.29 11.89 ± 0.38 16.48 ± 1.13 14.26 ± 1.36 21.46 ± 1.93 19.59 ± 1.07 16.27 ± 1.26 23.06 ± 1.38 21.05 ± 0.99 18.8 ± 1.04 24.48 ± 1.23

9.98 ± 0.28 9.59 ± 0.42 10.8 ± 0.55 8.66 ± 0.45 5.59 ± 0.59 11.3 ± 0.63 9.87 ± 0.26 6.28 ± 0.38 11.99 ± 0.56 10.66 ± 0.24 7.63 ± 0.39 12.9 ± 0.46 20.62 ± 1.34 17.03 ± 1.49 23.42 ± 1.78 21.61 ± 0.98 18.51 ± 1.12 24.04 ± 1.21 22.12 ± 0.67 19.3 ± 0.77 25.72 ± 0.98

73.19 ± 0.12 67.79 ± 0.16 77.94 ± 0.18 220.32 ± 0.31 145.94 ± 0.39 281.58 ± 0.54 251.9 ± 0.15 171.57 ± 0.33 294.26 ± 0.41 261.81 ± 0.18 182.01 ± 0.30 305.03 ± 0.36 723.89 ± 0.63 620.09 ± 0.78 816.32 ± 0.83 739.09 ± 0.42 636.15 ± 0.53 840.99 ± 0.59 753.71 ± 0.49 650.37 ± 0.51 874.08 ± 0.64

40.45 ± 0.37 44.68 ± 0.48 46.86 ± 0.49 194.32 ± 0.42 135.99 ± 0.49 250.19 ± 0.59 215.23 ± 0.27 148.37 ± 0.39 276.1 ± 0.51 228.73 ± 0.21 163.75 ± 0.26 310.24 ± 0.34 430.11 ± 0.78 372.04 ± 0.84 559.93 ± 1.11 511.21 ± 0.84 424.64 ± 0.96 601.56 ± 0.99 549.2 ± 0.61 490.61 ± 0.59 638.61 ± 0.67

55.18 ± 0.24 53.02 ± 0.38 59.73 ± 0.47 277.04 ± 0.41 178.92 ± 0.51 361.61 ± 0.49 315.92 ± 0.17 201.11 ± 0.31 383.66 ± 0.41 341.22 ± 0.19 244.06 ± 0.38 412.73 ± 0.29 659.83 ± 0.78 544.8 ± 0.86 749.43 ± 0.96 691.39 ± 0.59 592.33 ± 0.69 769.34 ± 0.76 707.8 ± 0.52 617.55 ± 0.69 823.03 ± 0.55

Fig. 14. Plateau stress, SEA and TEA variation with density for AAF (aec) and FFT (def) samples.

3.5. Compressive deformation mechanisms The quasi-compression test is used to investigate the energy absorption behaviour of the various tubular structures (circular, square and rectangular) filled with foam and unfilled. From results, it can be concluded that energy absorption performances of the structures with foam shows higher values compared to unfilled [69e71]. However, to understand the phenomenon the compressed samples are assessed. Fig. 16 presents the deformed AAFs, ETs and FFTs samples following compression tests.

In cases of circular tubes, most of the tube showed concertina mode of failure, and few showed diamond failure. In square only empty tubes from higher strain rate, showed the mixed type of failure. The rectangular samples showed the mixed type of failure in all cases. The tubular structure deforms with creating folds in them. These folds indicated the efficiency of energy absorption. The thickness of folds and distance between folds is effective parameter of efficient energy absorption. In case of a circular tube, it is more significant, when at 1 mm/s strain rate with the foam-filled tube, after formation of two folds at top and bottom another fold start

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Fig. 15. Mechanical properties (spl, SEA, TEA) results of investigated samples (ET, AAF, FFT) for 0.45 (aec), 0.65 (def) and 0.85 (gei) g/cm3 foam density at 10 mm/s.

Fig. 16. Deformed AAFs (aec), ETs (def) and FFTs (gei) samples after compression test.

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Fig. 17. Cross-section of foam-filled CT (a), ST (b) and RT (c) samples, together with the folds height comparison for an empty and foam-filled circular tube (d).

forming from the bottom and in case of 10 mm/s strain rate the fold starts at the middle section. Since the middle section has more isotropy in absorbing the crushing force; the energy absorption is increased. Also, the thickness of third fold varied in case of strain rate. With increasing of energy absorption, an increase in fold thickness was observed. The same phenomenon takes place in two other shapes too. For understanding enhancement in energy absorption capability, tubes were sliced open on WEDM. Therefore, Fig. 17aec shows the sliced open FFTs samples for different sample crosssections compressed at a strain rate of 10 mm/s. The ETs samples were easily crushed as they had no supporting filler material and there was no distance in their folds. The foam-filled samples had more energy absorption with a comparison to ETs and AAFs. As seen in Fig. 17d the height of folds of filled tubes are higher

than the empty tube, H2>H1. This indicates foam FFTs has higher absorption capability than that of ETs. The foam material undergoes band deformation. The plateau stress should remain constant throughout the stress-strain curve in ideal condition. However, for all FFTs samples plateau stress was varied in a staggering manner with increment in strain [72,73]. The presence of SiC in cell-walls causing this staggering behaviour in FFTs. The first band deforms, and the load is propagated to next band, the wall becomes strain hardened because of load, and thus, there is fluctuation. Therefore, the strain-hardening phenomenon is seen in the sample cell-walls during the compression test. The cut open FFTs were put to microstructure investigations to observe the cause of increment in energy absorption. The FESEM test is performed on the compressed specimen. The cracked foam cell-walls from SEM studies are shown in Fig. 18. The FFTs energy

Fig. 18. FESEM analysis of deformed sample showing fractured foam cell-walls.

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Main effects plot of shape and strain rate shows noticeable changes, reflected in their contribution to energy absorption. Whereas other factors do not show apparent variation like shape and strain rate, tend to exhibit low contribution to energy absorption. Interaction plot shows a complex relationship between individual factors and the dependent factor, i.e. energy absorption on various levels. The changes in shape, strain rate, pore size and density have different effects on the output that is indicated by an interaction plot.

Fig. 19. The plot of various contributing factors according to the percentage.

Table 6 Input parameters used for ANOVA. Strain rate (mm/s) Pore Size (mm)

0.1 1 10 0.1 1 10 0.1 1 10

Density (g/cm3)

Energy Absorption (MJ/m3)

CT

ST

RT

CT

ST

RT

CT

ST

RT

5.50 5.78 6.10 4.12 4.40 4.58 2.19 2.30 2.57

5.48 5.64 5.92 4.17 4.36 4.56 2.08 2.29 2.50

5.48 5.71 6.05 4.19 4.38 4.62 2.18 2.32 2.63

0.45 0.45 0.45 0.65 0.65 0.66 0.85 0.85 0.85

0.45 0.49 0.49 0.65 0.65 0.65 0.85 0.85 0.85

0.45 0.45 0.46 0.65 0.65 0.65 0.85 0.85 0.85

35.34 30.27 39.86 36.08 31.06 41.06 36.80 31.75 42.68

16.48 14.26 21.46 19.59 16.27 23.06 21.05 18.80 24.48

20.62 17.03 23.42 21.61 18.51 24.04 22.12 19.30 25.72

The data obtained from ANOVA are presented in Table 7. The predicted result considering mean square values and errors show that energy absorption is contributed 2.25% by density, 3.11% by pore size, 12.14% by strain rate and 81.59% by the shape of the specimen. The error in prediction is about 0.90%.

absorption is increased due to the main collapse mechanisms that occur in the foam microstructure during the compression test. The fractured cell-walls and friction between them largely affects plateau stress and also energy absorption performances. 3.6. Analysis of Variance (ANOVA) ANOVA in present research is employed for finding percentage contribution of various factors on specific energy absorption. This statistical tool gives an exact idea about contribution factor in energy absorption of foam-filled tubes. The input parameters used for this investigation are listed in Table 6. The analysis is performed in MINITAB 2018 software tool [49]. Figs. 20 and 21 show the main effect plot and interaction diagram for energy absorption from the ANOVA test. Main effects plot indicates the effect of an individual contributing factor on the energy absorption, neglecting the effect of other contributing factors.

4. Conclusions In the present research, AlSi10Mg AAF are fabricated by melt route method with a density of 0.45, 0.65 and 0.85 g/cm3. The synthesised alloy foam is characterized by microstructures and EDX analysis for understanding foam structure and pore size. Empty, foam filled and foam samples are also produced with varying geometries. An experimental study was done on the samples by analysing them under compression test for different strain rates viz. 0.1, 1 and 10 mm/s, for evaluating energy absorption capabilities. The comparison between energy absorption of circular, square and rectangular shape is made with obtained data from the stressstrain curve. Also, ANOVA is employed for investigating the most significant contributing factor affecting energy absorption. The following inferences can be made from the current research:  Foams of different densities can be obtained by varying foaming temperatures and by using TiH2 as a foaming agent. Also, pore diameter and porosity are a function of holding time and stirring time, which affects cell wall thickness.  FESEM analysis indicates that SiC particles strengthen the foam cell walls and enhances cell-wall stability through drainage restriction while cooling by reducing melt flow. The cell wall thickness of the foam structure increases with increasing density (80e110 mm for 0.45 g/cm3, 140e170 mm for 0.65 g/cm3 and 180e210 mm for 0.85 g/cm3).  The energy absorption of ETs, FFTs and AAFs circular samples is found to be maximum. Therefore, the optimal section is the circular shape, followed by rectangular and square shapes.  The strain rate affects the mechanical behaviour of the investigated samples. The maximum strength and energy absorption properties are obtained at a strain rate of 10 mm/s and minimum at 1 mm/s.  The main mechanical properties increase with increasing in foam density.  Compared to ETs, the specific energy absorption of FFTs at strain rate 10 mm/s with foam density 0.85 g/cm3 increased by 101.97% for a circular shape, by 144.09% for square shape and by 138.09% for a rectangular shape.

Table 7 The output obtained from ANOVA showing contribution of various factors. Source

DF

Seq. SS

Contribution

Adj. SS

Adj. MS

F-Value

P-Value

Density (g/cm3) Pore Size (mm) Strain rate (mm/s) Shape Error Total

1 1 2 2 20 26

0.3734 0.5168 2.0154 13.5406 0.1488 16.595

2.25% 3.11% 12.14% 81.59% 0.90% 100.00%

0.0077 0.0004 2.0154 13.5406 0.1488

0.00767 0.00042 1.00772 6.77028 0.00744

1.03 0.06 135.43 909.88

0.322 0.814 0 0

The results from Table 6 are presented by the circular statistical graphic from Fig. 19. This pie chart displays the percentage contribution of each factor to obtained energy absorption results. The shape of the specimen is a most influencing factor for energy absorption.

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Fig. 20. Main effect plot for energy absorption from ANOVA test.

Fig. 21. Interaction plot for energy absorption from ANOVA test.

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