According to Hunt's columnar-to-equiaxed transition (CET) criterion, which is generally accepted, a high-temperature gradient (G) in the solidification front is preferable to a low G for forming columnar grains. Here, we report the opposite tendency found in the solidification microstructure of stainless steels partially melted by scanning electron beam for powder bed fusion (PBF)-type additive manufacturing. Equiaxed grains were observed more frequently in the region of high G rather than in the region of low G, contrary to the trend of the CET criterion. Computational thermal-fluid dynamics (CtFD) simulation has revealed that the fluid velocity is significantly higher in the case of smaller melt regions. The G on the solidification front of a small melt pool tends to be high, but at the same, the temperature gradient along the melt pool surface also tends to be high. The high melt surface temperature gradient can enhance Marangoni flow, which can apparently reverse the trend of equiaxed grain formation.
Keywords: additive manufacturing; 316L stainless steel; 304 stainless steel; powder-bed fusion; electron-beam melting; computational thermal-fluid dynamics simulation
Recently, additive manufacturing (AM) technologies are emerging rapidly and being applied to various materials. In conventional forming processes, materials are cast, deformed, and/or subtracted from bulk by cutting tools. In contrast, materials are subsequently added to form parts with the desired shape in AM processes, and it enables us to build 3D parts with complicated geometry easily. Austenitic 316L and 304 stainless steels (hereafter denoted by SS) are commonly used in a wide range of fields, including plant piping, valves, tools, household equipment, food, and biomedical devices. AM technologies are proposed to be applied to fabricate SS parts as well [[
Among the AM processes applied to metals, a powder-bed fusion (PBF)-type AM has been most commonly used in this decade for its accuracy and degree of freedom in the shape of objects fabricated. In the PBF-AM process, 3D parts are fabricated by repeating the selective melting of metal powders by laser or electron beams and subsequent solidification. With optimized process parameters, AM-processed SS parts possessing a relative density higher than 99% can be fabricated with good reproducibility [[
Mechanical properties of metal parts largely depend on their microstructure. Therefore, many researchers have investigated the relationship between process parameters for PBF and microstructures in recent years [[
Microstructures of metals fabricated by the PBF process are solidification structures. In general, solidification microstructures can be predicted from solidification conditions defined by the combination of a temperature gradient, G, and a solidification rate, R, at a solid/liquid interface according to the columnar-equiaxed transition (CET) criterion proposed by Hunt [[
According to the CET criterion [[
(
where n and a are alloy constants. ∆T
In this study, to reveal the relationships between microstructures and solidification conditions, we have investigated the solidification microstructures of 316L and 304 SSs induced by electron-beam irradiation. In addition, the solidification conditions at the solid/liquid interface have been evaluated using a computational thermal-fluid dynamics (CtFD) simulation. The factors determining the formation of equiaxed grains are discussed with reference to the CET criterion. The roles of a fluid flow on the microstructure formation are discussed by utilizing the results of the microstructure analysis and the CtFD simulation.
Specimens of 316L and 304 SSs with a dimension of 20 mm × 50 mm × 10 mm were received. The specimens were irradiated with electron beams scanned along straight lines with a length of 5 mm using an electron beam machine (Mitsubishi Electric EBM-6LB-1, Mitsubishi Electric, Tokyo, Japan) under a helium atmosphere with a pressure of 0.5 Pa. Acceleration voltage and convergence current were fixed to be 60 kV and 1150 mA, respectively. The irradiations were conducted under 12 conditions combining three levels of beam power, P (
The top surfaces of the electron-beam irradiated samples were observed using a laser microscope (Keyence VK-X200/210, Keyence Corporation, Osaka, Japan) for measuring the widths and the surface topographies of the melt tracks. The samples were cut perpendicular to the beam-scanning direction for cross-sectional observation using a field emission scanning electron microscope (FE-SEM, JEOL JSM 6500, JEOL Ltd., Tokyo, Japan). Crystal orientation analysis was performed by electron backscatter diffraction (EBSD). The sizes of each crystal grain and their aspect ratio were evaluated by analyzing the EBSD datum.
CtFD simulations of electron-beam irradiations to 316L and 304 SSs were performed using a commercial 3D thermo-fluid analysis software (Flow Science FLOW-3D
Figure 1 shows a typical example of a surface laser microscope image and corresponding height map of the electron-beam irradiated region of 304 SS. The melt region can be seen in Figure 1a. The width of the melt regions tended to increase with increasing beam power. Additionally, the height map of Figure 1b shows that the surface of the melt region is not flat.
Figure 2 shows a cross-sectional SEM image taken from the electron-beam melt region of 304 SS. The fusion line can be seen, as indicated by dashed lines. The area of melt regions tend to increase with increasing beam power. The geometries of the melt regions in 304 SS for each of the same beam conditions are similar to those in 316L SS.
The width, height, and depth are measured from these surface and cross-sectional images. Figure 3 shows the width, height, and depth of melt tracks formed by scanning electron beam as a function of beam power. All of the width (Figure 3a), height (Figure 3b), and depth (Figure 3c) increased as the beam power increased. Under all process conditions, the melt regions formed in 316L SS were narrower and deeper than those in 304 SS.
Figure 4 shows the cross-sectional inverse pole figure (IPF) orientation maps of melt region in 316L SS and 304 SS samples irradiated with electron beam of various power at a scanning speed of 100 mm/s. Microstructures largely depend on the type of steels: in 316L SS samples (Figure 4(a1–a3)), equiaxed crystalline grains with diameters of 10–30 μm appear at the fusion line, and fine columnar crystalline grains with diameters of 20–50 μm appear at the center of the melt regions. In 304 SS (Figure 4(b1–b3)), coarse equiaxed grains with diameters of 5–20 μm are formed nearby the fusion line, and coarse columnar crystals with diameters of 5–10 μm are formed in the center. The morphology of the microstructures does not depend on the beam power significantly. Note that microstructures in the matrix of both steels are similar to each other, and the difference between the solidification microstructures in the melt region of the two SSs cannot be attributed to the difference in the microstructures in the matrix. From these EBSD data, average grain sizes and their aspect ratios in the melt regions were evaluated, as shown in Figure 5. The average grain size in 316L SS was larger than that of 304 SS under all process conditions, and the average grain size does not depend on beam power for both steels. Their average aspect ratios also do not depend on the process conditions, and are nearly the same for 316L and 304 SSs.
Figure 6 shows a snapshot of the CtFD simulation for 316L SS in the case of the electron-beam power, P, of 1200 W and scanning speed, V, of 100 mm/s, respectively.
Figure 7 compares a CtFD-simulated melt pool model of 316L SS with the EBSD IPF map of the corresponding cross section. By using a beam absorption efficiency of 0.8, the width and depth of the simulated melt region were in good agreement with these experimentally observed melt pools. On the other hand, there is a difference in the height between the experimentally observed melt pools and the simulated ones. The melt tracks have a rough surface, and the height depends on the cutting position. Thus, the height was excluded from the values, indicating the geometry of the melt region for examining the similarity of melt regions in the experiment to those in simulation in this study. The height will be included for further improvement of the model in future work. The value of the beam absorption efficiently is close to that reported in the literature [[
The solidification conditions at a liquid/solid interface were calculated from the CtFD simulation results. Figure 8 and Figure 9 show cross-sectional melt pools colored by solidification times (Figure 8(a1–c1) and Figure 9(a1–c1)), G (Figure 8(a2–c2) and Figure 9(a2–c2)), R (Figure 8(a3–c3) and Figure 9(a3–c3)), and U (Figure 8(a4–c4) and Figure 9(a4–c4)). Here, the solidification time is defined as the time when a liquid/solid interface has passed a mesh. Solidification times (Figure 8(a1–c1) and Figure 9(a1–c1)) indicate that the solidification starts at the region nearby the fusion line toward the center of the melt pool. In 316L SS, the G is highest in the regions near the fusion line and decreases as the solid–liquid interface moves toward the center of the melt pool (Figure 8(a2–c2)). On the other hand, the R is lowest near the fusion line and becomes higher as the interface approaches the center of the melt region (Figure 8(a3–c3)). In 304 SS, the regions solidified under the lowest G and R can be seen at the middle of the melt pools (Figure 9(a2–c2,a3–c3)). The distributions of G and R do not depend on beam power significantly in both 316L and 304 SSs. It is noted that the G became extremely large at the surface of the melt pool in both steels. It is suggested that the surface region was cooled mainly by external thermal radiation rather than by thermal diffusion through the metal substrate. As seen in Figure 8(a4–c4) and Figure 9(a4–c4), the fast fluid flow occurs in both steels, and the magnitude of flow velocity is larger in 316L SS than in 304 SS.
Figure 10a,b show the plot of the solidification conditions of each mesh in the G–R space. Except for the surface regions, all the regions exist under conditions of G in the range of 1.0 × 10
Each crystalline grain formed in melt regions corresponds with solidification conditions obtained by CtFD simulations. All the solidification conditions are plotted in the G–R space colored by the aspect ratio, as shown in Figure 11a,b. For a better visual understanding, average aspect ratios were calculated for each mesh of the double logarithmic grid using the points of solidification condition within each mesh as shown in Figure 11c,d.
Only equiaxed crystalline grains were formed in the 304 SS under the whole range of solidification conditions obtained in this study. On the other hand, equiaxed crystalline grains appeared in the high G region, whereas columnar crystals appear in the low G region in the G–R map of 316L SS. This relationship between the microstructures and solidification conditions is contrary to that predicted by the CET criterion.
In the welding process [[
Figure 13 shows the cross-sectional EBSD IPF-Z map of the bead solidified under P = 1200 W and V = 100 mm/s, and the corresponding flow velocity distribution map. Equiaxed crystalline grains were observed near the outmost part of the melt region. It is indicated that such regions were solidified under the condition with high flow velocities. These results also suggest that equiaxed crystals are formed owing to a high velocity of fluid flow even in the PBF-AM process, even though the G and the R are in the range for columnar grain formation. A similar trend has been reported for Co–Cr–Mo alloy [[
As shown in Figure 11, columnar crystal grains were formed in 316L SS, even in the ranges of G and R for the formation of equiaxed crystals grains formed in 304 SS. The CET line of 316L SS is suggested to be shifted downward significantly from that of 304 SS. According to Equation (
Thus, it is suggested that the CET line for 316L SS shifts toward lower G from that of 304 SS because of the smaller ∆T
Figure 14a compares the solidification conditions of 316L and 304 SSs except for those for the surface regions, which were evaluated by the CtFD. CET criteria was calculated by Equation (
We have investigated the solidification microstructures of 316L and 304 SSs induced by electron-beam irradiation for PBF-EB, and evaluated the solidification conditions at the solid/liquid interface using a CtFD simulation.
The width, height, and depth of melt track induced by electron-beam irradiation increased as the beam power increased. Under all process conditions, melt regions formed in 316L SS were narrower and deeper than those in 304 SS. EBSD analysis revealed that the average grain size in 316L SS was larger than that in 304 SS under all process conditions, while their average aspect ratios were nearly the same for 316L and 304 SSs. It was found that, contrary to the CET criterion, equiaxed grains were frequently formed under high G conditions in 316L SS. CtFD simulation revealed that there was a fluid flow with a velocity of up to approximately 400 mm/s, and suggested that equiaxed grains are formed owing to the effect of fragmentations of dendrites and the transport of the fragments. In 316L SS, columnar crystals were formed even in the case where the G and R were within the range of equiaxed crystals' grain formation in 304 SS. It is suggested that the CET line shifts downward because of the smaller ∆T
In this study, it was found that solidification microstructures formed in the PBF-EB process are intricately related to various factors such as temperature gradient, solidification rate, and flow velocity. The machine learning-assisted analysis is currently underway.
MAP: Figure 1 Typical examples of (a) a surface laser microscope image and (b) corresponding height map of 304 SS. The electron-beam power, P, and scanning speed, V, are 1200 W and 100 mm/s, respectively.
Graph: Figure 2 A typical example of a cross-sectional SEM image taken from the electron-beam irradiated region of 304 SS. P and V are 900 W and 100 mm/s, respectively. The dashed line indicates the fusion line.
Graph: Figure 3 (a) Width, (b) height, and (c) depth of melt tracks formed on 316L and 304 SSs as a function of beam power. The width and the height were measured by laser microscope and the depths were measured by cross-sectional SEM observation.
Graph: Figure 4 SEM electron backscatter diffraction (EBSD) IPF orientation maps on the transversal cross section of (a1–a3) 316L and (b1–b3) 304 SS samples irradiated with electron beams under V = 100 mm/s and various beam power conditions: (a1,b1) P = 600 W, (a2,b2) P = 900 W, and (a3,b3) P = 1200 W.
Graph: Figure 5 (a) Average grain size and (b) their aspect ratio evaluated from EBSD IPF orientation maps taken from the electron-beam irradiated regions in 316L and 304 SS samples.
Graph: Figure 6 Snapshot of CtFD simulation of electron-beam irradiation on 316L SS with process parameters of P = 1200 W and V = 100 mm/s. (a) Bird's eye view, (b) side view on the vertical cross section along the center of the scanning line. The color indicates the temperature.
Graph: Figure 7 Comparison of melt regions in (a) experimental SEM image and (b) CtFD simulation for the case with a beam diameter of 1200 µm, absorption rates of 0.8, beam power (P) of 1200 W, and beam scanning speed (V) of 100 mm/s.
Graph: Figure 8 CtFD simulated cross-sectional melt pools of 316L SS colored by (a1–c1) a solidification time, (a2–c2) a temperature gradient, G, (a3–c3) a solidification rate, R, and (a4–c4) a flow velocity, U. The beam powers were (a1–a4) P = 600 W, (b1–b4) P = 900 W, and (c1–c4) P = 1200 W.
Graph: Figure 9 CtFD simulated cross-sectional melt pools of 304 SS colored by (a1–c1) a solidification time, (a2–c2) a temperature gradient, G, (a3–c3) a solidification rate, R, and (a4–c4) a flow velocity, U. The beam powers were (a1–a4) P = 600 W, (b1–b4) P = 900 W, and (c1–c4) P = 1200 W.
Graph: Figure 10 G–R plots of (a) 316L and (b) 304 SSs colored by the beam power. (c) Average solidification conditions of each process parameter, and (d) magnified picture of (c).
Graph: Figure 11 G–R plots of (a) 316L and (b) 304 SSs colored by an aspect ratio of crystalline grains. Average aspect ratios of (c) 316L and (d) 304 SSs calculated for each mesh of the double logarithmic grid using the points of solidification condition within each mesh.
Graph: Figure 12 (a) G–R plot of 316L SS colored by a fluid velocity. (b) The average fluid velocity of 316L SS calculated for each mesh of the double logarithmic grid using the points of solidification condition within each mesh.
Graph: Figure 13 Comparison of (a) solidification microstructure (EBSD IPF map) of melt region in 316L SS formed by scanning electron beam and (b) a corresponding snapshot of CtFD simulation colored by fluid velocity.
Graph: Figure 14 Comparison between solidification conditions (dots and squares) evaluated by CtFD simulation and CET criteria (lines) calculated by Equation (
Table 1 Electron-beam irradiation conditions.
Line Energy, Scanning Speed, 100 300 1000 3000 Beam power, 600 6 2 0.6 0.2 900 9 3 0.9 0.3 1200 12 4 1.2 0.4
Table 2 Parameters used in CtFD simulations.
Name Symbol Value for 316L SS Value for 304 SS Density at 298.15 K 8000 a 7892.77 a Liquidus temperature 1710.26 a 1721.05 a Solidus temperature 1683.68 a 1619.15 a Viscosity at 7.83 a 7.35 a Specific heat at 298.15 K 440 a 453.66 a Thermal conductivity at 298.15 K 13.58 a 15.066 a Surface tension at 1.80216 a 1.78225 a Temperature coefficient of surface tension d −3.6616 × 10−4 a −3.5992 × 10−4 a Emissivity 0.27 [ Stefan–Boltzmann constant 5.67 × 10−8 [ Heat of vaporization Δ 6.21 × 10⁶ [ Vaporization temperature 3134 [
Table 3 Liquidus and solidus temperatures of 316L SS and 304 SS.
Name Symbol Value for 316L SS Value for 304 SS Liquidus temperature 1710.26 K a 1721.05 K a Solidus temperature 1683.68 K a 1619.15 K a Temperature difference between Δ 26.58 K 101.90 K
Conceptualization, Y.K. and T.N.; methodology, Y.M., M.O. and Y.K.; software, Y.M., M.O. and Y.K.; validation, Y.M., M.O. and Y.K.; investigation, Y.M., M.O. and Y.K.; data curation, Y.M., M.O. and Y.K.; writing—original draft preparation, Y.M., M.O. and Y.K.; writing—review and editing, M.O. and Y.K; supervision, Y.K. and T.N.; project administration, Y.K. and T.N.; funding acquisition, Y.K. and T.N. All authors have read and agreed to the published version of the manuscript.
This work was supported by JSPS KAKENHI Grant Number 17H01329 and by Cabinet Office, Government of Japan, Cross-ministerial Strategic Innovation Promotion Program (SIP), "Materials Integration for Revolutionary Design System of Structural Materials", (funding agency: The Japan Science and Technology Agency).
The authors declare no conflict of interest.
We would like to thank H. Kawabata for technical support for sample preparations and electron beam irradiation experiments.
By Yuichiro Miyata; Masayuki Okugawa; Yuichiro Koizumi and Takayoshi Nakano
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