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Compressive properties and energy absorption of aluminum foams with modified cellular geometry
Journal of Materials Processing Technology 214 (2014) 571–577
Contents lists available at ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Compressive properties and energy absorption of aluminum foams with modified cellular geometry P. Pinto ∗ , N. Peixinho, F. Silva, D. Soares CT2M – Centre for Mechanical and Materials Technologies, Minho University, Azurém, 4800-058 Guimarães, Portugal
a r t i c l e
i n f o
Article history: Received 2 September 2013 Received in revised form 7 November 2013 Accepted 8 November 2013 Available online 17 November 2013 Keywords: Aluminum foam Prototype Compressive properties Energy absorption
a b s t r a c t This study presents experimental results on the behavior of aluminum alloy metal foams with controlled pore morphology in compression. Two types of metal foams were analyzed, having uniform cell structure and with a dual-size cell arrangement seeking optimized mechanical properties. The structures were manufactured by lost-wax casting using 3D printed components for internal structure definition. Results for stiffness and energy absorption were obtained and compared on weight efficiency basis. The results are indicative of higher efficiency of the dual-size structures that may be considered for use in components subjected to impact or compression loading. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Metallic foams emerge as a new range of materials with great potential due to its excellent strength-density ratio which presents advantages for the development of components for the transportation industry, such as the automobile sector. In these industries, high energy absorption capacity combined with low density are interesting properties for use in stiffness related parts and passive safety structures (Banhart, 2001; Gibson and Ashby, 1988). Reducing vehicle weight is a major factor in the transport industry since it allows reducing fuel consumption. However, the decrease in vehicle weight cannot reduce passenger safety meaning that the materials used in the manufacturing cannot compromise stiffness and strength. Thus, it is important to correctly determine the behavior and properties of new materials to be used in vehicles (Song et al., 2005). Due to its low density, high strength and excellent energy absorption in compression, the use of metal foams in impactrelated parts has been increasingly considered in order to increase passive safety. Due to this excellent performance, there is a need for continuous improvement and to refine their manufacturing processes and production, in addition to the need to characterize mechanically (Banhart and Baumeister, 1998, 2000).
∗ Corresponding author at: Universidade do Minho, Centre for Mechanical and Materials Technologies (CT2M), Campus Azurém, P-4800-058 Guimarães, Portugal. Tel.: +351 253510732. E-mail address: [email protected] (P. Pinto). 0924-0136/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmatprotec.2013.11.011
The mechanical behavior of metal foams depends on the structure of cells, density and properties of the base material they are made. The efficiency obtained in the use of metallic foams in structural applications requires a detailed characterization of its deformation behavior for different loads and different geometries. The size and shape of the cells or pores determines their properties, namely their behavior depends on how the solid is distributed in the porous structure (Olurin et al., 2000). Advances in material and geometry characterization are required in order to develop material models suitable for reliable and efficient numerical simulation of the mechanical behavior of foams (Zaiser et al., 2013; Saadatfar et al., 2012). Although the relative density is the most dominant factor in determining the behavior and strength of a metal foam, other parameters such as distribution and configuration of the cells can also have great influence on the mechanical behavior. In a numerical simulation study Kou et al. (2008) proposed two types of open-cell foam structures using uniform and dual-size base cell configurations (Fig. 1). Uniform cell metal foams have a spherical shape and are closely compact. It is assumed that the cellular structure has a face-centered cubic arrangement. Dual-size foams have fillers forming a secondary link that is disposed in voids existing in uniform foam (Fig. 1). The distance between two adjacent centers of large fillers is a, the radius of large fillers and secondary fillers are R and r, respectively (Kou et al., 2008). According to the authors, the behavior of foams with dual-size structures is improved regarding uniform structures. It was found in their numerical study that the yield strength of a foam cell structure with dual-size is considerably higher than in a foam with uniform cell structure, for an equivalent density.
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P. Pinto et al. / Journal of Materials Processing Technology 214 (2014) 571–577 Table 2 Composition of the DC 500 resin (wt.%) (according to the manufacturer).
wt.%
Multi-functional acrylic monomers
Crystalline silica cristobalite
Radical photoinitiator
70–90
10–30
0.5–3
2.2. Experimental methods
Fig. 1. Compacted structures of fillers in open-cell arrangements: (A) uniform-size structure; (B) dual-size structure (Kou et al., 2008).
Fig. 2. CAD, resin and metal specimens obtained: (a) US cellular structure and (b) DS cellular structure.
In this work, experimental results on the compression behavior of uniform and dual-size metal foams are presented and discussed. The structures were manufactured by lost-wax casting using 3D printed components for structure definition (Fig. 2). The experimental protocol for manufacturing and testing is presented. Compression tests were performed on test samples. Results for stiffness and energy absorption were obtained and compared on weight efficiency basis. 2. Materials and experimental methods 2.1. Materials In this study, a commercial AlSi12 alloy (A413.1) was used for the manufacturing of cellular structures. This alloy was selected based on previous experience in manufacturing structures with very thin walls. The composition of the alloy is presented in Table 1. For the manufacturing process a preliminary 3D prototyping stage is used. The resin used in the rapid prototype (RP) machine was a photosensitive resin, DC 500 [DWS S.r.l., Zané, Italy], that is specifically designed to allow the production of high-definition, detailed parts and smooth surfaces. The nominal chemical composition of the resin is presented in Table 2. A commercial gypsum [Ranson & Randolph, Ultra-Vest, Maumee, OH, USA] was used in the lost wax casting as investing material.
Table 1 Nominal chemical composition of A413.1 aluminum alloy (wt.%).
wt.%
Si
Cu
Fe
Mg
Mn
Zn
Ni
Al
11.0–13.0
1.0
1.0
0.10
0.35
0.40
0.50
Balance
Based on the work by Kou et al. (2008), the idealized structures of open-cell metallic foams were designed using CAD software (SolidWorks). Cylindrical models with 40 mm height and 16 mm diameter were selected for the quasi-static compression tests (Fig. 3). Two types of structures were studied: one based on a single spherical open-cell with 2 mm radius (R) repeated in X, Y and Z directions, closely compacted, with fcc-like arrangement – uniformsize (US); and other based on two sized spherical open-cells, with 2 mm (R) and 0.85 mm (r) radius (r = 0.425 R) and organized in the same manner as for the uniform size – dual-size (DS) (Fig. 1). Both structures (Fig. 3c and f) were obtained by a Boolean subtraction operation of the solid cylinder (Fig. 3b) with the spheres bodies (Fig. 3a and d). The obtained models in CAD software were exported to a stereolithography (STL) machine (Digital Wax 008, DWS S.r.l., Zané, Italy). Standard build parameters were used and selected as follows: 0.03 mm for layer thickness; 0.04 mm for tool compensation; and 0.06 mm for hatching space. Eight resin samples were prototyped: four with uniform-size (US) cellular structure; and four with dual-size (DS) cellular structure. After each prototyping cycle, the resin models were cured for 30 min in an ultraviolet curing unit (Digital Wax Model S, DWS S.r.l., Zané, Italy) to final solidification. The investment flask was prepared following the manufacturer instructions (Ranson & Randolph, Ultra-Vest, Maumee, OH, USA). The procedure is presented in Fig. 4a–d. The metallic specimens were obtained by lost wax casting using a vacuum/pressure casting machine (Indutherm VC 400, Walzbachtal/Wössingen, Germany). The AlSi alloy was melt in a graphite crucible at 635 ◦ C on the top chamber under argon atmosphere (p1 = patm ) while the flask was placed in the bottom chamber under vacuum (p2 = 0.1 mbar) at 350 ◦ C (Fig. 5a). After the alloy’s melting, an over pressure of 0.75 bar (p3 ) was added to the top chamber followed by the pouring of the metal at 635 ◦ C (p4 = 0.1 mbar) (Fig. 5b) into the mold cavity, thus recreating the original wax tree with a metal replica (Fig. 5c). After casting, when the mold reached 500 ◦ C, it was inserted into a water container at room temperature that caused the disintegration of the investment. The residual investment in the metal tree was removed in an ultrasonic water cleaner for 10 min. Finally, the sprues were cut off and the metal in excess was trimmed using SiC-paper in a Double Desk Polishing Machine DC Motor. In order to analyze the geometry changes (% of shrinkage) occurring in the manufacturing steps of the two structures (US and DS), starting from the CAD models (Fig. 6a), to resin models (Fig. 6b) and finally getting the casted structures (Fig. 6c), a dimensional inspections was performed to the cross sectioned structures. For that purpose an optical microscope (Lampert SM 04, Germany) with a coupled digital camera (Canon Ixus I30, Japan) was used to obtain micrographs of the specimens. The images were analyzed using image analysis software (Image J) and the measurement data resulted from the average of three measurements. In order to analyze the foam’s mechanical properties the specimens were submitted to uniaxial compressive tests. The displacement rate was 10 mm/min and the tests stopped when the displacement reached 26 mm. Tests were performed in a universal testing machine (Instrom 8874, MA, USA) at room temperature and
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Fig. 3. Modeling steps to obtain the uniform size structure (c) and dual size structure (f): Boolean subtraction operation between spheres bodys (a), (d) and the solid cylinder (b).
Fig. 4. Investment flask preparation: (a) wax tree; (b) investing the metal flask; (c) investment after a stage of 2 h to allow for solification; (d) flask loaded into a preheated oven for wax extraction and cure of the investment mold.
ambient air. From the load–displacement acquired data, the maximum initial load (Loadmáx ), stiffness (Sf ) and the absorbed energy at 5 and 15 mm of displacement (E5 and E15 , respectively), were obtained. 3. Results and discussion
holes of the US and DS structures with larger diameters (d2) displayed shrinkage percentages in the same range, ∼9% in CAD–resin transition. Regarding the resin model–metal model transition, the hole expansion was ∼4.6% for the US structure and ∼2.9% for the DS structure. The differences displayed in resin–metal transition may be related to the geometric complexity and to the prototyping
3.1. Geometrical analysis Table 3 presents measurements for the diameters d1 and d2 (Fig. 6) and their variation percentage for the various productions steps, i.e. from the CAD model to resin model and from resin model to the metal sample. Results showed that the holes of the US and DS structures with smaller diameters (d1) displayed shrinkage percentages in the range of ∼5.7% and ∼11.7%, respectively, in CAD–resin transition. During the casting (resin–metal transition) the holes from the metal samples undergo an expansion percentage in the range of ∼9.1% for the US structure and in the range of ∼14.5% for the DS structure. On the other hand, the
Table 3 Measurements for the diameters d1, d2 and their variation percentage for the various productions steps.
CAD model Resin model Metal model CAD–resin diameter variation Resin–metal diameter variation CAD–metal diameter variation
Uniform size (US)
Dual size (DS)
d1
d2
d1
d2
1.74 mm 1.64 mm 1.79 mm −5.7% +9.1% +2.9%
4.00 mm 3.65 mm 3.81 mm −8.9% +4.6% −4.7%
1.34 1.18 1.35 −11.7% +14.5% +1.0%
4.00 3.64 3.74 −9.1% +2.9% −6.5%
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Fig. 5. Shematic of lost wax casting procedure used to obtain the metallic specimens, with (a) the metal melting phase, (b) the poured metal and (c) the obtained casted piece.
Fig. 6. Production steps of the metallic structures (US and DS): (a) started with the CAD model design; (b) was followed by the production of the resin model in a stereolitography laser machine; (c) and ended with the casted sample.
P. Pinto et al. / Journal of Materials Processing Technology 214 (2014) 571–577
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comparison. The two CAD models with different structures: uniform size (US) (Fig. 3c) and dual size (DS) (Fig. 3f), were produced having the theoretical masses of 2.06 and 1.55 g, respectively. Concerning the casted samples, the average mass of US structure was 3.15 g which accounts for an increase of over 53% relative to the designed CAD model. On the other hand, the DS samples exhibited an average mass of 3.02 g, yielding an approximately 95% increase in regard to its designed CAD model. These results reflected a technical limitation of the rapid prototyping machine for producing models with structures of increased complexity. Nevertheless, it is worth to mention that both structures had mass reductions of ∼86% in comparison with the solid cylindrical specimen. Fig. 7. Compressive tests: (a) initial stage and (b) final stage.
3.2. Compression tests
Fig. 8. Geometry changes occurring in the manufacturing steps (CAD–resin–metal) of the smaller holes [d1 variation – (a)] and larger holes [d2 variation (b)] in the cellular structure.
machine accuracy. It is worth to mention that the resin model undergoes two solidification processes: first, at the time of the construction of the model in the LASER rapid prototyping machine; and second, at the curing stage in the ultraviolet curing unit. So, the data showed that the prototyping stage leads to a sample oversizing and the solidification process (metal shrinkage), during the casting, leads to a hole expansion (Fig. 7). From the data of Table 3 it was possible to illustrate the geometrical behavior (Fig. 8) of the smaller holes [d1 variation – (a)] and larger holes [d2 variation (b)] in both structures. Regarding CAD model–metal model transition, holes with smaller diameter (d1) displayed an expansion percentage in the range of ∼2.9% for the US structure and ∼1.0% for the DS structure. However, holes with larger diameters displayed shrinkage percentages in the range of 4.7% for the US structures and 6.5% for the DS structure. In this study, a reference solid cylindrical specimen (˚ = 16 mm; h = 40 mm) (Fig. 3b) made out of a commercial aluminum alloy (A413.1) and with a mass of 21.7 g was used for mass
Compression tests results are presented in Fig. 9 for all metallic specimens of uniform-size (Fig. 9A) and dual-size structures (Fig. 9B). From the experimental results it was possible to extract: the maximum initial load (Pmáx ) in the first inflection point of the loading curve; the stiffness (Sf ), by the slope of the curve in elastic regime; and the absorbed energy at 5 and 15 mm of displacement obtained by calculating the area below the curve. These values and their specific values (per gram) are presented in Table 4. Force–displacement results were converted to stress–strain and are presented in Fig. 10 while Young’s modulus was calculated for the initial linear slope of stress–strain curves and presented in Table 4. As shown in Figs. 9 and 10, the compressive behavior of uniform size structure is similar to the dual size until the first layer collapses. At this stage dual size structure withstood a significantly higher initial load. From this stage, as the structure densification is unique for each sample, the compressive behavior is also different. This densification behavior is largely related to the extensive fracture that occurs within the sample’s geometry. Results show that the specific Pmáx (N/g) withstood by uniform size (US) structure was approximately 221 N/g whereas that withstood by the dual size (DS) structure was approximately 404 N/g, i.e. the resistance exhibited by the dual size structure was ∼83% higher than that of the uniform size. In what concerns specific stiffness, the dual size structure obtained an average value 29% higher than the uniform size structure. These values are consistent with values from numerical simulation presented in the study proposing the dual size structure (Kou et al., 2008). Stiffness expressed as Young’s modulus is approximately 14% higher for the dual size structure. This improvement in stiffness is related to the introduction of secondary cells within the structure (Kou et al., 2008).
Fig. 9. Compression tests results: (A) uniform-size structure and (B) dual-size structure.
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P. Pinto et al. / Journal of Materials Processing Technology 214 (2014) 571–577
Table 4 Values from mechanical behavior in the compression tests. Mass (g)
Young’s modulus (MPa)
US 1 US 2 US 3 US 4
3.23 3.27 3.02 3.07
230.2 192.8 158.7 199.5
744.9 662.3 660.4 716.1
230.6 202.5 218.7 233.2
10.7E+05 8.99E+05 7.20E+05 9.43E+05
3.31E+05 2.75E+05 2.38E+05 3.07E+05
1.97 1.22 1.65 1.67
0.61 0.37 0.55 0.54
5.94 4.32 7.07 6.05
1.84 1.32 2.34 1.97
Average Standard deviation
3.15 0.12
195.3 29.3
695.9 41.6
221.3 14.0
9.09E+05 1.46E+05
2.88E+05 0.40E+05
1.63 0.31
0.52 0.10
5.85 1.14
1.87 0.42
DS 1 DS 2 DS 3 DS 4
3.32 2.83 2.91 3.00
336.5 177.7 199.5 202.8
1454.9 1165.8 1165.2 1097.5
438.2 411.9 400.4 365.8
16.8E+05 8.71E+05 9.93E+05 9.89E+05
5.06E+05 3.08E+05 3.41E+05 3.30E+05
4.09 3.07 3.26 2.86
1.23 1.08 1.12 0.95
7.45 9.10 4.96 6.96
2.24 3.22 1.70 2.32
Average Standard deviation
3.02 0.21
229.1 72.4
1220.9 159.3
404.1 30.0
11.3E+05 3.71E+05
3.71E+05 0.91E+05
3.32 0.54
1.10 0.12
7.12 1.70
2.37 0.63
+103.7%
+111.5%
+21.7%
+26.7%
Variation
+14.7
Pmáx (N)
+75.4%
Specific Pmáx (N/g)
Stiffness (N/m)
Specimen
+82.6%
+24.3%
Specific stiffness (N/(m g))
+28.8%
Energy 5 (J)
Specific energy 5 (J/g)
Energy 15 (J)
Specific energy 15 (J/g)
Fig. 10. Compression stress strain results: (A) uniform-size structure and (B) dual-size structure.
Fig. 11. Compressive strength plotted against density for currently available metal foams (Ashby et al., 2000) and current results for uniform size ( cellular structures.
) and dual-size (
)
P. Pinto et al. / Journal of Materials Processing Technology 214 (2014) 571–577
Regarding specific absorbed energy registered until 5 mm of displacement, the dual size structure displayed an average absorbed energy significantly higher than the uniform size structure – around 112%. However, for a higher displacement (15 mm) the specific absorbed energy of the dual size structure was approximately 27% higher than that of the uniform size structure. This is attributed to the much higher initial load peak that contributes to the energy calculation in the first 5 mm of displacement. Based on the experimental data, one can conclude that the dual size structure exhibited general enhanced mechanical behavior over the uniform size structure. These improvements are highlighted in the maximum initial load supported (+83%) and in the absorbed energy until 5 mm of displacement (+112%). However, more realistic values of stiffness (29%) and energy absorption at 15 mm (27%) are to be considered for a validation of the modified geometry for mechanical applications. This analysis is based on the greater contribution of the maximum load and associated energy absorbed in the initial phase of collapse behavior. The improved results for stiffness and strength of dual size open-cell structures confirm previous numerical simulation results (Kou et al., 2008). The rational for such improved mechanical behavior was described by the authors as associated to a change of major plastic deformation concentration from incline struts that connect open spherical volumes (in uniform size structures) to dispersion of deformation between major struts and small struts that are present in the dual size structures. In the optimal condition of dual size open-cell structures, both major incline struts and small struts almost equally share the deformation (Kou et al., 2008). The introduction of secondary cells can therefore be used as an alternative to increasing density in order to improve mechanical properties if these secondary cells have a suitable size. Such appropriate design can be chosen with numerical simulation studies (Kou et al., 2008) and manufactured with a suitable process as described in the present study with a corresponding validation of mechanical properties. From the experimental stress–strain results and mass measurements of the tested structures, average compressive strength and density were calculated and presented in Fig. 11, for comparison with existing literature results on periodic and stochastic metal foams. The analysis of Fig. 11 highlights the possibilities with the method presented for manufacturing metal foams and, in particular, the scope of improvement possible with the dual-size structures. 4. Conclusions In this research work two types of metal foams were manufactured and analyzed, having different cell structures: uniform
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cell structure and dual-size cell arrangement. The structures were manufactured by lost-wax casting using 3D printed components for internal structure definition. Results for stiffness and energy absorption were obtained and compared on weight efficiency basis. The analysis of manufacturing parameters and geometry variation indicated that, the final specimen displayed a slightly higher value [1.0–2.9%] for smaller diameters (d1) and displayed a lower value [4.7–6.5%] for larger diameters (d2) than CAD model. This analysis is relevant for the definition of appropriate tolerances and CAD dimensions for part manufacturing. The compression tests showed that the specific Pmáx (N/g) withstood by the dual-size (DS) structure was approximately ∼83% higher than that of the uniform size, while stiffness had an improvement of 29%. Specific absorbed energy registered for 5 mm of displacement presented a significant improvement (around 112%). For a higher displacement (15 mm) the specific absorbed energy of the dual size structure was approximately 27% higher than that of the uniform size structure. These results are indicative of a higher efficiency of the dual-size structures that may be therefore considered for use in components subjected to impact or compression loading, both in stiffness and crash-energy absorption requirements. Acknowledgments The authors are grateful to the Portuguese Foundation for Science and Technology (FCT) who financially supported this work, through the project PTDC/EME-PME/115668/2009. References Ashby, M., Evans, A., Fleck, N., Gibson, L., Hutchinson, J., Wadley, H., 2000. Metal Foams: A Design Guide. Scripta Materialia, Butterworth-Heinemann. Banhart, J., Baumeister, J., 1998. Deformation characteristics of metal foams. Journal of Materials Science 33, 1431–1440. Banhart, J., 2000. Metallic foams: challenges and opportunities. In: Zitha, P., Banhart, J., Verbist, G. (Eds.), Proceedings Eurofoam 2000. , pp. 13–20. Banhart, J., 2001. Manufacture, characterisation and application of cellular metals and metal foams. Progress in Materials Science 46 (6), 559–632. Gibson, L., Ashby, M., 1988. Cellular Solids: Structure and Properties. Pergamon, Oxford. Kou, D.P., Li, J.R., Yua, J.L., Cheng, H.F., 2008. Mechanical behavior of open-cell metallic foams with dual-size cellular structure. Scripta Materialia 59, 483–486. Olurin, O., Fleck, N., Ashby, M., 2000. Deformation and fracture of aluminium foams. Materials Science and Engineering A 291, 136–146. Saadatfar, M., Mukherjee, M., Madadi, M., Schroder-Turk, G., Garcia-Moreno, F., Schaller, F., Hutzler, S., Sheppard, A., Banhart, J., Ramamurty, U., 2012. Structure and deformation correlation of closed-cell aluminium foam subject to uniaxial compression. Acta Materialia 60, 3604–3615. Song, H., Fan, Z., Yu, G., Wang, Q., Tobota, A., 2005. Partition energy absorption of axially crushed aluminum foam-filled hat sections. International Journal of Solids and Structures 42 (9–10), 2575–2600. Zaiser, M., Mil, F., Konstantinidis, A., Aifantis, K., 2013. Strain localization and strain propagation in collapsible solid foams. Materials Science and Engineering A 567, 38–45.
Contents lists available at ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Compressive properties and energy absorption of aluminum foams with modified cellular geometry P. Pinto ∗ , N. Peixinho, F. Silva, D. Soares CT2M – Centre for Mechanical and Materials Technologies, Minho University, Azurém, 4800-058 Guimarães, Portugal
a r t i c l e
i n f o
Article history: Received 2 September 2013 Received in revised form 7 November 2013 Accepted 8 November 2013 Available online 17 November 2013 Keywords: Aluminum foam Prototype Compressive properties Energy absorption
a b s t r a c t This study presents experimental results on the behavior of aluminum alloy metal foams with controlled pore morphology in compression. Two types of metal foams were analyzed, having uniform cell structure and with a dual-size cell arrangement seeking optimized mechanical properties. The structures were manufactured by lost-wax casting using 3D printed components for internal structure definition. Results for stiffness and energy absorption were obtained and compared on weight efficiency basis. The results are indicative of higher efficiency of the dual-size structures that may be considered for use in components subjected to impact or compression loading. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Metallic foams emerge as a new range of materials with great potential due to its excellent strength-density ratio which presents advantages for the development of components for the transportation industry, such as the automobile sector. In these industries, high energy absorption capacity combined with low density are interesting properties for use in stiffness related parts and passive safety structures (Banhart, 2001; Gibson and Ashby, 1988). Reducing vehicle weight is a major factor in the transport industry since it allows reducing fuel consumption. However, the decrease in vehicle weight cannot reduce passenger safety meaning that the materials used in the manufacturing cannot compromise stiffness and strength. Thus, it is important to correctly determine the behavior and properties of new materials to be used in vehicles (Song et al., 2005). Due to its low density, high strength and excellent energy absorption in compression, the use of metal foams in impactrelated parts has been increasingly considered in order to increase passive safety. Due to this excellent performance, there is a need for continuous improvement and to refine their manufacturing processes and production, in addition to the need to characterize mechanically (Banhart and Baumeister, 1998, 2000).
∗ Corresponding author at: Universidade do Minho, Centre for Mechanical and Materials Technologies (CT2M), Campus Azurém, P-4800-058 Guimarães, Portugal. Tel.: +351 253510732. E-mail address: [email protected] (P. Pinto). 0924-0136/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmatprotec.2013.11.011
The mechanical behavior of metal foams depends on the structure of cells, density and properties of the base material they are made. The efficiency obtained in the use of metallic foams in structural applications requires a detailed characterization of its deformation behavior for different loads and different geometries. The size and shape of the cells or pores determines their properties, namely their behavior depends on how the solid is distributed in the porous structure (Olurin et al., 2000). Advances in material and geometry characterization are required in order to develop material models suitable for reliable and efficient numerical simulation of the mechanical behavior of foams (Zaiser et al., 2013; Saadatfar et al., 2012). Although the relative density is the most dominant factor in determining the behavior and strength of a metal foam, other parameters such as distribution and configuration of the cells can also have great influence on the mechanical behavior. In a numerical simulation study Kou et al. (2008) proposed two types of open-cell foam structures using uniform and dual-size base cell configurations (Fig. 1). Uniform cell metal foams have a spherical shape and are closely compact. It is assumed that the cellular structure has a face-centered cubic arrangement. Dual-size foams have fillers forming a secondary link that is disposed in voids existing in uniform foam (Fig. 1). The distance between two adjacent centers of large fillers is a, the radius of large fillers and secondary fillers are R and r, respectively (Kou et al., 2008). According to the authors, the behavior of foams with dual-size structures is improved regarding uniform structures. It was found in their numerical study that the yield strength of a foam cell structure with dual-size is considerably higher than in a foam with uniform cell structure, for an equivalent density.
572
P. Pinto et al. / Journal of Materials Processing Technology 214 (2014) 571–577 Table 2 Composition of the DC 500 resin (wt.%) (according to the manufacturer).
wt.%
Multi-functional acrylic monomers
Crystalline silica cristobalite
Radical photoinitiator
70–90
10–30
0.5–3
2.2. Experimental methods
Fig. 1. Compacted structures of fillers in open-cell arrangements: (A) uniform-size structure; (B) dual-size structure (Kou et al., 2008).
Fig. 2. CAD, resin and metal specimens obtained: (a) US cellular structure and (b) DS cellular structure.
In this work, experimental results on the compression behavior of uniform and dual-size metal foams are presented and discussed. The structures were manufactured by lost-wax casting using 3D printed components for structure definition (Fig. 2). The experimental protocol for manufacturing and testing is presented. Compression tests were performed on test samples. Results for stiffness and energy absorption were obtained and compared on weight efficiency basis. 2. Materials and experimental methods 2.1. Materials In this study, a commercial AlSi12 alloy (A413.1) was used for the manufacturing of cellular structures. This alloy was selected based on previous experience in manufacturing structures with very thin walls. The composition of the alloy is presented in Table 1. For the manufacturing process a preliminary 3D prototyping stage is used. The resin used in the rapid prototype (RP) machine was a photosensitive resin, DC 500 [DWS S.r.l., Zané, Italy], that is specifically designed to allow the production of high-definition, detailed parts and smooth surfaces. The nominal chemical composition of the resin is presented in Table 2. A commercial gypsum [Ranson & Randolph, Ultra-Vest, Maumee, OH, USA] was used in the lost wax casting as investing material.
Table 1 Nominal chemical composition of A413.1 aluminum alloy (wt.%).
wt.%
Si
Cu
Fe
Mg
Mn
Zn
Ni
Al
11.0–13.0
1.0
1.0
0.10
0.35
0.40
0.50
Balance
Based on the work by Kou et al. (2008), the idealized structures of open-cell metallic foams were designed using CAD software (SolidWorks). Cylindrical models with 40 mm height and 16 mm diameter were selected for the quasi-static compression tests (Fig. 3). Two types of structures were studied: one based on a single spherical open-cell with 2 mm radius (R) repeated in X, Y and Z directions, closely compacted, with fcc-like arrangement – uniformsize (US); and other based on two sized spherical open-cells, with 2 mm (R) and 0.85 mm (r) radius (r = 0.425 R) and organized in the same manner as for the uniform size – dual-size (DS) (Fig. 1). Both structures (Fig. 3c and f) were obtained by a Boolean subtraction operation of the solid cylinder (Fig. 3b) with the spheres bodies (Fig. 3a and d). The obtained models in CAD software were exported to a stereolithography (STL) machine (Digital Wax 008, DWS S.r.l., Zané, Italy). Standard build parameters were used and selected as follows: 0.03 mm for layer thickness; 0.04 mm for tool compensation; and 0.06 mm for hatching space. Eight resin samples were prototyped: four with uniform-size (US) cellular structure; and four with dual-size (DS) cellular structure. After each prototyping cycle, the resin models were cured for 30 min in an ultraviolet curing unit (Digital Wax Model S, DWS S.r.l., Zané, Italy) to final solidification. The investment flask was prepared following the manufacturer instructions (Ranson & Randolph, Ultra-Vest, Maumee, OH, USA). The procedure is presented in Fig. 4a–d. The metallic specimens were obtained by lost wax casting using a vacuum/pressure casting machine (Indutherm VC 400, Walzbachtal/Wössingen, Germany). The AlSi alloy was melt in a graphite crucible at 635 ◦ C on the top chamber under argon atmosphere (p1 = patm ) while the flask was placed in the bottom chamber under vacuum (p2 = 0.1 mbar) at 350 ◦ C (Fig. 5a). After the alloy’s melting, an over pressure of 0.75 bar (p3 ) was added to the top chamber followed by the pouring of the metal at 635 ◦ C (p4 = 0.1 mbar) (Fig. 5b) into the mold cavity, thus recreating the original wax tree with a metal replica (Fig. 5c). After casting, when the mold reached 500 ◦ C, it was inserted into a water container at room temperature that caused the disintegration of the investment. The residual investment in the metal tree was removed in an ultrasonic water cleaner for 10 min. Finally, the sprues were cut off and the metal in excess was trimmed using SiC-paper in a Double Desk Polishing Machine DC Motor. In order to analyze the geometry changes (% of shrinkage) occurring in the manufacturing steps of the two structures (US and DS), starting from the CAD models (Fig. 6a), to resin models (Fig. 6b) and finally getting the casted structures (Fig. 6c), a dimensional inspections was performed to the cross sectioned structures. For that purpose an optical microscope (Lampert SM 04, Germany) with a coupled digital camera (Canon Ixus I30, Japan) was used to obtain micrographs of the specimens. The images were analyzed using image analysis software (Image J) and the measurement data resulted from the average of three measurements. In order to analyze the foam’s mechanical properties the specimens were submitted to uniaxial compressive tests. The displacement rate was 10 mm/min and the tests stopped when the displacement reached 26 mm. Tests were performed in a universal testing machine (Instrom 8874, MA, USA) at room temperature and
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Fig. 3. Modeling steps to obtain the uniform size structure (c) and dual size structure (f): Boolean subtraction operation between spheres bodys (a), (d) and the solid cylinder (b).
Fig. 4. Investment flask preparation: (a) wax tree; (b) investing the metal flask; (c) investment after a stage of 2 h to allow for solification; (d) flask loaded into a preheated oven for wax extraction and cure of the investment mold.
ambient air. From the load–displacement acquired data, the maximum initial load (Loadmáx ), stiffness (Sf ) and the absorbed energy at 5 and 15 mm of displacement (E5 and E15 , respectively), were obtained. 3. Results and discussion
holes of the US and DS structures with larger diameters (d2) displayed shrinkage percentages in the same range, ∼9% in CAD–resin transition. Regarding the resin model–metal model transition, the hole expansion was ∼4.6% for the US structure and ∼2.9% for the DS structure. The differences displayed in resin–metal transition may be related to the geometric complexity and to the prototyping
3.1. Geometrical analysis Table 3 presents measurements for the diameters d1 and d2 (Fig. 6) and their variation percentage for the various productions steps, i.e. from the CAD model to resin model and from resin model to the metal sample. Results showed that the holes of the US and DS structures with smaller diameters (d1) displayed shrinkage percentages in the range of ∼5.7% and ∼11.7%, respectively, in CAD–resin transition. During the casting (resin–metal transition) the holes from the metal samples undergo an expansion percentage in the range of ∼9.1% for the US structure and in the range of ∼14.5% for the DS structure. On the other hand, the
Table 3 Measurements for the diameters d1, d2 and their variation percentage for the various productions steps.
CAD model Resin model Metal model CAD–resin diameter variation Resin–metal diameter variation CAD–metal diameter variation
Uniform size (US)
Dual size (DS)
d1
d2
d1
d2
1.74 mm 1.64 mm 1.79 mm −5.7% +9.1% +2.9%
4.00 mm 3.65 mm 3.81 mm −8.9% +4.6% −4.7%
1.34 1.18 1.35 −11.7% +14.5% +1.0%
4.00 3.64 3.74 −9.1% +2.9% −6.5%
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Fig. 5. Shematic of lost wax casting procedure used to obtain the metallic specimens, with (a) the metal melting phase, (b) the poured metal and (c) the obtained casted piece.
Fig. 6. Production steps of the metallic structures (US and DS): (a) started with the CAD model design; (b) was followed by the production of the resin model in a stereolitography laser machine; (c) and ended with the casted sample.
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comparison. The two CAD models with different structures: uniform size (US) (Fig. 3c) and dual size (DS) (Fig. 3f), were produced having the theoretical masses of 2.06 and 1.55 g, respectively. Concerning the casted samples, the average mass of US structure was 3.15 g which accounts for an increase of over 53% relative to the designed CAD model. On the other hand, the DS samples exhibited an average mass of 3.02 g, yielding an approximately 95% increase in regard to its designed CAD model. These results reflected a technical limitation of the rapid prototyping machine for producing models with structures of increased complexity. Nevertheless, it is worth to mention that both structures had mass reductions of ∼86% in comparison with the solid cylindrical specimen. Fig. 7. Compressive tests: (a) initial stage and (b) final stage.
3.2. Compression tests
Fig. 8. Geometry changes occurring in the manufacturing steps (CAD–resin–metal) of the smaller holes [d1 variation – (a)] and larger holes [d2 variation (b)] in the cellular structure.
machine accuracy. It is worth to mention that the resin model undergoes two solidification processes: first, at the time of the construction of the model in the LASER rapid prototyping machine; and second, at the curing stage in the ultraviolet curing unit. So, the data showed that the prototyping stage leads to a sample oversizing and the solidification process (metal shrinkage), during the casting, leads to a hole expansion (Fig. 7). From the data of Table 3 it was possible to illustrate the geometrical behavior (Fig. 8) of the smaller holes [d1 variation – (a)] and larger holes [d2 variation (b)] in both structures. Regarding CAD model–metal model transition, holes with smaller diameter (d1) displayed an expansion percentage in the range of ∼2.9% for the US structure and ∼1.0% for the DS structure. However, holes with larger diameters displayed shrinkage percentages in the range of 4.7% for the US structures and 6.5% for the DS structure. In this study, a reference solid cylindrical specimen (˚ = 16 mm; h = 40 mm) (Fig. 3b) made out of a commercial aluminum alloy (A413.1) and with a mass of 21.7 g was used for mass
Compression tests results are presented in Fig. 9 for all metallic specimens of uniform-size (Fig. 9A) and dual-size structures (Fig. 9B). From the experimental results it was possible to extract: the maximum initial load (Pmáx ) in the first inflection point of the loading curve; the stiffness (Sf ), by the slope of the curve in elastic regime; and the absorbed energy at 5 and 15 mm of displacement obtained by calculating the area below the curve. These values and their specific values (per gram) are presented in Table 4. Force–displacement results were converted to stress–strain and are presented in Fig. 10 while Young’s modulus was calculated for the initial linear slope of stress–strain curves and presented in Table 4. As shown in Figs. 9 and 10, the compressive behavior of uniform size structure is similar to the dual size until the first layer collapses. At this stage dual size structure withstood a significantly higher initial load. From this stage, as the structure densification is unique for each sample, the compressive behavior is also different. This densification behavior is largely related to the extensive fracture that occurs within the sample’s geometry. Results show that the specific Pmáx (N/g) withstood by uniform size (US) structure was approximately 221 N/g whereas that withstood by the dual size (DS) structure was approximately 404 N/g, i.e. the resistance exhibited by the dual size structure was ∼83% higher than that of the uniform size. In what concerns specific stiffness, the dual size structure obtained an average value 29% higher than the uniform size structure. These values are consistent with values from numerical simulation presented in the study proposing the dual size structure (Kou et al., 2008). Stiffness expressed as Young’s modulus is approximately 14% higher for the dual size structure. This improvement in stiffness is related to the introduction of secondary cells within the structure (Kou et al., 2008).
Fig. 9. Compression tests results: (A) uniform-size structure and (B) dual-size structure.
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Table 4 Values from mechanical behavior in the compression tests. Mass (g)
Young’s modulus (MPa)
US 1 US 2 US 3 US 4
3.23 3.27 3.02 3.07
230.2 192.8 158.7 199.5
744.9 662.3 660.4 716.1
230.6 202.5 218.7 233.2
10.7E+05 8.99E+05 7.20E+05 9.43E+05
3.31E+05 2.75E+05 2.38E+05 3.07E+05
1.97 1.22 1.65 1.67
0.61 0.37 0.55 0.54
5.94 4.32 7.07 6.05
1.84 1.32 2.34 1.97
Average Standard deviation
3.15 0.12
195.3 29.3
695.9 41.6
221.3 14.0
9.09E+05 1.46E+05
2.88E+05 0.40E+05
1.63 0.31
0.52 0.10
5.85 1.14
1.87 0.42
DS 1 DS 2 DS 3 DS 4
3.32 2.83 2.91 3.00
336.5 177.7 199.5 202.8
1454.9 1165.8 1165.2 1097.5
438.2 411.9 400.4 365.8
16.8E+05 8.71E+05 9.93E+05 9.89E+05
5.06E+05 3.08E+05 3.41E+05 3.30E+05
4.09 3.07 3.26 2.86
1.23 1.08 1.12 0.95
7.45 9.10 4.96 6.96
2.24 3.22 1.70 2.32
Average Standard deviation
3.02 0.21
229.1 72.4
1220.9 159.3
404.1 30.0
11.3E+05 3.71E+05
3.71E+05 0.91E+05
3.32 0.54
1.10 0.12
7.12 1.70
2.37 0.63
+103.7%
+111.5%
+21.7%
+26.7%
Variation
+14.7
Pmáx (N)
+75.4%
Specific Pmáx (N/g)
Stiffness (N/m)
Specimen
+82.6%
+24.3%
Specific stiffness (N/(m g))
+28.8%
Energy 5 (J)
Specific energy 5 (J/g)
Energy 15 (J)
Specific energy 15 (J/g)
Fig. 10. Compression stress strain results: (A) uniform-size structure and (B) dual-size structure.
Fig. 11. Compressive strength plotted against density for currently available metal foams (Ashby et al., 2000) and current results for uniform size ( cellular structures.
) and dual-size (
)
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Regarding specific absorbed energy registered until 5 mm of displacement, the dual size structure displayed an average absorbed energy significantly higher than the uniform size structure – around 112%. However, for a higher displacement (15 mm) the specific absorbed energy of the dual size structure was approximately 27% higher than that of the uniform size structure. This is attributed to the much higher initial load peak that contributes to the energy calculation in the first 5 mm of displacement. Based on the experimental data, one can conclude that the dual size structure exhibited general enhanced mechanical behavior over the uniform size structure. These improvements are highlighted in the maximum initial load supported (+83%) and in the absorbed energy until 5 mm of displacement (+112%). However, more realistic values of stiffness (29%) and energy absorption at 15 mm (27%) are to be considered for a validation of the modified geometry for mechanical applications. This analysis is based on the greater contribution of the maximum load and associated energy absorbed in the initial phase of collapse behavior. The improved results for stiffness and strength of dual size open-cell structures confirm previous numerical simulation results (Kou et al., 2008). The rational for such improved mechanical behavior was described by the authors as associated to a change of major plastic deformation concentration from incline struts that connect open spherical volumes (in uniform size structures) to dispersion of deformation between major struts and small struts that are present in the dual size structures. In the optimal condition of dual size open-cell structures, both major incline struts and small struts almost equally share the deformation (Kou et al., 2008). The introduction of secondary cells can therefore be used as an alternative to increasing density in order to improve mechanical properties if these secondary cells have a suitable size. Such appropriate design can be chosen with numerical simulation studies (Kou et al., 2008) and manufactured with a suitable process as described in the present study with a corresponding validation of mechanical properties. From the experimental stress–strain results and mass measurements of the tested structures, average compressive strength and density were calculated and presented in Fig. 11, for comparison with existing literature results on periodic and stochastic metal foams. The analysis of Fig. 11 highlights the possibilities with the method presented for manufacturing metal foams and, in particular, the scope of improvement possible with the dual-size structures. 4. Conclusions In this research work two types of metal foams were manufactured and analyzed, having different cell structures: uniform
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cell structure and dual-size cell arrangement. The structures were manufactured by lost-wax casting using 3D printed components for internal structure definition. Results for stiffness and energy absorption were obtained and compared on weight efficiency basis. The analysis of manufacturing parameters and geometry variation indicated that, the final specimen displayed a slightly higher value [1.0–2.9%] for smaller diameters (d1) and displayed a lower value [4.7–6.5%] for larger diameters (d2) than CAD model. This analysis is relevant for the definition of appropriate tolerances and CAD dimensions for part manufacturing. The compression tests showed that the specific Pmáx (N/g) withstood by the dual-size (DS) structure was approximately ∼83% higher than that of the uniform size, while stiffness had an improvement of 29%. Specific absorbed energy registered for 5 mm of displacement presented a significant improvement (around 112%). For a higher displacement (15 mm) the specific absorbed energy of the dual size structure was approximately 27% higher than that of the uniform size structure. These results are indicative of a higher efficiency of the dual-size structures that may be therefore considered for use in components subjected to impact or compression loading, both in stiffness and crash-energy absorption requirements. Acknowledgments The authors are grateful to the Portuguese Foundation for Science and Technology (FCT) who financially supported this work, through the project PTDC/EME-PME/115668/2009. References Ashby, M., Evans, A., Fleck, N., Gibson, L., Hutchinson, J., Wadley, H., 2000. Metal Foams: A Design Guide. Scripta Materialia, Butterworth-Heinemann. Banhart, J., Baumeister, J., 1998. Deformation characteristics of metal foams. Journal of Materials Science 33, 1431–1440. Banhart, J., 2000. Metallic foams: challenges and opportunities. In: Zitha, P., Banhart, J., Verbist, G. (Eds.), Proceedings Eurofoam 2000. , pp. 13–20. Banhart, J., 2001. Manufacture, characterisation and application of cellular metals and metal foams. Progress in Materials Science 46 (6), 559–632. Gibson, L., Ashby, M., 1988. Cellular Solids: Structure and Properties. Pergamon, Oxford. Kou, D.P., Li, J.R., Yua, J.L., Cheng, H.F., 2008. Mechanical behavior of open-cell metallic foams with dual-size cellular structure. Scripta Materialia 59, 483–486. Olurin, O., Fleck, N., Ashby, M., 2000. Deformation and fracture of aluminium foams. Materials Science and Engineering A 291, 136–146. Saadatfar, M., Mukherjee, M., Madadi, M., Schroder-Turk, G., Garcia-Moreno, F., Schaller, F., Hutzler, S., Sheppard, A., Banhart, J., Ramamurty, U., 2012. Structure and deformation correlation of closed-cell aluminium foam subject to uniaxial compression. Acta Materialia 60, 3604–3615. Song, H., Fan, Z., Yu, G., Wang, Q., Tobota, A., 2005. Partition energy absorption of axially crushed aluminum foam-filled hat sections. International Journal of Solids and Structures 42 (9–10), 2575–2600. Zaiser, M., Mil, F., Konstantinidis, A., Aifantis, K., 2013. Strain localization and strain propagation in collapsible solid foams. Materials Science and Engineering A 567, 38–45.