Microstructure and Strengthening Mechanism of Fe-Supersaturated α Titanium alloy Produced by Laser Powder Bed Fusion

Abstract

In this study, α-Ti alloys with supersaturated iron (Fe) elements were fabricated by laser powder bed fusion, and their microstructures and mechanical properties were investigated to clarify the strengthening mechanism. The formation of β-Ti was not confirmed in the LPBF prepared Ti-Fe alloy, and Fe was solid soluted in the α-Ti grain. With solid solution of Fe, the α-Ti grain became fine, and the width of α-Ti lath was 530 nm with solid solution of 2 wt% Fe. 0.2% YS of LPBF Ti-Fe alloys increased with solid solution of Fe while maintaining a high elongation at break. The tensile strength of the Ti-2 wt% Fe alloy increased by 600 MPa compared to Ti-0 wt% Fe. The strengthening mechanism of LPBF Ti-Fe alloys was quantitatively clarified as Fe solid solution strengthening and grain refinement strengthening.

 

This Paper was Originally Published in Japanese in J. Jpn. Soc. Powder Powder Metallurgy, Advanced Publication by J-STAGE, https://doi.org/10.2497/jjspm.23-00068. The main text is slightly modified. The citation in Table 2 is corrected.

1. Introduction

In recent years, the use of titanium with excellent properties such as high specific strength, high corrosion resistance, and biocompatibility has been expanding in various industrial fields such as aerospace aircraft, chemical power plants, and medical equipment [1–3]. General purpose titanium alloys used in the above wide fields require the addition of rare metal elements such as vanadium (V), molybdenum (Mo) and zirconium (Zr) [4]. These rare metal elements are very unevenly distributed in terms of resources. For example, about 90% of the production of V, which is used in ASTM Gr. 5 alloy (Ti-6Al-4V), is dependent on China and Russia [5], and its price and supply are strongly influenced by geopolitics. In contrast, iron is one of the ubiquitous elements that are evenly distributed across the Earth. They are inexpensive and can be supplied stably [6]. It has been reported that Ti-Fe alloys produced by powder metallurgy have an excellent strength-ductility balance [7], and Ti-6 wt% Fe alloys have strength approaching 1200 MPa and elongation at fracture exceeding 20%. The main strengthening mechanism of these Ti-Fe alloys is the combined strengthening by hard β-Ti formed by the action of iron, a β-phase stabilizing element, and the amount of strengthening has a good correlation with the volume fraction of β-Ti.

On the other hand, the laser powder bed fusion (LPBF) method, which has attracted attention in recent years, forms a special microstructure due to its extremely high cooling rate of 10³–10⁸ K s⁻¹ [8, 9]. For example, in the case of Ti-6Al-4V alloys, the conventional method produces a microstructure consisting of α-Ti with a large amount of Al in solid solution and β-Ti with a large amount of V in solid solution, while the LPBF method produces fine acicular grains consisting of α/α′-Ti with homogeneous Al and V solid solution and high strength. In Ti-Fe alloys, it is believed that similar fine acicular grains consisting of α/α′-Ti in homogeneous solid solution of Fe is also exhibited, and a different strengthening mechanism is believed to operate than in Ti-Fe alloys prepared by the conventional method. In this study, we attempted to elucidate the strengthening mechanism of Ti-Fe alloys prepared by the LPBF method by investigating the effects of this method on the microstructures and mechanical properties.

2. Experimental Procedure

Pure Ti powder (99.7% purity, D₅₀ = 26.2 µm, TILOP-45, Osaka Titanium Technologies, Ltd.) and pure Fe powders (99.9% purity, D₅₀ = 4.8 µm, FEE16PB, Kojundo Chemical Laboratory Co., Ltd.) were used as starting powder. These powders were mixed with zirconia balls (φ10 mm, 10:1 by weight) in a plastic bottle to form Ti-x wt% Fe (x = 0, 0.05, 0.1, 0.2, 1.0, 2.0), and then mixed for 10.8 ks using a rocking mill (RM-05, Seiwa Giken Co., Ltd.). These powders were fabricated using an LPBF machine (TruPrint1000, Trumpf Corporation) with a power of 160 W, a hatch width of 0.11 mm, a layer thickness of 0.02 mm, and a scanning speed of 535 mm s⁻¹ to obtain a 10 × 50 × 10 mm (x × y × z) sample. The samples were then vacuum heat treated at 773 K for 3.6 ks to remove residual stresses.

These LPBF Ti-Fe alloys were characterized by X-ray diffraction (XRD, XRD-6100, Shimadzu Corporation), scanning electron microscopy (SEM, JSM-6500F, JEOL Ltd.), electron beam backscatter diffraction (EBSD, Digi Viewer IV detector, TSL Solutions, Inc.), and TEM-EDS (TEM, JEOL Ltd., JEM-2100F). For evaluation of tensile properties, a plate-shaped tensile specimen (parallel section width 2 mm, parallel section thickness 1 mm, parallel length 10 mm) was machined from the LPBF sample in the y-direction, and tensile tests were performed using an autograph (AG-X 50 kN, Shimadzu Corporation) at a strain rate of 5.0 × 10⁻⁴ s⁻¹.

3. Results and Discussions

Figure 1 shows the SEM-EDS observation results of the Ti and Fe raw powders used in this study and the Ti-1 wt% Fe composite powder prepared using these raw powders. Both raw powders are spherical powders with excellent flowability, which is advantageous for improving the powder bed density and the soundness of the LPBF sample [10–15]. The composite powder shows that Fe particles with relatively small diameters are uniformly adhered and dispersed on the Ti powder surface, indicating that the desired Ti-Fe composite powder was obtained.

Fig. 1

SEI of (a) pure Ti powder, (b) pure Fe particle, and (c-1) Ti-2 wt% Fe mix powder with (c-2) elemental map of Fe. (online color)

To understand the state of Fe in LPBF Ti-Fe alloys, XRD analysis was performed on LPBF Ti-Fe alloys and its starting powders. Figure 2 shows the XRD analysis results for Ti and Fe powders, as well as for LPBF Ti-0, 1, 2 wt% Fe alloys and for an extruded Ti-2 wt% Fe alloy [7]. The Fe raw powder had a peak at 44.4°, but the Fe peak disappeared in the LPBF Ti-Fe alloy. This means that Fe was completely decomposed in the LPBF process. In the Ti-2 wt% Fe alloys prepared by sintering and hot extrusion reported in previous studies [7], the added Fe atoms segregate into β-Ti during the cooling process, which stabilizes the β-Ti and allows it to remain at room temperature. As a result, with the addition of 1 or 2 wt% Fe, 4 or 7 vol% β-Ti is formed, and XRD analysis shows β-Ti peaks in addition to α-Ti peaks. In contrast, the β-Ti peak was not observed in the Ti-2 wt% Fe prepared by the LPBF method, and it was found to be composed of a single phase of α-Ti. This is considered to be because the rapid cooling characteristic of the LPBF method suppresses the diffusion and segregation of Fe in Ti, resulting in supersaturated solid solution of Fe in α-Ti.

Fig. 2

XRD profiles of Ti powder, Fe powder, LPBF Ti-0∼2 wt% Fe alloy and conventional Ti-2 wt% Fe PM extrudate.

The Inverse Pole Figure (IPF) maps of the LPBF Ti-Fe alloys are shown in Fig. 3. The Ti-0 wt% Fe alloy consists of coarse columnar grains, while the Ti-0.05∼2.0 wt% Fe alloy consists of fine acicular grains. The grain size of Ti-0.05∼2.0 wt% Fe consists of fine acicular grains, which become finer with increasing Fe content. Such changes have also been observed with the addition of O and N [16, 17]. Figure 4 shows the relationship between the average grain size (equivalent diameter) and average width of acicular grains and the amount of Fe added in the LPBF Ti-Fe alloy. The average grain size was 17.7 µm in Ti-0.05 Fe, while the size of the acicular grains became homogeneous throughout the Ti-0.2 wt% Fe alloy, and the average grain size was 4.1 µm. In the Ti-1.0 and 2.0 wt% Fe alloys, where the Fe content was increased, the grain size became finer, with an average grain size of about 1 µm. The width of the acicular grains was significantly reduced from 7.5 µm in Ti-0.05 Fe to 630 and 530 nm in Ti-1.0 and 2.0 wt% Fe, respectively. In addition, the prior β-Ti grains in Ti-0.05 wt% Fe showed coarse (50∼100 µm) and irregularly shaped, while those in Ti-0.2 wt% Fe consisted of a mixture of columnar prior β-Ti grains with a width of 30∼60 µm and equiaxed prior β-Ti grains with a diameter of about 10∼20 µm. With further increase in Fe addition, Ti-1.0 and 2.0 wt% Fe exhibits columnar grains of prior β phase with widths of 20–60 µm. The shape and size of both α-Ti and prior β-Ti grains were heterogeneous in Ti-0.05 wt% Fe, which was attributed to the heterogeneous distribution of Fe. It has been reported that LPBF Ti alloys exhibit fine acicular grains when a certain amount of solute element is added [16, 17]. Fine acicular grains are formed in melt pool in which the solid solution of Fe exceeds a certain amount, while coarse grains are formed in melt pool with less Fe. As a result, the shape and size of α-Ti and prior β-Ti grains in the Ti-0.05 wt% Fe became heterogeneous. No β-Ti formation was observed even in Ti-2 wt% Fe, which is consistent with the above XRD diffraction results.

Fig. 3

IPF maps of (a) Ti-0 wt% Fe, (b) Ti-0.05 wt% Fe, (c) Ti-0.2 wt% Fe, (d) Ti-1.0 wt% Fe, and (e) Ti-2.0 wt% Fe with prior β grain boundary as black line. (online color)

Fig. 4

Dependence of grain size and α lath width on Fe addition.

TEM-EDS analysis of LPBF Ti-2 wt% Fe was performed to clarify the distribution of these solid solution Fe atoms. The scanning transmission electron microscope (STEM) image and EDS analysis results at the same field of view are shown in Fig. 5. The distribution of Fe shows that the concentration of Fe decreases at the outer edges of the grains, and although Fe is abundant at the grain boundaries, Fe is also detected in the central part of the grains. Quantitative evaluation of Fe content shows that even the grain with the smallest amount of Fe detected in the center of the field of view has 0.14∼1.86 wt% of Fe. Although the amount of solid solution Fe decreases at the outer edge, the amount of solid solution Fe in the center is the same as that of the added amount. In contrast, the Fe solubility near the grain boundaries ranged from 1.90 to 3.76 wt%. Near-α titanium alloys containing a small amount of β-stabilizing elements produced by LPBF undergo martensitic transformation, a non-diffusion transformation, due to their rapid cooling rate, forming α′-Ti with forced solid solution of β-stabilizing elements. In the LPBF process, a heat-affected zone (HAZ) is formed around the molten pool and maintained at a high temperature for a very short time. In the HAZ, it is considered that some of the solid Fe at the grain periphery diffuses and segregates to the grain boundary. In previous studies, the solubility of Fe in α-Ti and β-Ti was reported to be 0.05–0.11 wt% and 7.98–9.94 wt%, respectively, in Ti-2 wt% Fe sintered and extruded alloys consisting of two phases of α-Ti and β-Ti. The maximum Fe concentration at the grain boundary of this Ti-2 wt% Fe LPBF alloy is 3.76 wt%, which is considered insufficient to stabilize the β-phase, suggesting that the formation of β-Ti is limited. Similarly, since the maximum Fe concentration is 3.76 wt%, no Ti-Fe intermetallic compound is formed.

Fig. 5

(a) STEM image of Ti-2 wt% Fe alloy and elemental map of (b) Ti and (c) Fe. (online color)

The stress-strain diagram and tensile properties of the LPBF Ti-Fe alloy during tensile testing are shown in Fig. 6. First, compared to Ti-0 wt% Fe without Fe, the ductility increased with Fe addition in the range of Ti-0.2 wt% Fe, and the maximum elongation at break was 30% for Ti-0.05 wt% Fe. A similar phenomenon was also observed in LPBF Ti-O/N alloys [16, 17] and is thought to be due to the change from coarse columnar grains to fine acicular grains. Subsequently, the ductility of the Ti-Fe alloy gradually decreased, showing 19.4% for Ti-1 wt% Fe, but decreased to 6.7% for Ti-2 wt% Fe. On the other hand, the strength properties increased with increasing Fe content, with a UTS of 418 MPa for Ti-0 wt% Fe and 624 MPa for Ti-0.05 wt% Fe, indicating that a strengthening of 206 MPa was achieved even at very low Fe content. The UTS of Ti-1 and 2 wt% Fe were 890 and 1024 MPa, respectively. In a previous study [7] on the mechanical properties of Ti-Fe sintered extrusion alloys, the UTS of Ti-0 wt% Fe was 600 MPa, while those of Ti-1 and 2 wt% Fe were 762 and 842 MPa, respectively. The UTS values for each composition and the amount of strengthening corresponding to the difference from the reference Ti-0 wt% Fe were found to be significantly superior for the LPBF Ti-Fe alloy.

Fig. 6

(a) Stress-strain curves of LPBF Ti-Fe alloys and (b) dependence of tensile properties of LPBF Ti-Fe alloys on Fe addition. (online color)

Here, we have attempted to quantitatively clarify the effect of Fe addition on the strength properties of LPBF Ti-Fe alloys by analyzing the strength of LPBF Ti-Fe alloys. The effect of residual unmelted Fe particles or the formation of Ti-Fe intermetallic compounds on strength is negligible because there is no evidence of them. Next, we consider the effect of grain size on strength properties. As mentioned above, Ti-0 wt% Fe is composed of coarse columnar grains, while Ti-0.05∼2.0 wt% Fe are composed of fine acicular grains. It is well known that the effect of grain size on strength properties can be quantitatively evaluated by the Hall-Petch law [18]. In the case of LPBF Ti alloys with acicular microstructure, it has been reported that their strength can be organized by the width of the acicular α-Ti grains [19]. However, Ti-0 wt% Fe exhibits a coarse columnar microstructure, which cannot be organized by the Hall-Petch rule together with Ti-0.05∼2.0 wt% Fe with acicular microstructure. Here, we study the change of crystal orientation and evaluate the orientation of each sample quantitatively by the Schmid factor of the columnar plane (10$\bar{1}$0) slip, which is the main slip plane of Ti. 0.4∼0.5 for Ti-0 wt% Fe, while it was widely distributed from 0 to 0.5 for Ti-0.05∼2.0 wt% Fe. This is due to a significant microstructural change from coarse, strongly oriented grains to randomly oriented fine acicular grains. The average values were 0.46 for Ti-0 wt% Fe and 0.30–0.32 for Ti-0.05∼2.0 wt% Fe. Since it is difficult to theoretically investigate the strength changes due to grain refinement strengthening and orientation changes associated with the change from coarse grains to fine acicular grains, this study mainly considers the strength analysis for Ti-0.05∼2.0 wt% Fe. Finally, the strength properties of Ti alloys are strongly influenced by solid solution elements. In the LPBF Ti-Fe alloys used in this study, the solid solution of Fe varies widely. In addition, a change in the solid solution of oxygen, an impurity element, is suspected. The oxygen content of the LPBF Ti-Fe alloys was measured, and the values ranged from 0.17 to 0.19 wt%, which were similar regardless of the Fe content. Since the amount of solid solution strengthening by oxygen can be calculated to be a maximum of about 30 MPa, the effect of oxygen on the strength properties in this study is considered to be limited. Therefore, the two main strengthening mechanisms in LPBF Ti-Fe alloys are grain refinement strengthening and solution strengthening by Fe. Solid solution strengthening by Fe is studied using the Labusch model expressed in eq. (1) [20].

  

\begin{equation} \Delta \sigma_{\text{YS}} = \frac{\tau }{m} = \frac{c^{2/3}}{m}\left(\frac{F_{M}{}^{4}w}{4Gb^{9}} \right)^{1/3}, \end{equation} (1)

where c is the amount of solid solution and m is the Schmid factor. They are variable values. F_M is the maximum value of the interaction force between the blade dislocation and solute atoms, w is a parameter that indicates the range of interaction between the blade dislocation and intruding solute atoms, G is the transverse modulus of elasticity, and b is the magnitude of the Burgers vector, which are constants specific to the material system. However, since it is difficult to theoretically calculate these constants for α-Ti with hcp structure, a method to experimentally derive these constants has been proposed [16, 21–23]. However, since this constant has not been reported for the Ti-Fe system, the contribution of solid solution strengthening by Fe is investigated in this study using the same method as in previous studies. The material factors used in the analysis of the strengthening mechanism are summarized in Table 1.

Table 1 Values of microstructural parameters required for tensile strength analysis in LPBF Ti-Fe alloys.

First, the amount of strengthening due to grain refinement was quantitatively evaluated based on the Hall-Petch law. The results are summarized in Table 2. The Hall-Petch coefficient was 147.8 MPa µm^1/2 calculated from the values reported in previous studies [19]. As a result, an increase in strength of 149 MPa was confirmed for the Ti-2 wt% Fe compared to the reference Ti-0.05 wt% Fe. Based on previous studies, the two main strengthening factors in LPBF Ti-Fe alloys are grain boundary strengthening by grain refinement and solid solution strengthening by Fe solute atoms. The amount of solid solution strengthening by Fe solute atoms can be determined by subtracting the amount of strengthening by grain refinement (calculated value) from the amount of strengthening of each Ti-Fe alloy for Ti-0.05 wt% Fe (experimental value). According to the Labusch model shown in eq. (1), the amount of solution strengthening is characterized by an increase in proportion to c^2/3/m. Therefore, we verified that this relationship holds for LPBF Ti-Fe alloys. Figure 7 shows the relationship between the amount of solution strengthening by Fe and c^2/3/m obtained by calculation. It can be seen that both are in good agreement with the Labusch model, with a coefficient of determination R² of 0.989, which is a very high value. The coefficient of proportionality (slope) is 6617.3 and from this value the material constant F_M is calculated to be 8.79 × 10⁻¹⁰ N. This value is in the same order of magnitude as the F_M value when oxygen and nitrogen are solute atoms in the α-Ti crystal.

Table 2 Strengthening factors of LPBF Ti-Fe alloys.

Fig. 7

Relationship between materials factor in Labusch model and increment of yield strength.

Therefore, the strength analysis of each Ti-Fe alloy with different amount of Fe addition is performed. First, the increase in strength from Ti-0.0 wt% Fe to Ti-0.05 wt% Fe was 175 MPa. Since the difference in Fe solid solution was limited, the change in grain size and orientation associated with the microstructure change from columnar to fine acicular grains was considered to be the main cause of this amount of strengthening. In addition, the amount of strengthening due to grain refinement of acicular grains calculated above and the amount of solid solution strengthening by Fe calculated using the derived material constants were summarized. The results are shown in Fig. 8 together with the experimentally obtained YS. It can be seen that the theoretically calculated strength analysis results are in good agreement with the experimental values for all samples. As the amount of Fe added increased, the strengthening due to acicular grain refinement and the solution strengthening due to Fe gradually increased, and the solution strengthening due to Fe reached a maximum in the case of Ti-2 wt% Fe. However, the proportion of the total strengthening was about 40%, and the contributions of other strengthening factors were about 30%, respectively. It was concluded that the high-strength properties of the LPBF Ti-Fe alloy are expressed by the fusion of solid solution strengthening by Fe, strengthening by microstructural change from columnar grains to fine acicular grains, and strengthening by refinement of acicular grains.

Fig. 8

Strengthening factor contribution to yield stress of LPBF Ti-Fe alloys.

4. Conclusion

In this study, Ti-Fe alloys were prepared by the LPBF method to improve mechanical properties by supersaturated solid solution of Fe to α-Ti, and each strengthening mechanism in the alloys was quantitatively clarified by microstructural analysis and evaluation of mechanical properties. As a result, the following findings were obtained.

1. (1)    Microstructural analysis showed that the added Fe powder was completely decomposed in the LPBF process, and the decomposed Fe was solidly dissolved in α-Ti, and no β-Ti or intermetallic compound formation was observed. The width of the acicular grains reached 530 nm for Ti-2 wt% Fe.
2. (2)    The LPBF Ti-Fe alloy exhibited excellent strength and ductility properties: UTS 418 MPa and elongation at break 20.2% for Ti-0 wt% Fe, UTS 890 MPa and elongation at break 19.4% for Ti-1 wt% Fe, and UTS 1024 MPa and elongation at break 6.7% for Ti-2 wt% Fe.
3. (3)    The strengthening mechanism of LPBF Ti-Fe alloys was analyzed, and the constant part of the Labusch model for the solid solution strengthening of Fe in α-Ti was calculated to be 6617. The main strengthening mechanisms of LPBF Ti-Fe alloys are solid solution strengthening by Fe, strengthening by microstructural change from columnar grains to fine acicular grains, and strengthening by refinement of acicular grains.

Acknowledgments

This research was supported by OU Master Plan Implementation Project.

REFERENCES

• 1)  Titanium Alloys-Towards Achieving Enhanced Properties for Diversified Applications, ed. by A.K.M.N. Amin, (InTech, London, 1928).
• 2)  Titanium and Titanium Alloys, ed. by J.C. Williams, (Springer-Verlag, New York, 1982).
• 3)  Titanium, ed. by G. Lütjering and J.C. Williams, (Springer-Verlag, New York, 2003).
• 4)   L.M.  Kang and  C.  Yang: A Review on High-Strength Titanium Alloys: Microstructure, Strengthening, and Properties, Adv. Eng. Mater. 21 (2019) 1801359. doi:10.1002/adem.201801359
• 5)  S.M. Jasinsk, Mineral commodity summaries 2023, (2023). doi:10.3133/mcs2023.
• 6)   M.  Niinomi,  T.  Hanawa,  M.  Ikeda,  A.  Chiba,  T.  Furuhara,  T.  Narushima,  K.  Tsuchiya,  S.  Emura,  T.  Nakano and  T.  Takenaka: Strategy for Ubiquitous Titanium Alloys, J. Japan Inst. Metal. 72 (2008) 915. doi:10.2320/jinstmet.72.915
• 7)   J.  Umeda,  T.  Tanaka,  T.  Teramae,  S.  Kariya,  J.  Fujita,  H.  Nishikawa,  Y.  Shibutani,  J.  Shen and  K.  Kondoh: Microstructures analysis and quantitative strengthening evaluation of powder metallurgy Ti–Fe binary extruded alloys with (α+β)-dual-phase, Mater. Sci. Eng. A 803 (2021) 140708. doi:10.1016/j.msea.2020.140708
• 8)   Q.  Yan,  B.  Chen,  N.  Kang,  X.  Lin,  S.  Lv,  K.  Kondoh,  S.  Li and  J.S.  Li: Comparison study on microstructure and mechanical properties of Ti-6Al-4V alloys fabricated by powder-based selective-laser-melting and sintering methods, Mater. Charact. 164 (2020) 110358. doi:10.1016/j.matchar.2020.110358
• 9)   S.  Liu and  Y.C.  Shin: Additive manufacturing of Ti6Al4V alloy: A review, Mater. Des. 164 (2019) 107552. doi:10.1016/j.matdes.2018.107552
• 10)   G.  Yablokova,  M.  Speirs,  J.  Van Humbeeck,  J.P.  Kruth,  J.  Schrooten,  R.  Cloots,  F.  Boschini,  G.  Lumay and  J.  Luyten: Rheological behavior of β-Ti and NiTi powders produced by atomization for SLM production of open porous orthopedic implants, Powder Technol. 283 (2015) 199–209. doi:10.1016/j.powtec.2015.05.015
• 11)   S.E.  Brika,  M.  Letenneur,  C.A.  Dion and  V.  Brailovski: Influence of particle morphology and size distribution on the powder flowability and laser powder bed fusion manufacturability of Ti-6Al-4V alloy, Addit. Manuf. 31 (2020) 100929. doi:10.1016/j.addma.2019.100929
• 12)   L.  Haferkamp,  L.  Haudenschild,  A.  Spierings,  K.  Wegener,  K.  Riener,  S.  Ziegelmeier and  G.J.  Leichtfried: The influence of particle shape, powder flowability, and powder layer density on part density in laser powder bed fusion, Metals 11 (2021) 418. doi:10.3390/met11030418
• 13)   M.  Mehrabi,  J.  Gardy,  F.A.  Talebi,  A.  Farshchi,  A.  Hassanpour and  A.E.  Bayly: An investigation of the effect of powder flowability on the powder spreading in additive manufacturing, Powder Technol. 413 (2023) 117997. doi:10.1016/j.powtec.2022.117997
• 14)   M.A.  Balbaa,  A.  Ghasemi,  E.  Fereiduni,  M.A.  Elbestawi,  S.D.  Jadhav and  J.P.  Kruth: Role of powder particle size on laser powder bed fusion processability of AlSi10mg alloy, Addit. Manuf. 37 (2021) 101630. doi:10.1016/j.addma.2020.101630
• 15)   S.  Ziri,  A.  Hor and  C.  Mabru: Combined effect of powder properties and process parameters on the density of 316L stainless steel obtained by laser powder bed fusion, Int. J. Adv. Manuf. Technol. 120 (2022) 6187–6204. doi:10.1007/s00170-022-09160-w
• 16)   E.  Ichikawa,  K.  Shitara,  J.  Umeda,  S.  Li,  B.  Chen and  K.  Kondoh: Microstructures and strengthening mechanism of oxygen soluted titanium by selective laser melting, J. Japan Soc. Powder Powder Metall. 68 (2021) 67–75. doi:10.2497/jjspm.68.67
• 17)   K.  Kondoh,  A.  Issariyapat,  J.  Umeda and  P.  Visuttipitukul: Selective laser-melted titanium materials with nitrogen solid solutions for balanced strength and ductility, Mater. Sci. Eng. A 790 (2020) 139641. doi:10.1016/j.msea.2020.139641
• 18)   E.O.  Hall: The deformation and ageing of mild steel III Discussion of results, Proc. Phys. Soc. B 64 (1951) 747–753. doi:10.1088/0370-1301/64/9/303
• 19)   W.  Xu,  E.W.  Lui,  A.  Pateras,  M.  Qian and  M.  Brandt: In situ tailoring microstructure in additively manufactured Ti-6Al-4V for superior mechanical performance, Acta Mater. 125 (2017) 390–400. doi:10.1016/j.actamat.2016.12.027
• 20)   R.  Labusch: A Statistical Theory of Solid Solution Hardening, Phys. Status Solidi 41 (1970) 659–669. doi:10.1002/pssb.19700410221
• 21)   S.  Kariya,  M.  Fukuo,  J.  Umeda and  K.  Kondoh: Quantitative Analysis on Light Elements Solution Strengthening in Pure Titanium Sintered Materials by Labusch Model Using Experimental Data, Mater. Trans. 60 (2019) 263–268. doi:10.2320/matertrans.Y-M2018849
• 22)   K.  Kondoh,  M.  Fukuo,  S.  Kariya,  K.  Shitara,  S.  Li,  A.  Alhazaa and  J.  Umeda: Quantitative strengthening evaluation of powder metallurgy Ti–Zr binary alloys with high strength and ductility, J. Alloy. Compd. 852 (2021) 156954. doi:10.1016/j.jallcom.2020.156954
• 23)   A.  Issariyapat,  P.  Visuttipitukul,  T.  Song,  J.  Umeda,  M.  Qian and  K.  Kondoh: Strength-ductility improvement of extruded Ti-(N) materials using pure Ti powder with high nitrogen solution, Mater. Sci. Eng. A 779 (2020) 139136. doi:10.1016/j.msea.2020.139136

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• This Paper was Originally Published in Japanese in J. Jpn. Soc. Powder Powder Metallurgy, Advanced Publication by J-STAGE, https://doi.org/10.2497/jjspm.23-00068. The main text is slightly modified. The citation in Table 2 is corrected.