Design and Applications of Additively Manufactured Porous Aluminum Alloys

Abstract

Additive manufacturing (AM) technology enables to manufacture many types of porous aluminum alloys. Present study focusses on AM porous Al–4.8Mg–0.7Sc alloys manufactured through laser powder bed fusion process. Eight types of ordered cell structures are designed by 3D-Voronoi division. AM porous Al–4.8Mg–0.7Sc alloys consisting of ordered cells show anisotropic compression behavior. Oscillated stress-strain curves are due to the heterogeneous deformation of cell struts. Post-annealed AM porous Al–4.8Mg–0.7Sc alloy shows excellent mechanical properties compared to post-annealed AM porous Al–10Si–0.3Mg alloy. This is because of solid solution hardening in Al–4.8Mg–0.7Sc alloy.

Compressive stress-strain curves of AM porous Al–4.8Mg–0.7Sc alloy specimens. Cell structures are (a) bcc-Voronoi, (b) fcc-Voronoi, and (c) hcp-Voronoi.

1. Introduction

Porous metals or cellular metals are focused on as a lightweight material for transport industries.^1,2) Main applications are lightweight construction, energy absorption and damping insulation. There have been reported many manufacturing processes of porous metals. Their cell structures strongly depend on the manufacturing process. The authors classify the manufacturing processes into two types [Table 1]. One is a foaming process using gas pressure and another is a non-foaming process without gas generation.

Table 1 Classified manufacturing processes of porous metals.

In classical porous metals, melt foaming^3,4) and powder metallurgical (PM) precursor processes^5,6) are known as two major foaming processes. The foaming process requires a foaming agent such as titanium hydride and calcium carbonate. The cell structure in a foaming process becomes a closed-cell structure. ALPORAS foams manufactured through the melt foaming process have spherical pores. In CYMAT aluminum foams,⁷⁾ aluminum melt is foamed by injecting gases using specially designed rotating impellers. Lotus-type porous metals have been manufactured by unidirectional solidification.^8,9) The hydrogen gas is ejected from the solid metal and forms long pores that are aligned parallel to the solidification direction. Since the hydrogen concentration dissolving in molten aluminum is small, the porosity of lotus-type porous aluminum is less than 30%. On the other hand, aluminum precursors are also manufactured from aluminum plates through accumulative roll bonding^10,11) or friction stir welding^12,13) processes.

Spacer process¹⁴⁾ is a typical non-foaming process. Aluminum sponges have been manufactured by infiltration of aluminum melt in a space holder filled mold followed by removal of space holders.¹⁵⁾ The combustion reaction process enables to manufacture porous intermetallic compounds.¹⁶⁾ A compacted powder is heated to ignite the reaction. Nanoporous metals have been manufactured through a dealloying process.¹⁷⁾ 3D-woven metals manufactured from metal fibers have ordered cell morphology.¹⁸⁾ The cell structure manufactured through a non-foaming process becomes both open- and closed-cell structures.

Many kinds of dense aluminum alloys have been manufactured through additive manufacturing (AM) process.^19,20) Al–10Si–0.3Mg alloy having excellent castability is widely used for laser powder bed fusion (LPBF) process. A low amount of magnesium is effective for age hardening. AM porous aluminum alloys are focused on their lightweight and energy absorption capacity. The mechanical property of AM porous metals strongly depends on their alloy composition as well as their cell structures. The strength of Al–10Si–0.3Mg alloy is relatively low compared to high strength aluminum alloys. Recently, Al–Mg–Sc–Zr alloy is focused on as a new AM alloy. The addition of Sc or Zr achieves age hardening due to Al₃(Sc,Zr) precipitates.²¹⁾ The present paper reviews the design process of cellular solids and the applications of AM porous aluminum using Al–Mg–Sc–Zr alloy.

2. Design of Cellular Solids by 3D-Voronoi Division

In AM porous metals, the cell structures are designed by 3D-CAD software. The design flexibility is significantly higher than that of classical foaming processes. The cellular solid consists of polyhedral unit cells. There have been reported several space-filling polyhedra. E.S. Fedorov²²⁾ discovered five space-filling polyhedra, parallelepiped, hexagonal prism, rhombic dodecahedron, elongated dodecahedron and truncated octahedron. Many studies on ordered AM lattice structures use Fedorov’s polyhedra as a unit-cell. Parallelepiped cell includes simple cubic lattice²³⁾ and bcc lattice^24,25) structures. Hexagonal prism cell, which is called honeycomb cell, has been used in porous Ti–6Al–4V alloy.²⁶⁾ Rhombic dodecahedron cells have been used in porous stainless steel.²⁷⁾ FEM analysis was carried out against truncated octahedron cell structures.²⁸⁾ These polyhedral unit-cells can be designed by 3D-Voronoi division. Therefore, 3D-Voronoi division is a powerful method for a design of cellular solids.

3D-Voronoi division²⁹⁾ enables to design both ordered and disordered cells.³⁰⁾ If the seed points are arranged to the non-periodic distribution, the resultant cell structure becomes disordered. If the seed points are arranged to the periodic and regular distribution, the resultant cell structure becomes ordered. Three kinds of ordered cells are designed in this study [Fig. 1]. At first, seed points are arranged on bcc [Fig. 1(a)], fcc [Fig. 1(b)] and hcp [Fig. 1(c)] lattice points. Next, the 3D-Voronoi division is carried out against respective seed points. As a result, three polyhedrons, truncated octahedron [Fig. 1(d)], rhombic dodecahedron [Fig. 1(e)] and trapezo-rhombic dodecahedron [Fig. 1(f)], are obtained. The trapezo-rhombic dodecahedron is not included in Fedorov’s space-filling polyhedra. In the case of 3D-Voronoi division, the number of seed points equals the number of cells. Truncated octahedron, which is also called Kelvin’s tetrakaidecahedron, consists of 6 squares, 8 hexagons, 36 edges and 24 vertices. Rhombic dodecahedron consists of 12 rhombi, 24 edges and 14 vertices. Trapezo-rhombic dodecahedron, which is also called squashed dodecahedron, consists of 6 rhombi, 6 trapezoids, 24 edges and 14 vertices.

Fig. 1

Seed points on (a) bcc, (b) fcc and (c) hcp lattice. Images of (d) truncated octahedron, (e) rhombic dodecahedron and (f) trapezo-rhombic dodecahedron unit-cells constructed by 3D-Voronoi division.

The volume, V, and the surface area, A, of cube, hexagonal prism, truncated octahedron, rhombic dodecahedron, trapezo-rhombic dodecahedron and sphere are summarized in Table 2. The edge length is a. Hexagonal prism with the height of c is assumed to be an ideal hcp lattice,   

\begin{equation} \frac{c}{a} = \frac{2\sqrt{6}}{3}. \end{equation} (1)

Trapezo-rhombic dodecahedron has three different edge lengths, a₁, a₂ and a₃, which are expressed as   

\begin{equation} \frac{3}{2}a_{1} = a_{2} = \frac{3}{4}a_{3}. \end{equation} (2)

Cube has the fewest faces. Sphere has infinite faces. The surface area at unit volume in truncated octahedron becomes 5.31 which is close to the value of 4.84 in sphere. In addition, the number of faces in truncated octahedron is 14 which is largest of the five polyhedra. Therefore, the unit-cell size of truncated octahedron becomes the smallest of the present five polyhedra.

Table 2 Comparison of space-filling polyhedra and sphere.

Truncated octahedron cells, rhombic dodecahedron cells and trapezo-rhombic dodecahedron cells are called bcc-Voronoi, fcc-Voronoi and hcp-Voronoi cells, respectively. As with the coordination number of the bcc lattice, one bcc-Voronoi cell is surrounded by nearest neighbor 8 cells and next nearest neighbor 6 cells. As with the coordination number of fcc and hcp lattice, one fcc- or hcp-Voronoi cell is surrounded by nearest neighbor 12 cells. The distance between nearest seed points, d, is expressed as   

\begin{equation} d = \sqrt{6}a\qquad \text{for bcc-Voronoi}, \end{equation} (3)

  

\begin{equation} d = \frac{2\sqrt{6}}{3}a\ \quad \text{for fcc-Voronoi}, \end{equation} (4)

  

\begin{equation} d = \frac{2\sqrt{6}}{3}a_{2}\quad \text{for hcp-Voronoi}. \end{equation} (5)

Therefore, the cell size is determined by the arrangement of seed points. Generally, the cell size or crystal grain size in 3D space is determined as an equivalent sphere diameter, D. Then, the diameter, D, is expressed as   

\begin{align} D &= \left(\frac{48\sqrt{2}}{\pi} \right)^{\frac{1}{3}}a = \left(\frac{8\sqrt{3}}{3\pi} \right)^{\frac{1}{3}}d \approx 1.14d\\ &\qquad \text{for bcc-Voronoi cell}, \end{align} (6)

  

\begin{align} D &= \left(\frac{32\sqrt{3}}{3\pi} \right)^{\frac{1}{3}}a = \left(\frac{3\sqrt{2}}{\pi} \right)^{\frac{1}{3}}d \approx 1.11d\\ &\qquad \text{for fcc-Voronoi cell}, \end{align} (7)

  

\begin{align} D &= \left(\frac{32\sqrt{3}}{3\pi} \right)^{\frac{1}{3}}a_{2} = \left(\frac{3\sqrt{2}}{\pi} \right)^{\frac{1}{3}}d \approx 1.11d\\ &\qquad \text{for hcp-Voronoi cell}. \end{align} (8)

The equivalent sphere diameters become about 10% longer than the distance between the nearest seed points.

The porosity determines the mechanical properties of the cellular solids. Here, open-cell structure consisting of cylindrical edges with diameter of t is considered. The porosity of the bcc-Voronoi cellular solid is calculated as   

\begin{align} p & = 1 - \frac{\sqrt{2} \pi}{16}\left(\frac{a}{t}\right)^{-3}\left(\frac{3a}{t} - 2 \right)\\ & = 1 - 6 \left(\frac{D}{t} \right)^{-3}\left(\frac{\sqrt{6}D}{2t}\left(\frac{\sqrt{3}\pi}{8} \right)^{\frac{1}{3}} {}- 2 \right)\\ & \quad \text{for bcc-Voronoi cell}, \end{align} (9)

and the porosity of fcc-Voronoi cellular solid is calculated as   

\begin{align} p & = 1 - \frac{3\sqrt{3} \pi}{16}\left(\frac{a}{t} \right)^{-3}\left(\frac{2a}{t} - \frac{4}{3} \right)\\ & = 1 - 6 \left(\frac{D}{t}\right)^{-3}\left(\frac{\sqrt{6} D}{2t}\left(\frac{\sqrt{2} \pi}{6} \right)^{\frac{1}{3}} {}- \frac{4}{3} \right)\\ & \quad \text{for fcc- and hcp-Voronoi cells} \end{align} (10)

where both ends of the cylindrical edges are assumed to be the shape of a cone. As-designed porosity is plotted against D/t in Fig. 2. The porosity increased with increasing D/t. At the same cell sizes, the porosity of bcc-Voronoi cell becomes slightly higher than that of fcc- and hcp-Voronoi cells. In other words, at the same porosities, the cell size of bcc-Voronoi cell becomes slightly smaller than that of fcc- and hcp-Voronoi cells.

Fig. 2

As-designed porosities of bcc- and fcc-Voronoi cells are plotted as a function of normalized cell size, D/t. D is the equivalent sphere diameter and t is the strut diameter.

In Fig. 3, eight types of cellular solids were designed using commercial 3D-CAD software, Rhinoceros 7. As-designed porosity and the strut diameter of all models are 90% and 1.0 mm, respectively. Compressive directions are parallel to [001], [011] and [111] directions in bcc- and fcc-Voronoi specimens and [0001] and $[\bar{2}110]$ directions in hcp-Voronoi specimens.

Fig. 3

3D-CAD imaged of as-designed compression specimens. (a) bcc-Voronoi [001], (b) bcc-Voronoi [011], (c) bcc-Voronoi [111], (d) fcc-Voronoi [001], (e) fcc-Voronoi [011], (f) fcc-Voronoi [111], (g) hcp-Voronoi [0001] and (h) hcp-Voronoi $[\bar{2}110]$. Compression direction is parallel to [001] for (a) and (d), [011] for (b) and (e), [111] for (c) and (f), [0001] for (g) and $[\bar{2}110]$ for (h). As-designed porosity is 90%.

3. Compression Behaviors of AM Porous Al–Mg–Sc-Alloys

Al–4.8Mg–0.7Sc alloy powder³¹⁾ supplied by Toyo Aluminium K.K., Japan was used as a starting material. This alloy is often referred to as “Scalmalloy”. Compression specimens were manufactured through the LPBF process. A building machine is LASERTEC 12 SLM, DMG MORI. Photographs of cubic specimens with 30 × 30 × 30 mm³ dimensions are shown in Fig. 4. The as-built porosities which are calculated from the specimen mass and outside dimensions are 85 ± 2%. Relatively low porosities may be caused by unmelted powder attached on the surfaces of the struts. All specimens are post-heat treated at 598 K for 4 h (T5) in atmosphere. This heat treatment condition is known as a suitable artificial aging condition due to Al₃Sc precipitates.³¹⁾

Fig. 4

Photographs of AM porous Al–4.8Mg–0.7Sc alloy specimens. (a) bcc-Voronoi [001], (b) bcc-Voronoi [011], (c) bcc-Voronoi [111], (d) fcc-Voronoi [001], (e) fcc-Voronoi [011], (f) fcc-Voronoi [111], (g) hcp-Voronoi [0001] and (h) hcp-Voronoi $[\bar{2}110]$. Compression directions are parallel to building direction.

Compression tests were carried out using a Shimadzu Autograph AGX-50kNVD universal testing machine. Crosshead moving speed was fixed at 1 mm/min. Non-lubricated platens were used in compression tests.

Compressive stress-strain curves are shown in Fig. 5. Initial peak stresses of bcc-Voronoi specimens were 16.2 MPa for [001], 16.5 MPa for [011] and 12.7 MPa for [111] [Fig. 5(a)]. Initial peak stresses of fcc-Voronoi specimens were 10.4 MPa for [001], 8.78 MPa for [011] and 10.8 MPa for [111] [Fig. 5(b)]. Initial peak stresses of hcp-Voronoi specimens were 16.3 MPa for [0001], 8.72 MPa for $[\bar{2}110]$ [Fig. 5(c)]. Though the hcp-Voronoi [0001] specimen showed the highest compressive strength, the hcp-Voronoi specimen showed high anisotropy of the strength. The anisotropy can be explained by the bending moment of the struts and the number of the struts.^32,33)

Fig. 5

Compressive stress-strain curves of AM porous Al–4.8Mg–0.7Sc alloy specimens. Cell structures are (a) bcc-Voronoi, (b) fcc-Voronoi, and (c) hcp-Voronoi.

Except for fcc-Voronoi [001] specimen, all specimens showed large stress oscillations during the compression tests. There are several factors related to stress oscillation in porous metals. One is the ductility of the base material. As-built AM porous Al–10Si–0.3Mg alloys with low ductility show the large stress oscillation.³⁴⁾ On the other hand, porous commercially pure titanium with high ductility shows small stress oscillation.³⁵⁾ Second is the cell regularity. The stress oscillation becomes small in AM porous aluminum with the disordered cells³⁰⁾ or a closed-cell aluminum foam with random pore distribution.⁴⁾ Third is the angle between the compressive directions and the strut axes. In Table 3, the relationship between the compressive directions and the strut axes is summarized for the present eight porous metals. In the bcc-Voronoi cell structure, the angles, θ, of 36 struts are classified to 0°, 35.3°, 45°, 60° and 90°. In the fcc-Voronoi cell structure, the angles of 24 struts are classified into 0°, 35.3°, 54.7°, 70.5° and 90°. In the hcp-Voronoi cell structure, the angles 24 struts are classified into 0°, 35.3°, 70.5° and 90°. Stress oscillation is caused by the heterogeneous deformation of the struts due to the different strut angles. It is noted that the fcc-Voronoi [001] type has only one angle between the compressive direction and the strut axes. This is the reason of the small oscillation observed in fcc-Voronoi [001] specimens. However, the mechanism of the stress oscillation is not sufficiently clear.

Table 3 Relationship between the compressive directions and the strut axes in bcc-, fcc- and hcp Voronoi cells.

4. Comparison between AM Porous Al–4.8Mg–0.7Sc and Al–10Si–0.3Mg Alloys

Al–10Si–0.3Mg alloy is a typical AM aluminum alloy. Most of AM porous aluminum alloys have been made of Al–10Si–0.3Mg alloy powder.^36,37) In the present study, AM porous Al–10Si–0.3Mg alloy specimens were manufactured by an EOS M280 LPBF machine in Koiwai Co., Ltd., Japan. The as-built porosity was 91.0%. As-built AM porous Al–10Si–0.3Mg alloy specimens were post-annealed at 803 K for 6 h in atmosphere. On the other hand, AM porous Al–4.8Mg–0.7Sc alloy specimens were built through the LPBF process and followed by post-annealing at 803 K for 8 h in atmosphere. Cell structures of all specimens were fcc-Voronoi [001] in order to remove the effects of stress oscillation. Both specimen dimensions are 30 × 30 × 30 mm³. Crosshead moving speed is 1 mm/min.

Compressive stress-strain curves are shown in Fig. 6. Both specimens showed smooth stress-strain curves and small stress oscillation. This is due to the cell structure of fcc-Voronoi [001] and post-annealing treatments. The plateau stresses which are determined as the average stress between 20% and 30% strains were 1.54 MPa for AM porous Al–4.8Mg–0.7Sc alloy and 0.62 MPa for Al–10Si–0.3Mg alloy. Therefore, the compressive strength of AM porous Al–4.8Mg–0.7Sc alloy is 2.5 times higher than that of AM porous Al–10Si–0.3Mg alloy.

Fig. 6

Compressive stress-strain curves of AM porous Al–4.8Mg–0.7Sc alloy and AM porous Al–10Si–0.3Mg alloy. Cell structures are fcc-Voronoi.

Tensile stress-strain curves of dense AM Al–4.8Mg–0.7Sc alloy bars (As-built and post-annealed) and dense AM Al–10Si–0.3Mg alloy bars (As-built and post-annealed) are shown in Fig. 7. Tensile directions are parallel to the building directions. AM Al–4.8Mg–0.7Sc alloys showed serrated stress-strain curves which were caused by solute Mg atoms. As-built Al–10Si–0.3Mg alloy showed the highest tensile strength of 393 MPa. On the other hand, post-annealed Al–10Si–0.3Mg alloy showed the lowest tensile strength of 136 MPa. As-built and annealed AM Al–4.8Mg–0.7Sc alloys showed tensile strengths of 361 MPa and 320 MPa, respectively. The tensile strength of annealed AM Al–4.8Mg–0.7Sc alloy was 2.4 times higher than that of annealed AM Al–10Si–0.3Mg alloy. Significant reduction in the tensile strength in post-annealed AM Al–10Si–0.3Mg alloy is due to the coarsened Si particles.³²⁾ On the other hand, Al–4.8Mg–0.7Sc alloy showed a small strength reduction due to the solid solution hardening. The difference between the compressive strength of AM porous Al–4.8Mg–0.7Sc and Al–10Si–0.3Mg alloys is due to the mechanical properties of the base material.

Fig. 7

Tensile stress-strain curves of AM Al–4.8Mg–0.7Sc alloys (as-built and annealed at 803 K for 8 h) and AM Al–10Si–0.3Mg alloys (as-built and annealed at 803 K for 2 h).

5. Summary

Many porous aluminum alloys have been manufactured through AM process. 3D-Voronoi division is a powerful method to design both ordered and disordered cells for AM process. In the case of ordered cell structure, the cell shape should be selected from space-filling polyhedra. Three kinds of ordered cell structures, truncated octahedron, rhombic dodecahedron and trapezo-rhombic dodecahedron cells were successfully manufactured by 3D-Voronoi division from bcc-, fcc- and hcp-lattice points, respectively. Compression tests revealed that the hcp-Voronoi cell showed the highest strength and highest anisotropy. Though the fcc-Voronoi cells have low strength, the fcc-Voronoi [001] showed smooth stress-strain curve without large stress oscillation. The bcc-Voronoi cells have relatively high strength and low anisotropy. Different mechanical properties caused by different cell structures should be considered for the design of practical porous metal applications.

Newly developed AM porous Al–4.8Mg–0.7Sc alloy showed about 2.5 times high strength compared to AM porous Al–10Si–0.3Mg alloy even at annealing conditions. Therefore, AM porous Al–4.8Mg–0.7Sc alloy has a potential as new structural and energy absorbing applications.

Acknowledgments

This study was supported in part by Light Metal Educational Foundation, Japan and Nikkeikin Aluminium Core Technology Co., Ltd.

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