Nondiffractive beam shaping for enhanced optothermal control in metal additive manufacturing.

High thermal gradients and complex melt pool instabilities involved in powder bed fusion–based metal additive manufacturing using focused Gaussian-shaped beams often lead to high porosity, poor morphological quality, and degraded mechanical performance. We show here that Bessel beams offer unprecedented control over the spatiotemporal evolution of the melt pool in stainless steel (SS 316L) in comparison to Gaussian beams. Notably, the nondiffractive nature of Bessel beams enables greater tolerance for focal plane positioning during 3D printing. We also demonstrate that Bessel beams significantly reduce the propensity for keyhole formation across a broad scan parameter space. High-speed imaging of the melt pool evolution and solidification dynamics reveals a unique mechanism where Bessel beams stabilize the melt pool turbulence and increase the time for melt pool solidification, owing to reduced thermal gradients. Consequently, we observe a distinctively improved combination of high density, reduced surface roughness, and robust tensile properties in 3D-printed test structures.

INTRODUCTION

Laser-based metal additive manufacturing (AM) or three-dimensional (3D) printing has gained immense traction in the last few decades as it offers a way forward for the rapid prototyping and manufacturing of intricate designs with superior mechanical properties beyond the realm of conventional manufacturing techniques (–). Laser powder bed fusion (L-PBF) has been the gold standard for metal 3D printing, where a scanning process laser beam irradiates a bed of metallic powder feedstock to sequentially melt and form structures of the desired shape. The high laser intensities (~MW/cm2) used in L-PBF lead to high solidification growth rates (R) and induce large thermal gradients (G) in the melt pool. Consequently, heat and mass transport mechanisms are dictated by instabilities resulting from complex melt flow dynamics and the cumulative effects of repeated heating and cooling cycles, which can unfavorably result in defects and porosity (–). High G/R ratios can also lead to columnar grain growth and residual stresses that are unfavorable for obtaining isotropic mechanical properties (–).

The intrinsic limitations of AM have been countered with some degree of success by incorporating such clever strategies as alloy design (), powder feedstock engineering (), and simple machine parameter optimization (–). Rather intuitively, the very laser intensity profile that initiates melting during L-PBF should affect the spatial distribution of the melt pool and, consequently, the thermal gradients and solidification dynamics. However, the intensity distribution of the process laser beam is often overlooked and only sparsely studied, perhaps due to the fact that most high-power commercial lasers output the TEM00 mode, commonly referred to as the Gaussian beam (). Gaussian beams are characterized by a strong intensity localization within the 1/e2 beam waist, which contains ~86% of the incident power. As a result of the high peak intensities delivered in a tightly focused region, Gaussian beam–induced melt pools are highly susceptible to (i) keyholing, which occurs due to the vaporization of the melt pool and the buildup of recoil pressure onto the underlying melt pool, and (ii) spatter generation, i.e., the ejection of nonmelted or melted powder particles. Both keyholing and spatter detrimentally affect macroscale and mesoscopic properties as they can result in pore formation and poor surface quality of printed products (, , ). The lack of flexibility in tailoring the thermal distribution presents a major challenge toward controlling other undesired effects resulting from melt pool hydrodynamics (, ), including laser-matter and laser-plume interactions (, ) and the interplay between porosity, relative density, and surface roughness. High surface roughness of as-printed products has been shown to contribute to drastic fatigue life reduction (, ).

Recently, laser beam shaping strategies have been used in the context of engineering light-matter interactions to tackle the drawbacks of using focused Gaussian beams in metal AM (, –). In particular, inverse Gaussian (annular) beams were shown to mitigate spatter generation () and reduce defects over a broader range of scan parameters compared to Gaussian beams (). Elliptical beam profiles were shown to strongly affect solidification microstructures in single-track studies () and increase the propensity for equiaxed grains (). Alternatively, flat-top beams were shown to achieve uniform temperature distributions and obtain dense structures at moderate energy densities (, , ). However, such Gaussian-like and super-Gaussian changes in radial intensity from the beam center to the edges impart large thermal gradients in the melt pools and limit the scan parameter space over which such beams can be efficacious. Critically, conventional focused beams are prone to strong diffraction (spreading). As a result, the uncertainty in positioning the build surface accurately at the beam focus can be very high due to mechanical positioning inconsistencies. In addition, the combination of high laser powers (up to kilowatts) and relatively long dwell times necessitated by L-PBF often leads to large thermal stresses on optical components and results in undesired effects such as thermal lensing, which can skew the intensity distribution on the build surface or shift the focus from its original position.

Bessel beams, on the other hand, are a broader class of nondiffractive beam shapes that are vital for several applications such as light sheet microscopy and optical trapping. Although there are several types of nondiffractive and spatially engineered beam shapes that can be envisioned and implemented, they often involve the use of multiple sophisticated optical elements and/or spatial light modulators, which may not be suitable for applications involving high laser powers. Zero-order Bessel beams can be generated using simple optical elements without posing substantial integrability challenges in commercial 3D printers. Bessel beams exhibit phenomenal optical properties including extended depth of focus (or the diffraction-free propagation range) and self-healing where the conical waves simply reconstruct beyond an obstacle placed in the path of propagation (–)—potentially mitigating deleterious effects caused by airborne spatter in L-PBF (). Crucially, very little is known about the effect of complex nondiffracting beams on material response in L-PBF despite the need to explore ways to control the laser-material interaction and improve final material properties. Here, we show that Bessel beams reduce the sensitivity for focal plane positioning during L-PBF (of SS 316L stainless steel). We also show that Bessel beams produce melt pools with larger aspect ratios (narrower and deeper) with a significantly reduced propensity for keyhole mode melting across a broad parameter space. Furthermore, we demonstrate that Bessel beams can significantly outperform Gaussian beams by enabling the production of denser and nearly defect-free structures over a broader parameter space. We also perform high-speed imaging of the melt pool dynamics and find that Bessel beams stabilize melt pool turbulence, increase their solidification times, and reduce spatter generation. Our experimental results are supported by simulations of G-R maps and nucleation mechanisms, which is accomplished by an integrated high-fidelity power-scale cellular automaton model.

RESULTS

Effect of larger depth of focus using Bessel beams

The intensity distribution of a Bessel beam I(r, ϕ, z) = ∣E(r, ϕ, z)∣2 ∝ J2(k), where E is the electric field, J is the Bessel function of nth order, and r, ϕ, and z are radial, polar, and longitudinal coordinates, respectively. For a zero-order Bessel beam, the field distribution can be represented aswhere U is the amplitude; k and k are the longitudinal and radial wave vectors, respectively, related by = 2π/λ; and λ is the wavelength of incident light (). The characteristic beam distribution of a typical zero-order Bessel beam, as shown in Fig. 1B, exhibits a bright central core surrounded by concentric rings separated by dark regions. The depth of focus of a laser beam is generally expressed as 2 × z, where z is the Rayleigh range, i.e., the axial distance over which the size of the beam increases by a factor of √2 (). That is, the depth of focus and the Rayleigh range quantify the size of the effective focal region of the beam or, indirectly, the tolerance for positioning the build surface in L-PBF. For a Gaussian beam, the Rayleigh range , where σ is the beam diameter at the focus (Fig. 1C). For a Bessel beam, the size of central core remains diffraction-resistant (in an idealized case) (), and for finite-sized apertures, the Rayleigh range is z ∝ (Dσ /λ), where D is the aperture diameter. Evidently, the depth of focus of Bessel beams can be significantly larger (by several orders of magnitude) than that of Gaussian beams (Fig. 1D) (, , ).

Fig. 1.

Schematic of the intensity distributions of Gaussian and Bessel beam shapes.

Schematic of (A) Gaussian and (B) zero-order Bessel beam profiles in the radial direction (x-y plane). (C and D) Cartoons representing the axial (z-axis) propagation and focusing properties of typical Gaussian and Bessel beams, respectively, indicating that the Rayleigh range of Bessel beams (z) is significantly larger than that of Gaussian beams (z). (E and F) Representative line profiles of radial intensity distributions (along the x axis) measured experimentally at the focus (z = 0, solid lines) and 200 μm away from focus (dashed lines) for Gaussian and Bessel beams, respectively. (G) The melt pool aspect ratios (d/w), where d and w are the melt pool depth and width, as a function of the defocusing distance (Δz), induced by Bessel (red) and Gaussian beams (gray). The solid markers represent the mean values of d/w normalized to the respective maxima across the defocusing range. Error bars indicate the SD, and the dashed lines are exponential fits to the data points. Schematic of a typical melt pool and corresponding dimensions (d, w, and height h) are shown in the inset of (G).

Experimentally, measured radial intensity distributions of Gaussian and Bessel beams, recorded at the focus (z = 0) and at a distance z = 200 μm away from the focus, are shown in Fig. 1 (E and F). The reader is referred to Materials and Methods and fig. S1 for details on the generation of Gaussian and Bessel beams. For Gaussian illumination, it is evident that defocusing leads to strong beam dispersion, where the full width at half maximum (FWHM) of the intensity distribution increases from 36 μm at the focus to 81 μm at z = 200 μm, i.e., ~2.2×. For the same defocus distance, the FWHM of the central core of the Bessel increases only by ~25%. The significantly weaker influence of defocusing on the beam size correlates well with the estimated Rayleigh range ~120 μm for the Gaussian beam and ~240 μm for the Bessel beam (fig. S2).

Figure 1G shows the influence of laser beam defocusing on the dimensions of melt pools, i.e., the tolerance for focal plane positioning (evaluated from single-track experiments). The details of single-track experiments are described in Materials and Methods (also see fig. S1 for a schematic of the optical setup). The scan parameters used for this set of experiments were power (P) = 250 to 550 W, velocity (v) = 68 to 1375 mm/s, and D4σ beam diameter (σ) = 65 to 280 μm, and the smallest beam diameter obtained in the case of Bessel beams was ~140 μm. The heights (h), widths (w), and depths (d) of the melt pools were evaluated from transverse cross sections of the melt tracks that were generated by defocusing the incident process laser beam relative to the build surface (see fig. S3). The average aspect ratio of melt pools (d/w) generated by each beam shape are normalized to their respective maxima (in the defocusing range) and plotted as a function of the defocusing distance (Δz) (Fig. 1G). It can be seen from Fig. 1G that, for tracks generated with Gaussian beams, the average melt pool aspect ratio (d/w) exhibits a ~5× reduction at a defocusing distance Δz = 250 μm. On the other hand, the tracks generated with the Bessel beam exhibit only a ~1.4× reduction for the same defocusing distance. Exponential fits (of the type y = Ae, where A and B are fit parameters) to the data points also emphasize the significantly stronger sensitivity to defocusing for the Gaussian beam. Note that the SD error is rather high for both beam shapes due to the broad scan parameter range and the uncertainty in mechanical positioning of the build plate following the measurement of beam intensity distribution with a beam profiling camera.

Influence of scan parameters on melt pool dimensions

Figure 2 shows the effect of changing scan parameters on the total aspect ratio of the melt pool—[(d + h)/w]. For simplicity, we consider the volumetric energy density Q (J/mm3), as detailed in Materials and Methods. We also limit the incident power P to 250 to 450 W and consider only those melt pools with h < 90 μm (~2 to 3× the powder particle diameter). From Fig. 2, we note that (d + h)/w is larger for the Bessel beam across most of the considered scan parameter space, i.e., for v < 500 mm/s, Q < 350 J/mm3, and σ ~ 100 to 300 μm. In addition, the variation in (d + h)/w remains more monotonic across a broader parameter space for the Bessel beam–induced melt pools. For instance, in the high-velocity (>300 mm/s) and low-energy density (<100 J/mm3) regime, we notice a nonmonotonic change in (d + h)/w, which can be attributed to a dip in absorptivity [as is typical for metals ()]. However, the Gaussian beam–induced melt pools exhibit a stronger variance within this regime. In the low-velocity (<75 mm/s) and high-energy density (>200 J/mm3) regime, (d + h)/w decreases as a function of energy density possibly due to the stronger interaction between the process laser beam and the melt vapor plume (), and the decrease is more drastic in the case of the Gaussian beam. In the moderate energy-density regime (100 > Q < 200 J/mm3), the melt pools induced by the Bessel beam are evidently larger (i.e., deeper and narrower).

Fig. 2.

Effect of beam shaping on melt pool dimensions.

The total size of melt pools [(d + h)/w]—evaluated from transverse cross-section scanning electron microscopy images, plotted as a function of input process parameters velocity (v), beam diameter (σ), and volumetric energy density (Q) for (A) Gaussian beam– and (B) Bessel beam–generated single tracks. The process parameters in this figure are limited to P = 250 to 450 W, v < 500 mm/s, Q < 350 J/mm3, and σ ~ 100 to 300 μm (for Gaussian beam experiments) and σ ~ 140 to 300 μm for the Bessel beam.

Effect of beam shaping on the propensity for keyholing

Increasing energy density to increase melt pool size is not a feasible route toward controlling melt pool geometry and size because, beyond a certain energy density threshold, the melting process transitions from the conduction to keyhole mode. As is well known from laser welding studies, the keyhole mode occurs due to more intense vaporization of the metal, which exerts stronger recoil forces on the melt pool, leading to the formation of a deep and narrow cavity. The melt pool aspect ratio (d/w) is a signature of the transition from conduction to keyhole mode melting, and as per convention, conduction regime occurs when d/w < 0.5, and d/w > 0.5 indicates keyholing (this is albeit only a crude metric to estimate the transition threshold) (). Because the parameter space used in our experiments is quite large, it is challenging to isolate the sole effect of the beam shape on melt pool geometry and consequently the melting mode from other parameters (as can be observed from Fig. 2). Although the volumetric energy density Q is an informative parameter to compare the effect of beam shaping qualitatively, making quantitative comparisons between the two beam shapes needs to be exercised with caution, especially when probing a broad parameter space (, , ). Hence, we use the normalized enthalpy (ΔH/h), which is the ratio of the absorbed energy density and the volumetric melting enthalpy, and takes into account the laser P, v, and σ to yield a dimensionless measure of the energy density (, ) (see Materials and Methods). ΔH/h scales linearly with the normalized melt pool depth d* = d/(σ/2) and has been proven to be useful in determining the keyhole threshold, as the slope of ΔH/h versus d* is expected to increase at the onset of keyholing (). Figure 3 shows the d* values plotted as a function of ΔH/h for both the beam shapes, and the d* values are segregated by the respective aspect ratio of the melt pool, i.e., d/w < 0.5 or d/w > 0.5. For the Gaussian beam–processed tracks, a clear increase in the slope (~6.7×) is observed in the transition from conduction-mode melting to keyholing. For tracks generated using Bessel beams, the change in slope due to the onset of keyholing is present but significantly reduced (~1.6×), as shown in Fig. 3B. This observation indicates that, when printing with Bessel beams, the melt pool aspect ratios are larger and the propensity for keyholing is reduced significantly across a broad scan parameter space. The chosen scan parameter space used in Fig. 3 was P = 150 to 550 W, v < 1100 mm/s, and σ = 90 to 280 μm, and results from Gaussian beam–induced single tracks (reported in Figs. 1 to 3) incorporate three different measurement sets, including those reported in () to ensure consistency.

Fig. 3.

Normalized melt pool depths as a function of energy density.

The normalized melt pool depth (d* = melt pool depth/beam radius) as a function of dimensionless energy density ΔH/h obtained using (A) Gaussian beam and (B) Bessel beam illumination. The points are segregated by whether the melt pool aspect ratios (d/w) are less than 0.5 (hollow markers) or greater than 0.5 (solid markers). The scan parameters were P = 150 to 550 W, v < 1100 mm/s, and σ = 90 to 280 μm.

High-speed imaging of melt pool dynamics

We perform high-speed imaging to gain additional insights into the dynamics of melt pool evolution during the L-PBF process, i.e., to visualize (i) the melt pool solidification dynamics, which control recrystallization, grain growth, and formation of subgrain structures, and (ii) the stability of the propagating melt pool and the ejection of spatter during single-track generation, both of which affect the propensity for pore formation. We perform two sets of high-speed imaging experiments for each beam shape. First, we image the evolution of melt pools generated by fixing the laser beam spot to one position on the powder bed surface for a defined “on” time. In the next set of high-speed experiments, we image the evolution of the melt pool propagation along a single track, i.e., with the process laser beam scanned along a line on the powder bed. In both cases, we obtain bird’s-eye (top-down) and side views of the melt pool simultaneously by positioning two cameras (see fig. S1). The details of the high-speed experiments are described in Materials and Methods. Figure 4 shows the time it takes for the melt pool to solidify (solidification time) as a function of the energy density ΔH/h, following a stationary single exposure on the powder bed with the “on” time = 5 ms. That is, the solidification time is the time at which the oscillations of the melt pool completely stop relative to the time at which the laser exposure was turned off. The high-speed videos corresponding to Fig. 4 are shown in movie S1. The process parameters used in this experiment were {P = 120 W, 175 W; σ = 90 to 175 μm} for the Gaussian beam illumination and {P = 250 W, 350 W; σ = 150 to 250 μm} for the Bessel beam illumination. The solidification times were evaluated at the center and at the edge of the melt pool (Fig. 4). From Fig. 4, we notice that melt pools induced by Bessel beams take longer to solidify across a broad input energy density range.

Fig. 4.

High-speed imaging of static melt pools.

High-speed snapshots of the melt pools induced by stationary (A) Gaussian and (B) Bessel beams with an illumination time = 5 ms. The snapshots are taken 0.87 ms (left, during solidification) and 5.1 ms (right, after full solidification) after the laser was turned off. The center and the peripheries of the melt pool are indicated by the red and yellow circles, respectively. Solidification times evaluated for Gaussian and Bessel beam illumination evaluated at the (C) center and (D) edge of the fluctuating melt pool. The solidification time is defined as the time at which the oscillations of the melt pool stop completely relative to the time at which the illumination laser exposure is turned off.

We observe that the difference in solidification times between the Gaussian- and Bessel-induced melt pools is higher (i.e., longer solidification times using Bessel beams) at the melt pool peripheries compared to the central regions (Fig. 4, C and D). We also notice that the solidification time for the Gaussian melt pool increases as a function of energy density toward the keyhole threshold region (ΔH/h ~ 5.5) followed by a decrease at higher energy densities. On the other hand, the Bessel beam exhibits a monotonic increase in the solidification time across the entire range of ΔH/h, due to which the solidification time is larger by ~60% for comparable energy densities.

Next, we perform high-speed imaging of melt pool propagation along single tracks processed with Bessel and Gaussian beam shapes (see Materials and Methods). Figure 5A shows the “side”-view snapshots of the melt pool captured at 0.12-ms intervals between 0.12 and 1.5 ms after the laser was turned on (the snapshots were narrowed down from movie S2). The scan parameters were chosen such that ΔH/h ~ 6.2 to 6.5, and the scan velocity was maintained at 143 mm/s for both beam shapes. Observing the evolution of the melt pool vapor along the single track (Fig. 5A), it is evident that the Gaussian beam generates more turbulent fluctuations in the melt pool compared to the Bessel beam characterized by strong variations of the vapor plume angle (with respect to the horizontal plane). Figure 5B shows the melt pool angle as a function of the time after laser illumination averaged over at least three repetitions for each beam shape. The melt pool induced by the Bessel beam exhibits a more stable evolution indicated by the smaller variance of plume angle in the early stages of single-track formation (up to 1.5 ms). While the melt vapor angle stays consistently between ~100° and 120° in the case of the Bessel beam, the Gaussian-induced melt vapor fluctuates between ~70° and 140°. Moreover, the larger spread of the vapor plume angles observed for the Gaussian-induced melt pools indicates a process that is more stochastic, although the variance of plume angles for the two beams becomes less distinguishable toward the end of the millimeter-long track, i.e., when the process reaches steady state (at ~6.5 ms), as shown in fig. S4. The highly turbulent nature of melt pool evolution using Gaussian beams also affects spatter generation. Thus, the number of cold ejecta (nonmelted spatter) from the powder bed is, on average, about twofold higher for the Gaussian beam–induced process (fig. S5). The velocity of ejection of molten spatter is also higher using Gaussian beams, indicating higher recoil forces generated by the Gaussian-like thermal distribution of the laser beam on the melt pool, resulting in the emanation of high velocity ejecta (fig. S6) ().

Fig. 5.

High-speed imaging of a propagating melt pool.

(A) Side-view snapshots of the melt pool captured (at 0.12-ms intervals) from high-speed movies between 0.12 and 1.5 ms after the illumination laser has been turned on induced by Gaussian (top, gray border) and Bessel (bottom, dashed red border). (B) Angle of the melt pool vapor with respect to the horizontal plane (the direction parallel to the build surface) as a function of time, evaluated from side-view high-speed imaging snapshots of melt pool propagation during a single-track scan on a SS 316L powder bed. The shaded error bars represent the SD of the data.

Printing ultrahigh-density parts with smoother surfaces and reduced porosity

Figure 6 (A and B) shows the average surface roughness values of the as-built cubes printed with the Gaussian and Bessel beams, respectively, as a function of their relative densities with the points color-mapped to ΔH/h values (see Materials and Methods for details on roughness and relative density measurements). Only those cubes with relative densities >98% are shown, and the laser scan parameters for the reported points are P = 250 to 380 W, v = 55 to 300 mm/s, and σ = 150 to 200 μm, corresponding to ΔH/h ~ 3 to 8. In the best case, cubes printed with the Gaussian beam do not exceed relative densities ~99%, but those printed using a Bessel beam profile exhibit relative densities that approach ~99.5%. Note that the relative density values approaching 99.9% are reported in literature, but the value can depend substantially on process parameters, measurement techniques, and printing strategies. In our experiments, the quantitative improvement of the relative density using the Bessel beam is in comparison to identical Gaussian beam processing conditions. Notably, the top-surface roughness [evaluated as the mean arithmetic height, S ()] of the cubes printed with the Gaussian beam decreases for denser cubes, but the side-wall roughness increases (Fig. 6A). Moreover, increasing the energy density beyond ~5.5 reduces the relative density and increases the trade-off between the side wall and top-surface quality, i.e., (side wall S)/(top surface S), as shown in fig. S7. This trade-off between the relative density, side-wall roughness, and top-surface roughness is evidently minimized in the case of Bessel beam–printed cubes (Fig. 6B), where energy densities ΔH/h > 5.5 result in nearly fully dense cubes (~99.5%) while maintaining the top surface S below ~10 μm and side wall S < 60 μm.

Fig. 6.

Effect of beam shaping on mechanical properties.

Mean surface roughness values (S) of cubes printed with (A) Gaussian and (B) Bessel beam illumination, as a function of their respective relative densities measured using the Archimedes method. The data points are color-mapped to the incident energy density (ΔH/h) values. BD indicates the build direction in the schematic. The measured yield stress (YS) (black markers) and uniform elongation (UE) (blue markers) of dog bone coupons printed using (C) Gaussian and (D) Bessel beams. Error bars represent the SD of the data.

We attribute the combination of high density and smoother topography that can be achieved using Bessel beams to (i) the reduced propensity for keyholing, which minimizes the side-wall roughness by mitigating keyhole porosity at the edges; (ii) reduced spatter owing to more stable melt pool dynamics, which reduces lack-of-fusion defects and porosity; and (iii) the tendency of the melt pool to remain in the liquid state for a longer period of time (as a consequence of the longer cooling rates), thereby minimizing spatial excursions. This hypothesis is supported by cross-sectional microscopy images of the polished cross sections of representative cubes (figs. S8 and S9), which show a reduction of the pore (spherical and nonspherical) fraction in cubes printed with the Bessel beam (at ΔH/h > 5). For ΔH/h ~ 8.7, the Bessel beam produces a nearly defect-free cube with the pore area fraction down to ~0.04%, which is ~3× lower than cubes printed using any combination of scan parameters with the Gaussian beam (figs. S8 and S9). However, note that Bessel beams require a larger critical energy density (ΔH/h ~ 5) to obtain high-density parts with respectable tensile properties in comparison to Gaussian beams (ΔH/h ~ 3), below which incomplete melting resulted in balling and lack-of-fusion defects.

Comparing mechanical properties

Figure 6 (C and D) shows the yield stress (YS) and uniform elongation (UE) values extracted from true stress-strain curves (eight tensile tests were performed per beam shape, with load applied along the build axis), as a function of energy density. Corresponding plots of ultimate tensile strength and total strain to failure as a function of energy density, and the raw stress-strain curves, are shown in figs. S10 and S11, respectively. Note that only the scan parameters that resulted in densities >98% were chosen, and the energy density range was limited to ΔH/h ~ 5 to 7.5 (see Materials and Methods). The strength and ductility of the Bessel beam (Fig. 6D) are comparable to those achieved with the Gaussian beam (Fig. 6C). However, the trends for both strength and ductility as a function of energy density are different for the two beams. It has been shown previously that, for SS 316L using Gaussian beams, below a certain energy density threshold, parts produced exhibit low ductility due to the formation of lack-of-fusion pores and voids (). From Fig. 6C, it is clear that the strength and ductility of the Gaussian builds decrease for ΔH/h > 5, which also corresponds to the threshold above which the density slowly drops (fig. S7). Evidently, even at very high energy density values, the parts printed with the Bessel beam are less susceptible to vaporization-induced degradation of the mechanical properties, owing to the reduced propensity for keyholing. Grain size analysis from electron backscatter diffraction (EBSD) maps of cubes printed with the two beam shapes indicates no significant differences in the grain size or texture (fig. S12), although filtering out large grains (with a grain aspect ratio of >0.4) and analyzing only those grains with diameter restricted to <15 μm reveal a 30% decrease in the average grain diameter using Bessel beams. Such a result could very well be due to the reduced thermal gradients as discussed below. However, a thorough understanding of the influence of beam shaping on the mechanical properties would require a study of subgrain cellular structures over mesoscopic length scales ().

Modeling and finite element simulations

The thermal gradient (G) and the velocity at the liquid-solid interface (R) under different beam shapes are compared to understand their possible influence on the microstructure. Local G and R in the solidifying region are extracted from the thermal profile history generated using ALE3D Multiphysics simulations [details of the approach have been reported elsewhere ()]. The accurate melt pool shape, dimensions, and thermal history profile predictions are derived by including a full laser ray tracing to capture laser absorption from multiple laser reflections in the melt pool () and accounting for thermocapillary and vapor recoil effects. The extracted G and R values are plotted on a reference solidification map for 316L SS () that shows the boundaries of the G-R regions in which the grain structure is predicted to be fully equiaxed, fully columnar, or mixed.

Figure 7 shows the temporal evolution of G and R for the two different beam shapes. A smaller thermal gradient G is achieved in the melt pool under the Bessel beam. For example, at time t = 323 μs, the smallest values of G is ~1.0 × 107 K/m for the Gaussian beam and 5.0 × 106 K/m for the Bessel beam, under otherwise identical conditions. In addition, at t = 523 μs, the smallest value of G remains at ~1.0 × 107 K/m for the Gaussian beam but drops to ~2.0 × 106 K/m for the Bessel beam. Moreover, the relative positions of points on the G-R map indicates that a melt pool formed under Bessel beam illumination could exhibit higher nucleation propensity of equiaxed grains. As shown in Fig. 7B, the lower-right portion of G-R pairs at t = 323 μs is closer to the equiaxed zone in the case of Bessel illumination, and at t = 523 μs, G-R pairs have drifted from the mixed columnar-equiaxed domain into the equiaxed region due to smaller Gs.

Fig. 7.

G-R solidification maps for the two beam shapes.

Temporal evolution of thermal gradient (G) versus solid/liquid interface velocity (R) for the (A) Gaussian (CG) and (B) Bessel (BES) beams. The superimposed reference solidification map was calculated using Hunt’s model with a nucleation density of N0 = 10 × 1015 m−3 and a critical undercooling of ΔT = 10 K. The processing parameters are power = 300 W and scanning speed = 1.8 m/s.

DISCUSSION

Regarding the detrimental nature of diffractive beam propagation, although the depth of focus can be increased simply by reducing the numerical aperture of the focusing lens, doing so would also increase the beam waist of the process laser beam and reduce the energy density delivered to the build surface. To this end, our work demonstrates that Bessel beams are the ideal replacement to conventional diffractive beam shapes due to their relatively greater degree of propagation invariance, thereby alleviating the need for the integration of adaptive optics for focal and aberration compensation (, , ), which presents unfeasible logistic complications by adding to the design complexity of AM machines. In addition, it has been proposed that at high energy densities, strong plume-laser interactions and the interaction of the laser beam with ejected nanoparticles could attenuate the power delivered to the build surface (, ). Although we have not explicitly studied such interactions in the present work, crude evidence of this can be garnered from Fig. 3, where the spread of Gaussian-induced melt pool aspect ratios increases significantly at higher energy densities. On the basis of our observations, we hypothesize that such deleterious interactions could potentially be mitigated using Bessel beams, owing to their unique self-reconstructing properties (). However, the topic warrants further investigation beyond the scope of this work.

Porosity remains an inevitable consequence of L-PBF and detrimentally affects the corrosion resistance and mechanical properties of printed products. We have shown here that engineering the laser intensity profile in the form of Bessel beams can significantly reduce porosity and increase relative densities of 3D-printed parts while minimizing the trade-off between top-surface and side-wall roughness. We attribute this notable result to several observations made using high-speed diagnosis. First, the redistribution of excess laser power from the center of the melt pool to the peripheries by switching from a Gaussian profile to a bull’s eye pattern in the form of Bessel beams stabilizes the melt pool turbulence during laser scanning.

Second, the thermal gradients in the melt pool are reduced, as deduced from G-R analysis (Fig. 7). Reducing the thermal gradient between the center and the periphery of the melt pool has been shown to stabilize heat and mass transport phenomena such as Marangoni and recoil forces, which are fundamentally the dominant cause of spatter and melt flow instabilities, resulting in porosity (, ). We noticed a reduction in cold spatter using Bessel beams, which can be attributed to the less “wavy” nature of induced vapor plumes and the consequent mitigation of the influence of laser wake fields on particle motion (, ). The improved tolerance for focal plane positioning also has a beneficial effect on printed part quality because a shift in the focal position by one Rayleigh length implies a fourfold decrease in the laser intensity, which is sufficient to degrade the quality of single tracks produced using L-PBF. However, pores, defects, and cracks can result from several other factors, including choice of scan strategy and residual stresses, and understanding their correlation (or the lack thereof) to beam shaping requires additional studies that are beyond the scope of this work. Nevertheless, it is worth noting that sector-wise (such as island or checkerboard patterns) printing and other scan strategies have been proposed and used to avoid accumulation of defects in the same location and reduce residual stresses during printing. However, such strategies using shorter tracks at the expense of greater number of scan “startups” are also more prone to defects and porosity at the beginning of a scan track, when the energy delivered by the laser beam is unstable (due to inertia arising from scanning components). In this regard, we have shown that Bessel beams minimize melt pool turbulence right from the beginning of a scan track, paving the way to incorporate complex scan strategies by minimizing start-of-scan detriments that conventional beam shapes are bound by.

The tensile properties as a function of energy density exhibited different trends for the two beam shapes, indicating differences in porosity and vaporization-induced effects (at higher energy densities). This observation correlates well with the fact that Bessel beam–induced melt pools require higher energy densities to form continuous and dense structures (without significant lack-of-fusion defects) compared to Gaussian beams. However, beyond such a critical energy density, Bessel beams significantly reduce the propensity for keyholing and the parameter space in which the density, strength, and ductility can be optimized is larger. Most significantly, Bessel beams resulted in a distinctively improved combination of high density, improved morphology, and robust tensile properties in 3D-printed test structures. Note that the power delivered by the core of the Bessel beam reduces proportionally to the number of rings. Moreover, the actual power delivered to the build surface is ~12% lower due to transmission losses through the axicons, which have not been accounted for in this work. Although we were unable to explore higher powers (beyond 380 W for full builds) due to limitations of our 3D printing system, doing so could lead to further improvements of mechanical properties (), which is not a luxury afforded with Gaussian beams due to the limit of keyholing.

Although our study does not consider powder size distribution effects in the context of beam shaping, we hypothesize that the beneficial results of using Bessel beams would hold for a wide distribution of powder particles with sizes close to or smaller than the beam diameter. In this regime, engineering the spatial distribution of Bessel beam could be used as a degree of freedom in such a way that only the central core of the beam exceeds the melting threshold, whereas power distribution in the wider Bessel rings could simply be used to anneal the powder bed or maximize heat retention. However, if the size of the powder particle approaches the wavelength of the process laser beam, Mie resonances or anomalous scattering effects could start to dominate and affect absorptivity of the powder bed or the strength of laser-plume interactions. We expect that the impact of Bessel beam shaping on optical and absorptivity-dependent thermal phenomena such as focal plane tolerance, melt pool turbulence, and keyholing propensity, as reported here for SS 316L, could qualitatively apply to a wide range of metals and alloys, although the resulting impact on microstructural and mechanical properties (which are significantly material-dependent) of other materials requires further studies.

MATERIALS AND METHODS

Optical setup used for printing single tracks

Single-track experiments were performed using a 600-W Yb fiber laser (JK Lasers, model JK600FL), emitting continuous-wave output with wavelength λ = 1070 nm. For Bessel beam experiments, the Gaussian output from the laser was collimated using a 35-mm lens and then routed through a pair of identical axicons (Thorlabs, AX255-C) with the half-angle of the prism, α = 5o, as depicted in fig. S1. The axicons were spaced ~5 cm apart to yield a collimated annular beam, which was directed through a three-axis galvanometer scanner (Nutfield Technology) into a vacuum chamber (15 cm by 15 cm by 15 cm) through a high-purity fused silica window. The annular beam was then directed through a focusing lens, which generated its Fourier transform at the focal plane and produced a zero-order Bessel beam (fig. S1). For generating Gaussian beam profiles, the output from the laser was collimated using a 50-mm lens and passed through the galvanometer scanner, with the two axicons removed from the beam path. The D4σ diameter of the focused Gaussian beam was varied between σ ~ 90 and 300 μm and that of the Bessel beam was varied between σ ~ 140 and 300 μm by defocusing and chosen depending on the type of experiment performed, as specified in the main text. The D4σ diameter is expressed as the second moment of the intensity distribution. Note that the D4σ diameter metric is extremely sensitive to the cutoff aperture for a 2D intensity distribution. Hence, to maintain consistency in evaluating the cutoff aperture and the beam size, we used a beam profiler (SP300, Ophir-Spiricon LLC) with a proprietary “Auto aperture” option to evaluate the aperture size. The accuracy of the measurements was confirmed by comparing the measured D4σ values with the more commonly used 1/e2 diameter of Gaussian beams with the error <15%, although, for an ideal Gaussian beam, the 1/e2 diameter is equal to the D4σ diameter. The D4σ diameter can be evaluated consistently using any beam profiling camera, if the noise level of the measurement is low and if good background subtraction techniques are used (including but not limited to image postprocessing methods).

Single tracks were generated on 316L stainless steel powder (15 to 45 μm; Additive Metal Alloys 316L, Holland, OH, USA), which was spread over 1-inch SS 316L substrates (McMaster-Carr). The substrates were 1/8 inch thick, and wire electrical discharge machining (EDM) was used to machine them into 1-inch-diameter discs. The powder layer was manually spread over each substrate using a glass coverslip. Although the powder layer thickness was not measured before each single-track experiment, the melt bead height (h) provides a good estimate of the powder layer thickness (t), which was assumed to be 50 μm in calculations. The single-track data reported in the paper are presented by filtering out any results, where h > 150 μm (~3 to 4 layers thick), to avoid any layer thickness-dependent effects. The powder-covered substrate was then positioned in a custom-built sample holder and placed at the focal plane of the incident build laser beam. For each set of single-track experiments, the vacuum chamber was evacuated using a turbomolecular pump and continually backfilled with argon (with the Ar flow direction parallel to the direction at which single tracks generated). The chamber pressure was maintained at ~1 atm.

Printing of density cubes

3D printing of full builds was performed inside an Aconity Lab L-PBF research machine (Aconity 3D, Aachen, Germany) equipped with a 400-W Yb fiber laser, as described elsewhere (). Considering the defined geometry of the optical setup within the L-PBF machine, the spacing between the axicon pair was adjusted accordingly to obtain focal spot diameter σ with minima ~150 μm for printing with Bessel beams. For density measurements and microstructural analyses, we printed SS 316L stainless steel cubes of dimensions 1 cm by 1 cm by 1 cm or 1.4 cm by 1.4 cm by 1 cm. The hatch spacing for all printed samples was maintained at 100 μm, and a serpentine scan strategy was used. The layer heights for all full builds were 50 μm. Build plates were 0.75 inch thick and made of SS 316L.

Energy density metrics

The volumetric energy density was evaluated as Q = (4 × P)/(π × v × σ2), where P is the power of the incident beam. v is the scan velocity of the beam, and σ is the beam diameter (D4σ). This metric is different from conventionally used metric for volumetric energy density, which incorporates hatch spacing and powder thickness (). However, as the hatch spacing is inconsequential in single-track measurements and the powder layer thickness can be assumed to be the same for comparative purposes, incorporating the area of the beam spot into the calculations of the energy density will better capture the effect of σ on the single-track melt pool dimensions and other characterized properties of full builds. For full builds, while the hatch spacing is an important process parameter, we maintain the hatch spacing constant at 100 μm for both beams across all the reported experiments, so for comparative purposes, the beam area is included in the equation for Q, in lieu of hatch spacing or powder layer thickness.

The normalized enthalpy metric used in the text is given aswhere A is the absorptivity, D is the thermal diffusivity, v is the scan velocity, and h ρcT is the enthalpy at melting with heat capacity c, density ρ, and melting temperature Tm. In our experiments, P, v, and σ were scan variables, as specified in the main text, D = 5 × 10−6 m2/s, ρ = 8 g/cm−3, Tm = 1660 K (). Although we perform absorptivity measurements for both the beam shapes, we assume A = 0.28 [according to prior estimates for the absorptivity minima in SS 316L ()] in the calculations of normalized enthalpy for the sake of simplicity.

Metallographic characterization

Metallographic samples were sectioned using a low-speed saw and cold-mounted in castable epoxy. The samples were ground using successively finer SiC abrasive paper from P500 to P4000 grit and polished using 3 μm followed by 1-μm diamond paste. Vibratory polishing was performed using 0.05-μm colloidal silica. For examination by optical microscopy, the samples were electrolytically etched at 6 V in a 10% oxalic acid solution. EBSD was performed on as-polished samples using an EDAX DigiView EBSD camera on an FEI XL-30 scanning electron microscope (SEM). Relative densities of the as-printed cubes were measured using the Archimedes method in Fluorinert (FC-43) and/or water. Evaluation of surface roughness of the top and side surfaces of as-printed cubes and porosity analysis of etched cube cross sections was performed using optical microscopy (Keyence, VHX 7000). To quantify the pore area fraction, microscopy images were postprocessed in ImageJ. Image processing consisted of thresholding the images (with identical pixel threshold values for both beam shapes) and filtering out any features that were less than 2 pixels.

High-speed imaging

For high-speed imaging experiments, the vacuum chamber that was used for single-track experiments was removed and the imaging experiments were performed in ambient atmospheres. Two high-speed cameras captured movies of single-track generation simultaneously. The first high-speed camera (Photron Fastcam SA-X2) was mounted at an angle ~28° from the axis of the process laser beam (fig. S1) to obtain side views. The camera was equipped with microscope optics (Mitutoyo 5×, 0.14 numerical aperture, plus a Navitar tube lens providing ×4.5 magnification). Top-down imaging was accomplished by imaging the melt pool through a 45° dichroic mirror, which was positioned in the path of the process laser beam (such that the process laser beam was transmitted). The scattered light from the build surface was reflected from the mirror and imaged by the second camera (Photron FASTCAM Mini AX200), equipped with an Infinity K2 Close-Focus Objective (CF-3). The resolution provided by both cameras is on the order of a few micrometers sufficient to resolve individual powder particles and the melt pool. The build surface was illuminated using a 810-nm pulsed laser with 500-W peak power (Cavitar, model Cavilux HF), and both cameras were equipped with appropriate neutral density filters and 10-nm band-pass filters, centered at 810 nm, to filter out melt pool incandescence. Imaging was performed at 30,000 frames per second. High-speed imaging was performed on single tracks, as well as single-exposure stationary shots on the powder bed, generated using the combination of scan parameters outlined in the main text. The exposure or “on” time of the laser for stationary beam experiments was 5 ms.

High-speed videos were postprocessed to enable better visualization of the melt pool vapor (see Materials and Methods), circumventing the need for more sophisticated imaging techniques such as Schlieren imaging (). Image postprocessing (contrast adjustments and thresholding), particle tracking, and velocity calculations were performed using ImageJ and Fiji (https://imagej.net/Fiji) with the aid of the MTrack () plugin. Solidification times were calculated by manually observing the frame at which the melt pool oscillations freeze, i.e., stop fluctuating, with respect to the frame at which the laser beam was turned off. Particle counting analysis, i.e., the number of hot or cold particles in each frame, was performed using a trainable image segmentation Fiji plugin that uses a collection of machine learning algorithms with a set of preselected features in the video/image to produce pixel-based segmentations (). The segmentation approach enabled the distinction of molten or partly molten spatter particles (which appear as bright pixels) from the “dark” powder ejecta or from the melt pool, which has a defined movement trajectory.

Mechanical testing

Tensile samples were cut with wire EDM from 10 mm by 10 mm by 40 mm plates printed using both beam shapes, as described in fig. S13. Samples were oriented with the tensile direction perpendicular to the build direction. Note that the position of the samples in the prints was chosen to consistently have the gauge region at the same distance from the build plate while staying away from any as-built surfaces by at least 1 mm. Because of print area constraints, the maximum allowable dimensions of the tensile samples prevented us from fully following the ASTM-E8 standard commonly used for pin-loaded specimens as it is the case here. Nevertheless, the tensile specimen gauge section was designed in respect of the ratio between gauge length and width, as dictated by the ASTM-E8 standard. Hence, the gauge region is 6.5 mm (length) by 2 mm (width) by 1.2 mm (thickness). As samples were pin-loaded, we used stiffening plates at the grip ends to prevent potential buckling. Note that no buckling was observed after test using a SEM and samples systematically failed near the middle of the gauge region (fig. S14). The yield strength was extracted at 0.2% offset following the ASTM-E8 standard. The UE used in this work corresponds to the true plastic elongation up to the onset of necking (strain localization). Tensile tests were carried out at 5 × 10−4/s with Instron 4444. A noncontact laser extensometer was used to allow for sufficient measurements across the large plastic strain of the L-PBF 316L SS. The scan parameters for the tensile samples were P = 250 to 380 W, v = 55 to 114 mm/s, and σ = 154 to 197 μm for the Bessel beam and P = 350 to 380 W, v = 114 to 190 mm/s, and σ = 150 to 170 μm for the Gaussian beam.

ALE3D simulations

ALE3D is a multiphysics code developed at Lawrence Livermore National Laboratory using arbitrary Lagrangian-Eulerian (ALE) techniques. For the simulations, ALE3D was run in the Eulerian mode. Figure S15 shows the pseudocode used for ALE3D simulations. The metal particles were overlaid on a uniform Cartesian background mesh and are represented as volume fractions that either fill a zone completely or not. The explicit hydrodynamics and heat conduction packages were integrated via operator splitting to simulate the thermo-mechanical evolution. The Lagrangian-motion phase moves material adiabatically in response to forces using single-point Gauss quadrature for strain mapping and nodal force calculations based on face normal. The thermal phase solves the heat diffusion equation and diffuses heat within the materials without any material motion, using a nodal temperature-based integration. The advection phase remaps the mesh back to its original configuration. All three phases occur sequentially at every time step.

The initial temperature is set to be at room temperature. In the thermal phase, all boundaries except the bottom were treated as insulated. The bottom face used a custom thermal boundary condition that mimics the response of a semi-infinite body at this interface. Furthermore, a heat sink thermal boundary condition was applied on the materials surface to mimic the evaporative cooling of boiling liquid metal and radiative cooling. The laser energy deposition model uses full laser ray tracing and acts as a heat source term for the thermal diffusion equation. For the hydrodynamical phase, surface tension and recoil pressure boundary conditions are applied at the interface between the material and ambient gas. These forces contribute to the Lagrangian-motion phase to advect material through the mesh.