Experimental approach for development of a powder spreading metric in additive manufacturing

The powder spreading is a vital step of powder-based additive manufacturing (AM) processes. The quality of spread powder can considerably influence the properties of fabricated parts. Poorly packed powder beds with high surface roughness result in printed part layers with large porosity and low dimensional accuracy, leading to poor mechanical properties. Therefore, the powder spreadability and its dependence on process parameters and powder characteristics should be quantified to improve the efficiency of powder-based AM methods. This study proposes a novel dimensionless powder spreadability metric that can be commonly used in different powder-based AM processes. The quality of spread powder in terms of powder bed density and surface roughness was evaluated by adjusting the process parameters including recoating velocity and layer thickness, and powder characteristics including particle size distribution. In addition, the dynamic repose angle was proposed and examined as another powder spreadability metric. The results showed that these two proposed metrics were strongly correlated and lower recoating velocity and larger layer thickness led to higher spreadability and lower dynamic repose angle.


Introduction
The conventional manufacturing methods include many steps such as machining, forming, assembling, and welding. [1][2][3][4][5][6]. The material and part handling among these steps can be very time-consuming in addition to the time and labor cost each of these steps takes to proceed with the production process. The advent of additive manufacturing (AM) decreased the need for several of these steps as it fabricates the parts in a single-step layer-based manufacturing fashion [4,7,8]. In AM processes, the part geometry data is sliced into several layers and is given to the AM machine. The material feedstock will be used to fabricate each part's layer. The final component is fabricated by repeating the material injection and production process for all part's layers [9]. Due to this layer-by-layer manufacturing process, the fabrication of high-complex geometry components with high accuracy and desirable part properties is possible [10,11].
Depending on the type of AM process, the format of material feedstock is different. For instance, laser foil printing (LFP) uses metal foils while Ceramic On-Demand Extrusion uses paste, and fused deposition modeling (FDM) uses filaments [12][13][14][15][16][17][18]. The powder is another widespread material format in AM, especially in powder-based AM processes [19][20][21]. Due to the higher formability of powder material, it is beneficial in fabricating parts with highly complicated geometries [22]. However, the specific fabrication conditions of AM, such as the creation of very thin layers, may adversely affect the powder characteristics and consequently deteriorate the powder performance in terms of powder spreadability. In addition, the process temperature should be accordingly controlled to avoid creation of defects in fabricated parts [23][24][25], and collision between fabricated part layers and powder recoater, which can be considered as a two fixed end beam [26].
The first step of fabricating each part's layer in powderbased AM methods is delivering the powder feedstock. As the delivered powder contributes to the fabrication of a single layer at a time, it should be deposited on the build plate (substrate) with the thickness of a part's layer. Although some techniques such as decreasing the part's surface roughness by adjusting layer thickness for different layers have been implemented to improve the part's quality, the properties of the spread powder layer may influence the quality of fabricated parts [27][28][29][30]. Each powder layer should be highly dense with low surface roughness to result in the desired part features including low porosity, high mechanical properties, and high dimensional accuracy [31][32][33][34]. Also, the powder should be rapidly delivered for each part's layer to minimize the fabrication time and maximize the process efficiency. Thus, the powder should be spread with a specific layer thickness (LT) and recoating velocity (RV) to quickly create a dense powder layer with low surface roughness.
Many researchers in recent years have studied powder spreadability and its dependence on spreading process parameters. As no spreadability metric was commonly used in the AM community, the researchers proposed some spreadability metrics and examined their validity. These spreadability metrics have been reported and extensively discussed in a comprehensive review paper by Sehhat et al. [35]. The observed empty areas on the substrate with various LTs were reported by Ahmed et al. [36]; they found that the lower layer thicknesses resulted in a greater number of empty areas in the substrate. Cordova et al. [37] proposed the relative density as the powder spreadability metric, defined as the ratio of apparent density over material density (ρ), and the relative density was evaluated in two different recoater designs. The funnel recoater, in which the particles were pushed down by the gravity forces of overhead particles, deposited a greater number of particles in the substrate and resulted in a higher relative density as the gravity forces dominated the Van der Waals forces among particles. Zhang et al. [38] considered the powder bed density as a powder spreadability metric; they found that powder bed density deteriorates at high RV and low LT due to powder splash and particle jamming, respectively. Surface roughness of spread powder was considered as a spreadability metric in a study by Parteli et al. [39], where higher RV resulted in larger surface roughness, i.e., lower spreadability.
Although several spreadability metrics have been proposed and investigated in the literature, the existence of a dimensionless powder spreadability metric that can be commonly used in different AM processes is still lacking. In this study, powder performance in terms of powder bed density and surface roughness was assessed, and a dimensionless powder spreadability metric was proposed based on them. To evaluate the powder spreadability as a metric independent on the material characteristics, the measured density of the spread layer (measured mass (m)/computed volume (v)) was divided by the material density, , and the resulting quantity was called powder bed density. Also, the measured surface roughness (Ra) was divided by the medium particle size of powder, D 50 , and the resulting quantity was called relative roughness, which is independent of the powder particles size. Since it is desired for the spread powder layers to be dense with little roughness, the powder bed density was divided by the relative roughness to create a dimensionless ratio that increases with improved powder bed quality. Thus, powder spreadability is defined as In addition, another powder spreadability metric, dynamic repose angle (DRA), was proposed and measured by the side view images obtained by the high-speed camera. Powders with higher flowability are known to result in smaller magnitudes of the angle of repose [40] similar to the flow behavior of granular material [41]. In a similar approach, smaller magnitudes of DRA indicate higher powder spreadability. The influence of spreading process parameters, including RV and LT, and powder characteristics, including particle size distribution (PSD), on these proposed spreadability metrics was evaluated. The trends for obtaining higher powder spreadability were determined. While in several research studies in the literature the researchers sufficed with the low-accuracy results of powder spreading manually with their hands, in this work, we report the high-accuracy results of powder spreading provided by an in-house fabricated automatic high-accuracy spreading setup.
The rest of this paper is organized as follows. Section 2 provides the information on the used material and the fabricated spreading setup for performing spreadability experiments. Section 3 discusses the impact of RV, LT, and PSD on powder spreadability and DRA, followed by the correlation relationship between them.

Material
The gas-atomized AISI 304L stainless steel powder was provided by LPW Technology (Carpenter Technology Corporation, USA). The manufacturer reported the powder density as 2.7 g/cm 3 and the powder particle size distribution as 13, 20, and 30 µm for D 10 , D 50 , and D 90 , where D 10 , D 50 , and D 90 are the 10th, 50th, and 90th percentiles, respectively, of the particle size distribution. As the particle size distribution will be discussed in the following sections, the powder size span can be used as a meaningful representative of powder PSD. The powder size span can be defined as with its larger values indicating higher PSD.

Fabrication of the powder spreading setup
Fabrication of an automatic high-accuracy and high-resolution spreading system was required to accurately study the different properties of the powder bed. Figure 1 shows the fabricated powder spreading setup with major components of a 3D gantry system, a laser line profiler, and a high-speed camera. The automatic gantry system is controlled with a computer numerical control (CNC) program and can provide a high motion resolution of 1 µm. The function of the gantry system is to move the powder recoater over the static table to spread the powder on the substrate, move the laser profiler over the spread powder layer to scan the coordinates of the spread layer, and move the high-speed camera for measurement of DRA. The deployed laser line profiler is a Gocator 2320 (LMI Technologies Inc., Canada) with a resolution of 1.8-3 µm in the Z direction and 14-21 µm in the X direction. It can provide coordinate information of 1280 data points per laser profile. By processing the obtained data points in the Mountains Map® software (Digital Surf, France), the required properties of the spread powder layer, such as volume and surface roughness, were computed.
The high-speed camera is an SC1 Edgertronic (Sanstreak Corp, USA) capable of capturing 700 frames per second (fps) at a resolution of 1280 × 720 pixels. The provided high fps of this camera makes the in situ capture of powder DRA possible during the powder spreading process. The camera is attached to the recoater's side and moves with it, i.e., although the camera is moving relative to the static table, the camera is static relative to the recoater's side. Thus, during the spreading process, the camera is watching a still frame of powder spreading with a changing powder DRA.

Design of experiments
The goal was to evaluate the impact of spreading process parameters on powder properties. The variable factors were recoating velocity (RV), layer thickness (LT), and particle size distribution (PSD). RV had 4 levels of 25% (32.5 mm/s), 50% (65 mm/s), 75% (97.5 mm/s), and 100% (130 mm/s). LT had 3 levels of 30, 50, and 70 µm. The virgin powder in its as-purchased condition was considered as one level of PSD (unsieved), and it was sieved by 45-and 25-µm screens to create the second level of PSD, including particles smaller than 45 µm but larger than 25 µm (25 < PSD < 45, hereafter called . Also, to distinctly investigate the impact of particle size (PS) on powder spreadability, three PSs of smaller than 25 µm (PS < 25 µm, hereafter called < 25), 25-45, and larger than 45 µm (45 < PS, hereafter called > 45) were studied. The particle size information of these three powder sizes is shown in Table 1. Adjustment of RV and LT was performed through the CNC program of the gantry system. The studied powder properties such as powder bed density, powder surface roughness, and powder DRA were considered as response variables. To evaluate the results' repeatability, each experiment was replicated three times, and their mean and standard deviations were reported.  The powder bed density was defined as the mass over the volume of spread powder. The powder mass was measured for each spreading experiment before spreading the powder on the substrate. To measure the volume of spread powder, the laser profiler should scan all the spread powder's top surface. Based on the point cloud obtained by the laser profiler, the Mountains-Map® software computed the volume, which would be the volume of space between the substrate and the scanned point cloud of powder layer. Then, the powder bed density was obtained by dividing the measured mass over the computed volume.
The powder surface roughness was measured by the MountainsMap® software. Figure 2a is an instance of the top view of a powder layer spread with RV 25% and LT 30 µm. The software can generate the surface roughness Ra parameter for each scanned profile. As shown in Fig. 2b, for measurement of surface roughness per spreading experiment, 12 profiles (with 10-mm gap distance) of the scanned surface were selected, and their individual Ra was measured. Then, the mean and standard deviation of these 12 Ra values were reported as powder layer's surface roughness.
To assess the impact of RV on the powder layers spread with a constant LT 30, the values of surface roughness at a representative location along the spreading direction Y60 are shown in Table 2. Increasing the RV resulted in a layer with higher surface roughness.
The increased surface roughness when increasing RV can be observed in the surface profiles of corresponding spread layers with a constant LT 30 in the middle of the spread layer (Y60), as shown in Fig. 3.
In addition, to evaluate the impact of LT on powder layers spread with a constant RV 100, the values of surface roughness at a representative location along the spreading  direction Y60 are shown in Table 3. The surface roughness of the spread layer slightly decreased when using larger LTs; this is mainly because the powder particles are packed to the larger underneath material thickness. The powder DRA was evaluated through performing image analysis on the side images obtained by the high-speed camera. Figure 4 shows an instance of the powder spreading process as watched by the high-speed camera. Figure 4a shows the powder released on the substrate in front of the recoater before spreading; the camera's view of this outlook is shown in Fig. 4b. As the spreading starts and the recoater makes contact with the powder, the powder pile is forced to move, which causes the creation of DRA in the powder pile. Figure 4c shows an instance of powder pile reaction during the spreading process, and the part of images used for DRA measurement is shown with a white rectangle. A closer look of the marked DRA can be seen in Fig. 4d. The ImageJ software [42] was used to measure the DRA angle between powder and substrate (α). For measurement of DRA per spreading experiment, 12 frames of the spreading process at the same locations of the 12 Ra profiles were investigated in image analysis. The angle in each frame was measured 10 times, and their mean was reported as the DRA for that specific frame. Then, the   Figure 5 illustrates the influence of RV and LT on powder spreadability. Increasing the RV from 25 to 100%

Impact of recoating velocity (RV) and layer thickness (LT) on spreadability
considerably decreased the powder spreadability, while increasing LT from 30 to 70 µm had a marginal impact on the powder spreadability. This behavior can be explained by the increased momentum of particles at higher RV; as the particles are being pushed faster, they maintain their gained speed for a longer distance and in an arbitrary direction. This unorganized particle motion causes particles to deposit at random locations, creating empty areas in the substrate and leaving empty space among particles which then will be transformed to porosity in the fabricated LPBF parts.
Running an analysis of variance (ANOVA) with a significance level of 0.05 showed that the results of different experimental runs were significantly different (P-value < 0.0001).  No significant interaction was found between the RV and LT (Table 4); they were independent factors and the effect of RV on spreadability remained the same irrespective of the used LT. Looking at the main effects of each factor, both RV and LT are significant factors as their P-values of < 0.0001 and 0.0025, respectively, were smaller than the 0.05 significance level.

Impact of particle size (PS) and particle size distribution (PSD) on spreadability
To assess the effect of PS on powder spreadability, some experiments with a constant RV of 100% and LT of 50 µm were performed with three different PS of − 25, 25 − 45, and + 45 µm. The results of powder spreadability for this set of experiments are shown in Fig. 6. The particles larger than 45 µm (+ 45) showed the highest spreadability, and the spreadability decreased by decreasing the particle size. Also, decreasing the particle size led to larger deviations in powder spreadability. This relation between particle size and powder spreadability can be explained by the dimensionless "bonding number (K)" [35], where for a constant density the larger particles have higher gravity forces which outweigh the Van der Waals forces present among particles. As a result, the larger particles are less likely to agglomerate and are more willing to deposit in the substrate. On the other hand, the smaller particles have lower gravity forces, larger surface/mass ratio, and larger Van der Waals forces. Thus, for smaller particles, the Van der Waals forces outweigh the gravity force and cause the powder to agglomerate and act more cohesively, which is detrimental to powder spreadability.
For evaluating the effect of PSD on powder spreadability, only the extremum PSDs of the unsieved powder (with the widest PSD) and the 25-45 (sieved) powder (with the narrowest PSD) were studied. Figure 7 shows the relationship between span and powder spreadability for both unsieved and 25-45 powders. The narrow size span of 25-45 powder indicates that the particles are more uniform without large size variations, while the large span of unsieved powder indicates that the powder is composed of non-uniform particles with various sizes; although this size non-uniformity may intuitively sound helpful for creating denser powder layers by smaller particles filling the voids among larger particles, the whole powder's increased surface/mass ratio and the great magnitude of Van der Waals forces among these non-uniform particles deteriorated the powder bed density and surface roughness [37,43]. Therefore, as the 25-45 powder had the narrowest size span, it showed higher spreadability than unsieved powder. Figure 8 shows the impact of RV and LT on DRA. Increasing the RV resulted in larger DRAs as the particles are forced to move and repose in a shorter time. This faster velocity also increases the particles' momentum, forcing them to move longer distances and create larger angles. Increasing the LT decreased the DRA as more powder passed through the larger gap between recoater and substrate; in other words, at larger LTs, there is less powder pile in front of the recoater. Consequently, this lower amount of powder in front of the recoater results in smaller DRAs. The influences of RV and LT on DRA agree with the results on the proposed powder spreadability metric, i.e., deploying lower RV and larger LT led to higher powder spreadability and lower DRA, although  the impact of RV on both metrics was more considerable than that of LT.

Impact of recoating velocity (RV) and layer thickness (LT) on dynamic repose angle (DRA)
Performing an ANOVA with a significance level of 0.05 on the DRA results showed that they are significantly different (P-value < 0.0001). Evaluating the effects of variable factors, as in Table 5, showed a significant interaction between the RV and LT (P-value = 0.0016), i.e., RV and LT are interdependently affecting the DRA. Also, the main effect tests indicated that both RV and LT are significant factors in determining the DRA.

Impact of particle size distribution on dynamic repose angle
The impact of PSD on DRA is shown in Fig. 9. The more uniform 25-45 powder with a narrower span showed higher spreadability with smaller DRA, while increasing the size span led to lower spreadability and larger DRA. This behavior can be explained by the higher cohesivity of powder with wider PSD. The Van der Waals forces exerted by smaller particles overcome their gravity forces; thus, the smaller particles are more willing to agglomerate. In addition, the heavier weight of larger particles forces them to stay still. These circumstances provide required conditions for the smaller particles to agglomerate around the larger particles, creating a cohesive powder with low powder bed density, high surface roughness, and large DRA.

Correlation between spreadability and dynamic repose angle
After experimenting the impact of recoating velocity and layer thickness on two metrics of powder spreadability and dynamic repose angle, it is necessary to investigate the correlation between these two metrics, i.e., whether spreadability shows similar behavior as dynamic repose angle under the same spreading conditions. Therefore, the correlation between spreadability and dynamic repose angle was evaluated, and the results are shown in Fig. 10. As the correlation coefficient R is very close to 1 (0.94), the spreadability and dynamic repose angle are very similar functions of RV and LT. Also, the R 2 being close to 1 (0.89) indicates that the results can be well fitted to a linear relationship. This great correlation shows that these two metrics can be interchangeably used depending on their ease of use for different applications. It also should be noted that the correlation between spreadability and dynamic response angle is inversely proportional, as a more spreadable powder (higher values of spreadability) results in a smaller repose angle.

Conclusion
The dependence of powder spreadability and dynamic repose angle (DRA) on the spreading process parameters showed that a significantly higher powder spreadability was obtained with lower recoating velocity (RV) due to the more organized particle motion caused by slower speed and less momentum. Layer thickness (LT) also had a statistically significant effect on powder spreadability, where larger LT slightly improved the powder spreadability as more powder was packed underneath the recoater. In addition, larger particle size with a narrower span led to higher spreadability. The heavier weight of larger particles overcame the Van der Waals forces, forcing the particles to deposit in the   Fig. 9 Effect of size span on DRA substrate at an early stage. For the powder with a wide span, the existence of light-weight smaller particles mixed with larger particles increased the interparticle Van der Waals forces, agglomerating the smaller particles around the larger ones, increasing the powder cohesivity, and deteriorating the powder spreadability due to the decreased powder bed density and the increased surface roughness. A high correlation was observed between the spreadability and DRA as they have strong correlation under different spreading parameters; the value of DRA decreases as the spreadability increases. Therefore, DRA can be used as a spreadability index.