Experimental quantification of inward Marangoni convection and its impact on keyhole threshold in laser powder bed fusion of stainless steel

Laser metal additive manufacturing has the potential to revolutionize the production of complex geometries with high precision across various industrial applications. To optimize the reliability of the process, a detailed understanding of the melt pool dynamics during the process is essential, particularly in the nearly pore-free regimes. In this study, the melt pool dynamics across conduction mode to keyhole mode in laser powder bed fusion processing of stainless steel 316 L have been investigated by means of in-situ synchrotron X-ray imaging utilizing tungsten particles as tracers. The spatial distribution of the fluid flow in the melt pool has been quantified with a resolution of ~10 µ m through automatic tracing all moving particles in the melt pool. The results identified the influence of the interplay between laser power and scanning speed on melt flow velocities. The measurements also revealed a pronounced impact of the inward Marangoni convection on the conduction-keyhole threshold, offering a new degree of freedom to broaden the pore-free process window of laser-based additive manufacturing. These findings contribute to a more comprehensive understanding of the melt pool dynamics during laser metal additive manufacturing and provide a valuable reference for calibrating high-fidelity computational fluid dynamics models.


Introduction
Laser powder bed fusion (LPBF) has emerged as a promising additive manufacturing (AM) technique for producing complex and customized metal parts with high accuracy and quality.However, it remains challenging to achieve a reproducible and defect-free fabrication process, which is required for the qualification of the final product.A complete understanding of the complex physical phenomena during the process, such as laser energy absorption, powder motion, fluid flow, heat transfer, and mass transfer, is essential to predict and control the melt pool dynamics.
The recent advancement of ultrafast synchrotron X-ray imaging has enabled in-situ and operando measurements of the rapid phenomena during laser-based AM [1].This approach has been extensively used to investigate the melt pool dynamics and defect formation mechanisms in LPBF, particularly in the keyhole mode [2][3][4][5][6][7].The keyhole mode refers to a laser melting regime that occurs when the absorbed laser energy exceeds a certain threshold [8][9][10].In the keyhole regime, a depression zone is created by the recoil pressure as a result of strong local evaporation of molten metal, and the recoil pressure and Marangoni effect drive the fluid away from the laser beam [2,11].The occurrence of a keyhole is accompanied by an abrupt increase in the effective absorptivity of the laser energy as a result of the multiple laser reflections in the cavity [8,12,13].If the absorbed laser energy continues to increase, the regime evolves from stable keyhole to unstable keyhole [5,6,10].More porous defects are prevalent in the unstable keyhole regime due to the pronounced chaotic interplay between recoil pressure, surface tension, and Marangoni force.Specifically, the keyhole pores undergo a series of events: they pinch off from the keyhole tip upon the collapse of the deep and narrow cavity, then are pushed away from the keyhole by the acoustic waves generated by the perturbative keyhole oscillation, and ultimately become trapped by the advancing solidification front [4][5][6].
The pressure instability within the keyhole is attributed to various factors, such as shadowing effects by spatters, agglomerates, and protrusion structures on the keyhole walls, Marangoni flow from the bottom to the opening of the keyhole, multiple reflections of the laser, and abrupt changes of the recoil force and surface tension [4][5][6]11,13,14].In the meantime, a fraction of pores can be entrained by the Marangoni convection, circulating in the rear of the melt pool [11,15,16].Besides in-situ X-ray imaging, high-speed camera and Schlieren imaging have also been used in previous studies to investigate the metal vapor ejection in the keyhole mode, which can lead to spattering and denudation of powder, resulting in the multiplication of defects [13,[17][18][19][20][21].
A practical takeaway of the aforementioned studies is that the nearly pore-free processing regime of LPBF is close to the conduction-keyhole threshold, i.e., the conduction mode and the stable keyhole mode [5,6,10,11,13].However, the melt pool dynamics in the nearly pore-free regime have not been fully explored experimentally, particularly in the conduction mode, as it is more challenging to characterize the melt flow behavior without the contrast of keyhole and pores.Micro-particles with high melting point, such as tungsten and tantalum, have been implemented in in-situ measurements as flow tracers to visualize the liquid flow in the melt pool [16,[22][23][24][25].However, the traced movements of a few particles within a few radiographs cannot serve as a reliable reference for the high-fidelity mechanistic modeling of the melt pool dynamics in this regime.Furthermore, it has been reported that the Marangoni convection plays an important role in the heat and mass transfer during laser melting, affecting the geometry, pore formation, and composition distribution of the melt pool [13,22,[26][27][28][29][30][31].Nevertheless, the fundamental mechanism of Marangoni convection during laser AM and its impact on the melt pool behavior, as well as on the optimization of processing parameters, remain incompletely understood.
This paper presents an experimental investigation of the melt pool dynamics during LPBF of a commercial stainless steel 316 L (SS316L) from the conduction mode to the conduction-keyhole transition.In-situ synchrotron X-ray imaging is employed with tungsten particles as tracers to investigate the spatial distribution of the fluid flow in the melt pool at different combinations of laser power and scanning speed.By automatically tracing hundreds of moving particles in the melt pool from thousands of consecutive frames, the fluid flow is visualized and quantified with an exceptional lateral resolution of approximately 10 µm.The findings reveal the presence of a prevalent inward fluid flow (from cold area to hot area on the melt pool surface) in the melt pool, which differs from the previously reported outward flow with other commercial LPBF materials [16,[23][24][25], along with the coexistence of outward and inward convections in the keyhole mode.This study primarily centers on gaining a deep understanding of the mechanisms underlying inward Marangoni convection and its dual impact on the behavior of the melt pool and the conduction-keyhole threshold within laser-based AM.This research provides valuable insights for the development of mechanistic models to accurately predict the melt pool dynamics in AM process and offers perspectives on extending the pore-free processing window by controlling melt flow direction through alloy design.

In-situ synchrotron X-ray imaging of melt pool dynamics with W tracer particles
A miniaturized LPBF device (MiniSLM) [32,33] was implemented in the beamline TOMCAT at the Swiss Light Source at Paul Scherrer Institute (PSI) to conduct in-situ and operando X-ray imaging of the melt pool dynamics during LPBF process.The chemical composition of the commercial LPBF SS316L powder (Oerlikon Metco Europe GmbH, Germany) used in this study is presented in Table 1.The SS316L powder (D90 = 52 μm) was mixed with 3 wt% tungsten powder (2 μm -10 μm) as tracer particles to visualize the fluid flow in the melt pool.The addition of 3 wt% tungsten equals 1.3 vol% tungsten in the melt pool of SS316L, ensuring a sufficient number of visible tracers without having a significant impact on the melt pool properties.Similar volume fractions of tungsten tracers have been employed in previous studies on melt pool dynamics [23][24][25].Thin-wall samples of 300 μm in thickness were produced on the build plates with the mixed powder using a SISMA MySint 100 (SISMA, Italy) LPBF machine before the synchrotron measurements.The sample geometry and experimental configuration are shown in Fig. 1(a).In the beamline, one layer of mixed powder (100 μm of thickness) was manually deposited in the slot (100 μm in width and depth) on the top of the thin wall, and a single-track scan was made with the 1064-nm laser system of MiniSLM.During the laser scanning, the sample was illuminated with a polychromatic X-ray beam with a peak energy around 20 keV.The transmitted radiation was converted to visible light with a LuAG:Ce 150 μm thick scintillator screen, magnified with a high numerical aperture (0.35) 4x magnification microscope (Optique Peter, Lentilly, France) and captured with the GigaFRoST detector system [34] with a frame rate of 15000 Hz and exposure time of 0.06 ms.The effective region of interest (ROI) was 1824×152 pixels (pixel size = 2.75 μm) and covered the full length of the laser track (5 mm).The measurements were conducted under a slightly overpressured argon environment with less than 0.15% oxygen.
The process was repeated with a constant beam diameter but different laser powers and scanning speeds to explore different levels of laser energy input.The ratio of the laser energy density to the melting enthalpy is described by the normalized enthalpy, which was originally proposed and applied in the welding field by Hann et al. [35] and then adapted to the LPBF field by King et al. [36].Recently, the normalized enthalpy has been widely used to guide the calibration of laser parameters to avoid process-related defects during LPBF [2,8,10,37,38].In this study, the definition of the normalized enthalpy follows the calibration of King et al. [36]: where A is the effective absorptivity, P is the laser power, u is the laser scanning speed, r is the laser beam radius.α = k ρCp is the thermal diffusivity, where k, ρ, and C p are the thermal conductivity, the density, and the specific heat capacity.The volumetric melting enthalpy is defined as , where T m is the liquidus melting point, T 0 is the substrate temperature, and L m is the latent heat of melting [37].More details about the normalized enthalpy are described in Supplementary Note 1. Detailed values of the material properties are provided in Supplementary Table 1.
After several preliminary tests to explore the processing parameters, seven samples were processed with single laser scan using different combinations of P and u varying from the conduction-keyhole transition (samples 'a' and 'b') to pure conduction mode (samples 'cg').The detailed values of P and u can be found in Table 2. Notably, the selected u values are lower than those typically used in LPBF of steels.This is primarily related to a necessary trade-off in frame rate, given the large ROI covering the entire laser track.A relatively large u will result in an

Image processing and particle tracing
All X-ray videos obtained from the measurements were processed using ImageJ [39] and Matlab©.A protocol was developed to automatically identify and trace the moving W particles from thousands of consecutive radiographs.The process contains the following steps: (1) The dynamic frames were cropped based on a smaller ROI (see an example frame in Fig. 2(a)) which is compatible with the size of the melt pool and moving with the same speed as the laser.To eliminate the geometric effect of the samples, the frames at the two edges of each sample were not included.For instance, a segment of the cropped video of sample 'a' is presented in Supplementary Movie 1. (2) Each frame of the cropped video was normalized into 16-bit greyscale image and inverted so that the W particles have the highest intensity, as shown in Fig. 2

Table 2
Laser processing parameters of the investigated samples.using a rolling ball algorithm [40] with a diameter of 10 pixels.( 4) Each image was converted to a binary image by separating the pixels into foreground and background based on Otsu's method [41].The white pixels correspond to the W particles. ( 5) The W particles beyond the melt pool region were excluded by applying a mask of melt pool profile.(6) The W particles in each binary image were identified and segmented with a pre-trained machine learning model, StarDist [42,43], as indicated by translucent circles in Fig. 2(c).( 7) The W particles in the liquid phase, as marked by red rectangle in Fig. 2(c), were extracted by detecting and eliminating the steady particles in the solid phase, as they show a uniform linear motion with the same speed as the laser scanning but in the opposite direction in the video.(8) The trajectories of all moving W particles in the melt pool were traced by the ImageJ plugin TrackMate [44,45] to analyze the melt flow dynamics, as shown in Fig. 2  (d).The video of the moving particles and their trajectories corresponding to the cropped video of sample 'a' can be found in Supplementary Movie 2. Supplementary material related to this article can be found online at doi:10.1016/j.addma.2024.104092.

Empirical model of melt flow velocities
To study the influence of laser parameters on the melt flow velocities, an empirical model of the fluid velocities is built as the function of the laser power, P, and the square root of scanning speed, ̅̅̅ u √ . For samples 'a' -'g', P and ̅̅̅ u √ are normalized into a range of − 1-1, as presented by P norm and ̅̅̅ u √ norm in Supplementary Table 5.To establish a mathematical representation, a quadratic model of P norm and ̅̅̅ u √ norm is employed, and the normalized coefficients, a i , are fitted using least-squares method under the concept of the following equation:

Validity of particle tracing approach
The projectional fluid velocities in the steady-state conduction mode were quantified by tracing hundreds of tungsten particles in around two thousand consecutive frames for each sample, as described in the subsection 2.2, Image processing and particle tracing.The high melting point of tungsten (3695 K) guarantees the stability of the tracer particles in the molten SS316L, of which the vaporization temperature is 3084 K under standard atmospheric pressure [46,47].The fidelity of the tracer particles to the fluid flow in this study can be validated by the value of Stokes number.The Stokes number plays a crucial role in understanding the behavior of particles suspended in fluid flow and serves as a measure of the fidelity of tracer particles in tracking melt flow.The Stokes number is defined as [48]: where v is the fluid velocity, d is the diameter of the W particles, and t 0 is the relaxation time of the particle under the drag of the fluid.For Stokes flow (Reynolds number < 1), t 0 can be calculated with [49]: where ρ p is the density of the W particle, and μ is the dynamic viscosity of the fluid.Taking v = 0. , where ψ(Re) can be calculated as [51,52]: where c = 0.158.Therefore, for a tracer particle with a diameter of d = 5 µm, the effective Stokes number is calculated as Stk e = 0.06 < 0.1 in this study, which implies that the error of tracing accuracy, i.e., the difference between the velocities of suspended particles and the fluid flow, is below 1% [48].

Quantitative analysis of melt flow
According to the time-series X-ray images captured from the in-situ measurements, the melt pool dynamics of all probed samples were predominantly characterized by the conduction mode with stable melt pool profile and fluid flow.Samples 'a' and 'b' were observed to enter the keyhole mode during the last 1/3 of the scan.This phenomenon arises from the heat accumulation ahead of the laser scanning, as indicated by the normalized thermal diffusion length [8], , where α, u, and r represent thermal diffusivity, laser scanning speed, and laser beam radius, respectively.For samples 'a' and 'b', the value of L * th is slightly above 1, showing that the characteristic length of thermal diffusion and the laser spot size are in the same order of magnitude, thereby inducing a slight heat accumulation in front of the laser advancement.Thus, the absorbed laser energy of samples 'a' and 'b' was very close to the threshold of conduction-keyhole transition.
The time-averaged fluid velocity field in the conduction mode of sample 'a' is presented in Fig. 3(a), where the origins of coordinates x and z correspond to the laser center and the melt pool surface, respectively.The majority of the melt pool exhibits smooth laminar flow, and the right half of the melt pool (behind the laser) shows clear Marangoni convection passing through the bottom, tail, and top of the melt pool, and towards the laser center.However, the measured fluid velocities in the left half of the melt pool (under the laser) display high circular variance, as shown in Fig. 3(b).The circular variance is an indicator of the spread of a directional data set, and it is defined as [53]: where v i represents the velocity vector of the i-th measured particle, and N is the total number of particles at the measured location.The circular variance will be close to zero if all vectors point into almost the same direction (e.g., the dark regions in Fig. 3(b)).The high circular variance observed in the regions under the laser spot is due to the three-dimensional (3D) nature of the melt pool convection, as the X-ray imaging measurements are essentially the projections of a 3D problem onto a 2D plane.The 3D effects in the melt pool will be discussed with more details in the subsection 3.3, 3D effects of the melt pool dynamics.
The Marangoni effect on the melt pool surface drives the liquid from the regions with low surface tension to the regions with high surface tension, resulting in the Marangoni convection.For most metals and alloys, the temperature coefficient of the surface tension is negative, resulting in an outward convection of the melt pool, which flows from high temperature to low temperature regions on the melt pool surface.However, different from the previously reported outward melt flow patterns during laser AM [11,15,16,[23][24][25], the melt pool dynamics of all samples in this study are featured with strong inward Marangoni convection.In fact, the inward convection is an important phenomenon for iron-based alloys in the welding community [22,54,55], but few experimental observations of this phenomenon have been reported in the field of laser AM [30].The inward melt flow on the melt pool surface can be induced by a slight variation of surface active elements in the molten metal, and previous studies have identified the critical values of sulfur (> 30 ppm) and oxygen content (> 17 ppm) in steels for the occurrence of inward flow [54][55][56].It is assumed that the surface tension of liquid SS316L in this work exhibits a positive relation with temperature within a certain temperature range because of the relatively high sulfur (40 ppm) and oxygen (500 ppm) contents as surface-active elements in the material (see Table 1) exceeding the above-mentioned critical values.Therefore, the Marangoni convection observed in this study is inward (towards the laser center on the melt pool surface).
In this study, the melt flow in the conduction mode is dominated by the Marangoni effect, as indicated by the estimation of the Marangoni number (Ma) and the Weber number (We) according to the quantified fluid velocities.The Marangoni number is defined as [57]: where dγ dT = 2×10 − 4 N⋅m − 1 ⋅K − 1 is a representative value for the temperature coefficient of the surface tension [54][55][56], α = 4.95×10 − 6 m 2 ⋅s − 1 is the thermal diffusivity, and ΔT is the temperature difference between the laser center and the liquidus point.Since a slight depression zone can be observed in the conduction mode, the local temperature at the laser center is close to the boiling point, thus ΔT is estimated to be 1400 K. Thus, the Marangoni number Ma is about − 3×10 3 in this work.Additionally, the Weber number, representing the ratio of the inertial pressure to the surface tension, is defined as [13]: where γ = 1.4 N⋅m − 1 is the surface tension of molten SS316L [54].Thus, the Weber number is calculated to be 0.08.It indicates that the inertia of the liquid flow cannot overcome the surface tension of the melt pool, showing that the melt pool is rather stable regardless the presence of a slight depression zone under the laser.Besides, the low Weber number implies that the surface tension alterations can significantly influence the melt flow velocities.Therefore, it can be concluded that the fluid velocities in the conduction-mode melt pool are dominated by the Marangoni effect.Since the Marangoni effect occurs only on the melt pool surface, the fluid velocities at the top of the melt pool with low circular variance (represented by points A, B, and C in Fig. 3(a)), are quantified for samples 'ae'.The absolute values of the projectional fluid velocities on the x direction, |v x |, are demonstrated in Fig. 3(c).Besides, the average accelerations on the x direction from A to B and from B to C are indicated in Fig. 3(c) to illustrate the importance of the surface tension gradient (Marangoni effect).In general, the x component of the fluid velocity increases from A to C as a result of the Marangoni effect.Samples 'c' and 'e' exhibit significantly higher acceleration from A to B, which are almost three times that of the other samples, suggesting relatively high temperature gradients between A and B. Additionally, it is interesting to observe that the acceleration between B and C is less pronounced than between A and B. Previous experiments revealed that the temperature gradient on the melt pool surface is higher when it is closer to the laser center [58].However, the temperature coefficient of surface tension is not a constant but decreases with temperature within a certain temperature range due to the sulfur/oxygen content in stainless steel [54][55][56]59].Thus, the surface tension gradient between B and C can be smaller than between A and B due to the elevated temperature, resulting in a reduction of the Marangoni force.It is also worth noting that sample 'd', with the same normalized enthalpy as 'c' and 'e', exhibits lower velocities at B and C and lower acceleration between A and B, suggesting lower peak temperature, smaller temperature gradient, and different surface tension responses on the melt pool surface.However, to the best of the authors' knowledge, the majority of simulation studies in the field of metal AM have employed a constant value of the surface tension coefficient.While a recent work [31] has considered the temperature-dependent nature of this coefficient, certain discrepancies still persist concerning the impact of inward melt flow on the melt pool dimensions and the influence of oxygen and sulfur content in stainless steels when compared to both the experimental observations in the present work and previous studies [22,54].Consequently, the integration of reliable experimental data will undoubtedly play a crucial role in further advancements and validation of computational mechanistic models to achieve more accurate prediction of the melt pool dynamics.
Furthermore, Fig. 3(d) shows the magnitude of fluid velocities from location 1-3 marked in Fig. 3(b), corresponding to the bottom, the tail, and the top of the melt pool, where the circular variance is relatively low to ensure reliable statistics.The fluid flow decelerates from location 1-2 and then accelerates to the peak velocity at location 3 for all seven samples.However, the different velocity magnitudes cannot be simply correlated with the normalized enthalpy, thus an empirical quadratic model of the velocities was introduced based on the method presented in the subsection 2.3, Empirical model of melt flow velocities.The fitted model as a function of P and ̅̅̅ u √ values without normalization was finally obtained: where v j represents the magnitude of fluid velocity at location j (j = 1, 2, 3), and the constant C j equals 1291, 1240, and 1335 for location 1, 2 and 3, respectively.The unit of the velocities in this model is [mm⋅s − 1 ] and the unit of power is [W].The graphical demonstration of the empirical model is shown in Fig. 4(a), where The fluid velocities at locations 1 and 3 are collapsed into the same level as location 2 by using the same constant C 2 , i.e., the average values of v ′ 1 and v ′ 3 are equivalent to the average of v 2 .It shows that the fluid velocity generally increases with the normalized enthalpy, while the highest velocity occurs for the intermediate modified normalized enthalpy ( ΔH Ahs = 11.7) when both the laser power and laser scanning speed are relatively low or high.Again, samples 'c' and 'e' show the highest velocities, which is consistent with their highest Marangoni accelerations.This phenomenon suggests a strong interplay between the laser power and laser scanning speed for the fluid flow behavior in the melt pool, which can be confirmed by the large value (second highest) of the normalized coefficient for the interplay term, P ̅̅̅ u √ , as illustrated in Fig. 4(b).The values of the normalized coefficients a i , along with their squared errors and p-values are provided in Supplementary Table 6.The reliability of the empirical model within the investigated process window can be confirmed by the low p-values and the added variable plot presented in Supplementary Fig. 1.

3D effects of the melt pool dynamics
The melt flow during LPBF is basically a 3D problem, thus it is challenging to fully quantify the melt pool dynamics using in-situ synchrotron X-ray imaging.Particularly, the region under the laser spot exhibit pronounced circular variance due to the 3D effect of the melt flow, as illustrated in Fig. 3(b).The averaged fluid velocities of the locations with high circular variance are actually the vector sum of numerous measured particle speeds with distinct directions, as shown in Fig. 5(a).For example, the fluid flow at location L1 and L2 mainly distributes in three directions, as shown in Fig. 5(b, c).Considering the inward Marangoni convections and the conservation of mass in steadystate melt pool, the downwards flow primarily occurs on the center plane (y = 0) beneath the laser spot, while the upwards flow dominates both sides as well as the front and the rear regions of the melt pool, as demonstrated in Fig. 5(d, e).The inward melt flow pattern of Fig. 5(e) is consistent with previous studies on the welding of stainless steels [22,55].
In addition, since the 3D effect is more pronounced in the region below the laser center, potential errors of particle tracking may arise in this region.Though qualitative flow patterns in the melt pool are accurately identified, as shown in Fig. 5, no quantitative analysis is carried out for this region with high circular variance in this study.

Correlation between melt pool size and normalized enthalpy
The average melt pool length and depth in both the conduction and keyhole modes of LPBF, as well as during the remelting of the bare surface, have been measured based on the X-ray radiographs.The melt pool size (depth and length) is found to be correlated with the modified normalized enthalpy, as presented in Fig. 6.Specifically, the depth of  to have the same average as v 2 ; (b) Diagram of half relative effects, where a i /a 0 is the ratio of i-th normalized coefficient to the normalized constant term in the quadratic model.The values of a 0 and a i can be found in Supplementary Table 6.
samples 'ag' in the conduction mode of LPBF show a linear relationship with ΔH Ahs , which is consistent with previous studies [8,[35][36][37].Also, the melt pool length exhibits similar correlation with ΔH Ahs .Notably, the measured melt pool size of LPBF is larger than that of the laser remelting of bare surface, while the later was processed with the same laser parameters as samples 'dg' and also characterized with X-ray imaging.Moreover, when the LPBF process enters the keyhole mode (samples 'a' and 'b', ΔH Ahs = 15.1), the melt pool length and depth both increase, as indicated by the circular spots in Fig. 6.
The discrepancies in melt pool size between the conduction-mode LPBF and remelting is primarily caused by their different effective absorptivity, which varies with the phase and morphology of the sample surface.In the conduction mode, the deposited laser energy is partially absorbed by the liquid melt pool while another portion goes into the solid phase with higher absorptivity [8,12,13,37].According to the in-situ absorptivity measurements conducted by Trapp et al. [12], the effective absorptivity during remelting of a bare SS316L surface in the conduction mode, A r , is 0.3.Considering the multiple reflections of a portion of the laser beam within the powder layer near the front of the melt pool, the effective absorptivity during the conduction-mode LPBF, A c , is expected to be slightly higher than A r .This hypothesis aligns with the results of absorptivity measurements reported in previous studies [8,12,60].Assuming that the linear relationship between the normalized enthalpy ΔH hs and the melt pool size is still valid in the vicinity of the presented processing conditions, the effective absorptivity of the powder bed can be estimated by aligning the average remelting melt pool size with the fitted line of LPBF in the conduction mode, as illustrated by the dashed lines on the left side of Fig. 6.This approach allows us to determine an equivalent ΔH Ahs for the conduction-mode LPBF, ΔHc Achs , to render the same melt pool size as the average of the remelting conditions.Thus, the following equation can be established: where A c is the effective absorptivity of the powder bed in the conduction mode.The average value of ΔH Ahs is known for the remelting  measurements, giving ΔHr Arhs = 10.7.The equivalent value of ΔH Ahs for the conduction-mode LPBF can be estimated according to Fig. 6, yielding ΔHc Achs = 8.2.Therefore, Ac Ar = 10.7 8.2 = 1.30 and A c = 0.39.When the LPBF process develops to the keyhole mode, the effective absorptivity increases because of the multiple reflections of the laser in the deep depression zone (keyhole).The effective absorptivity of the keyhole-mode LPBF observed in this work can also be estimated using similar approaches, i.e., A k Ac = 17.1 15.1 = 1.13 and A k = 0.44.Accordingly, the normalized enthalpy threshold of the conduction-keyhole transition for samples 'a' and 'b' is estimated to locate between ΔH hs = 5.9 (A c = 0.39) and ΔH h = 6.6 (A k = 0.44), which is higher than the previously reported universal conduction-keyhole threshold values, e.g., ΔH hs = 1.4 by Gan et al. [10] and ΔH hs = 2.5 ± 0.5 by Ye et al. [8].The critical normalized enthalpy values with detailed laser parameters in the present work and previous studies are compared in Supplementary Note 1.Moreover, the uncertainty of the keyhole threshold determination in this study is evaluated, as demonstrated in Supplementary Note 2. The shift of the conduction-keyhole threshold towards higher normalized enthalpy, following the previously mentioned comparison, is attributed to the effect of the inward Marangoni convection.Detailed mechanisms for the increased conduction-keyhole threshold will be discussed in the next subsection.

The role of melt flow in keyhole formation and stability
According to the in-situ measurements and multi-physics simulations in previous publications [8,10,12,13,15], the formation of a keyhole occurs when the recoil pressure as a result of local evaporation becomes strong enough to overcome the surface tension of the fluid below and create a depression zone.The multiple reflections of the laser in the keyhole enhance the local heat accumulation and increase the effective absorptivity.Simultaneously, the recoil pressure and the outward Marangoni flow displace the liquid away from the laser focal spot, facilitating the opening of the keyhole [2,6,16], which is the case for the metals and alloys with negative temperature coefficient of surface tension.
In contrast, the inward Marangoni convection plays a different role in keyhole formation according to the observation in this study.The inward mass flow can hinder the opening of the keyhole, and it becomes more difficult to reach the boiling point under the laser.This is due to the fact that the inward Marangoni flow drives the cold liquid from the rear of the melt pool to the laser center.This point can be confirmed by the high Péclet number of the melt flow, Pe = Lv α ≈ 20, where L is the length of the melt pool and v is the characteristic fluid velocity.It indicates that the heat convection dominates the heat transfer in the melt pool, as it is much more pronounced than heat conduction even in the conduction mode [61].Thus, the inward mass and heat transfer have an important offset effect on the formation of keyholes.
Moreover, as discussed in the subsection 3.2, Quantification of melt flow using in-situ X-ray imaging and particle tracing, the SS316L used in this study is assumed to have a positive temperature coefficient of surface tension within a certain range of temperatures, but the coefficient decreases with temperature and even turns negative at elevated temperature (around 2500 K) [31,[54][55][56]59].Therefore, outward Marangoni flow can occur near the keyhole region since the local temperature in this area is close to the boiling point.As shown in Fig. 7 (b), the particle movement marked in red indicates an outward Marangoni flow just behind the keyhole.Meanwhile, the Marangoni flow in the region further away from the keyhole is still inward (the particle movement marked in black).The two opposing fluid flows merge and move downwards together, as shown in Fig. 7(c, d).The corresponding X-ray video is provided as Supplementary Movie 3, which demonstrates the melt pool dynamics from the frame of Fig. 7(a) to the disappearance of the keyhole.According to the video, the inward Marangoni flow still dominates the right half of the melt pool, offsetting both the opening of the keyhole and the outward flow originating from the laser center.In addition, the counteractive interplay between the inward flow and the highly-dynamic recoil pressure, along with the outward Marangoni force, can provoke a pronounced oscillation.This oscillation is a reciprocal motion of the keyhole and the entire melt pool, characterized by a frequency of approximately 1500 Hz.Notably, this oscillatory pattern is different from previously reported two typical modes of keyhole oscillations [6].Ultimately, this oscillation leads to the closure of the keyhole.As soon as the keyhole disappears, the oscillation rapidly attenuates.Therefore, the formation and maintenance of the keyhole is more difficult in the melt pool with inward Marangoni flow, leading to an increase of the conduction-keyhole normalized enthalpy threshold.
Supplementary material related to this article can be found online at Previous research works suggest the process window for LPBF close to the conduction-keyhole threshold to achieve nearly pore-free components while maintaining an acceptable mass deposition rate [5,6,10,11,13,37].The reasons can be summarized into the following two main aspects: On one hand, an energy input far beyond the conduction-keyhole threshold leads to the increase of porosity.More keyhole pores are formed if the process enters the unstable keyhole mode [4][5][6].In the meantime, the powder denudation and spattering become pronounced in the keyhole mode due to the effect of the vapor plume and the associated vortex gas flow around it [17,[19][20][21].Besides, the melt flow in the keyhole mode becomes fast enough to overcome the constrains of the surface tension, i.e., the Weber number We > 1, leading to the ejection of liquid droplets or spatters that are detrimental for the printing quality [13].Consistently, powder spattering was observed in this work as a result of vapor jet when the keyhole formed (t = 9.00 ms in Supplementary Movie 4).By contrast, no spattering but only a slight powder denudation into the melt pool was observed in the conduction mode.As shown in Supplementary Movie 4, a few powder particles were driven by the inward gas flow in the region ahead of the melt pool, with speeds ranging from 100 to 550 mm/s within a certain distance to the melt pool (< 80 µm).
Supplementary material related to this article can be found online at doi:10.1016/j.addma.2024.104092.
On the other hand, a sufficient energy input is necessary to achieve a reasonable normalized melt pool depth (the ratio between melt pool depth and laser spot radius), allowing to fully melt the previously deposited layer under the powder layer to avoid lack-of-fusion defects.In this work, since the inward Marangoni convection drives the hot melt beneath the laser to the bottom of the melt pool, the normalized depth of the melt pool in the conduction mode is between 1.5 and 3, which is larger than the common value between 1 and 1.5 for the conduction mode [8,[27][28][29]37].
Hence, the inward Marangoni convection is expected to promote the expansion of the pore-free process window to accommodate higher energy input, coupled with an increase in the normalized melt pool depth.This improvement in the LPBF productivity can be achieved while ensuring the process in the conduction mode, thus mitigating issues such as porosity, powder denudation, and spattering.Consequently, a promising avenue for improving the reliability and sustainability of metal AM lies in directing research efforts towards harnessing the dynamics of the melt pool through control of surface-active elements.

Conclusion
The present study provides a comprehensive experimental investigation on the melt flow dynamics of SS316L during LPBF process in the nearly pore-free regimes.By employing in-situ synchrotron X-ray imaging measurements with a wide ROI spanning the entire 5 mm laser track, this study enables the statistical quantification of hundreds of tungsten tracer particles in the melt pool across thousands of frames.This groundbreaking approach allows for a detailed analysis of steadystate melt pool dynamics with an unprecedented resolution of approximately 10 μm.Consequently, this research sheds light on the fundamental mechanisms governing the melt pool dynamics in LPBF.The major findings of the study are as follows: Firstly, the study demonstrates that LPBF with commercial stainless steels can exhibit inward Marangoni convection because of high sulfur and oxygen contents in the material.The observed differences in fluid accelerations and the coexistence of outward and inward flow indicate the importance of calibrating the temperature coefficient of surface tension as a function of temperature, instead of relying on a constant value.This calibration is necessary to achieve more accurate predictions of melt pool dynamics using mechanistic models.
Secondly, a pioneering effort has been made in experimentally exploring the intricate relationship between processing parameters and fluid velocities in the melt pool.Notably, a robust interplay is identified between laser power and scanning speed, exerting substantial influence on melt flow velocities, even under identical normalized enthalpies.This observation suggests that the temperature gradient and the surface tension gradient can significantly alter the melt pool dynamics, particularly the fluid acceleration driven by the Marangoni effect.Thirdly, the melt pool length and depth in the conduction mode show linear relationships with the normalized enthalpy, and the increases in melt pool dimensions and effective absorptivity accompanying the transition to the keyhole mode are quantified.
Lastly, this study identifies a significant shift of the conductionkeyhole threshold towards higher normalized enthalpy in the presence of inward Marangoni convection.This shift is attributed to an offset effect by the inward flow on the keyhole opening, as well as a closing effect resulting from the oscillation of the entire melt pool stimulated by the contradictory recoil pressure and inward melt flow.
In summary, this study emphasizes the importance of a complete understanding on the melt pool dynamics in nearly pore-free regimes, particularly the mechanism of inward Marangoni convection, which has received limited attention within the metal AM community despite its significance.The results suggest that the inward fluid flow is a common phenomenon for the process with commercial LPBF stainless steel powder due to the contents of surface active elements.The study highlights the significant interplay between the laser power and the scanning speed on the melt flow velocities, and underscores the need for highfidelity computational fluid dynamic models to account for the nonconstant temperature coefficient of surface tension.Moreover, the presence of inward melt flow can double or even triple the absorbed laser energy required for the formation of a keyhole, and induce a new oscillation mode of the keyhole and the entire melt pool.These insights contribute to a step forward in understanding the melt pool dynamics during laser-based AM and provide valuable reference for validating high-fidelity mechanistic models of LPBF.In future work, the intricate melt pool dynamics with inward Marangoni convections under more realistic LPBF conditions will be investigated by integrating both modeling and experimental approaches.Furthermore, this study is expected to stimulate further research aimed at exploring the pore-free process window by controlling the melt flow directions with surface active elements as a new degree of freedom in AM alloy design.
insufficient number of captured images, e.g., only 75 frames with u = 1000 mm/s.These different P-u combinations were designed according to different levels of normalized enthalpy.As demonstrated on the P-̅̅̅ u √ map in Fig. 1(b), the investigated processing parameters are distributed on three isolines of the normalized enthalpy, ΔH hs .It should be mentioned that the values of modified normalized enthalpy, ΔH Ahs , instead of ΔH hs are indicated in Fig. 1(b).The effective value of A with the presence of the powder bed is carefully determined in the subsection 3.4, Correlation between melt pool size and normalized enthalpy.

Fig. 1 .
Fig. 1.In-situ characterization of melt pool dynamics during LPBF.(a) Schematic of the in-situ synchrotron X-ray imaging experiment; (b) Investigated laser powerspeed combinations.Each dashed line corresponds to a specific value of modified normalized enthalpy.The profiles in the X-Z plane of the melt pool for the probed samples 'ag' are indicated with a scale bar of 200 µm.

Fig. 2 .
Fig. 2. Demonstration of image processing.(a) Representative frame of raw image cropped with moving ROI; (b) Greyscale image after normalization and inversion of intensities; (c) Binary image corresponding to the W particles in the melt pool region (dashed line); (d) Trajectories of the moving particles within 30 neighboring frames.The particles in the red rectangle in (c) follow the fluid flow, while the others are stuck in the solid phase.
2 m⋅s − 1 , d = 5 µm, ρ p = 19300 kg⋅m − 3 , μ = 7 mPa⋅s [50], the Stokes number is calculated to be Stk = 0.15.However, the Reynolds number of the fluid flow in this study is estimated to be Re = ρvL μ ≈ 80, given the density of the molten SS316L ρ = 6881 kg⋅m − 3 and the characteristic dimension of the melt pool L = 400 µm.The Stokes number needs to be corrected to the effective Stokes number, Stk e = Stk • ψ(Re)

Fig. 3 .
Fig. 3. Quantification of fluid velocities in the melt pool.(a) Projectional fluid velocity field of sample 'a' with cell size of 13.1 µm; (b) Circular variance of the velocity field map of sample 'a'; (c) The x component of fluid velocities and average accelerations of sample 'ae' from point A to C indicated in (a); (d) The fluid velocity magnitudes of sample 'ag' from location 1-3 indicated in (b).x = 0 corresponds to the position of the laser center.

Fig. 4 .
Fig. 4. Empirical model of the fluid velocities at locations 1, 2, and 3 in Fig. 3(b).(a) Graphical demonstration of the fitted surface.v 1 and v 3 are shifted to v ′ 1 and v ′

Fig. 5 .
Fig. 5. 3D effects of the melt flow measurements.(a) Decomposed fluid flow at locations with circular variance > 0.7; (b, c) Circular plots demonstrating the directional distribution of measured fluid flow at locations L1 and L2 in (a); (d) Side view of melt flow pattern in the center plane (y = 0); (e) Front view of melt flow pattern.

Fig. 6 .
Fig. 6.Correlation between melt pool size (depth and length) and modified normalized enthalpy.The solid lines are the least square fitted lines.The dashed lines represent the estimation of equivalent modified normalized enthalpy of remelting (8.2) and keyhole (17.1).

Fig. 7 .
Fig. 7. Time-series X-ray images of keyhole mode.(ad) X-ray images of every second frame from t 0 .The trajectories of two particles illustrating the outward and inward Marangoni convections are marked by red and black arrows, respectively.

Table 1
Chemical composition in wt% of SS316L powder used in this study.