Interferometry of Gas-Phase Flows during Selective Laser Melting

Abstract

Gas-phase flows occurring in a plume in a processing zone during selective laser melting (SLM) can significantly affect the quality of the process. To further enhance SLM performance, the characteristics of the flows should be considered. In this article, the vapor-gas jet emerging from the laser processing zone was studied. It was visualized by interferometry to evaluate flow velocity, geometry and changes in refractory index depending on laser power. The velocity and pressure fields of the vapor jet and the entrained ambient gas were estimated by mathematical modeling. It was shown that the increase of laser power led to higher jet velocity and greater change in its refractory index. The latter also was used to evaluate the content of metal vapor in the plume and its influence on the absorption of laser radiation.

1. Introduction

Intensively developing additive technologies (AT) provide the ability to manufacture parts of complex shape directly from computer models, avoiding time-consuming operations of manufacturing special molds, tools and equipment settings. Normally, parts are manufactured layer-by-layer by consolidating powder, eliminating shape complexity as a technological restriction. It makes AT widely demanded due to their flexibility and the ability to quickly obtain final products. This dramatically changes the technology of product development in mechanical engineering, the technology of prosthetics in medicine and makes it possible to quickly prototype parts of complicated shape. Selective laser melting (SLM) is one of the key technologies due to its applicability to a wide range of structural and functional materials, including steel.

In the laser spot area, the melting temperature is easily reached even for refractory materials. However, due to the high scanning speed, the laser exposure time for each section of the material turns out to be very short, which is often not enough for complete powder consolidation. In addition, the temperature distribution in the laser exposure zone is very non-uniform. Under these conditions, the material may contain an unacceptable number of defects, such as pores, microcracks and extended defects in the metallurgical bond. On the other hand, the SLM process substantially depends both on a large number of process parameters, such as laser power and spot diameter; scanning speed and strategy; and powder layer thickness, and on parameters of the initial material. Therefore, one of the key problems of the SLM technology is the optimization of technological parameters to achieve stable process conditions and reduce the number of defects mentioned [1,2].

Increasing the productivity of the SLM process is one of the main objectives [3]. The productivity largely depends on the scanning speed of a laser beam when growing products. Along with power and diameter of the laser beam, scanning speed is a parameter that determines the manufacturing of high-quality objects without pores, cracks and other defects of micro and macrostructures [4]. The balance between productivity and stable quality is sometimes reduced to an integral indicator characterizing the amount of energy transferred to the powder material per unit area (1):

$$E_D=P/\left(DV\right),$$

(1)

where P is laser power, D is the laser beam diameter and V is the laser scanning speed [4]. Increasing the scanning speed without changing the laser power leads to low-energy instability of the fused material, resulting in the formation of individual droplets. Such an effect arises as the result of capillary instability of molten material. A gradual increase in power to compensate this effect leads to an increase in the energy density in the laser spot. Over the past few years, the phenomenon of intense evaporation during SLM with a high energy density has been discovered in various scientific groups [5,6,7]. Evaporation not only leads to loss of mass and energy in the laser spot but also causes a jet flow in the gas phase, which entrains the powder particles from the adjacent areas of the powder layer; thus, playing a key role in mass transfer [8,9]. This phenomenon was first explained by the evaporation of the material under laser irradiation and the entrainment of the ambient gas by the vapor jet due to Bernoulli effect [8]. This is the formation of the so-called denuded zone along the edges of the single track of molten material, which for a long time was an unresolved theoretical problem [10]. Besides, it was shown that the vapor recoil pressure significantly affects the melt pool and can lead to the formation of a keyhole. This effect determines the stability threshold of the melt pool and the entire SLM process at high energy densities, limiting the productivity [8,9]. It is also noted in some works that the resulting vapor-gas jet affects the absorption of laser radiation, reducing its useful power in the SLM [10,11,12,13].

Recent experimental works visualized the evaporation jet and particles it lifted and made it possible to estimate a typical jet velocity of several meters per second [5,14,15,16,17]. It experimentally confirms the importance of the gas-phase flow transporting the powder particles during SLM. Until now, theoretical concepts of the SLM mechanism have been based on the assumption of either direct interaction of laser radiation with powder particles, leading to their melting, or the absorption of a powder layer by a moving melt pool. New data suggests that the pool does not come in contact with the powder layer, and individual powder particles enter it together with the surrounding gas flow formed around the evaporation jet. Existing works on the visualization of the jet are limited by the use of a high-speed camera and a magnifying lens, which allows only considering in detail, the molten pool and the thermal radiation of the plume [5,8,16,17,18,19]. These works also reported that the resulting gas-vapor jet is not limited only to the zone of its own radiation, but also determines the zones of high and low pressure. To visualize not only the vapor jet but the induced entrainment flow of ambient gas, an improvement in the approach is required. It will provide more information about the impact of the gas-phase flow in the SLM process.

Thus, it is obvious that the formation of a gas-phase flow during the SLM process is unavoidable and its importance in achieving the required product quality increases with increasing technology productivity due to an increase in laser power density. In this work, the goal is to study the jet flow to identify the main mechanisms of its formation.

2. Materials and Methods

To register gas-phase flows in the zone of laser irradiation by interferometry, a compact setup has been developed that is placed above the desktop of the laboratory SLM unit. The optical setup is shown in Figure 1. It is based on Jamin interferometer, which was tested earlier in similar tasks and demonstrated the reliability of results [20,21,22]. Laser beam 1 (532 nm), expanded by lens 2, is divided into two beams (the probing one and the reference one) using plane-parallel glass plate 3. After the probing beam passes through the laser-interaction zone 4, both beams are brought together using the same glass plate 5. Next, lens 6 builds an image of the studied area together with a reference beam superimposed on it in the recording camera 7. The beams together create an interference pattern. The interferometer is configured so that in the absence of exposure, the interference pattern looks like closely spaced parallel fringes. The presence of a gas-phase jet leads to the change of the optical path length ΔS of the probe beam, which leads to the change of its phase Φ and, accordingly, to a local change in the position of interference fringes near the laser exposure zone. Interferograms were recorded using a high-speed Photron Fastcam SA 5 camera (Photron, Tokyo, Japan) with a frame rate of 5000 frames per second, which corresponds to an exposure time of 0.2 ms per frame.

The interpretation of the interferogram allows one to obtain the spatial distribution of the change in the optical path caused by the presence of a gas-phase jet. To interpret the interferograms, the spatial Fourier filtering method was used [23,24]. The decryption algorithm included a two-dimensional Fourier transform from the periodic intensity distribution in the interferogram, as a result of which the zero and ± first maxima were formed in the Fourier spectrum, reflecting the spatial frequency of the interference fringes. The first-order maxima contained information on phase distribution Δϕ(x,y) in the cross-section of the working beam. To obtain this distribution, only the 1st maximum was highlighted by filtering and shifted to the center of the Fourier plane, which meant the elimination of the spatial frequency in the phase distribution Δϕ(x,y), and the inverse Fourier transform was performed. The resulting complex-valued function:

$$I\left(x,y\right)=a{e}^{i\Delta \phi \left(x,y\right)}$$

(2)

contains the required function Δϕ(x,y):

$$\Delta \phi \left(x,y\right)={\tan }^{-1}\frac{\mathrm{Im}\left(t\right)}{\mathrm{Re}\left(t\right)}.$$

(3)

Using Equation (3), the spatial distribution of the increment Δϕ of the phase of the probing laser beam caused by the interaction of the working laser with the processed substrate was obtained. Since the phase found in this way is a multivalued function and can break at the points where it takes the values ±π/2, phase unwrapping algorithm is used to remove discontinuities by adding a constant value ±π to all values of the Δϕ after every discontinuity. As a result, a continuous smooth phase surface Δϕ (x,y) was obtained.

According to this scheme, the process of powder melting of corrosion-resistant steel 12X18H10T (Polema LLC, Tula, Russia) with an average particle size of 20–63 μm was recorded (Figure 2). The same steel was used as the substrate (

Table 1. Chemical composition of the 12X18H10T steel, %wt.

Material	Fe	C	Si	Cu	Mn	Ni	Cr	Ti
12X18H10T	bal.	<0.12	<0.8	<0.3	<2.0	9–11	17–19	0.4–1

). The gas-phase jet was recorded when the powder was treated with the Nd:YAG working laser with a wavelength of 1064 nm (IPG Photonics LK-200, Fryazino, Russia) across the probing beam of the probing laser. The experiments were carried out in air atmosphere at a constant scanning speed of the working laser beam of 50 mm/s, with a variable laser power of 50, 90, 130 and 170 W.

To estimate the velocity fields and pressure changes in the area of gas-phase flow formation, a mathematical model of gas flow during SLM was developed (Appendix A), taking into account the presence of a solid surface, which allows calculation of shear stresses on this surface (Figure A1). The calculations were made for an argon atmosphere at normal atmospheric pressure and a temperature of 298 K (

Table A1. Gas-phase flow velocity.

Parameter	Density ρ0, kg/m3	Dynamic Viscosity η, Pa∙s	Kinematic Viscosity v, m2/s
Value	1.634	22.3 × 106	13.65 × 106

). The dynamic viscosity of argon and air differ slightly, as a result of which the data obtained are applicable to the present experiment (

Table A2. Jet parameters at evaporation spot of D = 50 μm.

No	Reynolds Number Re	Mass Flow M, μg/s	Dynamic Force F0, nN	Impulse Flow F/F0	Dimensionless Impulse Flow F/(ηv)	Landau Parameter A
1	10	8.757	30.43	1.06	111	1.284
2	20	17.51	121.7	0.99	415	1.0760
3	30	26.27	273.9	0.98	924	1.0347

).

3. Results

Information contained in the interference patterns can be decrypted locally, at individual points of interest in the observation area, or globally for all pixels of the interference pattern. Powder particles emitted during laser processing in separate frames are the cause of artifacts, but in general do not have a critical effect on the quality of the interference pattern. Information about the object observed lies in the change in the optical length of the probing laser beam passing through the zone of interest of the object field. In gas-phase flows, temperature and gas concentration are functions of spatial coordinates. As a result of this, the optical path length of the probe beam of the interferometer was modulated by the studied object, and a phase increment Δϕ (x,y) arises, associated with the average change in the refractive index ⟨Δn⟩:

$$\Delta \phi \left(x,y\right)=2\pi L⟨\Delta n⟩/\lambda ,$$

(4)

where L is the geometric length of the optical path of the probing laser beam in the affected area and λ the wavelength of the probing laser.

Previous works on the study of gas-phase flows in SLM indicate several aspects that accompany their formation: changes in pressure, temperature and concentration of metal vapor [5,25,26,27,28]. These three components affect the refractive index. Therefore, unlike ordinary high-speed recording, registration of the spatial change in the refractive index gives more information about the plume. The interferograms obtained during processing made it possible to visualize the gas-vapor flow (Figure 3). The differential interferogram (Figure 3b) shows the presence of a bright spot near the substrate, the width of which correlates with the diameter of the plume at its base in Figure 3c,d and probably corresponds to the evaporation spot. The interferograms show that the optical path length of the probe beam increases in the plume compared to the length in the unaffected zone outside. For instance, in the gas-phase flow shown in Figure 3, the phase increment Δϕ increases up to 45 radians due to a change in the optical path. Varying working laser parameters made it possible to reveal their effect on the geometry of the jet and a change in the optical path length of the probe laser (Figure 4 and Figure 5). To make sure that the steady-state process was analyzed, the first 0.1–0.15 s of laser spot movement were ignored.

At laser power of 50 W, stable plume formation and particle emission were not observed (Figure 4a). In this case, parameter Δϕ attains the maximum directly at the zone of interaction of the laser beam with the powder layer. Figure 4b–d shows that the region of the greatest phase change is formed at a certain distance from the laser processing zone. With increasing power, the distance from the substrate to the Δϕ maximum increases, as does the value of the maximum itself, and the gas jet becomes more stable.

To evaluate the jet velocity, 10 consecutive frames of the processed interferograms of the steady-state jet were analyzed (Figure 6). Qualitatively, modes of 90, 130 and 170 W share the same gas-phase flow behavior (Videos S2–S4). In this regard, Figure 6 represents two different patterns of gas-phase flows depending on energy input. Having the exposure time of the frame and the scale of the observed region known, the flow velocity was calculated through tracking movements of jet inhomogeneities (Figure 6,

Table 2. Gas-phase flow velocity.

Laser Power, W	Average Velocity, m/s
50	0.35 ± 0.1
90	1.8 ± 0.4
130	2.3 ±0.4
170	2.6 ± 0.5

). For laser power from 90 to 170 W, the average calculated velocity over 10 frames is presented. However, Figure 6b shows acceleration of the gas-phase flow as it moves away from the substrate. At laser power of 50 W, the plume pulsation was not observed and the mode of its expansion did not change throughout the laser-processing period (Video S1).

4. Discussion

The interferometry clearly visualizes optical inhomogeneities. It made possible the calculation of the average velocity of the jet outflow for all the processing modes (Figure 7). The obtained data correlate with the previously obtained results when observing the gas-phase flow [5,9]. The effect of power on the flow rate is obvious: an increase in the energy input leads to more intense evaporation of the material. Moreover, flow acceleration common for all the observed modes starting from 90 W and above is observed at a distance of 3–4 mm from the substrate. Laser power of 50 W seems to be insufficient for stable evaporation of the metal in the treatment zone; thus, no gas-phase flow was observed.

It is known that submerged jets with moderate Reynolds numbers are laminar in the initial flow segment, and, starting from a certain critical distance, go into turbulent mode [29]. In the laminar zone, the jet is thin, and upon transition to turbulence, it begins to expand sharply. It is possible that the maxima in the interferograms arise in the turbulence zone (Figure 4). The laminar zone can be so thin that the image resolution is not enough.

The works on the denuded zone in the SLM indicate a collective motion of powder particles from the periphery to the melt pool [5,8,14]. The movement itself is caused by the emerging Bernoulli effect when the vapor jet creates a zone of reduced pressure, which entrains ambient gas. The gas flows drag particles and transfers them to the molten pool.

To evaluate the pressure change, a gas flow model was developed for SLM for various Reynolds numbers taking into account the presence of a solid surface and allowing calculating the shear stresses on this surface (Appendix A). The stresses are responsible for the detachment of particles of the powder layer and the formation of the denuded zone. The numerically calculated flow (Figure 8) qualitatively corresponds to the obtained experimental data. It should be mentioned that a fast jet flow is formed near the axis and a much slower-induced flow in the rest of the half-space. With an increase in the Reynolds number Re, the jet becomes less divergent and extends further along the axis. The velocity of the induced entrainment flow at a certain point, increases with increasing Reynolds number. It can be noted that at a large distance from the origin, the velocity vector of the induced flow is directed approximately along the radius (see blue flags in Figure 8). In the axial region, the flow is directed from the center. Near the surface, the flow is directed toward the center. The half-angle of the cone, at which the direction of flow velocity changes to the opposite one, decreases with increasing the Reynolds number.

Bidare et al. [28] numerically solved the system of mass, momentum and energy conservation laws for the laser plume and calculated the fields of temperature and flow velocities of vapor and ambient gas. Their results reviled the formation of a slender high-velocity vapor jet surrounded with a low-velocity induced entrainment flow of ambient gas. The estimated maximum vapor temperature ranged from approximately 3000 K to approximately 6000 K, depending on the laser power. The maximum was attained in the laser spot on the surface. Vapor temperature gradually decreased downstream the slender jet. The estimated temperature rise in the ambient gas was much less. The model of laser plume applied in the present work is based on mass and momentum conservation (see Equation (A1)), but does not use the energy equation to avoid consideration of particular thermo-kinetic processes, which can affect the generality of the results. The velocity and pressure fields shown in Figure 8 are applicable outside the heat-affected zone; namely, in the whole domain of the ambient-gas entrainment flow, as follows from the results [28].

According to the calculations in absolute terms, the pressure change is small and amounts to about 1 Pa. Such a difference is not able to significantly increase the refractive index of the gaseous medium through which the probing laser passes. An increase in temperature, which sharply increases in the laser exposure zone and reaches several hundred degrees [30], is a factor that reduces the Δϕ parameter, since density of gas reduces as temperature increases. Nevertheless, the present experiments indicate that the optical path length in the plume itself increases, which can be explained by an increase in the concentration of metal vapor due to its evaporation from the molten pool.

In gas-phase flows, temperature and vapor concentration are functions of spatial coordinates (x,y). The refractive index of a gas depends on its composition and density. As a result, the optical path length of the probing laser is modulated by the object being studied. All local changes Δn of the refractive index along the ray path are integrated, and an increase in the phase Δϕ of the interference fringes is observed in any pixel of the interference pattern. It is associated with a change in the optical length of the probing laser beam by Equation (4). If the size L of the perturbed region is estimated from the interferogram as the size of the domain within which the interference fringes change their position during laser processing, then Equation (4) allows estimating the value of ⟨Δn⟩ from the recorded values of Δϕ. In the experiments performed at laser power of 130 W, Δϕ was about 4π rad. For the observed size L ≈ 2 mm of the perturbed region, the quantity ⟨Δn⟩, as follows from Equation (4), was 0.000532. This value almost doubles the maximum possible change in the refractive index of the air when the air is heated to T → ∞. Indeed, in this case, the air density tends to zero, and the refractive index tends to unity. The maximum possible change in the refractive index of air is thus limited and amounts to n_a − 1, where n_a is the refractive index of air under normal conditions (1.0002926 [31]). A comparison of the maximum possible change in the refractive index of air 0.0002926 with the real value ⟨∆n⟩ = 0.000532 indicates that the change in the refractive index does not decrease, but increase. In this case, this can be caused only by the presence in the recorded zone of another gas with a refractive index greater than the refractive index of air; for example, iron.

Evaporated material can affect the intensity of working laser radiation in the case of resonance absorption. According to the data presented in literature [32], the intensity of absorption of radiation by iron vapor in the visible and near-infrared ranges generally decreases with increasing wavelength and it should be expected that absorption of laser radiation with a wavelength of 1064 nm is not significant. Given the short laser path inside the plume (≈1 cm), the absorption of laser radiation is most likely negligible.

Based on the assumption that the evaporated material is a significant part of the vapor-gas jet, the refractive index of iron vapor was estimated. The refraction of any substance is determined by the polarizability of its molecules and its density. In turn, the polarizability of nonpolar molecules or atoms is determined by their volume. To estimate the refractive index of iron vapor, the following equation can be used [29]:

$$\frac{n^2-1}{n^2+2}=\alpha \frac{4\pi N_a}{3M}d,$$

(5)

where α is the polarizability of atoms, N_a the Avogadro number, M the molar mass and d the vapor density. If we take into account the relationship of the density d with pressure P and temperature T according to the ideal gas law:

$$d=\frac{PM}{RT},$$

(6)

where R is the universal gas constant; then, Equation (6) becomes:

$$\frac{n^2-1}{n^2+2}=\alpha \frac{4\pi P}{3kT},$$

(7)

where k is the Boltzmann constant. According to [33], the polarizability of iron α is close to the atomic volume (7.7 ų). From Equation (7), the refractive index of iron vapor is n_Fe = 1.00127 under normal conditions (P = 10⁵ Pa, T = 273 K). The estimations in Figure 8 show that pressure, and hence the concentration of the gas mixture in the jet, does not differ significantly from normal conditions. Therefore, the changes in gas parameters do not exceed the limit of applicability of the ideal gas model. Thus, it can be concluded that the optical density of iron vapor is an order of magnitude higher than the optical density of air.

In the mixture of two gases with different polarizabilities, the contribution of each gas to the total refractive index n of the mixture can be estimated as [33]:

$$\frac{n^2-1}{n^2+2}=V_{Fe}\frac{n_{Fe}{}^2-1}{n_{Fe}{}^2+2}+V_A\frac{n_A{}^2-1}{n_A{}^2+2 },$$

(8)

where V_Fe and V_A are the volume fractions of iron and air vapors in the mixture, respectively; n_Fe and n_A are the refractive indices of iron and air vapors under normal conditions; and n is the refractive index of the mixture. Equation (8) makes it possible to find the volume fraction V_Fe of iron vapor in air from the experimentally measured refractive index n of the mixture and the known refractive indices n_Fe and n of its components. In fact, in the experiments, not the absolute value of the refractive index n of the mixture was found, but its relation to the refractive index of the unperturbed air in the support arm of the interferometer (9):

$$⟨\Delta n⟩=n-n_A.$$

(9)

For the above example, where ⟨∆n⟩ = 0.000532, from Equation (8) the value of the volume fraction of iron vapor is V_Fe = 0.545. This shows that a significant part of the flow consists of evaporated metal.

5. Conclusions

In this work, a method for studying the vapor-gas jet that arises during SLM process based on interferometry with subsequent digital processing was applied. Registration of spatial changes in the refractive index made it possible to evaluate the geometry of the jet and the manner of its propagation. No jet was observed above the laser zone, and the observation zone changed slightly with time at scanning speed of 50 mm/s and laser power of 50 W. The increase in power leads to the emergence of a stable gas-phase flow, a significant part of which is vaporized metal. From the obtained interferograms, the volume fraction of iron vapor was calculated, which at 130 W was V_Fe = 0.545.

The flow rate estimated from the tracking movement of inhomogeneities inside the plume also increases with increasing specific power due to more intense evaporation. The maximum velocity of 2.6 ± 0.5 m/s was achieved at 170 W. This provokes the movement of the surrounding gas in the direction of the jet, which explains the appearance of denudation zones during SLM. Qualitatively, the experimental data correspond to the simulated data on the pressure change and the resulting gas flow velocity.