Anisotropic Compression Behavior of Additively Manufactured Porous Titanium with Ordered Open-Cell Structures at Different Temperatures

Shiyue Guo; Xuezheng Yue; Koichi Kitazono

doi:10.2320/matertrans.MT-M2021149

Abstract

Anisotropic compression behavior of open-cell porous titanium is evaluated at different temperatures. Porous titanium specimens with truncated octahedron unit cells are designed by 3D-Voronoi division. Cubic specimens with the porosities of 85 and 92% are manufactured from commercially pure titanium powder using an electron beam melting process. Compression tests are carried out at different temperatures of 300, 473 and 673 K for three different compression directions of [001], [011] and [111]. In all specimens, the flow stress of [001] direction is highest and the flow stress of [111] direction is lowest. Anisotropic compressive strength can be explained by comparing the bending moment of cell struts. Activation energy obtained by Arrhenius plot is the same as that of base titanium and is independent of the compression direction.

Anisotropic compression behavior of ordered open-cell porous titanium.

1. Introduction

Lightweight porous metals and metal foams have excellent properties such as energy absorption, sound absorption and biocompatibility.¹⁾ Titanium has excellent physical and chemical properties such as low density, high strength, corrosion resistance, heat resistance, low coefficient of thermal expansion, low thermal conductivity and biocompatible.²⁾ Therefore, there have been investigated many porous metals based on titanium. Conventional porous titanium was manufactured through the powder metallurgical (PM) foaming process³⁾ or the space holder method.⁴⁾ These have disordered cell structures which cause a variation in the mechanical properties.

Recently, many porous titanium alloys with ordered cell structures have been manufactured through additive manufacturing (AM) process.⁵^,⁶⁾ The mechanical properties of AM porous titanium are determined by both the cell structure and the material property of base material. The cell structure includes porosity, cell size, cell shape, cell distribution. There are many researches on the deformation behavior of disordered porous metals at high temperatures. The high temperature mechanical properties of disordered porous metals are the same as those of cell walls or edge materials.⁷⁾ On the other hand, various studies of the mechanical characteristics of ordered porous titanium at room temperature have been published.⁸^,⁹⁾ The authors also reported that the compression behavior of ordered AM porous Ti–6Al–4V alloys depended on the post heat treatment.¹⁰⁾ There are few studies on the anisotropic deformation behavior of ordered cellular solids at different temperatures.

In the present study, mechanical properties of ordered AM porous titanium are evaluated at different temperatures and in the different compression directions. The unit cell structure is determined as a truncated octahedron (so-called Kelvin’s tetrakaidekahedron) which is one of space-filling polyhedrons.¹¹⁾ Ordered cell structures are designed by 3D-CAD software and cellular titanium specimens are manufactured through AM process.

2. Experimental Procedure

Unit cell structure of the present porous titanium is a truncated octahedron which has 14 faces (8 hexagons and 6 squares), 36 struts and 24 vertexes. CAD models of the specimen for AM process were designed by the 3D-Voronoi division using commercial 3D-CAD software, Rhinoceros 6. First, the seed points of periodic bcc lattice arrangement were put in the space. Second, 3D-Voronoi division was carried out against the seed points. As a result, ordered truncated octahedron unit cell structures are obtained in the space. Here, the center of the unit cell is the same as the original bcc lattice point. Finally, CAD model of the cylindrical specimen was manufactured after cutting the bcc-Voronoi region. The compressive direction of truncated octahedron open-cell geometries can be defined as bcc-Voronoi [u v w] by miller index. Three types of the unit cell structures (bcc-Voronoi [001], bcc-Voronoi [011] and bcc-Voronoi [111]) with the nominal porosity, p_N, of 80% and 90% are shown in Fig. 1. The strut lengths, a, of the specimens with the porosity of 80% and 90% are 2.04 and 2.88 mm, respectively. Strut shape is cylinder with the diameter, t, of 1 mm. The nominal porosity increases with increasing a/t.

Fig. 1

3D-CAD images of truncated octahedron unit cells. (a), (d) bcc-Voronoi [001], (b), (e) bcc-Voronoi [011] and (c), (f) bcc-Voronoi [111]. Nominal porosities are (a), (b), (c) 80% and (d), (e), (f) 90%. Compression direction is parallel to the z-axis.

Compression test specimens were manufactured by Arcam A2X electron beam melting (EBM) machine. The electron beam output was 210 W, the scanning speed was 232.4 mm/s. Commercial pure titanium, Grade 2, powder was used as a starting metal. The chemical composition is 0.01%C, 0.08%Fe, 0.13%O, 0.004%N, 0.001%H and remaining titanium. The shape of the specimens is a cylinder with a diameter of 30 mm and a height of 30 mm. Building direction is parallel to the cylinder axis. Post heat treatment was not applied to the AM porous titanium specimens.

The experimental porosity of the specimen is calculated as

\begin{equation} p = 1 - \frac{\rho^{*}}{\rho_{s}} \end{equation}

(1)

where $\rho ^{*}$ is the density of specimen and ρ_s is the density of cell edge material. $\rho ^{*}$ is determined from the mass and the size of the specimen.

Cross sections of the strut parallel and perpendicular to the building direction were observed by field emission scanning electron microscope (JEOL, JSM-IT800(SHL)). The acceleration voltage is 15 kV and the working distance is 22–25 mm. A scan-step size of 1 µm was used to analysis the orientations of microstructures using electron backscatter diffraction (EBSD) equipped with an OIM 7.3 (TSL solutions) system.

Compression tests were carried out at room temperature of 300 K using a Shimadzu Autograph AG-50kNISD universal testing machine and high temperatures of 473 and 673 K using a Shimadzu CONCRETO 2000X compression testing machine. The initial strain rate was fixed at 5.6 × 10⁻³ s⁻¹ (10 mm/min). Compression behaviors were observed using a commercial high definition digital video camera.

3. Results

Photographs of the AM porous titanium specimens are shown in Fig. 2. Though the nominal porosities were designed as 80% and 90%, the experimental porosities of the specimens were 85% and 92%, respectively. This is because of the defects during EBM process. This is mainly due to the inevitable defects in the additive manufacturing process, such as laser melting powder splash occurs at times. Therefore, the experimental porosity often becomes higher than the nominal porosity.

Fig. 2

Photographs of AM porous titanium specimens with bcc-Voronoi cell structures. Porosities are (a), (b), (c) 85% and (d), (e), (f) 92%. Compression and building directions are parallel to [001] ((a) and (d)), [011] ((b) and (e)) and [111] ((c) and (f)).

The EBSD inverse pole figures in Fig. 3 display the microstructures of the EBM manufactured commercial pure titanium samples in both building and scanning direction cross-sections. The microstructure of the AM porous sample in the scanning direction cross-section is composed of fine-grains due to rapid cooling of the molten pool. In scanning direction cross-section, the average grain size of AM porous titanium is 6.9 µm. (bcc-Voronoi [001]), 6.6 µm (bcc-Voronoi [011]) and 5.3 µm (bcc-Voronoi [111]), respectively. The average grain size of AM porous titanium in building direction cross-section is 10.1 µm (bcc-Voronoi [001]), 12.0 µm (bcc-Voronoi [011]) and 9.1 µm (bcc-Voronoi [111]), respectively.

Fig. 3

EBSD inverse pole figure maps of (a), (d) bcc-Voronoi [001], (b), (e) bcc-Voronoi [011] and (c), (f) bcc-Voronoi [111] specimens. Images (a), (b), (c) are cross sections perpendicular to the building direction. Images (d), (e), (f) are cross sections parallel to the building direction.

Compressive stress-strain curves of open-cell AM porous titanium with 85% porosity are shown in Fig. 4 at temperatures of 300 K, 473 K, 673 K. Photographs of the specimens at 25% strain are shown in Fig. 5. All specimens showed linear elastic, plateau and densification regions. The flow stress decreased with increasing the temperature. The flow stress of bcc-Voronoi [001] was highest and the flow stress of bcc-Voronoi [111] was lowest. Anisotropy of the compression behavior does not depend on the test temperature. Photographs at the strain of 25% showed local layered deformations of the cells which is typical of the plateau region of the cellular solids.

Fig. 4

Compressive stress-strain curves of AM porous titanium specimens with the porosity of 85%. Test temperatures are (a) 300 K, (b) 473 K and (c) 673 K.

Fig. 5

Photographs of AM porous titanium specimens with the porosity of 85% at compressive strain of 25%. Temperatures are (a), (b), (c) 300 K and (d), (e), (f) 473 K. Cell structures are bcc-Voronoi (a), (d) [001], (b), (e), [011], (c), (f) [111].

Compressive stress-strain curves of open-cell AM porous titanium with 92% porosity are shown in Fig. 6 at temperatures of 300 K, 473 K, 673 K. Photographs of the specimens at 25% strain are shown in Fig. 7. Similar to the low porosity specimens, all specimens showed linear elastic, plateau and densification regions. However, the flow stress showed oscillation in the plateau region at 300 K. No oscillation of the flow stress was found in the curves over 473 K. Photographs at 25% strain showed macroscopic shear deformation in specimens only at 300 K. The clear shear band was observed in the bcc-Voronoi [111] specimen of 92% at 300 K [Fig. 7(c)]. These results are typical for ordered AM porous metals.⁹⁾

Fig. 6

Compressive stress-strain curves of AM porous titanium specimens with the porosity of 92%. Test temperatures are (a) 300 K, (b) 473 K and (c) 673 K.

Fig. 7

Photographs of AM porous titanium specimens with the porosity of 92% at compressive strain of 25%. Temperatures are (a), (b), (c) 300 K and (d), (e), (f) 473 K. Cell structures are bcc-Voronoi (a), (d) [001], (b), (e) [011], (c), (f) [111]. The arrow shows a shear band during compressive deformation.

4. Discussion

Plateau stresses, σ_p of AM porous titanium specimens with 85% and 92% porosities were plotted as a function of temperature [Fig. 8]. The plateau stress is determined by using average value of the flow stress between 20% and 30% of the strain. All plateau stresses were monotonically decreased with increasing the temperature. At all temperatures, the plateau stresses of bcc-Voronoi [001] specimens were the highest. On the other hand, the plateau stresses of bcc-Voronoi [111] specimens were the lowest. The anisotropic mechanical property can be explained by the simple beam theory of the cell struts. The angular relationship between 36 struts in the unit cell and the compression direction is summarized in Table 1. When the compressive force, F, is applied on a strut, the maximum bending moment, M, is expressed as¹²⁾

\begin{equation} M = \frac{1}{2} Fa \sin\theta \end{equation}

(2)

where θ is the angle between the strut axis and the compressive force. In the case of bcc-Voronoi [001] specimens, the major deformation occurs in 24 struts with the angle of θ = 45 deg. In the case of bcc-Voronoi [011] specimens, the major deformation occurs in 24 struts with the angle of θ = 60 deg. In the case of bcc-Voronoi [111] specimens, the major deformation occurs in 18 struts with the angle of θ = 90 deg. Therefore, the maximum bending moment of the strut in [001], [011] and [111] compressive directions are expressed as

\begin{equation} M_{[001]} < M_{[011]} < M_{[111]}. \end{equation}

(3)

In the case of the deformation mode of the bending, the bcc-Voronoi [001] specimens show the highest plateau stress because of the lowest bending moment of the struts. Of course, there are other deformation modes, yielding and buckling, in the cellular solid. The dominant deformation mode will change according to the porosity, the compressive strain, the temperature, the strain rate. Further studies such as finite element analysis are necessary for evaluation of the mechanical properties of porous titanium. Yamanaka et al.¹³⁾ have investigated anisotropy of mechanical properties of additively manufactured pure titanium and obtained isotropic mechanical properties. The weak texture in Fig. 3 further shows that the base material’s anisotropy has minor effect on the porous pure titanium.

Fig. 8

Plateau stresses of AM porous titanium specoimens with the porosity of (a) 85% and (b) 92% are plotted as a function of temperature.

Table 1 Number of struts (total 36) in three bcc-Voronoi unit cells are listed. Five angles between the strut axis and the compression direction (z-axis) are 0, 35.3, 45, 60 and 90 deg.

The compressive flow stress decreased with increasing the temperature. In general, the solid cell edge material deforms according to the power-law creep equation expressed as

\begin{equation} \dot{\varepsilon} = A\sigma^{n} \exp \left( -\frac{Q}{RT} \right) \end{equation}

(4)

where $\dot{\varepsilon }$ is the steady state strain rate, n is the stress exponent, Q is the activation energy, R is the gas constant, T is the temperature and A is the constant. In the case of disordered open-cell porous metals, the modified creep constitutive equation⁷⁾ is reported as

\begin{equation} \dot{\varepsilon}^{*} = A\frac{0.6}{n+2}\left( \frac{1.7(2n + 1)}{n} \right)^{n} \sigma_{p}{}^{n} \left( \frac{\rho^{*}}{\rho_{s}} \right)^{-\frac{3n+1}{2}}\exp \left(-\frac{Q}{RT}\right) \end{equation}

(5)

where σ_p is the plateau stress. Equation (5) can be rewritten in logarithmic form as

\begin{align} &n\ln \sigma_{p} - \frac{3n+1}{2}\ln \left( \frac{\rho^{*}}{\rho_{s}} \right) - \ln\dot{\varepsilon}^{*} \\ &\quad = -\ln\left[ A\frac{0.6}{n+2}\left( \frac{1.7(2n+1)}{n} \right)^{n}\right] + \frac{Q}{RT}. \end{align}

(6)

In Fig. 9, the experimental data are plotted against the reciprocal of temperature according to eq. (6). Here, the stress exponent of n = 6.0 and the apparent activation energy of Q = 48.0 kJ/mol are used from previous creep experiments.¹⁴⁾ All experimental data on the present AM porous titanium specimens showed good agreement with eq. (6). At 300 K, the experimental values were slightly small compared the fitting line. This is because of the stress oscillation shown in Figs. 6(a) and 8(a). Therefore, the stress exponent and activation energy of AM porous titanium can be explained by those of the cell edge material. Therefore, it can be concluded that the cell structures of porous titanium do not affect the activation energy, which means the structure has a limited effect on the temperature dependence, which is only related to the property of the base material.

Fig. 9

Results of compression tests are plotted as a function of reciprocal temperature according to eq. (6). Data for PM titanium foams are plotted on the same graph.

Results of high temperature compression tests on PM titanium foams with disordered cell structure³⁾ are plotted in Fig. 9. Plateau stress of PM titanium foams were relatively higher than that of present AM porous titanium specimens. It was reported that the strength of disordered AM porous aluminum alloys was lower than that of ordered AM porous aluminum alloys.¹⁵⁾ In addition, rapidly cooled AM metals shows high strength compared to sintered metals because of the fine crystal grain size. Discrepancy between the previous and the present experimental results may be caused by the size effect of cellular solids.¹⁶⁾ Dimension of the PM titanium foam specimen is a 22 mm cube and the average cell size is 180 µm. On the other hand, the average cell sizes of the present AM porous titanium specimens are 6.5 mm in 85% porosity and 9.0 mm in 92% porosity. The ratio of the specimen width to the average cell size in PM titanium foams becomes 120, and the ratio of AM porous titanium specimens become 4 in 85% porosity and 3 in 92% porosity. The strength of porous metals decreases with decreasing the ratio. Therefore, the relatively low strength of AM porous titanium specimens is caused by the size effect in cellular solids.

5. Conclusions

Open-cell porous titanium with ordered cell structure was designed and manufactured through EBM process. Compression tests were carried out at different temperatures and at different compression directions. Some conclusions were summarized as follows.

(1) Flow stress of AM porous titanium decreased with increasing the porosity. Flow stress oscillation due to the macroscopic shear deformation was observed in high porosity specimens.
(2) Mechanical properties in the [001] compressive direction was highest of all. Anisotropic deformation can be explained using the bending moment of the cell struts.
(3) Flow stress of AM porous titanium decreased with increasing the temperature. At high temperature, the flow stress oscillation was suppressed. The stress exponent and the activation energy were the same as those of dense titanium. Temperature dependence of AM porous titanium is mainly determined by that of base materials.

Acknowledgment

This study was supported in part by The Light Metal Educational Foundation, Japan.

REFERENCES

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