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Plastic deformation and compressive mechanical properties of hollow sphere aluminum foams produced by space holder technique
Materials & Design 83 (2015) 352–362
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Plastic deformation and compressive mechanical properties of hollow sphere aluminum foams produced by space holder technique J. Kadkhodapour a,⇑, H. Montazerian a, M. Samadi a, S. Schmauder b, A. Abouei Mehrizi c a
Mechanical Engineering Department, Shahid Rajaee Teacher Training University, Tehran 16758-136, Iran Institute for Materials Testing, Materials Science and Strength of Materials (IMWF), University of Stuttgart, Stuttgart, Germany c Biomechanics Lab, Life Science Engineering Department, Faculty of New Sciences and Technologies, University of Tehran, Amir Abad, North Kargar Street, Tehran, Iran b
a r t i c l e
i n f o
Article history: Received 8 December 2014 Revised 20 May 2015 Accepted 31 May 2015 Available online 19 June 2015 Keywords: Hollow sphere Space holder technique Centrifugal casting Regular and irregular pore distribution Compressive properties Failure mechanism Finite element method
a b s t r a c t In this study, experimental procedure and numerical methods were utilized to evaluate the effect of regular and irregular pore distribution as well as loading direction on compressive properties and deformation mechanism of hollow sphere aluminum foams. In order to study scaling laws, different volume fractions of the regular samples were produced and loaded in horizontal and vertical directions to address the loading conditions effects. For this purpose, expanded polystyrene (EPS) grains were expanded to a designed diameter size and positioned in different configurations. Compression test results showed higher elastic properties for irregular sample due to the thicker cell walls while energy absorption capability at high strains was found to be reduced due to the non-uniform deformation in comparison with regular foams. In regular samples, a nonlinear behavior in the elastic regime was observed since the imperfections during casting procedure. Furthermore, similar deformation mechanisms were found for the set of samples with similar pore configurations indicating the feasibility of controlling deformation mechanism by manipulating morphological characteristics. Finite element results well predicted deformation mechanism of structures and plastic properties of regular hollow sphere samples especially for plateau stress with less than 12% relative error. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Development of metallic foams has attracted great consideration in the two past decades due to the unique and controllable properties of cellular materials in different scales [1]. Metal foams have made advancement in many areas owing to their superior multi-physics properties such as excellent strength to density ratio [2], desirable buckling behavior [3], vibration attenuation [4], great energy dissipation thanks to the plastic collapse [5], controllability on mechanical response [6], and high specific mechanical properties [7]. Application of metal foams in transportation industry is growing increasingly since safety implies use of low density materials with high energy absorption to reduce impact stresses [8]. Nowadays, many industries such as railway industry, filtration, heat exchangers, sound absorbers, building structure and insulation [9], and even sport equipment, enjoy the advantages of metal foams [10]. Hence, more sophisticated analysis
⇑ Corresponding author. E-mail address: [email protected] (J. Kadkhodapour). http://dx.doi.org/10.1016/j.matdes.2015.05.086 0264-1275/Ó 2015 Elsevier Ltd. All rights reserved.
methodologies are required to design metal foams for performance in multi-functional situations. For instance, in automotive industry, weight reducing in addition to increasing the ability of energy absorption is satisfied by increasing porosity of components, while it lead the strength and stiffness to decrease [11]. Such challenges implies a compromise between design parameters thorough suitable optimization methods. It is intuitively obvious that many morphological parameters as well as sintering conditions play a prominent role in physical and mechanical characteristics of foams. Structure of cells, density of materials, porosity, pore size, and distribution affect mechanical strength and Young’s modulus as well as shear modulus, ability of energy absorption, strain rate sensitivity, and fatigue behavior [12–14]. Moreover, deformation behavior of foams is directly influenced by pore architecture and specifies mechanical efficiency and elastic properties of foams. Many approaches have been also developed for fabricating metal foams [15–20], Most of which lead to forming irregular pore architectures in foams, which are not mechanically as efficient and ideal as regular ones due to the lack of controllability and theoretical predictability on mechanical properties.
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Fig. 1. Procedure of preparing aluminum foam samples using space holder technique through vertical centrifugal casting. (a) Initial EPS grains, (b) EPS grains after expansion procedure, (c) expanded EPS grains coated with an incombustible material, (d) framework preparation with the controlled pore distribution, (e) mini Foundry casting machine setup, and (f) schematic representation of centrifugal casting procedure.
Table 1 Morphological characterization of final aluminum foam samples produced by centrifugal casting procedure; regular samples with 20 mm cube length are labeled combining relative density and loading direction. The irregular sample with 30 ⁄ 20 ⁄ 20 mm dimensions was labeled as 35.0-IRR. Sample label
Relative density
Loading direction
L (mm)
D (mm)
Pore configuration
27.3-V 27.3-H 38.4-V 38.4-H 50.0-V 50.0-H 35.0-IRR
0.273 0.273 0.384 0.384 0.500 0.500 0.350
Vertical Horizontal Vertical Horizontal Vertical Horizontal –
1 1 2 2 2 2 –
3.5 3.5 3.5 3.5 3.5 3.5 3.5
BCC BCC BCC BCC SC SC –
It is reported in the literature that spherical cell foams, named hollow sphere foams, have provided improved conditions for dynamic shock and energy absorption [15]. Mechanical properties of such structures are more predictable than those produced by other production methods. Hollow sphere foams are commonly fabricated by consolidating hollow spheres with the melt or by compacting the spheres through powder metallurgy [16–18]. In this area, Bafti and Habibolahzadeh [3] investigated the effect of cell shape, size, and relative density on the compressive behavior of aluminum foams produced by space holder technique utilizing Carbamide powder as the space route. They theoretically analyzed the constant values in scaling laws and relationships for
densifications strain and plateau stress for metallic foams and concluded that spherical cells provided higher mechanical properties in the structure. Szyniszewski et al. [6] executed a comprehensive study on the mechanical characterization of hollow sphere steel foams in terms of compression and tension and investigated elastic and plastic parameters applying calibrated Deshpande-Fleck plasticity to mechanical simulations of steel foams. They finally claimed that such structures had high bending rigidity and energy dissipation potential. Moreover, Luong et al. [19] studied compressive failure mechanisms under diverse strain rates ranging to cover quasi-static and high strain rates for hollow sphere aluminum foams and reported higher compressive and plateau stress than ash cenosphere filled aluminum matrix syntactic foams. Ming et al. [20] assessed the tensional failure mode of hollow sphere filled syntactic epoxy-ceramic foams using experimental and numerical procedures. They found finite element results in good agreement with the experimental observations and reported the domination of brittle fracture mechanism under tensile load. Effect of particle clustering on failure mechanism was numerically studied by Ming et al. [21]. They stated that the elastic behavior of syntactic foams was insensitive to the degree of particle clustering and could considerably affect strength and failure modes. Since the mechanical aspects of aluminum hollow sphere foams with regular pore architecture have been inadequately addressed, in this work, we investigated morphological parameters effect on compressive behavior of hollow sphere structures by controlling pore distribution in production procedure. In addition, effect of
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Fig. 2. Framework configuration considered to form void phase and distribute spheres in the aluminum foam samples with gluing plaster columns and coated EPS grains following (a) SC and (b) BCC crystal systems.
loading direction on compressive behavior of aluminum foam samples with regular pore architectures (with BCC and SC configuration) in addition to irregular pore distribution was studied using numerical and experimental procedures. Furthermore, to address the structure–property correlations, compressive deformation mechanisms and scaling analysis of mechanical properties were studied. 2. Materials and methods 2.1. Sample production To evaluate effect of spherical pore distribution and morphological parameters on compressive behavior of hollow sphere aluminum foams, position of pores are controlled using interconnections to generate regular pore distribution and the mechanical properties are compared with that of foams having irregular pore architecture. In order to fabricate aluminum foam samples, Al6063-T6 with the reported chemical composition of 97.5Al, 0.45–0.9 Mg, 0.2–0.6Si, 0.1Cr, 0.1Mn, 0.1Ti, 0.1Cu, and 0.35Fe (wt.%) was used as the matrix material. Space holder framework was prepared by positioning the hollow spheres through the interconnections to form internal pore architecture for the samples with regular pore architecture. In the case of irregular sample, space holder grains with the same material and grain size as regular samples were prepared without connections and regularity. The aluminum alloy used as the matrix material had the density of 2.7 g/cc and its melting point was 616–654 °C with the mechanical properties of 214 MPa for yield strength and 241 MPa for ultimate strength. It had the Young’s modulus of 68.9 GPa and elongation at break was 12%. An overall view of sample production procedure is shown in Fig. 1. EPS grains expand proportional to temperature between 110 and 150 °C in the presence of water and NaCl. Moreover, it is feasible to control pore size of the samples by setting ambient parameters during the expansion procedure of EPS, expanded polystyrene (EPS) grains with the initial diameter of 0.8 mm (Fig. 1(a)) were utilized to shape the internal pores. To this end, 6 g of EPS grains was mixed with saltwater and kept at 115 °C and 2.5 bar for 45 min to obtain spherical grains with 3.5 mm diameter (Fig. 1(b)). EPS grains extremely shrink by increasing temperature after final stages of expansion and then vaporize under temperatures of less than that for aluminum melting. Hence, in order to lead melted aluminum to form internal spherical pores with the same
size as the prepared EPS grains, the spherical EPS grains and plaster columns were coated with incombustible materials. Then, polymeric grains were kept at 80 °C for 20 min to dehydrate (which led to 0.2% decrease in the diameter of spheres) and tipped with the incombustible paste prepared by mixing 10 g glass wool powder, 19 g silicon, and 15 g calcium oxide. The EPS grains were trundled between two surfaces tripped with an incombustible paste until a layer with 0.5–1 mm thickness coated them. Then, the polymeric grains coated with an incombustible paste were heated up to 120 °C and a hard spherical coat with high heat resistance (1560 °C) was formed on the spherical EPS grains (Fig. 1(c)). In order to take shape interconnections between spherical grains for the regular samples, calcium sulfate was mixed with water to form a paste. Then, it was passed through a loophole with 1 mm diameter dried after 20 min. Plaster strings were cut into some slices with the length of 1 and 2 mm to form interconnections and cell walls between spherical pores. For the regular samples, three frameworks with different morphological characteristics (presented in Table 1) were made such that their EPS grain sizes and consequently pore sizes were similar (3.5 mm) for all and plaster connections perpendicular to the melt injection were unilaterally holding the coated EPS grains in space, as shown schematically in Fig. 2. For the sample with 50.0% relative density, the grains were located with SC configuration, while BCC configuration was considered for the samples with 38.4% and 27.3% volume fraction. Furthermore, 1 mm plaster connections were used between the grains for the samples with 50% and 38.4% volume fractions. The grains in the samples with 27.3% volume fraction were located using 1 mm length plasters. To produce irregular aluminum foam, the coated EPS grains were put into the casting lacuna without any connection and regularity. The frameworks were heated and kept at 380 °C for 20 min for the polymeric content of the spheres to vaporize. After vaporizing EPS content, the frameworks with incombustible hollow spheres with the plaster columns were heated up to 700 °C to facilitate melt penetration into the cells of frameworks and then they were placed into the rotary kiln for casting procedure. Centrifugal casting technique was utilized in order to lead melted aluminum into the cylindrical lacuna containing the framework with 100 mm diameter and 50 mm height (Fig. 1(d)). Mini Foundry machine with the molding diameter of 50–450 mm and height of 400 mm was employed (Fig. 1(e)) to perform casting procedure. The framework was set into the machine and casting was performed under 1200 rpm rotation speed to inject melted aluminum. In order to prepare aluminum melt, Al6063 bars were heated in the furnace
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Fig. 3. Model mesh and geometry representation of FE model corresponding to the samples with (a) 27.3%, (b) 38.4%, and (c) 50% volume fractions.
Fig. 4. Experimental compressive stress–strain curves of the samples in total strain domain with different volume fractions and loading direction. Stress strain curves for all the regular samples are followed by plateau region with strain hardening behavior up to the beginning of densification, while the irregular sample shows strain softening during plateau regime.
Ultrasonic vibration was utilized to clean the aluminum foam samples of the incombustible materials used to prepare framework. It peeled almost 98% of such materials of aluminum foam samples and the reminder was cleaned by water pressure in the regular samples. Finally, two cubic samples with 20 mm length corresponding to each regular framework and 30 ⁄ 20 ⁄ 20 mm for irregular foam were cut of the produced cylindrical foams and polished by a p2000 sandpaper to get prepared for compression test procedure. Then, the samples were weighted and their volume fractions were calculated. As it is shown in Table 1, Values of 50%, 38.4%, and 27.3% corresponding to the frameworks with SC configuration with 2 mm plaster column and BCC configurations having 2 and 1 mm plaster column were achieved, respectively. The specimens were named by combining their volume fractions with the loading direction relative to the melt injecting. For instance, 27.3H refers to the sample with 27.3% volume fraction which is horizontally loaded, while 27.3V refers to the sample with the same volume fraction which is loaded vertically (Fig. 2). Fig. 5. Detailed representation of elastic regime in the stress–strain curves of the experimental samples. Nonlinear behavior in elastic regime is attributed to narrow cell walls and imperfections formed during the casting procedure.
up to 850° for 25 min. Rotation in the centrifugal casting was kept on up to the time the mold temperature was risen to 600 °C. Then, solidification was initiated at the ambient temperature and finally the samples were taken out of the casting machine.
2.2. Mechanical compressive test Compressive test was implemented on the samples in order to assess their mechanical properties under compression. Standard ISO/DIS 1334 suggests a square cross section for the compressive testing of porous and cellular materials [22]. In order to prevent buckling during the test, a height to width ratio of less than 1.5
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Table 2 Compressive mechanical properties of the samples obtained by the experimental stress strain data. Sample label
Young’s modulus (MPa)
Compression strength (MPa)
Plateau stress (MPa)
Densification strain
Densification stress (MPa)
Energy absorption at densification (kJ/g)
27.3-H 27.3-V 38.4-H 38.4-V 50.0-H 50.0-V 35.0-IRR
194.7 151.8 430.3 218.3 690.4 686.7 657.4
7.5 5.4 14.6 13.2 33.5 20.8 19.3
19.6 14.7 33.9 23.7 54.4 46.4 32.7
0.553 0.557 0.393 0.346 0.263 0.328 –
30.4 23.0 50.9 34.8 72.7 66.0 –
10.2 7.8 12.5 7.3 12.5 14.1 –
was considered in designing the samples. Furthermore, rectangular jaws were utilized at the bottom and top and the specimens were aligned relative to loading direction to distribute force as uniform as possible. A preload was applied to the samples until the gaps between the sample and jaws disappeared. Then, compression test was initiated with the cross head speed of 2 mm/min corresponding to 0.0334 mm/s using Zwick Roell testing machine at room temperature and compressive force against displacement was plotted corresponding to each sample. In order to extract compressive stress versus strain, initial cross sectional area of 400 mm2 for all of the samples and initial height of 20 mm and 30 mm were defined for the regular and irregular foams, respectively. To study the effect of loading direction and role of unilateral interconnections on mechanical response for the regular samples, compression tests were conducted parallel and perpendicular to the interconnections (melt injection was performed perpendicular to the interconnection direction) for each volume fraction. In order to interpret mechanical properties for the samples, an idealization approach was performed on the resulted stress strain curves. To this, elastic modulus was considered as the slope of linear fit to data in the stress range of 30–70% of compressive strength. Yield stress was calculated by intersecting 0.002 offset line with the stress strain curve. Since the incomplete densification process, intersection of the lines on the most linear regions of densification and plateau regime used to obtain densification stress and strain. The average value of stress in stress strain curve from yield point up to the onset of densification was assigned to the plateau stress. Furthermore, to calculate specific absorbed energy (strain energy per unit of gram), the area under stress strain curve was divided by (density sample volume fraction) to address the capability of material in energy absorption for each sample. 2.3. Finite element simulation procedure In order to investigate stress distribution patterns, plastic deformation behavior of the samples, and the predictability of regular hollow sphere foams, finite element method was conducted on the CAD models of the structures. CAD model of unit cells were designed by the negative image of the frame work shown in Fig. 2 with the dimensions presented in Table 1. Then, the constitutive unit cell was patterned along three global coordinates such that cubic porous structures comprised of 3 3 3 unit cells were designed with 20 mm length for each sample. Then, the models were automatically meshed using 10-node second-order tetrahedral elements with the element size range of 900 lm (Fig. 3) with respect to the sensitivity analysis performed on the models. Moreover, an elastoplastic material model was considered with the elastic modulus of 68.9 Mpa, yield strength of 214 Mpa, and Poisson’s ratio of 0.33. Then, compressive load was applied to all the 3D models with the strain rate matching experimental tests. FE calculations were executed by ABAQUS explicit code and Mises stress, plastic deformation contours, and stress strain curves were extracted based on the initial dimensions of the specimens.
3. Results and discussion 3.1. Interpreting experimental stress strain curves Compressive stress strain results for all the samples and loading directions are presented in Fig. 4. Global trend of the curves for the specimens with regular pore architecture was similar to that of cellular materials with strain hardening behavior in plateau region. Softening behavior in plateau region was observed in stress strain curve of irregular sample, while in regular samples such a behavior was not observed. No fluctuation in stress strain curves is seen implying ductile deformation in plastic region. For regular samples, no material separation was occurred and densification happened at high strains as it can be seen in Fig. 4. Despite the ductile deformation procedure, for irregular sample, a considerable material separation was occurred due to non-uniform deformation of the structure and no densification can be observed in compression test. In order to investigate the elastic region more precisely, the elastic region was zoomed from the stress strain curves of Fig. 4 and illustrated in Fig. 5. Stress variations in elastic regime was found to be nonlinear and it is explained by the imperfections and defects during the casting procedure. The compressive mechanical properties of the samples is presented in Table 2. The data shows that the higher mechanical properties were found for the horizontal loading compared with vertical loading direction. 3.2. Mechanical properties versus relative density (scaling laws analysis) Many theoretical studies on cellular materials declared the exponential variations of mechanical properties versus relative density thereby mechanical properties such as elastic modulus, yield strength, and plateau region are characterized through scaling by volume fraction of porous structure [23]:
n X q ¼C qs Xs
ð1Þ
As it is stated by Ashby [24], in scaling laws analysis of Young’s modulus, the exponents (n) near 2 refer to the structures with more tendency to bending deformation, while the exponents close to 1 show the tendency to stretching deformation in compression loading. Hence, deformation modes, namely bending dominated or stretch dominated, can be evaluated by scaling laws analysis. 3.2.1. Elastic properties Normalized Young’s modulus of the samples was calculated and plotted against volume fraction in Fig. 6(a). In order to calculate constant values of scaling laws, power fitting was performed on n the data for the regular samples EEs ¼ C qq and exponential s
value of 2.177 with strengthening coefficient of 0.0452 was obtained (with the regression of 0.921) matching with that of cellular materials in which bending is dominated on their
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(a)
357
compressive deformation. Moreover, horizontally loaded samples exhibited stiffer behavior compared with vertically loaded ones at the same volume fractions. Besides, elastic behavior of irregular sample was found to be improved compared to the regular samples. This implies the role of cell wall thickness in stiffness behavior of hollow sphere structures. 3.2.2. Compression strength Normalized compression strength versus volume fraction is illustrated in Fig. 6(b). Fitting to data was performed on the regular samples to obtain the scaling constants for yield stress n ry q . Similar to the elastic analysis, the exponential value ry;s ¼ C q s
(b)
of scaling laws is indicative of the deformation behavior of structure such that the n near to 1.5 implies bending dominated deformation and (n = 1) refers to the stretching dominated structures [24]. Curve fitting results showed the exponential value of 2.112 with the strengthening coefficient of 0.553 (with regression of 0.829) indicating the trend of regular structures to bending dominated deformation which is in line with the results obtained in elastic analysis. It can be seen that among regular structures, horizontally loaded samples exhibited more strength meeting the requirements of structural applications. Moreover, yield stress for the irregular sample was found to be improved compared with the regular samples. 3.2.3. Plateau stress Normalized Plateau stress is plotted versus volume fraction and demonstrated in Fig. 6(c). As well as elastic properties, scaling analysis of normalized plateau stress for regular samples n rpl q was performed and the results indicated strengthry;s ¼ C q s
ening coefficient of 0.760 and exponential value of 1.683 (with regression of 0.916). The theoretical correlations between deformation mode and scaling analysis of plateau stress is similar to what stated for yield stress (the n near to 1 and 1.5 refers to stretching and bending dominated deformations, respectively). Hence, scaling plateau stress confirms domination of bending on deformation mechanism of regular hollow sphere structures. Moreover, for regular configurations, horizontal loading conditions were found to increase plateau stress.
(c)
Fig. 6. Variation of (a) Young’s modulus, (b) yield stress, and (c) plateau stress versus volume fraction for scaling laws analysis. Scaling laws confirms the domination of bending on the overal deformation and illustrates the improved elastic properties is found for the horizontally loaded samples.
3.2.4. Energy absorption In order to highlight the effect of morphological parameters on energy absorption of hollow sphere aluminum foams, the specific strain energy (the energy absorbed per unit of mass) was plotted at different strains and the results are illustrated in Fig. 7. Normally, analysis of plateau stress is indicative of energy absorption capability of porous structures. Although, comparing the results of specific energy versus strain for different structures gives better insight into the role of morphological parameters effect on structural efficiency of hollow sphere aluminum foams in energy absorption. As it can be seen in Fig. 7, increasing volume fraction for the set of regular structures improved specific energy absorption. On the other hand, irregular sample (with 35% relative density) in comparison with the regular structure at the nearest relative density (38.4%) showed the higher specific energy absorption especially at lower strains (less than 0.46). By the way, at higher stages of deformation, material separation leads the irregular sample to lose its energy efficiency relative to regular one. 3.2.5. Densification strain Fig. 8 shows the densification strains versus the samples’ volume fraction. An almost linear trend can be observed which is well in line with many theoretical studies on densification behavior of cellular materials [25]. Chan [26] presented the more accurate
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Fig. 7. Strain energy absorption extracted from stress strain curves for different loading directions and relative densities in total strain domain. Irregular sample absorbs higher energy due to more bending deformation of its thicker walls than the regular samples.
Fig. 8. Variation of densification strain with relative density for the regular specimens.
theoretical relationship to describe densification behavior of metallic foams in the form of Eq. (2):
3 !
q q þ 0:4 eD ¼ C 1 1:4 qs qs
ð2Þ
where the constant coefficient of C varies for different materials and structures. With considering Eq. (2) for the experimental results, the constant value was found to be C = 0.84 for the regular samples. Bafti and Habibolahzadeh [3] illustrated the densification strain versus volume fraction for the closed cell hollow sphere structures with irregular pore architecture and characterized the densification behavior by Eq. (2) with C = 0.95. The results of Fig. 8 shows that the effect of loading direction on densification strain becomes more considerable as volume fraction increases. 3.3. Failure mechanism and plastic deformation procedure The deformation procedure of the regular samples under both vertical and horizontal compression is represented in Figs. 9, 10, and 11 for the samples with 27.3%, 38.4%, and 50%
relative densities. Internal narrow walls is observable in Fig. 10(f). The nonlinear behavior in elastic regime can be explained by these defects as previously stated. It can be deduced from deformation patterns that the set of samples with the same pore configuration and morphological characteristics followed similar deformation mechanisms and it indicates that controlling deformation mechanism is feasible by manipulating morphological parameters. In the samples with BCC pore configuration in horizontal loading, shear band of 45° was observed thanks to the side wall inclination as can be seen in Figs. 9(d) and 10(e). On the other hand, a layer by layer failure mechanism was seen for the SC configuration in horizontal loading (Fig. 11(d)). In the vertically loaded samples, a global barreling was found thanks to the cell wall buckling (Fig. 9(i), 10(i), and 11(i)). Deformation mechanism was found to be accompanied by cell wall bending which confirms the analysis of deformation by scaling the mechanical properties of the samples. The deformation procedure for the sample with irregular pore distribution is illustrated in Fig. 12. It was also well seen that crushing was accompanied by an overall barreling with the localizations (Fig. 12(c)) which caused material separation at higher strains. 3.4. Simulation results and validation Fig. 13 demonstrates Mises stress and plastic strain distribution contours of the deformed samples computed by finite element method for the structures with regular pore architecture. Shear band of 45° in the plastic strain contour of the samples with BCC pore configuration in horizontal loading (Fig. 13(h) and 13(l)) is confirmed by experimental deformation procedure shown in Figs. 9(d) and 10(d). A layer by layer failure owing to the bending of cell walls between hollow spheres was apparent in the regular sample with SC pore configuration in horizontal loading; i.e. 50.0-H (Fig. 13(d)) which is confirmed by experimental observations (Fig. 11(d)). Furthermore, barreling mode of deformation in experimental deformation mechanism of the samples with vertical loading is also observable in the simulation results. Numerical stress strain results for the samples with regular pore architecture are compared with the experimental stress strain curves in Fig. 14. Overestimations in the elastic region can be
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Sample
(I)
(II)
(III)
(IV)
(V)
0.57
0.94
0.17
0.18
0.30
(a)
(b)
(c)
(d)
(e)
0.55
0.12
0.18
0.29
0.35
(f)
(g)
(h)
(i)
(j)
27.3 -H
Strain
27.3 -V
Strain
Fig. 9. Deformation procedure and failure mechanism of horizontally and vertically loaded samples with 27.3% relative density; shearing band of 45° for the horizontally loaded and barreling deformation mode for vertically loaded samples is observed in deformation mechanisms.
Sample
(I)
(II)
(III)
(IV)
(V)
0.03
0.09
0.24
0.26
0.39
(a)
(b)
(c)
(d)
(e)
0.07
0.21
0.32
0.34
0.40
(f)
(g)
(h)
(i)
(j)
38.4-H
Strain
38.4 -V
Strain
Fig. 10. Deformation procedure and failure mechanism of horizontally and vertically loaded samples with 38.4% relative density; shearing band of 45° for horizontally loaded and barreling deformation mode for vertically loaded samples is observed in deformation mechanisms.
Sample
(I)
(II)
(III)
(IV)
(V)
0.06
0.11
0.14
0.17
0.20
(a)
(b)
(c)
(d)
(e)
0.13
0.25
0.38
0.43
0.50
(f)
(g)
(h)
(i)
(j)
50-H
Strain
50-V
Strain
Fig. 11. Deformation procedure and failure mechanism of horizontally and vertically loaded samples with 50.0% relative density; a layer by layer failure pattern for horizontally loaded sample and barreling deformation is observed for vertically loaded sample.
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Sample
(I)
(II)
(III)
(IV)
(V)
0.05
0.13
0.21
0.34
0.55
(a)
(b)
(c)
(d)
(e)
35.0-IRR
Strain
Fig. 12. Deformation mechanism of the irregular sample with 35.0% relative density; material separation, thanks to high bending deformation during the test, causes stress softening in plateau regime.
SC pore configuration Mises Stress Plastic Strain 50.0-V
(a)
BCC pore configuration Mises Stress Plastic Strain 50.0-H
(b)
(c)
38.4-V
(f)
(e)
(g)
27.3-V
(h) 27.3-H
(j)
(i)
(d) 38.4-H
(k)
38.4-V
50-H
(l) 23.7-H
Legends
Fig. 13. Mises stress and plastic strain distribution contours on the deformed shape of simulated regular sample models matching with the morphological characteriation described in sample production procedure (Section 2.1) for different volume fractions, loading directions and internal pore architectures.
explained by the imperfections (lack of material) which formed during the casting procedure. The numerical stress strain data were found to fit well to experimental data especially at higher strains. Hence, it can be inferred that the effect of internal imperfections becomes negligible at higher stages of deformation. In order to address the reliability of FE method in predicting plastic mechanical properties of described hollow sphere structures, the
relative errors between the numerical and experimental results are presented in Table 3. The results show that plateau stress is well predicted by the presented approach. Hence, FEM showed a good potential to predict the mechanical behavior of hollow sphere cellular materials with regular pore architecture and higher reliability was achieved in predicting plastic properties; e.g. plateau stress.
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(a)
Table 3 Validating mechanical properties predicted by FE method. The results show good predictability of plateau stress with the developed model. Sample label
27.3-H 27.3-V 38.4-H 38.4-V 50.0-H 50.0-V
(b)
(c)
Fig. 14. Validating stress strain curves resulted by FE simulation with the experimental data at (a) 27.3, (b) 38.4, and (c) 50.0 relative densities with different loading directions; Despite the imperfections formed in casting procedure, a good agreement is found between numerical and experimental results.
4. Conclusions In this work, effects of pore distribution and loading direction were investigated on the compressive behavior of hollow sphere aluminum foams for different volume fractions using an experimental procedure and numerical methods. To this end, the regular aluminum foam samples with controlled internal pore configurations of BCC and SC were produced by a centrifugal casting process and different volume fractions were prepared to study scaling laws on the specific mechanical properties for both vertical and
Compression strength (Mpa)
Plateau stress (MPa)
Energy absorption at densification (kJ/g)
Simulation
% Error
Simulation
% Error
Simulation
% Error
3.8 2.9 6.5 5.6 25.9 10.6
49.2 46.1 55.2 57.8 22.8 49.0
18.3 14.3 29.7 22.1 50.0 42.4
6.6 2.8 12.1 6.6 8.0 8.5
13.7 10.9 16.0 7.5 9.9 10.4
34.1 40.2 28.2 1.9 20.9 26.5
horizontal loading directions. The aluminum foam sample with irregular pore architecture was also fabricated using the same technology to be compared with the regular specimens. Experimental stress strain curves showed the same strain hardening behavior for the regular samples, while strain softening behavior in plateau region was observed for the irregular sample. Moreover, a nonlinear trend in the elastic regime due to imperfections during the casting procedure and formation of narrow cell walls was observed. Scaling laws analysis of Young’s modulus, yield strength, and plateau stress confirmed the high trend of hollow sphere structures to bending dominated deformation. Evaluating the resulted mechanical properties showed that an elastic property for irregular sample was higher than that of foams with regular architecture and it was attributed to the cell walls thickness. Although the elastic properties were found to be improved in irregular sample, the energy absorption ability was reduced in comparison with the regular samples since the non-uniform deformation and the material separation occurred at higher strains. Moreover, comparing mechanical response resulted by vertical and horizontal loadings indicates that vertical positioning of interconnections (horizontal loading) led the plateau to be enlarged and consequently energy absorption to be improved. Generally, horizontally loaded samples exhibited higher mechanical properties. Furthermore, densification analysis of all the samples versus relative density showed the constant value of C = 0.84 in Eq. (2). For horizontally loaded samples, experimental and numerical deformation mechanisms showed a layer by layer failure in the samples with SC pore configuration. Moreover, deformation mechanism of the horizontally loaded samples with BCC pore architecture was developed by shearing bands of 45°. Vertically loaded samples also deformed thanks to overall barreling of structure along with the cell walls buckling. The results of deformation mechanism showed that failure patterns can be controlled by manipulating the positioning state of pores. Furthermore, deformation mechanism for stochastic sample was accompanied by high localizations leading the non-uniform compression and finally material separations at high strains. Numerical results of the FE analysis were in good agreement on deformation procedure as well as plastic properties of regular samples with regular pore configurations. Plateau stress was well predicted by less than 12.1% relative error implying the high predictability of mechanical behavior of regular hollow sphere foams by FE method. References [1] J.H. Cadena, I. Alfonso, J.H. Ramírez, V. Rodríguez-Iglesias, I.A. Figueroa, C. Aguilar, Improvement of FEA estimations for compression behavior of Mg foams based on experimental observations, Comput. Mater. Sci. 91 (2014) 359–363. [2] J. Banhart, Manufacture, characterisation and application of cellular metals and metal foams, Prog. Mater Sci. 46 (2001) 559–632.
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[3] H. Bafti, A. Habibolahzadeh, Compressive properties of aluminum foam produced by powder-Carbamide spacer route, Mater. Des. 52 (2013) 404–411. [4] R. Neugebauer, T. Hipke, Machine tools with metal foams, Adv. Eng. Mater. 8 (2006) 858–863. [5] V. Marcadon, S. Kruch, Influence of geometrical defects on the mechanical behaviour of hollow-sphere structures, Int. J. Solids Struct. 50 (2013) 498–510. [6] S.T. Szyniszewski, B.H. Smith, J.F. Hajjar, B.W. Schafer, S.R. Arwade, The mechanical properties and modeling of a sintered hollow sphere steel foam, Mater. Des. 54 (2014) 1083–1094. [7] A.M. Parvanian, M. Saadatfar, M. Panjepour, A. Kingston, A.P. Sheppard, The effects of manufacturing parameters on geometrical and mechanical properties of copper foams produced by space holder technique, Mater. Des. 53 (2014) 681–690. [8] D.X. Sun, Y.Y. Zhao, Static and dynamic energy absorption of Al foams produced by the sintering and dissolution process, Metall. Mater. Trans. B 34 (2003) 69–74. [9] L.J. Gibson, M.F. Ashby, Cellular Solids: Structures and Properties, second ed., Cambridge University Press, 1997. [10] S. Bazzaz Bonabi, J. Kahani Khabushan, R. Kahani, A. Honarbakhsh Raouf, Fabrication of metallic composite foam using ceramic porous spheres ‘‘Light Expanded Clay Aggregate’’ via casting process, Mater. Des. 64 (2014) 310–315. [11] P. Pinto, N. Peixinho, F. Silva, D. Soares, Compressive properties and energy absorption of aluminum foams with modified cellular geometry, J. Mater. Process. Technol. 214 (2014) 571–577. [12] O.B. Olurin, N.A. Fleck, M.F. Ashby, Deformation and fracture of aluminium foams, Mater. Sci. Eng., A 291 (2000) 136–146. [13] J. Zare, H.D. Manesh, A novel method for producing of steel tubes with Al foam core, Mater. Des. 32 (2011) 1325–1330. [14] M. Malekjafarian, S.K. Sadrnezhaad, Closed-cell Al alloy composite foams: production and characterization, Mater. Des. 42 (2012) 8–12.
[15] J. Fan, J. Zhang, Z. Wang, Z. Li, L. Zhao, Dynamic crushing behavior of random and functionally graded metal hollow sphere foams, Mater. Sci. Eng., A 561 (2013) 352–361. [16] J. Brown, L. Vendra, A. Rabiei, Bending properties of Al–steel and steel–steel composite metal foams, Metall. Mater. Trans. A 41 (2010) 2784–2793. [17] B.P. Neville, A. Rabiei, Composite metal foams processed through powder metallurgy, Mater. Des. 29 (2008) 388–396. [18] O. Friedl, C. Motz, H. Peterlik, S. Puchegger, N. Reger, R. Pippan, Experimental investigation of mechanical properties of metallic hollow sphere structures, Metall. Mater. Trans. B 39 (2008) 135–146. [19] D.D. Luong, O.M. Strbik Iii, V.H. Hammond, N. Gupta, K. Cho, Development of high performance lightweight aluminum alloy/SiC hollow sphere syntactic foams and compressive characterization at quasi-static and high strain rates, J. Alloy. Compd. 550 (2013) 412–422. [20] M. Yu, P. Zhu, Y. Ma, Experimental study and numerical prediction of tensile strength properties and failure modes of hollow spheres filled syntactic foams, Comput. Mater. Sci. 63 (2012) 232–243. [21] M. Yu, P. Zhu, Y. Ma, Effects of particle clustering on the tensile properties and failure mechanisms of hollow spheres filled syntactic foams: a numerical investigation by microstructure based modeling, Mater. Des. 47 (2013) 80–89. [22] ISO/TC TC. Compression Test for Porous and Cellular Metals, 2011.. [23] M.F. Ashby, A.G. Evans, N.A. Fleck, L.J. Gibson, J.W. Hutchinson, H.N.G. Waldey, Metal Foams: A Design Guide, Butterworth-Heinemann, 2000. [24] M.F. Ashby, The properties of foams and lattices, Phil. Trans. R. Soc. A: Math. Phys. Eng. Sci. 364 (2006) 15–30. [25] Q.M. Li, I. Magkiriadis, J.J. Harrigan, Compressive strain at the onset of densification of cellular solids, J. Cell. Plast. 42 (2006) 371–392. [26] K.C. Chan, L.S. Xie, Dependency of densification properties on cell topology of metal foams, Scripta Mater. 48 (2003) 1147–1152.
Contents lists available at ScienceDirect
Materials & Design journal homepage: www.elsevier.com/locate/matdes
Plastic deformation and compressive mechanical properties of hollow sphere aluminum foams produced by space holder technique J. Kadkhodapour a,⇑, H. Montazerian a, M. Samadi a, S. Schmauder b, A. Abouei Mehrizi c a
Mechanical Engineering Department, Shahid Rajaee Teacher Training University, Tehran 16758-136, Iran Institute for Materials Testing, Materials Science and Strength of Materials (IMWF), University of Stuttgart, Stuttgart, Germany c Biomechanics Lab, Life Science Engineering Department, Faculty of New Sciences and Technologies, University of Tehran, Amir Abad, North Kargar Street, Tehran, Iran b
a r t i c l e
i n f o
Article history: Received 8 December 2014 Revised 20 May 2015 Accepted 31 May 2015 Available online 19 June 2015 Keywords: Hollow sphere Space holder technique Centrifugal casting Regular and irregular pore distribution Compressive properties Failure mechanism Finite element method
a b s t r a c t In this study, experimental procedure and numerical methods were utilized to evaluate the effect of regular and irregular pore distribution as well as loading direction on compressive properties and deformation mechanism of hollow sphere aluminum foams. In order to study scaling laws, different volume fractions of the regular samples were produced and loaded in horizontal and vertical directions to address the loading conditions effects. For this purpose, expanded polystyrene (EPS) grains were expanded to a designed diameter size and positioned in different configurations. Compression test results showed higher elastic properties for irregular sample due to the thicker cell walls while energy absorption capability at high strains was found to be reduced due to the non-uniform deformation in comparison with regular foams. In regular samples, a nonlinear behavior in the elastic regime was observed since the imperfections during casting procedure. Furthermore, similar deformation mechanisms were found for the set of samples with similar pore configurations indicating the feasibility of controlling deformation mechanism by manipulating morphological characteristics. Finite element results well predicted deformation mechanism of structures and plastic properties of regular hollow sphere samples especially for plateau stress with less than 12% relative error. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Development of metallic foams has attracted great consideration in the two past decades due to the unique and controllable properties of cellular materials in different scales [1]. Metal foams have made advancement in many areas owing to their superior multi-physics properties such as excellent strength to density ratio [2], desirable buckling behavior [3], vibration attenuation [4], great energy dissipation thanks to the plastic collapse [5], controllability on mechanical response [6], and high specific mechanical properties [7]. Application of metal foams in transportation industry is growing increasingly since safety implies use of low density materials with high energy absorption to reduce impact stresses [8]. Nowadays, many industries such as railway industry, filtration, heat exchangers, sound absorbers, building structure and insulation [9], and even sport equipment, enjoy the advantages of metal foams [10]. Hence, more sophisticated analysis
⇑ Corresponding author. E-mail address: [email protected] (J. Kadkhodapour). http://dx.doi.org/10.1016/j.matdes.2015.05.086 0264-1275/Ó 2015 Elsevier Ltd. All rights reserved.
methodologies are required to design metal foams for performance in multi-functional situations. For instance, in automotive industry, weight reducing in addition to increasing the ability of energy absorption is satisfied by increasing porosity of components, while it lead the strength and stiffness to decrease [11]. Such challenges implies a compromise between design parameters thorough suitable optimization methods. It is intuitively obvious that many morphological parameters as well as sintering conditions play a prominent role in physical and mechanical characteristics of foams. Structure of cells, density of materials, porosity, pore size, and distribution affect mechanical strength and Young’s modulus as well as shear modulus, ability of energy absorption, strain rate sensitivity, and fatigue behavior [12–14]. Moreover, deformation behavior of foams is directly influenced by pore architecture and specifies mechanical efficiency and elastic properties of foams. Many approaches have been also developed for fabricating metal foams [15–20], Most of which lead to forming irregular pore architectures in foams, which are not mechanically as efficient and ideal as regular ones due to the lack of controllability and theoretical predictability on mechanical properties.
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Fig. 1. Procedure of preparing aluminum foam samples using space holder technique through vertical centrifugal casting. (a) Initial EPS grains, (b) EPS grains after expansion procedure, (c) expanded EPS grains coated with an incombustible material, (d) framework preparation with the controlled pore distribution, (e) mini Foundry casting machine setup, and (f) schematic representation of centrifugal casting procedure.
Table 1 Morphological characterization of final aluminum foam samples produced by centrifugal casting procedure; regular samples with 20 mm cube length are labeled combining relative density and loading direction. The irregular sample with 30 ⁄ 20 ⁄ 20 mm dimensions was labeled as 35.0-IRR. Sample label
Relative density
Loading direction
L (mm)
D (mm)
Pore configuration
27.3-V 27.3-H 38.4-V 38.4-H 50.0-V 50.0-H 35.0-IRR
0.273 0.273 0.384 0.384 0.500 0.500 0.350
Vertical Horizontal Vertical Horizontal Vertical Horizontal –
1 1 2 2 2 2 –
3.5 3.5 3.5 3.5 3.5 3.5 3.5
BCC BCC BCC BCC SC SC –
It is reported in the literature that spherical cell foams, named hollow sphere foams, have provided improved conditions for dynamic shock and energy absorption [15]. Mechanical properties of such structures are more predictable than those produced by other production methods. Hollow sphere foams are commonly fabricated by consolidating hollow spheres with the melt or by compacting the spheres through powder metallurgy [16–18]. In this area, Bafti and Habibolahzadeh [3] investigated the effect of cell shape, size, and relative density on the compressive behavior of aluminum foams produced by space holder technique utilizing Carbamide powder as the space route. They theoretically analyzed the constant values in scaling laws and relationships for
densifications strain and plateau stress for metallic foams and concluded that spherical cells provided higher mechanical properties in the structure. Szyniszewski et al. [6] executed a comprehensive study on the mechanical characterization of hollow sphere steel foams in terms of compression and tension and investigated elastic and plastic parameters applying calibrated Deshpande-Fleck plasticity to mechanical simulations of steel foams. They finally claimed that such structures had high bending rigidity and energy dissipation potential. Moreover, Luong et al. [19] studied compressive failure mechanisms under diverse strain rates ranging to cover quasi-static and high strain rates for hollow sphere aluminum foams and reported higher compressive and plateau stress than ash cenosphere filled aluminum matrix syntactic foams. Ming et al. [20] assessed the tensional failure mode of hollow sphere filled syntactic epoxy-ceramic foams using experimental and numerical procedures. They found finite element results in good agreement with the experimental observations and reported the domination of brittle fracture mechanism under tensile load. Effect of particle clustering on failure mechanism was numerically studied by Ming et al. [21]. They stated that the elastic behavior of syntactic foams was insensitive to the degree of particle clustering and could considerably affect strength and failure modes. Since the mechanical aspects of aluminum hollow sphere foams with regular pore architecture have been inadequately addressed, in this work, we investigated morphological parameters effect on compressive behavior of hollow sphere structures by controlling pore distribution in production procedure. In addition, effect of
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Fig. 2. Framework configuration considered to form void phase and distribute spheres in the aluminum foam samples with gluing plaster columns and coated EPS grains following (a) SC and (b) BCC crystal systems.
loading direction on compressive behavior of aluminum foam samples with regular pore architectures (with BCC and SC configuration) in addition to irregular pore distribution was studied using numerical and experimental procedures. Furthermore, to address the structure–property correlations, compressive deformation mechanisms and scaling analysis of mechanical properties were studied. 2. Materials and methods 2.1. Sample production To evaluate effect of spherical pore distribution and morphological parameters on compressive behavior of hollow sphere aluminum foams, position of pores are controlled using interconnections to generate regular pore distribution and the mechanical properties are compared with that of foams having irregular pore architecture. In order to fabricate aluminum foam samples, Al6063-T6 with the reported chemical composition of 97.5Al, 0.45–0.9 Mg, 0.2–0.6Si, 0.1Cr, 0.1Mn, 0.1Ti, 0.1Cu, and 0.35Fe (wt.%) was used as the matrix material. Space holder framework was prepared by positioning the hollow spheres through the interconnections to form internal pore architecture for the samples with regular pore architecture. In the case of irregular sample, space holder grains with the same material and grain size as regular samples were prepared without connections and regularity. The aluminum alloy used as the matrix material had the density of 2.7 g/cc and its melting point was 616–654 °C with the mechanical properties of 214 MPa for yield strength and 241 MPa for ultimate strength. It had the Young’s modulus of 68.9 GPa and elongation at break was 12%. An overall view of sample production procedure is shown in Fig. 1. EPS grains expand proportional to temperature between 110 and 150 °C in the presence of water and NaCl. Moreover, it is feasible to control pore size of the samples by setting ambient parameters during the expansion procedure of EPS, expanded polystyrene (EPS) grains with the initial diameter of 0.8 mm (Fig. 1(a)) were utilized to shape the internal pores. To this end, 6 g of EPS grains was mixed with saltwater and kept at 115 °C and 2.5 bar for 45 min to obtain spherical grains with 3.5 mm diameter (Fig. 1(b)). EPS grains extremely shrink by increasing temperature after final stages of expansion and then vaporize under temperatures of less than that for aluminum melting. Hence, in order to lead melted aluminum to form internal spherical pores with the same
size as the prepared EPS grains, the spherical EPS grains and plaster columns were coated with incombustible materials. Then, polymeric grains were kept at 80 °C for 20 min to dehydrate (which led to 0.2% decrease in the diameter of spheres) and tipped with the incombustible paste prepared by mixing 10 g glass wool powder, 19 g silicon, and 15 g calcium oxide. The EPS grains were trundled between two surfaces tripped with an incombustible paste until a layer with 0.5–1 mm thickness coated them. Then, the polymeric grains coated with an incombustible paste were heated up to 120 °C and a hard spherical coat with high heat resistance (1560 °C) was formed on the spherical EPS grains (Fig. 1(c)). In order to take shape interconnections between spherical grains for the regular samples, calcium sulfate was mixed with water to form a paste. Then, it was passed through a loophole with 1 mm diameter dried after 20 min. Plaster strings were cut into some slices with the length of 1 and 2 mm to form interconnections and cell walls between spherical pores. For the regular samples, three frameworks with different morphological characteristics (presented in Table 1) were made such that their EPS grain sizes and consequently pore sizes were similar (3.5 mm) for all and plaster connections perpendicular to the melt injection were unilaterally holding the coated EPS grains in space, as shown schematically in Fig. 2. For the sample with 50.0% relative density, the grains were located with SC configuration, while BCC configuration was considered for the samples with 38.4% and 27.3% volume fraction. Furthermore, 1 mm plaster connections were used between the grains for the samples with 50% and 38.4% volume fractions. The grains in the samples with 27.3% volume fraction were located using 1 mm length plasters. To produce irregular aluminum foam, the coated EPS grains were put into the casting lacuna without any connection and regularity. The frameworks were heated and kept at 380 °C for 20 min for the polymeric content of the spheres to vaporize. After vaporizing EPS content, the frameworks with incombustible hollow spheres with the plaster columns were heated up to 700 °C to facilitate melt penetration into the cells of frameworks and then they were placed into the rotary kiln for casting procedure. Centrifugal casting technique was utilized in order to lead melted aluminum into the cylindrical lacuna containing the framework with 100 mm diameter and 50 mm height (Fig. 1(d)). Mini Foundry machine with the molding diameter of 50–450 mm and height of 400 mm was employed (Fig. 1(e)) to perform casting procedure. The framework was set into the machine and casting was performed under 1200 rpm rotation speed to inject melted aluminum. In order to prepare aluminum melt, Al6063 bars were heated in the furnace
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Fig. 3. Model mesh and geometry representation of FE model corresponding to the samples with (a) 27.3%, (b) 38.4%, and (c) 50% volume fractions.
Fig. 4. Experimental compressive stress–strain curves of the samples in total strain domain with different volume fractions and loading direction. Stress strain curves for all the regular samples are followed by plateau region with strain hardening behavior up to the beginning of densification, while the irregular sample shows strain softening during plateau regime.
Ultrasonic vibration was utilized to clean the aluminum foam samples of the incombustible materials used to prepare framework. It peeled almost 98% of such materials of aluminum foam samples and the reminder was cleaned by water pressure in the regular samples. Finally, two cubic samples with 20 mm length corresponding to each regular framework and 30 ⁄ 20 ⁄ 20 mm for irregular foam were cut of the produced cylindrical foams and polished by a p2000 sandpaper to get prepared for compression test procedure. Then, the samples were weighted and their volume fractions were calculated. As it is shown in Table 1, Values of 50%, 38.4%, and 27.3% corresponding to the frameworks with SC configuration with 2 mm plaster column and BCC configurations having 2 and 1 mm plaster column were achieved, respectively. The specimens were named by combining their volume fractions with the loading direction relative to the melt injecting. For instance, 27.3H refers to the sample with 27.3% volume fraction which is horizontally loaded, while 27.3V refers to the sample with the same volume fraction which is loaded vertically (Fig. 2). Fig. 5. Detailed representation of elastic regime in the stress–strain curves of the experimental samples. Nonlinear behavior in elastic regime is attributed to narrow cell walls and imperfections formed during the casting procedure.
up to 850° for 25 min. Rotation in the centrifugal casting was kept on up to the time the mold temperature was risen to 600 °C. Then, solidification was initiated at the ambient temperature and finally the samples were taken out of the casting machine.
2.2. Mechanical compressive test Compressive test was implemented on the samples in order to assess their mechanical properties under compression. Standard ISO/DIS 1334 suggests a square cross section for the compressive testing of porous and cellular materials [22]. In order to prevent buckling during the test, a height to width ratio of less than 1.5
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Table 2 Compressive mechanical properties of the samples obtained by the experimental stress strain data. Sample label
Young’s modulus (MPa)
Compression strength (MPa)
Plateau stress (MPa)
Densification strain
Densification stress (MPa)
Energy absorption at densification (kJ/g)
27.3-H 27.3-V 38.4-H 38.4-V 50.0-H 50.0-V 35.0-IRR
194.7 151.8 430.3 218.3 690.4 686.7 657.4
7.5 5.4 14.6 13.2 33.5 20.8 19.3
19.6 14.7 33.9 23.7 54.4 46.4 32.7
0.553 0.557 0.393 0.346 0.263 0.328 –
30.4 23.0 50.9 34.8 72.7 66.0 –
10.2 7.8 12.5 7.3 12.5 14.1 –
was considered in designing the samples. Furthermore, rectangular jaws were utilized at the bottom and top and the specimens were aligned relative to loading direction to distribute force as uniform as possible. A preload was applied to the samples until the gaps between the sample and jaws disappeared. Then, compression test was initiated with the cross head speed of 2 mm/min corresponding to 0.0334 mm/s using Zwick Roell testing machine at room temperature and compressive force against displacement was plotted corresponding to each sample. In order to extract compressive stress versus strain, initial cross sectional area of 400 mm2 for all of the samples and initial height of 20 mm and 30 mm were defined for the regular and irregular foams, respectively. To study the effect of loading direction and role of unilateral interconnections on mechanical response for the regular samples, compression tests were conducted parallel and perpendicular to the interconnections (melt injection was performed perpendicular to the interconnection direction) for each volume fraction. In order to interpret mechanical properties for the samples, an idealization approach was performed on the resulted stress strain curves. To this, elastic modulus was considered as the slope of linear fit to data in the stress range of 30–70% of compressive strength. Yield stress was calculated by intersecting 0.002 offset line with the stress strain curve. Since the incomplete densification process, intersection of the lines on the most linear regions of densification and plateau regime used to obtain densification stress and strain. The average value of stress in stress strain curve from yield point up to the onset of densification was assigned to the plateau stress. Furthermore, to calculate specific absorbed energy (strain energy per unit of gram), the area under stress strain curve was divided by (density sample volume fraction) to address the capability of material in energy absorption for each sample. 2.3. Finite element simulation procedure In order to investigate stress distribution patterns, plastic deformation behavior of the samples, and the predictability of regular hollow sphere foams, finite element method was conducted on the CAD models of the structures. CAD model of unit cells were designed by the negative image of the frame work shown in Fig. 2 with the dimensions presented in Table 1. Then, the constitutive unit cell was patterned along three global coordinates such that cubic porous structures comprised of 3 3 3 unit cells were designed with 20 mm length for each sample. Then, the models were automatically meshed using 10-node second-order tetrahedral elements with the element size range of 900 lm (Fig. 3) with respect to the sensitivity analysis performed on the models. Moreover, an elastoplastic material model was considered with the elastic modulus of 68.9 Mpa, yield strength of 214 Mpa, and Poisson’s ratio of 0.33. Then, compressive load was applied to all the 3D models with the strain rate matching experimental tests. FE calculations were executed by ABAQUS explicit code and Mises stress, plastic deformation contours, and stress strain curves were extracted based on the initial dimensions of the specimens.
3. Results and discussion 3.1. Interpreting experimental stress strain curves Compressive stress strain results for all the samples and loading directions are presented in Fig. 4. Global trend of the curves for the specimens with regular pore architecture was similar to that of cellular materials with strain hardening behavior in plateau region. Softening behavior in plateau region was observed in stress strain curve of irregular sample, while in regular samples such a behavior was not observed. No fluctuation in stress strain curves is seen implying ductile deformation in plastic region. For regular samples, no material separation was occurred and densification happened at high strains as it can be seen in Fig. 4. Despite the ductile deformation procedure, for irregular sample, a considerable material separation was occurred due to non-uniform deformation of the structure and no densification can be observed in compression test. In order to investigate the elastic region more precisely, the elastic region was zoomed from the stress strain curves of Fig. 4 and illustrated in Fig. 5. Stress variations in elastic regime was found to be nonlinear and it is explained by the imperfections and defects during the casting procedure. The compressive mechanical properties of the samples is presented in Table 2. The data shows that the higher mechanical properties were found for the horizontal loading compared with vertical loading direction. 3.2. Mechanical properties versus relative density (scaling laws analysis) Many theoretical studies on cellular materials declared the exponential variations of mechanical properties versus relative density thereby mechanical properties such as elastic modulus, yield strength, and plateau region are characterized through scaling by volume fraction of porous structure [23]:
n X q ¼C qs Xs
ð1Þ
As it is stated by Ashby [24], in scaling laws analysis of Young’s modulus, the exponents (n) near 2 refer to the structures with more tendency to bending deformation, while the exponents close to 1 show the tendency to stretching deformation in compression loading. Hence, deformation modes, namely bending dominated or stretch dominated, can be evaluated by scaling laws analysis. 3.2.1. Elastic properties Normalized Young’s modulus of the samples was calculated and plotted against volume fraction in Fig. 6(a). In order to calculate constant values of scaling laws, power fitting was performed on n the data for the regular samples EEs ¼ C qq and exponential s
value of 2.177 with strengthening coefficient of 0.0452 was obtained (with the regression of 0.921) matching with that of cellular materials in which bending is dominated on their
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(a)
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compressive deformation. Moreover, horizontally loaded samples exhibited stiffer behavior compared with vertically loaded ones at the same volume fractions. Besides, elastic behavior of irregular sample was found to be improved compared to the regular samples. This implies the role of cell wall thickness in stiffness behavior of hollow sphere structures. 3.2.2. Compression strength Normalized compression strength versus volume fraction is illustrated in Fig. 6(b). Fitting to data was performed on the regular samples to obtain the scaling constants for yield stress n ry q . Similar to the elastic analysis, the exponential value ry;s ¼ C q s
(b)
of scaling laws is indicative of the deformation behavior of structure such that the n near to 1.5 implies bending dominated deformation and (n = 1) refers to the stretching dominated structures [24]. Curve fitting results showed the exponential value of 2.112 with the strengthening coefficient of 0.553 (with regression of 0.829) indicating the trend of regular structures to bending dominated deformation which is in line with the results obtained in elastic analysis. It can be seen that among regular structures, horizontally loaded samples exhibited more strength meeting the requirements of structural applications. Moreover, yield stress for the irregular sample was found to be improved compared with the regular samples. 3.2.3. Plateau stress Normalized Plateau stress is plotted versus volume fraction and demonstrated in Fig. 6(c). As well as elastic properties, scaling analysis of normalized plateau stress for regular samples n rpl q was performed and the results indicated strengthry;s ¼ C q s
ening coefficient of 0.760 and exponential value of 1.683 (with regression of 0.916). The theoretical correlations between deformation mode and scaling analysis of plateau stress is similar to what stated for yield stress (the n near to 1 and 1.5 refers to stretching and bending dominated deformations, respectively). Hence, scaling plateau stress confirms domination of bending on deformation mechanism of regular hollow sphere structures. Moreover, for regular configurations, horizontal loading conditions were found to increase plateau stress.
(c)
Fig. 6. Variation of (a) Young’s modulus, (b) yield stress, and (c) plateau stress versus volume fraction for scaling laws analysis. Scaling laws confirms the domination of bending on the overal deformation and illustrates the improved elastic properties is found for the horizontally loaded samples.
3.2.4. Energy absorption In order to highlight the effect of morphological parameters on energy absorption of hollow sphere aluminum foams, the specific strain energy (the energy absorbed per unit of mass) was plotted at different strains and the results are illustrated in Fig. 7. Normally, analysis of plateau stress is indicative of energy absorption capability of porous structures. Although, comparing the results of specific energy versus strain for different structures gives better insight into the role of morphological parameters effect on structural efficiency of hollow sphere aluminum foams in energy absorption. As it can be seen in Fig. 7, increasing volume fraction for the set of regular structures improved specific energy absorption. On the other hand, irregular sample (with 35% relative density) in comparison with the regular structure at the nearest relative density (38.4%) showed the higher specific energy absorption especially at lower strains (less than 0.46). By the way, at higher stages of deformation, material separation leads the irregular sample to lose its energy efficiency relative to regular one. 3.2.5. Densification strain Fig. 8 shows the densification strains versus the samples’ volume fraction. An almost linear trend can be observed which is well in line with many theoretical studies on densification behavior of cellular materials [25]. Chan [26] presented the more accurate
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Fig. 7. Strain energy absorption extracted from stress strain curves for different loading directions and relative densities in total strain domain. Irregular sample absorbs higher energy due to more bending deformation of its thicker walls than the regular samples.
Fig. 8. Variation of densification strain with relative density for the regular specimens.
theoretical relationship to describe densification behavior of metallic foams in the form of Eq. (2):
3 !
q q þ 0:4 eD ¼ C 1 1:4 qs qs
ð2Þ
where the constant coefficient of C varies for different materials and structures. With considering Eq. (2) for the experimental results, the constant value was found to be C = 0.84 for the regular samples. Bafti and Habibolahzadeh [3] illustrated the densification strain versus volume fraction for the closed cell hollow sphere structures with irregular pore architecture and characterized the densification behavior by Eq. (2) with C = 0.95. The results of Fig. 8 shows that the effect of loading direction on densification strain becomes more considerable as volume fraction increases. 3.3. Failure mechanism and plastic deformation procedure The deformation procedure of the regular samples under both vertical and horizontal compression is represented in Figs. 9, 10, and 11 for the samples with 27.3%, 38.4%, and 50%
relative densities. Internal narrow walls is observable in Fig. 10(f). The nonlinear behavior in elastic regime can be explained by these defects as previously stated. It can be deduced from deformation patterns that the set of samples with the same pore configuration and morphological characteristics followed similar deformation mechanisms and it indicates that controlling deformation mechanism is feasible by manipulating morphological parameters. In the samples with BCC pore configuration in horizontal loading, shear band of 45° was observed thanks to the side wall inclination as can be seen in Figs. 9(d) and 10(e). On the other hand, a layer by layer failure mechanism was seen for the SC configuration in horizontal loading (Fig. 11(d)). In the vertically loaded samples, a global barreling was found thanks to the cell wall buckling (Fig. 9(i), 10(i), and 11(i)). Deformation mechanism was found to be accompanied by cell wall bending which confirms the analysis of deformation by scaling the mechanical properties of the samples. The deformation procedure for the sample with irregular pore distribution is illustrated in Fig. 12. It was also well seen that crushing was accompanied by an overall barreling with the localizations (Fig. 12(c)) which caused material separation at higher strains. 3.4. Simulation results and validation Fig. 13 demonstrates Mises stress and plastic strain distribution contours of the deformed samples computed by finite element method for the structures with regular pore architecture. Shear band of 45° in the plastic strain contour of the samples with BCC pore configuration in horizontal loading (Fig. 13(h) and 13(l)) is confirmed by experimental deformation procedure shown in Figs. 9(d) and 10(d). A layer by layer failure owing to the bending of cell walls between hollow spheres was apparent in the regular sample with SC pore configuration in horizontal loading; i.e. 50.0-H (Fig. 13(d)) which is confirmed by experimental observations (Fig. 11(d)). Furthermore, barreling mode of deformation in experimental deformation mechanism of the samples with vertical loading is also observable in the simulation results. Numerical stress strain results for the samples with regular pore architecture are compared with the experimental stress strain curves in Fig. 14. Overestimations in the elastic region can be
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Sample
(I)
(II)
(III)
(IV)
(V)
0.57
0.94
0.17
0.18
0.30
(a)
(b)
(c)
(d)
(e)
0.55
0.12
0.18
0.29
0.35
(f)
(g)
(h)
(i)
(j)
27.3 -H
Strain
27.3 -V
Strain
Fig. 9. Deformation procedure and failure mechanism of horizontally and vertically loaded samples with 27.3% relative density; shearing band of 45° for the horizontally loaded and barreling deformation mode for vertically loaded samples is observed in deformation mechanisms.
Sample
(I)
(II)
(III)
(IV)
(V)
0.03
0.09
0.24
0.26
0.39
(a)
(b)
(c)
(d)
(e)
0.07
0.21
0.32
0.34
0.40
(f)
(g)
(h)
(i)
(j)
38.4-H
Strain
38.4 -V
Strain
Fig. 10. Deformation procedure and failure mechanism of horizontally and vertically loaded samples with 38.4% relative density; shearing band of 45° for horizontally loaded and barreling deformation mode for vertically loaded samples is observed in deformation mechanisms.
Sample
(I)
(II)
(III)
(IV)
(V)
0.06
0.11
0.14
0.17
0.20
(a)
(b)
(c)
(d)
(e)
0.13
0.25
0.38
0.43
0.50
(f)
(g)
(h)
(i)
(j)
50-H
Strain
50-V
Strain
Fig. 11. Deformation procedure and failure mechanism of horizontally and vertically loaded samples with 50.0% relative density; a layer by layer failure pattern for horizontally loaded sample and barreling deformation is observed for vertically loaded sample.
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Sample
(I)
(II)
(III)
(IV)
(V)
0.05
0.13
0.21
0.34
0.55
(a)
(b)
(c)
(d)
(e)
35.0-IRR
Strain
Fig. 12. Deformation mechanism of the irregular sample with 35.0% relative density; material separation, thanks to high bending deformation during the test, causes stress softening in plateau regime.
SC pore configuration Mises Stress Plastic Strain 50.0-V
(a)
BCC pore configuration Mises Stress Plastic Strain 50.0-H
(b)
(c)
38.4-V
(f)
(e)
(g)
27.3-V
(h) 27.3-H
(j)
(i)
(d) 38.4-H
(k)
38.4-V
50-H
(l) 23.7-H
Legends
Fig. 13. Mises stress and plastic strain distribution contours on the deformed shape of simulated regular sample models matching with the morphological characteriation described in sample production procedure (Section 2.1) for different volume fractions, loading directions and internal pore architectures.
explained by the imperfections (lack of material) which formed during the casting procedure. The numerical stress strain data were found to fit well to experimental data especially at higher strains. Hence, it can be inferred that the effect of internal imperfections becomes negligible at higher stages of deformation. In order to address the reliability of FE method in predicting plastic mechanical properties of described hollow sphere structures, the
relative errors between the numerical and experimental results are presented in Table 3. The results show that plateau stress is well predicted by the presented approach. Hence, FEM showed a good potential to predict the mechanical behavior of hollow sphere cellular materials with regular pore architecture and higher reliability was achieved in predicting plastic properties; e.g. plateau stress.
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(a)
Table 3 Validating mechanical properties predicted by FE method. The results show good predictability of plateau stress with the developed model. Sample label
27.3-H 27.3-V 38.4-H 38.4-V 50.0-H 50.0-V
(b)
(c)
Fig. 14. Validating stress strain curves resulted by FE simulation with the experimental data at (a) 27.3, (b) 38.4, and (c) 50.0 relative densities with different loading directions; Despite the imperfections formed in casting procedure, a good agreement is found between numerical and experimental results.
4. Conclusions In this work, effects of pore distribution and loading direction were investigated on the compressive behavior of hollow sphere aluminum foams for different volume fractions using an experimental procedure and numerical methods. To this end, the regular aluminum foam samples with controlled internal pore configurations of BCC and SC were produced by a centrifugal casting process and different volume fractions were prepared to study scaling laws on the specific mechanical properties for both vertical and
Compression strength (Mpa)
Plateau stress (MPa)
Energy absorption at densification (kJ/g)
Simulation
% Error
Simulation
% Error
Simulation
% Error
3.8 2.9 6.5 5.6 25.9 10.6
49.2 46.1 55.2 57.8 22.8 49.0
18.3 14.3 29.7 22.1 50.0 42.4
6.6 2.8 12.1 6.6 8.0 8.5
13.7 10.9 16.0 7.5 9.9 10.4
34.1 40.2 28.2 1.9 20.9 26.5
horizontal loading directions. The aluminum foam sample with irregular pore architecture was also fabricated using the same technology to be compared with the regular specimens. Experimental stress strain curves showed the same strain hardening behavior for the regular samples, while strain softening behavior in plateau region was observed for the irregular sample. Moreover, a nonlinear trend in the elastic regime due to imperfections during the casting procedure and formation of narrow cell walls was observed. Scaling laws analysis of Young’s modulus, yield strength, and plateau stress confirmed the high trend of hollow sphere structures to bending dominated deformation. Evaluating the resulted mechanical properties showed that an elastic property for irregular sample was higher than that of foams with regular architecture and it was attributed to the cell walls thickness. Although the elastic properties were found to be improved in irregular sample, the energy absorption ability was reduced in comparison with the regular samples since the non-uniform deformation and the material separation occurred at higher strains. Moreover, comparing mechanical response resulted by vertical and horizontal loadings indicates that vertical positioning of interconnections (horizontal loading) led the plateau to be enlarged and consequently energy absorption to be improved. Generally, horizontally loaded samples exhibited higher mechanical properties. Furthermore, densification analysis of all the samples versus relative density showed the constant value of C = 0.84 in Eq. (2). For horizontally loaded samples, experimental and numerical deformation mechanisms showed a layer by layer failure in the samples with SC pore configuration. Moreover, deformation mechanism of the horizontally loaded samples with BCC pore architecture was developed by shearing bands of 45°. Vertically loaded samples also deformed thanks to overall barreling of structure along with the cell walls buckling. The results of deformation mechanism showed that failure patterns can be controlled by manipulating the positioning state of pores. Furthermore, deformation mechanism for stochastic sample was accompanied by high localizations leading the non-uniform compression and finally material separations at high strains. Numerical results of the FE analysis were in good agreement on deformation procedure as well as plastic properties of regular samples with regular pore configurations. Plateau stress was well predicted by less than 12.1% relative error implying the high predictability of mechanical behavior of regular hollow sphere foams by FE method. References [1] J.H. Cadena, I. Alfonso, J.H. Ramírez, V. Rodríguez-Iglesias, I.A. Figueroa, C. Aguilar, Improvement of FEA estimations for compression behavior of Mg foams based on experimental observations, Comput. Mater. Sci. 91 (2014) 359–363. [2] J. Banhart, Manufacture, characterisation and application of cellular metals and metal foams, Prog. Mater Sci. 46 (2001) 559–632.
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