A simple method for assessing powder spreadability for additive manufacturing

: Additive manufacturing based on powder spreading is attracting great interest, but one key 6 weakness is that narrow gaps used for spreading produce non-uniformity in the spread layer due to 7 transient jamming. We propose a simple technique for assessing the powder spreadability, a measure 8 of the ease with which a powder is spread uniformly without the formation of empty patches. A cutter 9 blade, with a segment cut along its length to produce a gap, is used to manually spread a small heap of 10 powder. The frequency of formation of empty patches and their size, which are a manifestation of 11 jamming as the particles are spread, are analysed for several gap heights. The sizes of the empty 12 patches and frequency of their formation are determined by image analysis. The outcomes correlate 13 well with a Discrete Element Method simulation of the same system. A criterion is proposed for 14 diagnosing the empty patch formation.


Introduction
uniformly as a thin layer of a few multiples of particle size without the formation of any empty patches, 1 presence of agglomerates and rough surfaces. 2 The majority of the studies conducted so far address powder flowability instead of spreadability [14- inter-related. The former, which is the focus of the work here, is affected by powder flow behaviour 10 in narrow clearances, where the shearing zone is only a few multiple of particle size, thus the discrete 11 nature and properties of particles, such as size distribution, shape and surface properties are highly works have been done on the powder spreading [10,[29][30][31][32][33][34], there is no experimental technique so far 21 to assess powder spreadability. 22 Hence, in this work we use a model metal powder commonly used for additive manufacturing and 23 propose a simple and quick experimental technique for characterising its spreadability as a function of 24 the spreading gap height. The analysis is performed on the same metal powder as previously characterised for particle shape, interfacial adhesion and friction and used in the simulations by DEM 1 [10]. A laser cut Stanton cutter blade of various gap heights positioned vertically is used to manually 2 spread a pile of powder particles on frictional Emery paper to produce a spread layer. The generated 3 particle spread layer contains empty patches (manifestation of jamming). The characteristics of empty 4 patches in terms of size and frequency of appearance is analysed, providing a quick and simple method 5 for characterising the spreadability of metal powders. The results are compared with numerical 6 simulations by DEM. The test powder is gas-atomised 316 L stainless steel particles, obtained from Sandvik Osprey Ltd., 10 Neath, UK. Its particle size distribution is in the range 15-55 µ m, with the characteristic measures of 11 the distribution D10, D50 and D90 by number given as 20 µm, 32 µm and 45 µ m, respectively. Nan et 12 al. [10] have shown that the most appropriate characteristic measure of particle size that describes 13 transient jamming and powder flow through narrow gaps is D90 by number (will be denoted as D in 14 this work). As we use the same powder in our work, the relevant particle properties are those reported 15 by Nan et al. [10]. The particle size distribution is classified into four sizes classes as reproduced here  µm and 45 µm, respectively [10]. 20 A Stanton cutter blade is used for powder spreading. It is cut along its length by laser to create a gap   To provide an appropriate amount of powder for spreading, a makeshift cardboard stencil (25 mm×2.5 9 mm) was made to deliver a consistent amount of powder for every spreading experiment, shown as a 10 CAD model in Figure 4(a). The Emery paper is cut to the size of a standard microscope glass slide 11 (75 mm×25 mm), and is glued to the glass slide (i.e. the right slide in Figure 4(b)) with a thin glue and 12 compressed by dead-weight to ensure flatness. The glass slide is placed next to another glass slide (i.e.  . Two threshold images are applied via default auto-threshold methods, one for the voids 15 and one for the particles to ease analysis in the following steps, as shown in Figure 6. The size analysis 16 is initiated and the two images are passed to MATLAB R2018a for analysis. The image of particles is 17 first dilated by five pixels (established by trial-and-error). This is done to filter out the noise in the 18 image analysis process brought by the small empty patches/areas, and they are also of no interest, as 19 they do not constitute empty patches, due to their extreme small sizes (<6 μm), and to define specific  The frames that captured the spreading process were counted, and the time taken for the spread was 8 ascertained from the FPS and the average spreading speed was hence calculated from the spreading 9 distance (25 mm) and time, as described later below.

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The experiments were repeated three times to check for reproducibility for each of the individual gap 12 height. The gap heights were actually 1, 1.5, 2, 2.5 and 3 multiples of D90, respectively, as the work of 13 Nan et al. [10] had previously shown that D90 of the particle size distribution by number was 14 accountable for transient jamming, and hence the quality of spreading. The results of the three repeats 15 are denoted as R1, R2 and R3, respectively. However for brevity only the results of R1 is reported 16 here, but all the three repeats are used in the analysis. The SEM images of R1 for the five gap heights to the simulation results of the spreading of the same powder layer reported by Nan et al. [10] based on visual observations. This is shown in Figure 9 for the simulation work along with the experimental 1 results obtained here.  8 where a similar pattern of empty patches is observed in both works. 9 The threshold images are analysed quantitatively by MATLAB to calculate the length, area and  Table 1.  The frequency of formation of empty patches of different lengths can now be calculated using both  Figure 10 for all the gap heights tested.
There is a significant decrease in the frequency of empty patches with increasing empty patch length. 1 This is correlated with the jamming events of particle flow in the gap region. The jamming events with 2 shorter survival times produce smaller empty patches, and have a much larger occurrence frequency 3 [10]. Additionally, with increasing gap height, it is apparent that the frequency decreases rapidly and 4 for increased empty patch lengths, the frequency is mainly composed of small gap heights (i.e. the 5 spread layer is more uniform with large gap heights). The simulation predictions of Nan et al [10] for 6 exactly the same system is reproduced as Figure 11 for comparison, where a good correlation is 7 observed.   [10]. 2 As it could be seen from Figures 12 and 13, with increasing patch lengths, the probability of formation 3 of longer patches decreases. Additionally, for the smallest patch lengths (2-3), it could be concluded 4 that it is almost certain that all the empty patches generated by large gap heights (3 and 2) fall within 5 this size criterion, while it becomes less frequent with greater patch lengths and roughly non-present 6 in the greatest size range (≥10). This indicates that large gap heights (above (2-3)/D) give a more 7 uniform spread layer without the formation of empty patches, due to less jamming, as intuitively 8 expected. So spreadability can be defined based on a criterion for empty patch formation, considering 9 the largest patch size which is acceptable for spreading and its formation frequency. This is obviously 10 correlated with frequency and period of transient jamming. The location of the empty patches is 11 predicted based on its size following the approach of Nan et al. [10]. The particle layer is divided into 12 bins of size ∆ = 1.25 and ∆ = 2 in the y and x directions, respectively. The location of each 13 empty patch is estimated based on its size. So if the particle fraction in the bin falls below a critical 14 value, the bin is designated as empty. The following criterion (equation 1) was proposed by Nan et al. 15 [10] based on trial and error.
where is the particle volume, and is the critical gap (1.0D). In practise it is difficult to account 17 for volume measures from a 2-D image, hence the area of each particle ( ) is considered instead.

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Therefore the volume criterion is modified to fit the particle area by considering that the analysed 19 image is 2-D, the particle fraction becomes the number of particles in a given area (area of the bins) 20 and thus the term ( − ) is neglected (see Figure 14). Instead a 2-D criterion (equation 2) is adopted 21 by trial and error. It is found that the following criterion gives equivalent locations of empty patches. The area of the particles is determined through MATLAB using the threshold image of the particles 3 for each gap height as given previously in Figure 8. Similar to Nan et al.'s work [10], an overlap of 4 adjacent bins by 50% is considered to ensure that any of generated empty patches are of size 2D and 5 greater. The locations of the empty patches for R1 are shown in Figure 15, along with the simulation 6 results in Figure 16 reported by Nan et al. [10] 7 Figure 15: Illustration of the location of the empty patches of R1 as identified by equation (2) based 8 on experimental results, where the legends/markers indicate the location of empty patches present in 9 their respective x/D values, and the connected markers indicate that the legend/markers are related 10 to the same empty patch.
11 Figure 16: Illustration of the location of empty patches as identified by simulation [10].

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Similar to the trend observed by Nan et al. [10], Figure 15, has legends/markers that indicate the