The Pennsylvania State University

The Graduate School

College of Engineering

UNDERSTANDING POWDER SPREADABILITY IN POWDER BED FUSION

ADDITIVE MANUFACTURING

A Thesis in

Mechanical Engineering

by

Zackary Snow

© 2018 Zackary Snow

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Master of Science

August 2018

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The thesis of Zackary Snow was reviewed and approved* by the following:

Richard P. Martukanitz

Senior Research Associate at the Applied Research Laboratory

Thesis Adviser

Sanjay Joshi

Professor of Industrial and Manufacturing Engineering

Timothy W. Simpson

Paul Morrow Professor of Engineering Design and Manufacturing

Professor of Mechanical and Nuclear Engineering

Guha Manogharan

Assistant Professor of Mechanical and Nuclear Engineering

Mary Frecker

Professor of Mechanical and Nuclear Engineering

Associate Head for Graduate Programs

*Signatures are on file in the Graduate School.

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ABSTRACT

Additive manufacturing (AM) represents a class of rapidly developing manufacturing

technologies in which material is selectively added layer-by-layer as opposed to traditional,

subtractive methods. The layered approach employed in AM decomposes complicated, three-

dimensional manufacturing designs into simple, planar geometries, allowing for unprecedented

design freedom unencumbered by constraints of traditional manufacturing. While topics such

as design for additive manufacturing (DfAM), thermal distortion and residual stress, and process

modelling efforts have received recent attention, studies related to powder feedstock

requirements for powder bed fusion (PBF) and directed energy deposition (DED) systems

remain scarce, and only recently have researchers begun to investigate the influence of powder

characteristics on the AM process. Furthermore, standard characterization techniques used in

industry, having originated in the powder metallurgy industry, fail to capture powder

characteristics relevant to AM. Existing powder quality metrics are related to packing efficiency

and flowability, but have found little merit when applied to the dynamics of spreading in PBF.

While newer techniques such as powder rheometry and dynamic avalanche testing have shown

promise, they are encumbered by an excess of output data, and both techniques fail to relate

their results to the ability of a powder to spread in a PBF system. To date, no powder

characterization technique is able to predict the spreadability of AM feedstock. In fact, no such

spreadability metrics exist.

This work endeavors to establish viable powder spreadability metrics through the

development of a spreadability testing rig that emulates the recoating conditions present in PBF

AM systems. These metrics are then correlated to the results of bulk powder characterization

methods, such as the angle of repose and powder rheometry, to correlate powder quality

indicators to spreadability performance. A belt-driven gantry mounted to a rigid laser table acts

as the main frame of the spreadability tester outfitted with a variety of sensing technologies to

study powder performance. As no metrics for spreadability currently exist, seven possible

metrics are proposed and evaluated in a 24 full factorial experimental design. These seven

metrics are (1) a qualitative visual inspection, (2) the percentage of the build plate covered by

spread powder, (3) the rate of powder deposition, (4) the average avalanching angle of the

powder, (5) the rate of change of the avalanching angle, and the roughness of the spread powder

iv

layer as measured by (6) a portable microscope and (7) a laser profilometer. The influence of

the layer height, recoating speed, the recoater blade material, and the powder quality on each of

the proposed metrics are evaluated under the construct of the experimental design, and each of

the proposed metrics are analyzed using analysis of variance (ANOVA) to test their suitability

as a powder spreadability metric. Two samples of gas atomized, Al10SiMg PBF powder,

representing differing degrees of quality, were used as the high and low levels of the powder

quality input variable. As no powder quality metrics has been shown to be indicative of powder

spreadability in PBF, the angle of repose, a simple, inexpensive, and accessible bulk powder

characterization method, is used as the powder quality indicator. The powder samples chosen

had angle of repose values of 30 and 40° with the lower values being indicative of higher quality

powder.

Of the seven metrics evaluated, the microscope layer roughness, laser profilometer layer

roughness, and deposition rate metrics lacked any statistically significant correlation with the

results of the spreading testing and were not considered further. Additionally, the rate of change

of the avalanching angle, although found to be statistically dependent on the powder quality,

displayed poor model fitness to the measured responses with an R2 value of only 58%, too low

to be a viable spreadability metric. Of the four remaining metrics, the visual inspection is purely

qualitative and subject to external biases. However, the percentage of the build plate covered

during spreading and the average avalanching angle of the powder wave are both quantitative

metrics capable of predicting spreading performance as a function of both user-defined

processing variables and the quality of the powder feedstock. Additionally, the speed of the

recoat showed little correlation with either of these two metrics, while the layer height and

recoater blade material both had statistically significant impacts on the spread quality.

Additionally, powder spreading simulations using the discrete element method (DEM),

were performed to investigate the interaction between the particle size distribution and the layer

height as well as the impact of interparticle cohesion. A commercially available DEM software,

EDEM 2017, was used to record the average deposited powder size as a function of the layer

height. Increasing layer thicknesses were found to increase the average deposited particle

diameter at every timestep in the simulation while the introduction interparticle cohesion

v

provided powder avalanching behavior indicative of physical spreading experiments.

Preferential deposition of smaller particles at the beginning of a spread was also noted.

vi

TABLE OF CONTENTS

List of Figures .............................................................................................................................. viii

List of Tables ............................................................................................................................... xiii

Chapter 1. Introduction ................................................................................................................... 1

Chapter 2. Background ................................................................................................................... 5

2.1 Powder Production Methods for Additive Manufacturing ............................................... 5

2.1.1 Water Atomization (WA) ................................................................................... 5

2.1.2 Gas Atomization (GA) ........................................................................................ 7 2.1.3 Plasma rotating electrode process (PREP) ......................................................... 8 2.1.4 Spheroidization ................................................................................................... 9

2.2 Feedstock Characterization Techniques for Additive Manufacturing ............................ 10

2.2.1 Standards According to ASTM F3049 ............................................................. 11 2.2.1.1 Hall and Carney Flowmeters .................................................................... 11

2.2.1.2 Apparent and Tapped Density .................................................................. 12 2.2.1.3 Angle of Repose......................................................................................... 13 2.2.1.4 Laser Diffraction Particle Sizing .............................................................. 14

2.2.1.5 Scanning Electron Microscopy ................................................................. 15

2.2.2 Novel Powder Characterization Methods ......................................................... 16 2.2.2.1 Avalanche Tester ....................................................................................... 16 2.2.2.2 Powder Rheometry .................................................................................... 18

2.2.2.3 Image Analysis .......................................................................................... 19 Chapter 3. Literature Review ........................................................................................................ 22

Chapter 4. Design of a Spreadability Testing Rig ........................................................................ 32

4.1 Mechanical Design Overview ......................................................................................... 32

4.2 Sensing Equipment and Spreadability Metrics ............................................................... 39

4.2.1 Qualitative Visual Inspection ........................................................................... 39 4.2.2 Overhead Camera ............................................................................................. 40

4.2.3 DinoLite Microscope ........................................................................................ 40 4.2.4 Keyence Laser Profilometer ............................................................................. 46

4.3 Using the Spreadability Tester ........................................................................................ 48

Chapter 5. Experimental Procedure .............................................................................................. 58

5.1 Powder Characterization ................................................................................................. 58

5.2 Experimental Design ....................................................................................................... 59

Chapter 6. Results and Discussion ................................................................................................ 64

6.1 Powder Characterization ................................................................................................. 64

6.2 Metric Evaluation............................................................................................................ 67

6.3 Influence of Input Factors on Statistically Relevant Metrics .......................................... 70

6.3.1 Visual Inspection and Percent Coverage .......................................................... 70

vii

6.3.2 Average Angle .................................................................................................. 73 6.4 Conclusions from Physical Spreadability Experiments .................................................. 75

Chapter 7. PBF Spreading Simulations Using EDEM.................................................................. 77

7.1 Discrete Element Method (DEM) Background .............................................................. 77

7.2 Simulation Setup ............................................................................................................. 81

7.3 Results ............................................................................................................................. 84

Chapter 8. Conclusions and Future Work ..................................................................................... 91

References ..................................................................................................................................... 95

Appendix A – Supplemental Material for the Experimental Design .......................................... 103

Appendix B – Equations in the Hertz-Mindlin with J.K.R. Cohesion ........................................ 125

Appendix C – Raw Data from Various Powder Characterizations ............................................. 128

viii

LIST OF FIGURES

Figure 1. Schematic representation of powder bed fusion additive manufacturing [3]. ................ 2

Figure 2. Residual stresses in metal additive manufacturing can be sufficiently large to induce

delamination of layers [5]. ............................................................................................ 2

Figure 3. Typical powder characterization studies attempt to relate flowability metrics directly

to spreading in PBF systems. No metrics for spreadability currently exist [8], [13]. .. 4

Figure 4. Schematic representation of the water atomization process [17]. .................................. 6

Figure 5. Schematic representation of the gas atomization process [20]....................................... 7

Figure 6. Schematic representation of the PREP atomization process [21]. ................................. 8

Figure 7. Representative images of AM powder feedstock produced via water atomization (a),

gas atomization (b), and PREP (c) [22], [23]. .............................................................. 9

Figure 8. Raw, irregular powder feedstock (left) after it has been spherodized (right) [19]. ...... 10

Figure 9. Dichotomy of powder characterization techniques available for additive

manufacturing. ............................................................................................................ 11

Figure 10. A Hall Flowmeter apparatus to measure the flowability of particulate matter. ......... 12

Figure 11. Loosely packed powder (left) representative of apparent density and consolidated

powder (right) representative of tapped density. ........................................................ 13

Figure 12. Determination of the angle of repose for particulate matter ...................................... 14

Figure 13. Schematic representation of a laser diffraction particle size distribution analyzer

[30]. ............................................................................................................................. 15

Figure 14. Example SEM image showing gas atomized Inconel 718 powder. ............................. 16

Figure 15. Mercury Scientific’s REVOLUTION powder analyzer [9]. ........................................ 17

Figure 16. Side view of the REVOLUTION’s testing apparatus showing the powder wave

generated from the rotation of the drum [9]. .............................................................. 17

Figure 17. Freeman Technology’s FT4 Powder Rheometer [8]................................................... 18

Figure 18. Schematic of the FT4 Powder Rheometer. As the propeller plunges into the powder,

force and torque measurements are used to generate quality metrics [35]. ............... 19

Figure 19. Two commercial morphological image analysis tools: static analysis in the Malvern

Morphologi G3 (left) and dynamic analysis in the Camsizer X2 (right) [36], [37]. ... 20

Figure 20. Schematic representation of the difference between the mechanical layer height and

the physical layer height. ............................................................................................ 27

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Figure 21. Investigation of the effect of volumetric consolidation on the physical layer thickness

in PBF AM. ................................................................................................................. 28

Figure 22. Schematic overview of the spreadability testing rig with all of its major subassemblies

and components. ......................................................................................................... 33

Figure 23. Stepper motor and linear rail subassembly. The stepper motors, one on each of the

two actuator rails, are outfitted with a toothed roller to engage the belt drive (right).

..................................................................................................................................... 34

Figure 24. Mounting bracket for the xPRO V3 Stepper microcontroller. Built in holes in both the

bottom (left) and top (right) of the case allow for easy connections to power and the

stepper motors while protecting the wiring. ............................................................... 34

Figure 25. The build plate subassembly (left) is outfitted with four rigid mounts to the laser table

which interface with the spring-loaded corners of the build plate (right), allowing for

four points of levelling. ............................................................................................... 35

Figure 26. Corner bracket mounts for the build plate. Eight ¼”-20 holes located on the

perimeter of the bracket interface with the laser table while another off-center hole is

used to attach to the build plate. ................................................................................. 35

Figure 27. The recoating subassembly has two configurations: one for the tool steel blade

(shown) and another for the silicon blade. ................................................................. 36

Figure 28. Overhead camera subassembly which interfaces with the laser table, allowing for

consistent imaging of the build plate before and after spreading. ............................. 37

Figure 29. Subassembly for the Keyence laser profilometry system. The yellow mounting system

allows for quick and repeatable connection to the spreading subassembly. .............. 38

Figure 30. The DinoLite microscope subassembly allows for quick adjustment of both the height

through the slotted crossbeams and of the focal plane. .............................................. 39

Figure 31. Representative low, medium, and high scores for visual inspection of the layer of

spread powder. ............................................................................................................ 39

Figure 32. Image processing scheme for the overhead image analysis. This analysis yields the

percentage of the build plate covered by the spread layer. ........................................ 40

Figure 33. Sample frame from the avalanching video taken from the DinoLite microscope. The

region in which image analysis is performed is highlighted in red. ........................... 41

x

Figure 34. Sample raw (a, c, e) and processed images (b, d, f) from the avalanching data. The

progression of powder deposition through time can be estimated using the triangular

area in the processed images. ..................................................................................... 43

Figure 35. Sample avalanche area data from Run #1 showing a linear decrease in area through

time. The slope of this line is used as a potential metric for powder spreadability.... 44

Figure 36. Sample dynamic avalanche angle data from Run #1. The red and green lines denote

the average and time derivative of the avalanching angle during spreading............. 45

Figure 37. Sample raw data (left) and processed images (right) from a side layer roughness

video. The regular black columns denote the ticks on the ruler and represent 1/100th

of an inch (0.254mm). ................................................................................................. 46

Figure 38. The Keyence profilometer collecting data during an experimental run. .................... 47

Figure 39. Sample data from the Keyence blue laser profilometer. ............................................. 48

Figure 40. There are four positions used during spreading: the home position, the end position,

the cleaning position, and the levelling position. ....................................................... 49

Figure 41. Procedural overview of how to use the spreadability testing rig decomposed into

three main sections: Assembly, Testing, and Disassembly. ........................................ 50

Figure 42. The tool steel (left) and silicon (right) recoater blades and their corresponding braces

prior to assembly......................................................................................................... 51

Figure 43. Tightening or loosening each of the four spring-loaded corner mounts allows the

build plate to the levelled relative to the recoater blade. ........................................... 53

Figure 44. Powder is loaded into the powder dispenser manually and is prevented from falling

by a thin, metallic insert spanning the length of the funnel. ....................................... 54

Figure 45. Following the initial spread, the microscope position is adjusted to account for the

shift in focal plane from the change in magnification. ............................................... 55

Figure 46. Once the spread is complete, the recoating system is positioned off the build plate and

the overhead camera is mounted to the laser table. ................................................... 55

Figure 47. Lighting configuration for collecting overhead images. Example images from Run #7

show the difference between ambient lighting (b) and the auxiliary lighting (c). ...... 56

Figure 48. Split-plot designs run a factorial design of split-plot factors within the levels of the

whole-plot factors. ...................................................................................................... 62

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Figure 49. SEM images of the two powder samples of varying powder quality: (a) is the 30°

powder and (b) is the 40° powder. .............................................................................. 65

Figure 50. Predicted response versus measured response for dθdt shows poor correlation,

indicating a poor model fitness. .................................................................................. 69

Figure 51. Streaking in the powder bed due to electrostatically adhered powder to the recoating

mechanism................................................................................................................... 70

Figure 52. Measured response versus the predicted response for both the visual inspection (a)

and the percent coverage (b). ..................................................................................... 71

Figure 53. The correlation between the qualitative visual inspection and the quantitative percent

coverage is very high at R2 = 93.2%. ......................................................................... 72

Figure 54. Raw and processed overhead images for the 30° powder (a and b) and the 40°

powder (c and d) with the other input variables being equal. The corresponding

scores for the visual inspection and percent coverage are also given. ...................... 72

Figure 55. Avalanching angle as a function of time for the low-quality powder. ........................ 73

Figure 56. Avalanching angle as a function of time for the high-quality powder. As opposed to

the low-quality powder, the angle increases linearly throughout the spread............. 74

Figure 57. Measured average avalanching angle versus the model’s predicted value. ............... 75

Figure 58. Architecture of a discrete element method algorithm. ................................................ 78

Figure 59. Definition of particle overlap criteria for determining reactionary forces [68]. ........ 79

Figure 60. Pictorial representation of the difference between the base Hertz-Mindlin contact

model and the modified model with J.K.R. cohesion [72]. ......................................... 80

Figure 61. Effect of reducing the shear modulus on simulation accuracy [75]. .......................... 82

Figure 62. Angle of repose calibration simulation (left). The simulation is analyzed as a 2D Hall

Flowmeter (right) to reduce computational requirements [76]. ................................. 82

Figure 63. Average deposited particle diameter for varying layer thicknesses. .......................... 84

Figure 64. Side views of the simulated powder wave without interparticle cohesion at one second

intervals....................................................................................................................... 85

Figure 65. Average deposited powder diameter for 30µm and 90µm layers with increasing levels

of interparticle cohesion. ............................................................................................ 86

Figure 66. Isometric views of the simulated powder depositions three seconds into the simulation

(a) without interparticle cohesion and (b) with a surface energy of 20 J/m2. ............ 87

xii

Figure 67. Number of particles deposited for 30µm and 90µm layers with increasing levels of

interparticle cohesion. ................................................................................................ 87

Figure 68. Side views of the simulated powder wave with interparticle cohesion set at 20 J/m2 at

one second intervals. ................................................................................................... 88

Figure 69. Simulated avalanche angle for varying levels of interparticle cohesion. ................... 89

Figure 70. Reflections from the opposing stepper motor created a large circular object in the

videos, making automated image analysis challenging. ............................................. 92

Figure 71. Transition from low to high avalanching angles for the 40° powder was not captured

by the current metrics. ................................................................................................ 93

Figure 72. Small region of good powder deposition which potentially corresponds to the shift in

the avalanching behavior displayed in Run #13. ........................................................ 94

Figure 73. SEM image of the 30° powder: Al10SiMg from LPW. .............................................. 129

Figure 74. SEM image of the 40° powder: Al10SiMg from Eckhart. ......................................... 130

xiii

LIST OF TABLES

Table 1. List of shape factors commonly applied to morphological image analysis. ................... 21

Table 2. Summary of characterization techniques employed for powder characterization. The

quantity of powder required and relevant specifications are also given. ...................... 58

Table 3. The angle of reposes measured for each of the seven potential feedstocks tested. Their

vendor name and composition is also given. ................................................................. 61

Table 4. High and low factor levels for each of the input variables. ............................................ 61

Table 5. Required mass of powder for different treatment combinations of the experiment. ....... 63

Table 6. The D10’s, D50’s, and D90’s for each of the powders used in the experiment. ............ 64

Table 7. Summary of the powder rheology results from the FT4. ................................................ 66

Table 8. Summary of the dynamic avalanche results from the REVOLUTION. ........................... 66

Table 9. Summary of statistically relevant terms for each response variable and the

corresponding model fitnesses. ...................................................................................... 68

Table 10. Coefficient levels for the DEM calibration procedure. ................................................ 83

Table 11. Uncoded experimental design matrix in run order. .................................................... 103

Table 12. List of kinematic variables in EDEM’s simulation models......................................... 125

Table 13. List of material properties in EDEM’s Hertz-Mindlin with cohesion model. ............ 125

Table 14. Summary of Powder Characterization Results ........................................................... 128

1

Chapter 1. INTRODUCTION

Additive manufacturing (AM) represents a class of rapidly developing manufacturing

technologies in which material is selectively added layer-by-layer as opposed to traditional,

subtractive methods [1]. The layered approach employed in AM decomposes complicated, three-

dimensional manufacturing designs into simple, planar geometries, allowing for unprecedented

design freedoms. In AM, a part is constructed digitally, usually from a computer aided design

(CAD) software, and discretized into a series of layers of a prescribed height. The now two-

dimensional geometries are processed in a slicing software, creating G-code specifying the tool

path and machine instructions for each layer. The printer then processes the G-code and begins to

build individual layers onto a build platform. Once a layer is completed, the platform is lowered,

and a new layer of material is applied and processed on top of the previous one. Through the

joining of previous layers to subsequent ones, a three-dimensional part is constructed. While there

are many types of 3D printers and materials available, all AM processes follow this generalized

processing scheme, and it is the layer-by-layer construction of parts that gives AM its unique

properties and advantages.

Characterized by economically viable small lot sizes and the ability to build complicated,

optimized geometries, AM of metal components is of significant interest to the aerospace, medical,

and oil and gas industries [2]. In metal powder bed fusion (PBF) AM, the main focus of this work,

the layer is created by spreading a thin layer of powder which is subsequently fused using an

energy source or binders to create the solid layer geometry. The mechanics of spreading involve a

reservoir of fine metal powder that is raised a small amount, exposing a thin layer of powder. Then,

a recoating system, typically a blade, rake, or roller, translates across the exposed powder, pushing

it across the build chamber where it is deposited onto a build plate. The powder is then selectively

melted via a focused heat source, either a laser or electron beam, to form a two-dimensional layer

of the three-dimensional component. Once a layer has been completed, the build plate is lowered

by a specified distance, commonly referred to as the layer thickness, and a new layer of powder is

spread over the build plate for the next layer. The newly melted material fuses with previously

deposited layers, forming a three-dimensional component (see Figure 1).

2

Figure 1. Schematic representation of powder bed fusion additive manufacturing [3].

As additive manufacturing (AM) continues to mature as a viable manufacturing process,

several challenges continue to hinder widespread adoption in industry. The layered manufacturing

approach coupled with the small melt pool size yields complex thermal histories, resulting in

significant thermally-induced residual stresses. These stresses, augmented by solidification

shrinkage effects, are large enough to cause gross part deformation both during part construction

and upon cooling. Deformation during the build process can cause build failures due to part

interference with the recoating mechanism or delamination (see Figure 2), and distortion in general

can cause part dimensions to come several millimeters out of tolerance [4]. This is particularly

detrimental for components for high-value applications and makes the process economically

impractical. Support structures can be built to mitigate these effects, but the geometric complexity

inherent in the AM process makes the design of these supports unintuitive. Thermo-mechanical

modelling efforts are underway to predict part deformation during the design stage but often

require significant computational requirements due to the range of size scales in AM.

Figure 2. Residual stresses in metal additive manufacturing can be sufficiently large to

induce delamination of layers [5].

3

Additively manufactured components also exhibit surface roughnesses comparable to those

found in castings, limiting the application of AM for many fatigue sensitive components[6].

Whereas traditional castings are designed for post-processing operations to improve the surface

quality, many of these techniques, such as machining, are limited by the complexity of AM

designs. Furthermore, classical inspection techniques like ultrasonic and die penetrant inspection

are hindered by poor surface quality, presenting challenges for qualifying AM components.

Traditional qualification approaches also require significant quantities of test specimens to

establish statistically significant design values, and the small lot sizes characteristic of current AM

technology makes this process economically cumbersome [7].

While topics such as design for additive manufacturing, thermal distortion and residual stress,

and process modelling efforts continue to receive attention, only recently have researchers begun

to investigate the influence of powder characteristics on the AM process. Standard characterization

techniques for industry are defined in ASTM F3049: Standard Guide for Characterizing Properties

of Metal Powders Used for Additive Manufacturing Processes, but, having originated in the

powder metallurgy industry, these techniques often fail to capture powder characteristics relevant

to powder bed fusion (PBF) AM. Consequently, efforts have been made to develop and evaluate

novel characterization techniques. Newer devices such as the Freeman FT4 Powder Rheometer [8]

and Mercury Scientific’s REVOLUTION Powder Analyzer [9] have improved powder assessment

capabilities, but both produce tremendous amounts of data which the AM community is struggling

to correlate to spread quality.

More pressingly, there are currently no metrics in existence relating powder characteristics to

its ability to be uniformly spread across a build plate, i.e., the spreadability of the powder. In situ

investigations of powder spreadability are challenged by the closed architecture of most

commercial PBF systems, resulting in an abundance of studies relating powder characteristics to

flowability, a remnant of the powder metallurgy industry with limited evidence showing its

relationship to spreadability. Consequently, development of feedstock requirements,

specifications, and qualification procedures have been stunted due to a lack of correlation of

flowability metrics with powder performance in PBF systems (see Figure 3). Simulation studies

utilizing discrete element method (DEM) algorithms are gaining popularity to overcome

experimental challenges [10]–[12], but without a physical corollary, progress has been slow.

4

Figure 3. Typical powder characterization studies attempt to relate flowability metrics

directly to spreading in PBF systems. No metrics for spreadability currently exist [8],

[13].

This work seeks to establish viable powder spreadability metrics and correlate them with

relevant powder quality indicators in an effort to accelerate the development of powder feedstock

specifications. First, a review of literature related to AM feedstock characterization was performed

to identify both traditional and novel characterization techniques employed in industry, and a suite

of these techniques were then performed on a wide variety of powder samples. As no metrics for

spreadability currently exist, seven metrics are proposed and evaluated. A spreadability testing rig

is constructed to physically spread powder across a PBF build plate, and a variety of sensing

techniques are used to study powder performance and assess the proposed metrics. Using two of

the previously characterized powder samples, the influence of the layer height, recoating speed,

recoater blade material, and the powder quality are evaluated in a 24 full factorial design. Each of

the seven proposed metrics are analyzed using analysis of variance (ANOVA) to test their

suitability as a powder spreadability metric. DEM simulations are also performed to study the

influence of the particle size distribution and interparticle cohesion on spreading performance.

5

Chapter 2. BACKGROUND

This chapter presents various background topics to provide context for the remainder of

the document. First, several powder production methods used for making AM feedstock are

reviewed and differences in powder produced by these processes is discussed. Current techniques

used in industry to characterize the resulting feedstock are discussed. Both traditional powder

metallurgy and novel techniques are presented. Finally, the effect of feedstock characteristics on

the quality of additively manufactured parts is reviewed.

2.1 Powder Production Methods for Additive Manufacturing

While a variety of different methods exist for producing particulate material, not all are of

potential use for additive manufacturing. For example, grinding and milling processes have

frequently been used for powder production of materials used in the powder metallurgy industry;

however, the resulting sizes and morphology have proven to be unsuitable for additive

manufacturing due to issues with powder flowing and spreading and are rarely used [14]. Similar

issues exist with chemical techniques such as the hydride-dehyride process. This is particularly

true for PBF processes – as opposed to directed energy deposition – where powder requirements

are much more stringent. For this reason, the following discussion of powder production

techniques includes only those methods which have been used in the past, are currently used, or

are currently being adopted by the AM community for PBF.

2.1.1 Water Atomization (WA)

Water atomized powder [15] are the cheapest and most readily available form of feedstock

for PBF processes and, consequently, was one of the first types of feedstock attempted for powder

bed fusion. Water atomization, like all atomization techniques, starts by melting metal – usually

through inductive heating. For WA, a metal ingot is melted in a furnace and then transferred to a

crucible called a tundish. The tundish is transported to the atomization chamber and connected.

The molten material is allowed to flow due to gravity though the tundish’s bottom orifice where

regulation of the molten liquid’s flow rate occurs. As the liquid falls into the atomization chamber,

it is blasted with high pressure water, creating a partial vacuum under the tundish orifice which

helps to continue the flow of the molten material. The interaction of the water with the molten

metal breaks the metal into droplets via cratering, splashing, stripping, and bursting phenomena

6

[16]. The natural surface tension in the metal droplets drives them to form spherical particles.

However, the droplets, via convection with the atomization fluid, are also being cooled. The

competition between the solidification and spheroidization of the droplets results in irregular,

semi-spherical powder particles. Finally, the wetted particles are then collected from the bottom

of the atomization chamber and dried.

Figure 4. Schematic representation of the water atomization process [17].

The size distribution, 𝐷, and morphology of the resultant powder is dependent on the flow

rate of the water and molten metal, the nozzle geometry, and angle of incidence of the water stream

with the molten liquid through [1].

𝐷 =𝛽 ln (𝑃)

𝑉 𝑠𝑖𝑛(𝛼) [1]

where 𝛽 is an empirical constant that accounts for different materials and the atomizer geometry,

𝑃 is the water pressure, 𝑉 is the water’s velocity, and 𝛼 is the angle of incidence for the water jets.

Typically, the morphology of WA powders is far too irregular for proper spreading in the PBF

process. In addition, WA is prone to contamination and inclusions when compared to gas and

plasma atomization techniques. This is because the furnace where the input material is melted is

not directly coupled to the atomization chamber, leaving the molten, highly-reactive liquid

exposed to the environment. Consequently, these powders are rarely used in PBF AM [18], [19].

However, these powders are still commonly used in the press-and-sinter industry.

7

2.1.2 Gas Atomization (GA)

Gas atomization is similar to water atomization in that powder feedstock is melted in a melt

chamber, fed into an atomization chamber, and then spherodized via an atomization fluid.

However, it has several key features that distinguish it from water atomization. First, the melting

chamber is directly coupled to the atomization chamber, helping to prevent any contamination

from the environment. Second, the atomization fluid is a gas as opposed to a liquid. Because of

the lower heat capacity of gases, the solidification time for the atomized droplets is longer

compared to the spheroidization time. This results in much more spherical parts than WA powders.

Although air can be used as the atomization fluid, argon or nitrogen gas are typically used since

these gases may be chemically inert. This again improves the prevention of contaminates when

compared to WA.

Figure 5. Schematic representation of the gas atomization process [20].

Gas atomized powder is the most common form of powder feedstock currently used in AM

due to its relatively low cost and high sphericity. Although satellite particles or irregular particles

are still present, the quality of powder from spreading in PBF is much higher compared to WA

powder. Like WA, empirical models have been developed to predict the mean particle size of GA

powder. First, the Weber number, 𝑊𝑒, is defined as:

𝑊𝑒 =𝜌𝑔𝑉2𝑑𝑙

2𝛾𝑚 [2]

8

where 𝜌𝑔 is the gas density, 𝑉 is the gas velocity, 𝑑𝑙 is the melted ligament, and 𝛾𝑚 is the surface

energy density of the molten liquid. Then the mean particle size, 𝐷, can be estimated according to

[3]:

𝐷 =𝐾𝑑

𝑊𝑒(1 +

𝑀𝑚

𝑀𝑔)

𝜂𝑚

𝜂𝑔 [3]

where 𝐾 is an empirical constant, 𝑑 is diameter of the melt stream, and 𝑀𝑚, 𝑀𝑔, 𝜂𝑚, and 𝜂𝑔 are

the mass flow rate and fluid viscosity for the molten liquid, 𝑚, and the atomization gas, 𝑔.

2.1.3 Plasma rotating electrode process (PREP)

While a variety of plasma atomization (PA) techniques exist, PREP powder is the most

commonly used in PBF AM. Figure 6 describes the process schematically. A high amperage circuit

composed of a stationary cathode and a rotating electrode raises the temperature of the electrode.

The electrode, whose composition matches that of the final powder, reaches its melting

temperature, and the liquid metal is ejected from the spinning electrode. The atomization process

is performed in an inert gas chamber, and the size of the chamber dictates the spheroidization time.

The resulting powder is highly spherical and contains very little contamination due to the lack of

powder interaction with the sides of the chamber, making PREP useful for processing highly

reactive material like titanium alloys.

Figure 6. Schematic representation of the PREP atomization process [21].

9

The resulting powder size distribution is a function of the angular velocity of the electrode,

𝜔, the surface energy of the molten material, 𝛾, the melt density, 𝜌𝑚, and the electrode radius, 𝑅,

through the following relationship:

𝐷 = 𝐴

𝜔√

𝛾

𝜌𝑚𝑅 [4]

where A is an empirical constant. Whereas both WA and GA produce a wide range of particle

sizes at a high yield rate, most powder produced via PREP is above 80µm and has an average

diameter of 250µm [15]. For PBF processes, typical powder sizes are below 60µm, making PREP

powder relatively expensive. For reference, Figure 7 shows representative images of water

atomized, gas atomized, and PREP powder.

Figure 7. Representative images of AM powder feedstock produced via water atomization

(a), gas atomization (b), and PREP (c) [22], [23].

2.1.4 Spheroidization

Spheroidization is a post-processing technique in which irregular particles or particles with

satellites are made more spherical through exposure to high heat in a plasma induction furnace and

can be used as a low cost alternative to traditional gas or plasma atomized powder [19]. The raw,

irregular powders are fed into the spherodizer where they are subjected to high temperature plasma.

The powder feed rate is kept sufficiently high that the powders do not achieve a full melt, but their

surfaces are fluid enough that surface tension effects can drive the particles to form a spherical

shape. Figure 8 shows an example of irregular stainless steel 316L powder before and after

exposure to the spheroidization process. Note that the spheroidization process can lead to a small

decrease in the mean particle size, which requires the input feedstock to be larger than the intended

particle size distribution.

10

Figure 8. Raw, irregular powder feedstock (left) after it has been spherodized (right) [19].

2.2 Feedstock Characterization Techniques for Additive Manufacturing

Due to the lack of standards found within the AM, ASTM formulated a committee, ASTM

F42, to generate a pool of standards applicable to AM. Almost all of these standards, including

feedstock characterization methods, were pulled from other industries in an attempt to accelerate

the adoption of AM in industry. The standards outlined in ASTM F3049: Powder Characterization

Techniques for Additive Manufacturing are comprised mainly of pre-existing standards adopted

from the powder metallurgy (PM) industry. Techniques such as the Hall flowmeter and apparent

and tapped density, while still relevant to additive processing, were designed for PM, and their

applicability to AM has been debated [24], [25]. In other cases, some standards which are no longer

in circulation, such as the angle of repose, are frequently reported within AM feed stock literature.

Before discussion of the different powder characterization techniques, it is important to

distinguish between two classes of techniques defined in this work: specific characterization

techniques and bulk characterization techniques (see Figure 9). Specific characterization

techniques are defined as those that measure a specific trait of a powder particle. This can include

techniques for measuring the particle size, morphology, surface and bulk chemistry, density, etc.,

and can be used to explain why one powder performs better than another. In contrast, bulk

characterization techniques, like the Hall flowmeter or angle of repose, measure the collective

effect of all of the specific characteristics of that powder. Bulk characterization techniques cannot

be used to explain why one powder flows or spreads better than another, only that there is a

difference in powder performance.

11

Figure 9. Dichotomy of powder characterization techniques available for additive

manufacturing.

2.2.1 Standards According to ASTM F3049

The following summarizes techniques outlined in ASTM F3049 commonly utilized in

industry for powder feedstock characterization.

2.2.1.1 Hall and Carney Flowmeters

The Hall Flowmeter [26] is an essential component of current powder characterization

techniques and can be used to determine several powder characteristics including: apparent

density, tapped density, angle of repose, and flow time. However, the primary function of the Hall

Flowmeter is to measure the flow time for the powder (see Figure 10). In this setup, twenty-five

grams of the particulate being tested is placed into the funnel while the user’s fingertip covers the

orifice at the bottom of the funnel, allowing the specimen to settle into the funnel and reach

equilibrium. Then, the user removes his/her fingertip while simultaneously starting a stopwatch.

At this point, the powder flows from the orifice into a collection cylinder, and the time for all the

powder to leave the Flowmeter is recorded. The test is repeated five times at minimum to reduce

the effect of human variability, and the average flowtime is used as a powder characteristic.

12

Figure 10. A Hall Flowmeter apparatus to measure the flowability of particulate matter.

For some samples, the powder will not flow freely through the orifice. In this case, ASTM

B213 Section 10.1.6 permits a single tap to help initiate flow. If the excitation does not cause flow,

then the sample is considered non-flowable. For some particulate matter, the orifice and angle of

the Hall Flowmeter are not conducive to flow. In this case, the Carney Flowmeter [27] can be used.

The larger orifice diameter and steeper angle are better suited for low-flowability powders.

However, it should be noted that flow times taken from the Hall Flowmeters should not be

compared to flow times taken from a Carney Flowmeter; measurements taken with a particular

flowmeter design should only be used for comparison to measurements using the same flowmeter.

2.2.1.2 Apparent and Tapped Density

Not to be confused with a material’s specific density, the apparent density and tapped

density are both measures of the packing behavior of particulate matter. In many applications

involving powder, material is loaded into a storage container. In the case of laser powder bed

fusion additive manufacturing, hoppers are often used to store powder prior to application across

the build plate. Initially, the powder is loosely filled inside the confines of the hopper. Apparent

density is a good indicator of this storage condition as it quantifies the mass of powder required to

fill a given volume under loose packing conditions. Following the initial loading of the powder,

the machine operator will agitate the powder to increase the packing efficiency of the powder,

resulting in more a more consolidated packing condition. Tapped density is the analog to apparent

density for the tightly packed condition as shown in Figure 11.

13

Figure 11. Loosely packed powder (left) representative of apparent density and

consolidated powder (right) representative of tapped density.

The Hausner ratio is a common metric for understanding the flow behavior of granular

material, and it is defined as the ratio of the tapped density to the apparent density [28]. For any

granular material, the unconsolidated packing density is always going to be smaller than that of

the consolidated density. The theory behind the Hausner ratio, however, is that flowable powders

will have Hausner ratios that are close to one, indicating that the packing behavior of the powder

was already near optimal prior to external excitation. Conversely, large values of the Hausner ratio

indicate that the unconsolidated packing behavior was severely non-optimal, indicating that the

powder sample is likely to have unfavorable flow characteristics. In general, powders having a

Hausner ratio greater than 1.25 are considered to have low flowability [28], [29].

2.2.1.3 Angle of Repose

The angle of repose is representative of the friction conditions and cohesive behavior of

particulate matter. For this test, 100 grams of the sample material are loaded into the Hall

Flowmeter with the user’s fingertip plugging the orifice. Once the flowmeter is fully loaded, the

orifice is unplugged, and the powder flows freely onto a plate. This creates a mound of powder,

and the angle relative to the base plate, called the angle of repose, can be used to assess the level

of friction in a powder sample. Steeper angles are indicative of higher friction while lower angles

indicate lower friction. Additionally, interparticle forces - such as electrostatic effects, liquid

bridging, magnetic effects, etc. – can all increase the angle of repose. Thus, the angle of repose is

14

a measure of the effects of these factors collectively. Note that for samples that cannot flow through

the Hall Flowmeter, the Carney Flowmeter can be used instead.

Figure 12. Determination of the angle of repose for particulate matter

2.2.1.4 Laser Diffraction Particle Sizing

Perhaps the most important and widely reported particle characteristic is the size

distribution. In powder bed fusion processes, the layer thickness are roughly 30-60µm, meaning

that powder particles must be have diameters on the same order of magnitude as the layer thickness

for good spreadability as particles larger than the physical layer thickness will have a harder time

being deposited during the recoating process. Conversely, fine particles increase interparticle

friction and act as a driving force for particle agglomeration, decreasing the flowability and

spreadability [16]. Thus, the minimum, maximum, and range of particle sizes in PBF AM

feedstock, play a crucial role is determining the suitability of a particular powder.

While a variety of techniques for generating particle size distributions exist, laser

diffraction particle sizing is the most common. Using automated laser diffraction particle sizers,

the powder is suspended in a liquid, commonly deionized water, and then propelled across a

sensing region. The powder is then exposed to a laser which interacts with individual powder

particles, generating diffraction patterns that are captured by a detector array (see Figure 13).

15

Figure 13. Schematic representation of a laser diffraction particle size distribution

analyzer [30].

The diameter of the powder particle can be determined from the diffraction pattern of small

particles using Brownian motion through [5]:

𝐷 =𝑘𝑇

3𝜋𝜂𝐷𝑇 [5]

where 𝐷 is the particle diameter, 𝑘 is Boltzmann’s constant, 𝑇 is the temperature in Kelvin, 𝜂 is

the viscosity of the suspension fluid, and 𝐷𝑇 is the translational diffusivity. Note that if a sample

is not suspended in enough fluid, then particles can overlap or agglomerate, distorting the results.

Similarly, irregular powder morphologies can detrimentally impact the sizing as the analysis

assumes that the input particles are spherical. It is recommended that the suspension be composed

of less than 1% solid by volume [16].

2.2.1.5 Scanning Electron Microscopy

Another common technique used when characterizing powder particles is the use of

scanning electron microscopy (SEM), which allows a snapshot view of the overall quality of the

powder and can also be used to identify possible contamination. SEM imaging is used primarily

for qualitative morphological analysis of the powder, and, as shown in Figure 14, a wide range of

particle qualities are present even within the nominally spherical gas atomized powder below. The

majority of particles are spotted with satellites and many particles show fracture surfaces and other

surface irregularities. The limited field of view in SEM images makes obtaining statistically

relevant impressions of the powder quality cumbersome; however, automated image analysis can

16

be utilized to gain a quantitative understanding of the powder’s morphological characteristics (see

Section 2.2.1.3).

Figure 14. Example SEM image showing gas atomized Inconel 718 powder.

In addition to qualitative inspection, chemical analysis tools such as energy dispersive

spectroscopy (EDS) and electron backscatter diffraction (EBSD) can also be used in conjunction

with SEM imaging for compositional analysis, but the spherical nature of the particles presents

challenges for these analyses [31]. Furthermore, these techniques suffer from the same statistical

limitations as morphological characterization.

2.2.2 Novel Powder Characterization Methods

The testing methodologies discussed in the next section represent a collection of newer or

non-standard characterization techniques that are applicable to particulate matter.

2.2.2.1 Avalanche Tester

Many of the standard powder characterization techniques are static tests: the powder is

unaffected by external forces except for gravity. In the Hall Flowmeter, the powder is allowed to

fall naturally through the funnel orifice; for the angle of repose test, the powder is kept stationary

once it has formed a peak, the apparent and tapped densities completely constrain the powder.

17

However, the spreading process in PBF is highly dynamic, and the powder is constantly moving,

flowing, and reacting to shear stresses. Consequently, newer powder characterization techniques

are attempting to understand the powder’s response to dynamic excitation. One such device is

Mercury Scientific’s REVOLUTION (see Figure 15).

Figure 15. Mercury Scientific’s REVOLUTION powder analyzer [9].

In this instrument, the powder is loaded into a drum that is rotated at a controlled velocity.

The powder, reacting to both the friction of the drum walls and gravity, begins to form a wave

until the potential energy is released in the form of an avalanche. The entire process is recorded

using a high-speed camera, and the angle of the powder pile relative to the horizontal is recorded

in conjunction with the torque required to rotate the drum. This angle can be considered as the

dynamic analog to the angle of repose. A variety of metrics, including the average avalanche angle,

the avalanche energy, specific energy, etc. can also be generated through analyzing the potential

energy of each pixel through a variety of image analysis tools. Several investigations are underway

to understand how these metrics relate to performance in PBF systems [25].

Figure 16. Side view of the REVOLUTION’s testing apparatus showing the powder wave

generated from the rotation of the drum [9].

18

2.2.2.2 Powder Rheometry

Whereas most bulk powder characterization techniques assess the flowability of powder,

rheometric techniques like Freeman Technology’s FT4 Powder Rheometer assesses a powder’s

response to shear loading (see Figure 17). Flowability metrics are used to study a powder’s

behavior under the influence of gravity alone and other sources of excitation are not considered.

In contrast, the addition of external shear forces is more indicative of the spreading behavior in

PBF AM, and thus has been the subject of several studies related to powder quality in AM [2],

[32]–[34].

Figure 17. Freeman Technology’s FT4 Powder Rheometer [8].

The testing apparatus for the FT4 Powder Rheometer consists of an aerated graduated

cylinder placed beneath a propeller. The bottom of the cylinder is outfitted with a force transducer

while the propeller has an analogous torque transducer. Powder is loaded into the graduated

cylinder and is levelled and weighed to control both the volume and mass of the powder sample.

Then, the propeller plunges into the powder sample at a controlled linear and rotational speed,

exposing the powder to shear forces and causing it to rotate within the cylinder. Because the

translational and rotational speed of the propeller are controlled, the normal force and torque

required to perform this action can be recorded as a function of the plunge depth (see Figure 18).

The resulting curves can be manipulated in a variety of ways to generate numerous powder quality

metrics. Several other testing configurations are available, some including aeration or other

19

applicators, and each generates new metrics. Repeated tests can also be used to study electrostatic

charging effects.

Figure 18. Schematic of the FT4 Powder Rheometer. As the propeller plunges into the

powder, force and torque measurements are used to generate quality metrics [35].

2.2.2.3 Image Analysis

ASTM F3049 is the de facto standard for AM powder characterization requirements and

references several methods for testing the size, chemistry, and flow properties of metal powders.

However, in Section 5.3: Morphology Characterization, is states that “no standards describe a

means of quantifying the morphology of metal powder particles.” Although ASTM B243 calls out

qualitative definitions for particle morphologies, the lack of standard quantitative techniques has

garnered a response from the academic and industrial community. There are now several

commercially available morphological analysis tools, all of which make use of image analysis

techniques.

20

Figure 19. Two commercial morphological image analysis tools: static analysis in the

Malvern Morphologi G3 (left) and dynamic analysis in the Camsizer X2 (right) [36],

[37].

Image analysis techniques take images or video frames as input data and perform a variety

of image processing methods, such as histogram equalization, thresholding, and segmentation, to

identify individual powder particles. Once a particle has been identified, the shape of the

thresholded particle is analyzed using an array of metrics, called shape factors, for determining the

circularity, eccentricity, roughness, etc. of the particle. Additionally, an approximation of the

spherical equivalent diameter can be generated. By analyzing all of the particles in the input data,

distributions of the particle size and any of the shape factors can be analyzed. In the case of the

size distribution, the results from image analysis can even be compared to laser diffraction particle

size distributions once the number-based distribution from image analysis is converted to a

volume-based distribution [16]. Table 1 provides a summary of basic morphological powder

metrics commonly employed in morphological image processing.

21

Table 1. List of shape factors commonly applied to morphological image analysis.

Image analysis is performed either statically or dynamically. Static systems have stationary

particles and the dynamic systems have moving particles and both configurations have present

challenges for analysis. In static systems, there is a tendency for the particles to fall onto the sample

platform in their lowest energy state, which is thought to bias the particle size and morphology

distribution data. Furthermore, because the particles are stationary, there is only one orientation

you can view the particles from. In dynamic systems, however, the particles are moving and video

is being recorded as they fall. A particle tracking algorithm identifies the particles through multiple

frames and gets images from multiple perspectives of the same particle. Dynamic systems perform

the analysis faster but analyzing too much powder at once can make distinguishing one particle

from another difficult. Standards ISO 13322-1 and ISO 13322-2 provide further explanations of

the differences between the two methods [38], [39].

22

Chapter 3. LITERATURE REVIEW

As noted by Clayton [2], the characterization, control, and optimization of powder

characteristics is crucial to qualification efforts for high value applications in the automotive,

aerospace, and medical applications. While many traditional characterization techniques can

provide valuable insight into the flow properties of AM feedstock, the dynamic nature of powder

utilization in both directed energy deposition and PBF applications calls into question their

applicability. For example, the Hall Flowmeter is unable to compare powders that are non-flowable

through the funnel orifice that may be able to be spread in PBF. To illustrate the importance of

dynamic testing, Clayton (CITE) used a Freeman Technology FT4 Powder Rheometer to

understand the basic flow energy of virgin, used, and mixtures of an unnamed AM powder

feedstock. The basic flow energy (BFE) is defined as the “energy required [to displace] a powder

during non-gravitational, forced flow, i.e. its resistance to flow in a constrained environment”

(CITE). Clayton found that the basic flow energy of the virgin powder was substantially less than

that of the raw and sieved recycled powder. Furthermore, mixtures of virgin and used powder

showed a mostly linear increase in the basic flow energy starting with 1350mJ using virgin powder

to 1550mJ at 25% virgin/75% used powder. Comparatively, the basic flow energy of the used

powder was roughly 1850mJ, a 37% increase relative to the virgin feedstock.

Clayton expanded on this work in 2015 through several case studies, two of which are

relevant to this work [33]. The first involved assessing the specific energy and permeability of

three powder feedstocks: two of the feedstocks, Powders A and B, produced high density parts

while Powder C was prone to blockages, resulting in print errors during direct digital deposition.

Furthermore, all three samples had similar particle size distributions, flow times, and angles of

repose. The specific energy (SE) measures the energy required to induce gravity driven flow, while

the permeability is determined through the pressure drop across the powder when flowing air

through the sample. Powders A and B produced similar specific energies and pressure drops. In

contrast, Powder C had a specific energy of rough 2.95 mJ/g, a 28.3% increase relative to Powders

A and B. Similarly, the pressure drop across Powders A and B was approximately 3.8 mbar, and

the pressure drop across powder C was 8 mbar, nearly double that of the other feedstocks. This is

indicative of a low permeability powder and is possibly the reason for the difference in

performance during deposition.

23

The second case study investigated variability in rheological performance between

suppliers and atomization techniques. Three samples were studied: two produced via gas

atomization from different supplier and a third produced by plasma atomization from one of the

same suppliers of the gas atomized powder. Shear cell testing using the FT4 showed lower shear

stresses in the plasma atomized powder relative to both gas atomization samples, suggesting that

plasma atomized powder would exhibit improved performance in both DED and PBF applications.

Similarly, variations were also found in the BFE and SE between the two gas-atomized powders.

Note that neither Clayton’s initial work in 2014 (CITE) nor these more recent case studies (CITE)

name the composition of any of the powders tested, making comparison to other literature difficult.

However, these works demonstrate the ability of rheological powder characterization techniques

to detect differences in performance which some traditional techniques are unable to address.

As Seifi et al. [7] note, qualification of feedstock for additive manufacturing represents a

significant hurdle to the industry, and defining specifications and standards for powder to be used

in both DED and PBF requires an understanding of the minimum performance requirements. For

this reason, recent literature has focused on the influence of powder characteristics on measurable

performance metrics in additively manufactured components, including final part density, surface

quality, and mechanical properties. For example, Nguyen et al. [32] explored various

characteristics of both virgin and recycled Inconel 718 powder and investigated the impact of

recycling on tensile properties. Laser diffractions particle sizing using a Horiba LA-960 was

performed in addition to traditional powder characterization techniques like the Hall flow time,

apparent and tapped densities, and scanning electron microscopy. The basic flow energy and

specific energy were also recorded through powder rheometry, and all tensile specimens were

solutionized and precipitation hardened according to AMS 5664. The recycled powder was

sampled after ten uses, and compositional analysis showed little change in the alloying elements.

Similarly, both the virgin and recycled powder exhibited comparable particle sizes distributions,

flow times, and apparent and tapped packing efficiencies. Small but statistically significant

differences in the basic flow energies and specific energies were detected between the virgin and

recycled powder. Due to the similarity between the two feedstocks and the post-process heat

treatments, it is unsurprising that both powders were able to produce highly dense tensile

specimens with little difference in tensile properties. The ultimate strengths for the virgin and

24

recycled powders were 1404±32MPa and 1369±35MPa, respectively, while the corresponding

elongations were 18.5±1.6% and 17.4±1.7%.

Ardila et al. [40] also studied the effect of powder recycling on Inconel 718 powder.

Samples of gas atomized Inconel 718 powder from LPW Inc. were processed on an SLM 250

using nominal processing parameters, and the remaining powder was sieved to achieve a particle

size distribution of 15-45µm and subsequently sampled for laser diffraction particle sizing and

compositional analysis using energy dispersive spectroscopy (EDS). New components were then

fabricated using the recycled powders and characterized for porosity, microstructure, and

mechanical properties. After 14 reuses of the powder, a 10% increase in the particle size

distribution was found. Additionally, a slight decrease in the nickel content of the powder was

observed through EDS and was attributed to partial oxidation during processing. Like Nguyen et

al., however, the quality of the fabricated components appeared unaffected by the changes in

powder properties. No trends in either porosity, measured via optical microscopy, or

microstructure, observed through scanning electron microscopy, were detected. Furthermore,

Charpy impact testing was performed on samples heat treated according to AMS 5662, showing

no discernable relationship between material toughness and the number of powder reuses. Given

the sieving procedure and relatively low reactivity of nickel superalloys, it is not surprising that

recycling did not affect part quality.

In contrast, compositional changes during electron beam PBF of titanium alloys has been

observed to affect mechanical properties. Tang et al. [41] investigated the effect of continued

processing of recycled powder on the powder’s characteristics, as well as the final part’s

mechanical properties using virgin extra low interstitial (ELI) Ti-6Al-4V powder. The powder was

processed in an Arcam A2 using default parameters and recycled a total of twenty-one times. Each

build consisted of a series of tensile specimens built in the vertical direction, and processed powder

was sieved through a 177 μm mesh to remove agglomerated particles and characterized for size

distribution, morphology, composition, and flowability using standard techniques defined in

ASTM F3049. Mechanical specimens from the initial build using virgin powder and powder from

builds 2, 6, 11, 16, and 21 were machined according to ASTM E8 and tested in tension at a rate of

5 mm/min. No significant compositional changes were detected aside from a gradual increase in

the oxygen content in the feedstock. Additionally, the particles became more spherical due to the

25

removal of satellite particles separated during part excavation in the powder recovery system. This

in conjunction with the continued sieving after AM processing resulted in a narrower particle size

distribution with the same mean diameter, leading to improved powder flowability as measured by

the Hall flow meter. Finally, a gradual increase in the oxygen content with continued powder reuse

improved the yield and ultimate strengths compared to builds with virgin powder without a loss in

ductility. As noted by Yan et al. [42], oxygen contents below 0.33% by weight in Ti-6Al-4V does

not detrimentally affect ductility, and the final oxygen content reached was only 0.19% after 21

reuses.

Strondl et al. [34] also made use of powder rheometry to characterize the flow properties

of AM powders. Virgin and recycled nickel and titanium alloys for laser and electron beam PBF

were analyzed using the FT4 powder rheometer for the basic flow energy, specific energy, and

apparent and tapped densities. Morphological image analysis was also performed on each sample

to generate particle size distributions as well as quantitative information on the feedstocks’ aspect

ratios. Finally, tensile and Charpy V impact specimens were made using virgin and recycled nickel

powders to evaluate the effect of recycling on part quality. Both the nickel and titanium powders

showed a change in the size distribution following recycling although the nickel powder showed

an increase in size while the titanium powder showed a decrease. This difference was attributed to

differences in the recommended recycling practices between laser and electron beam PBF. For

both powders, recycling appeared to have no significant impact on the aspect ratios of the powder,

indicating that recycling does not affect powder morphology. Rheological analysis shows that

recycling the nickel powder results in lower basic flow and specific energies and is attributed to

the changes in the particle size distribution. For the same reason, the recycled titanium powder

displayed increased flow energies and lower flowability. Finally, mechanical testing of the virgin

and recycled powder specimens showed similar strengths (although exact values are not reported)

but lower ductility and decreased toughness. Compositional analysis showed increases in oxygen

content in the recycled power and is attributed to the decrease in mechanical performance.

Despite the wealth of literature available pertaining to the characterization of powder

feedstock for additive manufacturing, very few powder-related design rules have been generated.

Karapatis et al. [43] optimized the powder lay density via a theoretical approach in which wall and

boundary effects are considered to increase the final part density in PBF AM. The authors noted

26

that previous works that develop theory for maximizing the packing density are not applicable in

AM since the layer thickness is of the same order of magnitude as the powder particles themselves.

Thus, wall and boundary effects play a significant role in the packing behavior during the spreading

process. A theoretical model of percentage of voids in a spread layer is developed which compares

the volume fraction of voids due to wall and boundary effects to that of the bulk packing efficiency.

Using this approach, they estimated that 40% of all of the voids within a spread layer are due to

boundary effects. The authors found that a multimodal PSD with a mean size ratio of 1:10 for

coarse to fine particles produces a 15% improvement in the packing efficiency relative to typical

monomodal distributions found in AM. While these findings were corroborated via experimental

results, the smallest layer thickness investigated was 500um. However, typical powder layer

thicknesses used are 80µm for most PBF systems (prior to lasing), which is outside the scope of

their work. Furthermore, the introduction of multimodal PSDs, while beneficial to the packing

behavior, can lead to difficulties in the spreading process.

Bimodal distributions to improve powder packing density were first suggested by McGeary

in 1961 [44] and corroborated for AM applications by Karapatis et al. [43]. In 2016, Spierings et

al. [25] investigated the flow behavior of several powder feedstocks with bimodal distributions

compared to those with monomodal distributions. The particle sizes were analyzed using an optical

image analysis system called the PowderShape system, and the flowability of each powder was

evaluated both qualitatively through visual inspection and quantitatively using the REVOLUTION

powder analyzer. Several parameters, including the avalanche angle and the avalanche surface

fractal parameter, a measure of powder cohesivity, were measured for each powder sample. Using

the results from the avalanche testing system, the flowability of the bimodal powders was found

to be less than that of the monomodal powders as evidenced both by the visual inspection an

empirically derived metric for flowability using quantitative results from the avalanche testing.

This proposed metric, however, lacks correlation to corresponding performance during the

spreading process. Without such physical evidence, the development of this new metric correlates

purely with the visual inspection results and does not appear to be indicative of powder

performance during spreading.

Like Karapatis et al., Spierings and Levy [45] were able to generate powder feedstock

design requirements for PBF AM. Several definitions are made. First, the mechanical layer

27

thickness, 𝑡𝑚, is defined as the physical distance the build plate moves downward between layers.

For the first layer only, the mechanical layer height and the physical height of the powder layer, 𝑡𝑝,

are equivalent. Once material in a layer has been melted, the volume of the powder is consolidated,

resulting in a reduction in the height of the material. This height is defined as the consolidated

height, 𝑡𝑐. The difference between the consolidated height and the mechanical layer thickness is

called the height difference, 𝑑. Once a new layer has been spread, powder is added to make up for

the height difference as well as the additional powder for the new layer. This causes an increase in

the physical layer height relative to the mechanical layer height in regions where material has been

deposited. This process can be seen schematically in Figure 20.

Figure 20. Schematic representation of the difference between the mechanical layer

height and the physical layer height.

Assuming full consolidation of the spread powder, the height difference between the

mechanical and physical layer thicknesses can be represented according to [6]:

𝑑𝑖+1 =𝑒

2𝑑𝑖 + 𝑡𝑚(𝑁𝑖 + 1 − 𝑒) [6]

where 𝑑𝑖+1 and 𝑑𝑖 are the height differences for the next and current layer, 𝑁𝑖 is the current

number of layers, and 𝑒 is the packing efficiency of the spread layer. The packing efficiency is

defined as the ratio of the volume of the packed powder in a unit space to the volume of that space.

Typical values for packing efficiency of AM powder feedstock on the build plate are 45%-55%

[46], [47]. Implementation of this scheme assuming a mechanical layer height of 30µm and a

packing efficiency of 50% yields the two graphs shown in Figure 21. As shown, the height

28

difference reaches a steady-state condition wherein the height difference is equal to the mechanical

layer height, and the physical layer height is doubled (a factor of 1

𝑒 ). Though subtle, this difference

in layer height plays a crucial role in the suitability of a particle powder feedstock for PBF AM

applications. For example, Al10SiMg powder, a common material used in PBF, commonly has

powder particles 60-70µm in diameter but is processed with mechanical layer thicknesses of 30µm.

Thus, the larger powder particles will be unable to fit through the thin gap between the build plate

and the recoating mechanism for the initial layers. This problem is accentuated when the powder

quality is poor and can lead to build failures in the early stages of a print.

Figure 21. Investigation of the effect of volumetric consolidation on the physical layer

thickness in PBF AM.

Spierings and Levy (CITE) produced density coupons out of stainless steel 316L powders

of three different particle size distributions, denoted Type I, II, and III. All powders exhibited

similar packing efficiencies in the tapped state but had drastically different size distributions. The

first powder sample, Type I, had a relatively small size distribution compared to nominal PBF

powder with sizes from 6-30µm. Type II had a typical PBF particle distribution of 20-40µm, and

the third sample, Type III, had the widest size distribution from 15-60µm. Scanning electron

microscopy showed no discernable differences between the powder morphologies. Density couple

were produced on a Concept Laser M1 system using nominal processing parameters for 30 and

45µm layers except for the scanning velocity, which was graded from 250-800mm/s in either

29

25mm/s or 50mm/s increments. The density of each specimen, three for each testing conditions,

was measured four times per sample, and the resulting data was plotting against the energy density,

defined as:

𝐸𝑑 =𝑃

𝑣∗𝑠∗𝑡 [7]

where 𝐸𝑑 is the volumetric energy density, 𝑃 is the laser power, 𝑣 is the scanning velocity, 𝑠 is the

hatch spacing, and 𝑡 is the layer thickness. Density measurements for the 30µm layer samples

showed that Type I and III powders obtained the highest densities, roughly 99% of the theoretical

density, whereas the Type II powder with a nominal size distribution of 20-40µm showed densities

as low as 94%. However, increasing the layer size reversed this behavior, resulting in the Type II

powder outperforming the Type III powder. This was attributed to the discrepancy between the

mechanical layer thickness and physical layer thickness for the two layer thicknesses.

The increased layer thickness allowed the passage of the larger particles for the Type II

powder, resulting in a wider particle size distribution and reducing the packing efficiency of the

spread layer. Using their results, the authors expanded upon the feedstock design rules developed

by Karapatis et al. (CITE) for polymeric PBF AM and suggested the following guidelines:

𝑡𝑝

𝐷90≈ 1.5 [8]

𝐷90

𝐷10≈ 5 [9]

where 𝑡𝑝 refers to the physical powder layer thickness, and 𝐷10 and 𝐷90 are the 10th and 90th

percentile equivalent particle diameters by volume. Equation [8] implies that the largest particles

in a particular feedstock should not exceed the physical powder layer thickness during processing

to avoid aggregation of large particles in the powder wave and poor material deposition. Similarly,

Equation [9] is defined to place a maximum on the width of the particle size distribution, which is

known to lead to poor powder flowability. It should be noted that while useful, these design rules

have arbitrary definitions as no experimental evidence was obtained to generate the exact

numerical values above (hence the approximate signs).

In a follow-up study, Spierings [48] also determined that the particle size distribution also

has an influence on the surface quality and mechanical properties of the as-deposited components.

30

The powders used in the prior study were used to construct surface roughness and tensile coupons

using a Concept Laser M1 at 30 and 40µm layers. As expected, the samples built using the Type I

powder with the smallest and tightest particle size distribution produced the lowest surface

roughness, while the Type II and III powders both had similar but worse roughness compared to

Type I. Tensile testing according to ISO 6892-1 showed that the powder samples with the smaller

and tighter particle size distributions, i.e., Type I and II, produced the best ultimate and yield tensile

properties. Conversely, the Type III powder had an ultimate tensile strength of roughly 600MPa

in the xy-orientation in 30µm layers, 110 and 130 MPa less than the corresponding values for the

Type I and Type II powder. Additionally, it was shown that both the percent elongation and yield

strengths for the 45µm layers than the 30µm layers.

The lack of design guidelines for AM powder feedstock is driven by the lack of tests

evaluating the spreadability of powder. An abundance of flowability studies have been performed

showing which powder characteristics are important for feedstock qualification, but without a

correlation to spreading performance, flowability metrics will continue to struggle developing

minimum performance requirements for AM feedstock. To date, only one study has been published

that investigates powder quality by assessing a spread layer of powder. Sun et al. [49] evaluated

the efficacy of a spheroidization process, dubbed a proprietary manipulation technology (PMT),

for a titanium powder precursor obtained from the Kroll process. Raw, unprocessed titanium

powder is compared to both virgin and recycled Ti-6Al-4V powder (nominally 45-100µm) for

electron beam PBF and the titanium precursor after PMT processing. The size and shape of all

powder samples were analyzed using images taken from scanning electron microscopy and a

commercial image analysis software, Image Pro Plus. The flowability of all samples were

characterized using traditional Hall Flowmeter techniques but were found to be insufficient for

determining their suitability for spreading. Instead, a spreading rig analogous to the recoating

system found in an Arcam A1 electron beam PBF system was constructed to evaluate powder

spreadability. All powders were spread at the nominal speed of 14m/min, and the spreadability

was evaluated via an overhead camera and lighting system. In this configuration, the tallest point

in the spread layer shows as high intensity pixels whereas low spots are defined by low pixel

values. Images were analyzed in Matlab and used to form digital surface profiles of the spread

layers; however, no quantitative analysis was performed on the surface profiles.

31

The present work demonstrates the need for quantitative investigations into the

spreadability of powder feedstocks for PBF AM. While flowability metrics may prove to be

adequate in evaluating powder quality, quantitative relationships between various flowability

metrics, i.e., Hall flow time, angle of repose, basic flow energy, specific energy, and spreadability

metrics must first be established. As little of the AM powder characterization literature actually

spreads powder, no such spreadability metrics are in existence. This work seeks to fill this gap in

the literature through the construction of a powder spreadability testing rig similar to that presented

by Sun et al. (CITE). However, a variety of sensing technologies are used to generate quantitative

spreadability metrics, each of which are evaluated to determine their ability to predict spreading

behavior. The design of this testing rig and its associated metrics are presented in the following

chapter.

32

Chapter 4. DESIGN OF A SPREADABILITY TESTING RIG

This chapter outlines the mechanical design and data collection instruments for the

spreadability testing rig. First, a review of the mechanical design of the rig as well as its major

subassemblies is presented. Next, the sensing instrumentation and their corresponding metrics are

reviewed. Finally, a step-by-step procedure of how to operate and collect data from the testing rig

is discussed.

4.1 Mechanical Design Overview

Figure 22 shows a schematic representation of the spreadability testing rig. The rig is

composed of seven main components and subassemblies: (1) the stepper motor and linear rails, (2)

the microcontroller and power supply, (3) the build plate subassembly, (4) the spreading

subassembly, (5) the overhead camera subassembly, (6) the laser profilometer subassembly, and

(7) the microscope subassembly. Each of the above subsystems plays a vital role in successfully

measuring the spreadability of a given powder feedstock. The sensing instrumentation and

potential spreading metrics being evaluated are discussed in detail in Section 4.2. A laser table ─

a large platform with a series of ¼”-20 threaded holes placed at one inch intervals ─ acts to rigidly

attach the four corner mounts of the spreadability tester, minimizing any part deflection during

testing and ensuring repeatable results.

33

Figure 22. Schematic overview of the spreadability testing rig with all of its major

subassemblies and components.

The main frame of the spreadability testing rig is composed of a series of slotted, aluminum

extrusions with acrylic brackets interfacing between the rails and two stepper motors ─ one for

each side of the testing rig (see Figure 23). The brackets connect to the frame via four rubber

wheels designed to fit into the slots in the rails. Actuation of the stepper motors spins a toothed

gear on the end of the motor shaft which connects to a rubber belt with the negative of the gearing.

The drive belt is rigidly attached to the ends of the linear rail, resulting in motion of the stepper

motor and bracket relative to frame when the motor is activated. The speed of translation is dictated

to the stepper motors by the commands given from the microcontroller. Both stepper motors are

wired to spin at the same speed for the same amount of time so that the motion is balanced during

spreading.

34

Figure 23. Stepper motor and linear rail subassembly. The stepper motors, one on each

of the two actuator rails, are outfitted with a toothed roller to engage the belt drive

(right).

The microcontroller used for this application is an xPRO V3 Stepper Driver

microcontroller. This board runs on GRBL, an open source G-code reader used to translate the

commands sent via USB from the computer to commands that the stepper motors can read. There

are a total of four stepper connection ports although only two are used for the spreadability tester.

The board is powered through a 24V power supply and is given commands from the open source

laser computer numeric control (CNC) software, LaserWeb. The microcontroller is housed inside

of custom designed bracket that interfaces directly with one of the stepper motor brackets and had

built-in holes for power, control, and stepper motor connections. This configuration enables quick

assembly and disassembly of the system while still protecting the microcontroller from external

contaminants [50].

Figure 24. Mounting bracket for the xPRO V3 Stepper microcontroller. Built in holes in

both the bottom (left) and top (right) of the case allow for easy connections to power and

the stepper motors while protecting the wiring.

35

Next, the build plate assembly (see Figure 25) is composed of an aluminum build plate

from an EOS M280 with a build area of 250mm x 250mm and a thickness of one and a half inches.

The plate attaches to the laser table through four ¼”-20 x 1.5” bolts going through the mounting

points at the corners of the plate. The ends of the bolts each mount to corner bracket printed on a

Stratasys Fortus 400mc in ULTEM 9085, a high strength thermoplastic (see Figure 26). The corner

brackets convert the metric system dimensions of the EOS built plate to the Imperial system

dimensions of the laser table, allowing for the build plate to be rigidly attached to the laser table.

The eight ¼”-20 holes around the perimeter of the corner brackets are countersunk so that the bolts

that attach the brackets to the laser table do not interfere with the other components of the

assembly. A smaller hole is located off-center and is hand tapped to ¼”-20 following completion

of the print. The bolts that connect the build plate to the corner brackets thread through this hole

and are spring-loaded to facilitate leveling the build plate prior to spreading.

Figure 25. The build plate subassembly (left) is outfitted with four rigid mounts to the

laser table which interface with the spring-loaded corners of the build plate (right),

allowing for four points of levelling.

Figure 26. Corner bracket mounts for the build plate. Eight ¼”-20 holes located on the

perimeter of the bracket interface with the laser table while another off-center hole is

used to attach to the build plate.

36

The most important subassembly of the spreadability tester is the spreading subassembly.

This subsystem is composed of two mounting brackets, the powder dispenser, either the silicon or

tool steel recoating mechanism, and the corresponding recoater blade braces. These braces

conform around either side of the recoater blade. The two mounts are then fixtured together using

six M5 bolts, immobilizing the recoater blades (see Figure 27). Once fixtured, the recoating blade

can then be mounted to slots on the brackets on the aluminum framing which crosses the build

area, allowing the height of the blade relative to the build plate to be easily adjusted in between

runs to prevent the spread layer from being disturbed prior to measurement (see Section 4.3). A

central slot on the mounting brackets allows the powder dispenser, an elongated funnel which

spans the width of the build plate, to also be attached to the spreading subassembly.

Figure 27. The recoating subassembly has two configurations: one for the tool steel blade (shown) and

another for the silicon blade.

The three following subassemblies entail the entirety of the sensing technologies utilized

in this work. The first of these sensors is an overhead camera to image the overall area covered by

an individual spreading test. Additional aluminum framing leftover from the main frame of the

spreadability tester was used to construct a mounting system for the overhead camera so that

images taken from the top of the spread would be taken from the same perspective. The overhead

37

camera mount assembly, like the test rig frame and the build plate subassembly, can be bolted into

the laser table to minimize any differences between runs. Additionally, a custom mount for the

camera, a Nikon EOS Rebel T6i, was designed by reverse engineering a computer aided design

(CAD) model from a point cloud representation of the surface geometry obtained from a FARO

Arm laser coordinate measurement machine (CMM). Reverse engineering is design technique is

which a CAD model of a component is created from a preexisting part, commonly through a point

cloud scanning technique [51]. Once a CAD model representation of the camera had been

constructed, the mount, again printed in UTEM 9085, was designed around the camera so as to

interface with the aluminum extrusions. Furthermore, a Keyence blue light laser profilometer, is

attached onto the back of the spreading subassembly through an ULTEM-printed mounting bracket

and is used to generate a height map of the spread layer via interferometry.

Figure 28. Overhead camera subassembly which interfaces with the laser table, allowing

for consistent imaging of the build plate before and after spreading.

38

Figure 29. Subassembly for the Keyence laser profilometry system. The yellow mounting

system allows for quick and repeatable connection to the spreading subassembly.

Finally, the microscope subassembly is composed of a DinoLite portable microscope, a

conformal microscope mount, two custom designed C-rings, and two cross brackets that connect

the subassembly to the aluminum framing. The microscope mount was again designed around a

reversed engineered CAD model of the microscope using the FARO laser scanner. Two C-rings

warp around the microscope mount along self-supporting slots to snap the microscope mount into

position. The ends of the C-rings are outfitted with cylindrical protrusions which fit through the

two slots of the cross brackets. Like the recoating mechanism, this facilitates readjustment of the

microscope height to align the viewing window with the region of interest during spreading. The

cross brackets are connected to linear rails using the same rubber wheel design as the stepper motor

brackets described above. This allows the position of the focal plane to be more quickly aligned

with the powder wave (see Section 4.2).

39

Figure 30. The DinoLite microscope subassembly allows for quick adjustment of both the

height through the slotted crossbeams and of the focal plane.

4.2 Sensing Equipment and Spreadability Metrics

Given the lack of established, quantitative metrics of powder spreadability, a suite of

potential metrics is evaluated in this work. The following sections detail these metrics and are

organized by the sensing device used to create the metrics.

4.2.1 Qualitative Visual Inspection

The first metric evaluated was a simple, visual inspection performed by five different

judges. Each judge was shown an overhead image taken from a randomly selected run performed

in the experiment (see Figure 31). The judges were shown all 24 images first to allow them to

acclimate to the ranges of spread qualities and were then asked to judge each image based on the

uniformity and extent of the powder spread. The average score of each run was used as the metric

score.

Figure 31. Representative low, medium, and high scores for visual inspection of the layer

of spread powder.

VI ≈ 1 VI ≈ 4 VI ≈ 7

40

4.2.2 Overhead Camera

While the visual inspection is important for establishing a comparative baseline,

quantitative metrics are required for objectively evaluating the spreadability of a given powder.

To this end, an 18-megapixel (MP) Nikon EOS Rebel T6i camera was mounted above the build

plate so that images of the build plate could be taken (see Figure 32). Once captured, the images

were rotated and cropped to the spread area in Matlab 2015b and subsequently thresholded using

a built-in, adaptive thresholding tool.

Figure 32. Image processing scheme for the overhead image analysis. This analysis

yields the percentage of the build plate covered by the spread layer.

Some images, particularly those of poor spreads, show a significant portion of the build

plate as opposed to the spread powder and consequently show a reflection of the camera mount in

the image. This reflection drastically alters the thresholding process. Thus, these regions were also

cropped out of the image using the impoly tool from the Matlab Image Processing Toolbox. The

ratio of white pixels to black pixels could then be taken as the percentage of the build plate covered

during spreading.

% 𝐶𝑜𝑣𝑒𝑟𝑎𝑔𝑒 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑊ℎ𝑖𝑡𝑒 𝑃𝑖𝑥𝑒𝑙𝑠

𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐵𝑙𝑎𝑐𝑘 𝑃𝑖𝑥𝑒𝑙𝑠 𝑥 100 [10]

4.2.3 DinoLite Microscope

The most important sensing device utilized in this work is the DinoLite Microscope, a

portable microscope capable of magnification from 15x to 220X. The camera can take 5MP images

and record 1MP video at 30fps, a frame from which is presented in Figure 33. A total of four

potential spreadability metrics were generated via the DinoLite microscope, each of which are

discussed next.

41

Figure 33. Sample frame from the avalanching video taken from the DinoLite

microscope. The region in which image analysis is performed is highlighted in red.

The first three microscope-based metrics attempt to capture the avalanching behavior of

the powder as it is spread: (1) the powder deposition rate, (2) the time-averaged avalanching angle,

and (3) the rate of change of the avalanching angle during spreading. For highly flowable powders,

the powder should behave like a fluid as it is being pushed across the build plate, uniformly

depositing powder without any major clumping or avalanching of the powder. Conversely,

powders with poor flowability will not be able to deposit material as readily and will exhibit

significant clumping and avalanching behavior [2], [31], [52]. For data collection, the microscope

is adjusted to its lowest magnification setting to get a holistic representation of the recoater blade

and the powder wave. Once the video has been collected, a frame-by-frame image analysis is

performed on the video to extract out the relevant data.

First, the user is asked to enter the physical width of the recoater blade being used. The

user is then prompted to select two points on the recoater blade corresponding to the dimension

given. By determining the Euclidean distance between the two selected points and knowing the

corresponding physical distance, the pixel distances in subsequent video frames can be converted

to physical distances. Because image analysis only needs to be performed on the region of the

42

image with powder, the user is prompted again to select two additional points in the image frame

which represent the upper right and lower left points of the region of interest in the frame, i.e., the

powder. This significantly reduces the computational requirements of the image processing and

also improves image thresholding.

Once the image frame is cropped to the region of interest, each frame of the video,

originally RBG images, is further processed to extract only the red pixels as these provide the best

contrast between the powder and the background. Histogram equalization is then performed using

the Matlab function histeq to accentuate the contrast in the image, exposing the powder wave.

Figure 34 shows three raw images and their corresponding processed image taken at three points

in time. As shown, the cross-sectional area of the powder wave gradually decreases as the powder

is spread. Furthermore, the user is asked to manually identify the upper right-hand corner and

lower left-hand corner of the powder wave using the command ginput. The pixel coordinates from

each of those points are then used to creating a triangular approximation to the powder wave in

each frame of the video of which both the area and angle relative to horizontal can be tracked as a

function of time.

43

Figure 34. Sample raw (a, c, e) and processed images (b, d, f) from the avalanching data.

The progression of powder deposition through time can be estimated using the triangular

area in the processed images.

As shown in the sample data in Figure 35, the cross-sectional area of the powder wave

decreases linearly as a function of time, and the slope of this decrease is used as a potential metric

for the powder’s spreadability. Note that the rapid increase and decrease at the beginning and end

of the graph represent the initiation of the powder spread when the blade first collects the deposited

powder and when the blade reaches the end of the build plate. For more flowable powders, the

slope of this line is expected to have a greater magnitude than those from runs with low flowability

powder.

44

Figure 35. Sample avalanche area data from Run #1 showing a linear decrease in area

through time. The slope of this line is used as a potential metric for powder spreadability.

Similarly, the angle that the triangle makes with the build plate, dubbed the avalanching

angle, can be tracked throughout the spread. As shown in Figure 36, some powder samples exhibit

a gradual increase in the avalanching angle whereas others remain relatively constant. To address

this, two metrics are extracted from the avalanching angle data: (1) the time-averaged avalanching

angle (red) and (2) the slope of the avalanching angle versus time curve (slope). Like the

avalanching area plots, the initial collection of the dispensed powder and the end of the spread can

be identified by the perfectly flat regions at the beginning and end of the plot.

45

Figure 36. Sample dynamic avalanche angle data from Run #1. The red and green lines

denote the average and time derivative of the avalanching angle during spreading.

The final spreadability metric collected from the DinoLite microscope is the deviation in

the layer height. For this data to be collected, the microscope’s magnification is adjusted to 220X,

and the focal plane is realigned with the edge of the build plate. Magnifications of this level allow

imaging of individual powder particles used in PBF. However, the frame rate of the microscope is

too low to resolve individual parts when travelling at realistic powder spreading speeds. Instead,

the speed of the spreading mechanism is dropped to 1mm/s and video is taken of the powder layer

after it has been spread. In this configuration, the spatial and temporal resolution is sufficient for

imaging the spread layer. Figure 37 shows a representative frame taken from this data type.

46

Figure 37. Sample raw data (left) and processed images (right) from a side layer

roughness video. The regular black columns denote the ticks on the ruler and represent

1/100th of an inch (0.254mm).

Prior to taking video, a high precision ruler with intervals of roughly 250µm is fixtured to

the edge of the build plate to provide a physical dimension from which the pixel distances can be

converted into physical distances. The ticks of the ruler are seen by the regular block column

shown in the above figure. Individual video frames are then thresholded using the graythresh and

im2bw commands in Matlab, resulting in the right-hand image in Figure 37. To generate the

deviation in the height of a spread layer, the first column of pixels is searched to find the first white

pixel that corresponds to the top of the leftmost powder particle in a given frame. This process is

repeated for all frames, resulting in a vector containing the height of the spread layer in each frame.

Finally, the RMS deviation in this height is calculated and used as a metric for powder

spreadability.

4.2.4 Keyence Laser Profilometer

The final powder spreadability metric evaluated in this work is generated from a Keyence

blue laser profilometer. Profilometry is an interferometry technique which uses the speed of light

to generate a height map of a given surface. A laser of a given wavelength, in this case blue light,

is emitted and split from the sensor. One of the beams travels to the surface being interrogated,

reflects, and rebound back to the sensor where the signal is captured by a detector screen. The

other beam is sent to a reference geometry at a known distance away. By comparing the travel

time of the two respective beams, the height of the interrogated surface can be inferred [53]. The

Keyence laser line profilometer is an industrial-grade sensor with a sampling frequency of 1000Hz

47

and a height resolution of 0.2µm [54]. Data is collected over a 40mm wide line in 50µm increments

(see Figure 38).

Figure 38. The Keyence profilometer collecting data during an experimental run.

The Keyence profilometer, which is mounted onto the back of the spreading assembly,

collects data starting at the beginning of the spread and generates a height map of the spread surface

as the layer is being deposited (see Figure 39). The profilometry data is analyzed as a matrix in

Matlab 2015 where the columns of the matrix represent a given x-position while the rows represent

a given distance from the start of the spread. The standard deviation along each column is then

averaged to generate a planar standard deviation of the layer height which is unaffected by any

misaligned of the Keyence system relative to the build plate like that seen Figure 39. This standard

deviation is the final spreadability metric evaluated in this work.

48

Figure 39. Sample data from the Keyence blue laser profilometer.

4.3 Using the Spreadability Tester

During assembly and testing, there are four primary positions which the recoating system

may be in: the “home position”, the “end position”, the “cleaning position”, and the “levelling

position” (see Figure 40). The home position is the starting point for all spread tests and is located

30mm from the back edge of the build plate, denoted as the “zero position.” Once in position, the

home position is set for all runs in the LaserWeb software, allowing the user to return to this

position at any point during testing. Once a test has been properly set up, the recoating system

travels 250mm at a specified speed until it is positioned off of the build plate at the end position.

The cleaning position is used to facilitate assembly and disassembly, as well as capturing overhead

images, by positioning the recoating system 30mm off of the build plate. Unlike the home position,

the recoating system can be sent to the cleaning position by running a custom program in the

LaserWeb software. Finally, the levelling position is used to properly level the front of the plate

and is located 30mm from the front of the plate (220 mm from the zero position).

49

Figure 40. There are four positions used during spreading: the home position, the end

position, the cleaning position, and the levelling position.

Once a test has been performed on the spreadability tester, the majority of the components

must be disassembled and cleaned to prevent cross-contamination from previous runs. To

minimize the chance of experimental deviations between runs, a set testing procedure was

established so that experiments were performed in the same manner every time. A schematic

overview of this procedure is presented in Figure 41.

50

Figure 41. Procedural overview of how to use the spreadability testing rig decomposed

into three main sections: Assembly, Testing, and Disassembly.

51

Starting with properly cleaned and dried components, the four corner brackets are mounted

onto the laser table using four ¼”-20 x 1” bolts. The central hole on each of the corner brackets is

outfitted with a 3/8” x R0.5in compression spring sandwiched between two ¼” washers. The build

plate is then placed on top of the four springs, which are stable enough to remain upright. The ¼”-

20 x 1.5” steel bolts are then inserted through the four mounting holes and threaded into the corner

brackets, constraining the built plate. All bolts are then tightened until the springs are fully

compressed so that each run of the experiment has the same starting point for levelling.

Figure 42. The tool steel (left) and silicon (right) recoater blades and their

corresponding braces prior to assembly.

Next, the two recoater blades used in this work, a flexible silicon blade and a rigid tool

steel blade, are mounted into their corresponding braces (see Figure 42) and fixtured using six M5

x 12mm bolts. The back ends of the braces are fully threaded so that the bolts can rigidly attach

and fully constrain the motion of the blades through friction. For the silicon blade, a small ledge

on the inside of each of the braces restricts the vertical motion of the blade during assembly so that

three millimeters of the blade are exposed on the bottom of the brace. Similarly, both of the braces

for the tool steel blade conform around the parallelogrammatic cross-section of the recoater,

locking its degrees of freedom while exposing the bottom three millimeters of the blade.

Additionally, the front brace for each recoater blade has a 45° chamfer added to mimic the

geometry of the recoater blade mounting system used in an EOS M280. Once assembled, the

recoater blade being used can be attached to the central brackets in the spreading subassembly

through the two slots on the brackets’ exteriors. Two M5 x 40mm bolts, four washers, and

matching locking nuts are then used to fixture the recoater to the main frame. The slotted design

is used to adjust the height of the blade in between steps during testing and assembly.

52

Once the recoater blade has been attached, the powder dispenser can be attached through a

similar procedure through brackets’ central slot. At this point, it is important to fully tighten the

two bolts on the outer slots to fully constrain the recoater blade so that the blade will not move

during testing. The blade can then sent to the home position to begin the plate levelling process.

The spring-loaded corner brackets allow the height of the build plate to be controlled at

four different points. Once in the home position, all four corner bolts are loosened until the top of

the build plate is close, but not touching, the bottom of the recoater blade. The blade is then sent

to the levelling position for the first fine tuning of the build plate height. A set of feeler gauges is

used to determine when the build plate is the correct distance from the bottom of the recoater blade.

For example, if an experimental run uses a layer height of 40µm layer height, then the bolt at one

corner is either tightened or loosening until a 40µm feeler gauge is just able to freely travel along

the bottom of the blade (see Figure 43). The gap is probed again with an 80µm feeler gauge to

ensure that the gap is not too large and the experimental design can distinguish between the levels

of the experiment. Similarly, a 120µm feeler gauge is used for an 80µm layer. Once both of the

two front corners are level, the blade is sent back to the home position so that the back two corners

can be levelled. This process is repeated at the front and back of the plate until all four corners are

level with the recoater blade.

53

Figure 43. Tightening or loosening each of the four spring-loaded corner mounts allows

the build plate to the levelled relative to the recoater blade.

Once the build plate has been levelled, the powder is loaded into the powder dispenser

funnel. The funnel is designed to accommodate a fixed volume of powder which represents enough

powder to just barely cover the entirety of the plate (see Section 5.2). The powder is weighed out

on a balance and then manually deposited into the funnel (see Figure 44). A metal insert is placed

in the funnel to prevent powder from falling to the build plate, allowing the user to evenly distribute

powder along the width of the plate. Once the funnel is loaded, the insert is removed, and the

powder falls to the build plate.

54

Figure 44. Powder is loaded into the powder dispenser manually and is prevented from

falling by a thin, metallic insert spanning the length of the funnel.

The microscope is then put into position by sliding it along the cross railing until the focal

plane is aligned with the side of the build plate. After checking that both the microscope and the

laser profilometer are both connected to power and are able to collect data, the powder is spread

across the build plate at a user-specified speed while collecting both video from the microscope

and laser profilometer. The microscope and profilometer stop taking data at the end of the spread

and the resulting files, a .WMV for the microscope and a .CSV file for the profilometer, are saved.

The powder dispenser is then removed while care is taken not to disturb the spread layer. The

recoater blade mounts are also loosened so that the blade can be raised above the build plate. The

recoating assembly is sent back to then home position, the magnification of the microscope

increased to maximum for the side layer roughness data, and then traverses back over the already

spread layer at 1mm/s, a speed slow enough for the camera to resolve each individual particle

while collecting data. A high precision ruler is also mounted to the side of the build plate to convert

pixels to physical distances (see Figure 45).

55

Figure 45. Following the initial spread, the microscope position is adjusted to account

for the shift in focal plane from the change in magnification.

Figure 46. Once the spread is complete, the recoating system is positioned off the build

plate and the overhead camera is mounted to the laser table.

56

Finally, the recoating assembly is sent to the cleaning position so that images can be taken

without obstructing the camera’s view. The camera mount is connected to the laser table and then

the camera is placed inside the custom designed mount (see Figure 47). To improve the contrast

between the build plate and the deposited powder in the overhead images, the room lights were

turned off and a stand lamp illuminated the plate from the side.

Figure 47. Lighting configuration for collecting overhead images. Example images from

Run #7 show the difference between ambient lighting (b) and the auxiliary lighting (c).

Once all of the data for a given run has been taken, the camera mount can be removed and

the parts disassembled for cleaning. If the same powder is being used again for the next run, then

the build plate and recoater blades simply need to be cleaned to remove any powder from the

previous run. The build plate should also be lowered again so that all of the corner springs are fully

compressed, and the recoater blade should be removed, regardless of whether or not the next run

is using the same blade material. If the next run is using a different powder, then all of the

components need to be removed and hand-washed with soap and water to remove all traces of

powder from the previous run to prevent cross-contamination. The majority of powder from a

spread is collected onto a thin plastic sheet covering the laser table, preventing powder from falling

through its holes. The powder on this sheet can be quickly collected and disposed of following

proper material handling procedures.

57

In the next chapter, powder characterization methodologies employed in this work and the

design of the spreadability experimented is presented.

58

Chapter 5. EXPERIMENTAL PROCEDURE

This chapter outlines the experimental design chosen to develop an understanding of

powder spreadability. Additionally, the powder characterization methods employed to understand

the results of the experiment are also presented.

5.1 Powder Characterization

This work endeavors to understand the influence of power spreading parameters, such as

the layer height and recoating speed, on the quality of a recoat in PBF for two powder feedstocks

of varying quality, each of which was evaluated according to the techniques outlined in Table 2.

The purpose of these characterizations is not to understand how a specific powder characteristic,

such as morphology, affects spreadability but to explain why one powder feedstock performs better

than another. The particle size distribution and morphology, as well as several bulk

characterization methods, were evaluated for both feedstocks (see Section 2.2 for detailed

descriptions of each characterization method).

Table 2. Summary of characterization techniques employed for powder characterization.

The quantity of powder required and relevant specifications are also given.

Test Name Quantity

Required Properties Measured

Measurement

Quality

Relevant

Specifications

1 Scanning Electron

Microscopy 1 g

Size Distribution Qualitative ---

Morphology Qualitative

2 Laser Diffraction 10 g Size Distribution Quantitative ASTM B822 [55]

3 Malvern

Morphologi 20 cc

Size Distribution Quantitative ASTM B243 [56]

Morphology Quantitative

4 Apparent/Tapped

Density 100 g Packing Density Quantitative

ASTM B212 [57]

ASTM B527 [58]

5 Hall Flowmeter 50 g Flowability Quantitative ASTM B213 [26]

ASTM B855 [59]

6 Angle of Repose 50g Static Avalanching Quantitative ASTM C1444 [60]

(Withdrawn)

7 Avalanche Test 100 cc Dynamic Avalanching Quantitative ---

8 Powder

Rheometry 85 cc Powder Shear Behavior Quantitative ASTM D7891 [61]

59

5.2 Experimental Design

There are four processing parameters that have potential impact on the spreading

performance of AM feedstock in PBF. The first of these parameters is the layer thickness chosen

for the build. In addition to having direct impact on the feature resolution and surface quality [48]

of additively manufactured components, the layer thickness also impacts the spreadability of

powder feedstock: smaller layer thicknesses decrease spreadability while larger layer thicknesses

facilitate more uniform spreading behavior. The speed of the recoat can also have an impact on the

uniformity and packing efficiency of a powder layer and has been known to affect spreadability

[10], [11]. Additionally, recoater blades are commonly available in a range of materials, including

flexible silicon blades and rigid tool steel and ceramic blades. Note that recoating mechanisms that

use rollers as opposed to blades are not considered in this work.

These three parameters are all user-defined and are readily adjustable to suit the needs of a

particular application. In contrast, the quality of the powder itself, although having direct

ramifications on the quality of a spread layer, is often dictated by the feedstock supplier, and the

AM supply chain has not developed an appropriate understanding of the influence of specific and

bulk powder characteristics on powder spreadability to dictate powder quality needs to the vendor.

Hence the goal of this work is to break the cyclic nature of this interaction by (1) evaluating the

potential spreadability metrics described in Section 4.2, (2) understanding the influence of the

user-controllable parameters on the spreadability of a given powder, and (3) demonstrate the angle

of repose’s suitability as a simple, quantifiable metric of powder quality that AM users can dictate

to potential vendors when procuring feedstock.

The experimental design used in this work is a 24 full factorial design wherein all input

factors − the layer thickness (A), the recoating speed (B), the recoater blade material (C), and the

powder quality (D) − have two levels. The design of the experiment was generated and analyzed

in JMP 12.0. Layer thicknesses in PBF typically range from 30-60µm while recoating speeds are

nominally 100mm/s on an EOS M280. The high (+1) and low (−1) values for the layer thickness

were selected as 80µm and 40µm, respectively. The low value was chosen to be 40µm instead of

30µm because the smallest available feeler gauge was 40µm while the high value was set to 80µm

instead of 60µm because the smallest repeatable adjustment in layer height enabled by the testing

rig’s current design is 40µm. Similarly, the high and low values for the recoating speed are set to

60

150mm/s and 50mm/s to span the typical processing window in PBF. A silicon recoater blade is

designated as the low value for the recoater blade material while the tool steel blade is considered

the high value. Both the layer thickness and the recoating speed are considered numerical factors

while the recoater material is a categorical factor.

The final input factor, the powder quality, is designed to have two levels representing

“good” and “bad” powder. However, the lack of powder quality metrics that has hindered supply

chain development in AM also makes objectively choosing a representative “bad” or “good”

feedstock challenging. Furthermore, defining the powder quality as a categorical factor would

allow a full analysis of variance (ANOVA) and would be an adequate solution from an

experimental design perspective. However, this strategy prevents the usage of response surface

modelling approaches which could be employed if the levels of powder quality were numeric.

Instead, it is desirable to have a numerical representation of the powder quality that both provides

objectivity and enables fully numeric experimental models. An ideal candidate for the powder

quality metric would be a single number that represents the overall quality of the powder and takes

into account all of the specific powder characteristics of the feedstock, i.e., the particle size

distribution, the powder morphology, chemistry, etc. As described in Section 2.2, bulk powder

characterization methods test the collective effects of the specific powder characteristics and are a

viable option for an objective powder quality metric.

In this work, three testing instruments were used for bulk powder characterization. Both

the Mercury Scientific Avalanche Tester and Freeman FT4, while the most technologically

advanced, suffer from an abundance of data. Both instruments output several dozens of potential

metrics, and several academic pursuits are underway to understand which of these metrics best

correlate with powder spreadability [25], [62]–[64]. Similarly, many of the metrics associated with

the Hall Flowmeter have been criticized in the AM literature for a lack of applicability to powder

spreading. For example, the flow time measurement has been shown to be an ineffective predictor

of powder spreadability where powder that is unable to flow through the funnel orifice is still

spreadable in commercial PBF systems [25]. However, the angle of repose, although relatively

simplistic, has not received such criticism and still provides a quantitative, unbiased measure of

the overall quality of the powder. Furthermore, the test’s simplicity and relative equipment cost

61

makes it more accessible to AM users than the Mercury Scientific and Freeman Technology

systems. Thus, the angle of repose was selected as the powder quality metric used in this study.

Table 3. The angle of reposes measured for each of the seven potential feedstocks tested.

Their vendor name and composition is also given.

Material Vendor

Angle of

Repose

1 Inconel 718 Praxair 27

2 Al10SiMg LPW 30

3 Al10SiMg Valimet 30

4 SS316L LPW 35

5 SS316L LPW 37

6 Al10SiMg Eckhart 40

7 Al10SiMg EOS 50

Next, two powder feedstocks were chosen for the levels of powder quality. To this end, the

angle of repose of seven different gas-atomized, metallic PBF powders of various compositions,

densities, particle size distributions, and morphologies were determined according to ASTM

C1444. The powders selected, shown in red in Table 3, have angles of repose spanning the breadth

of potential values and are spaced at regular intervals, making them ideal candidates for the powder

quality levels. Additionally, prior testing showed the 50° powder from EOS to be too cohesive to

collect any data according to the metrics described in Section 4.2 and was consequently not

considered for selection. Similarly, the two powder samples chosen are both aluminum alloys

displaying similar particle size distributions, minimizing the risk of confounding the results of the

experiment with particle and density effects. Table 4 summarizes the levels chosen for each of the

design variables.

Table 4. High and low factor levels for each of the input variables.

Low (-1) High (+1)

A Layer Thickness 40 μm 80 μm

B Recoating Speed 50 mm/s 150 mm/s

C Recoater Material Silicon Tool Steel

D Powder Quality 30° 40°

62

Given that only 16 runs are required in a 24 factorial design, a full factorial design was

chosen as opposed to a fractional factorial. This provides a better estimate of the experimental

variance, improves the degrees of freedom in the ANOVA, and removes any alias structure from

the experimental analysis [65]. However, the design is not fully randomized. A fully randomized

design requires a full disassembly of the spreadability tester to prevent cross-contamination

between runs containing different powder feedstocks – a process that takes roughly three hours to

complete. In situations in which a factor is difficult or cumbersome to change between runs, in this

case powder quality, split-plot experimental designs can be employed [65]. Split plot designs

divide experimental factors into two categories: (1) hard-to-change factors in whole plots and (2)

easy-to-change factors in split plots.

Figure 48. Split-plot designs run a factorial design of split-plot factors within the levels

of the whole-plot factors.

Within a single whole plot level, a fully randomized experimental design of the easy-to-

change, split-plot factors is run (see Figure 48). This is repeated for each level of the hard-to-

change, whole-plot factors, and the order in which the whole plots are run is also randomized. This

experimental scheme maximizes the randomization necessary for an ANOVA while significantly

reducing the experimental time. The cost of this experimental design is a loss of randomization at

the whole-plot level; so, factors expected to have a statistically significant effect on the results are

preferred for whole-plot factors [65].

Finally, it is important to normalize the amount of powder supplied to the spreadability

tester between runs. The mass required for a single experimental run (see Equation 11) is a function

of the area of the build plate, 𝐴𝑝𝑙𝑎𝑡𝑒, the layer thickness, 𝑡, a fudge factor, 𝐹, representing the

63

percentage of the build plate that is going to be covered during the spread, and the apparent density

of the powder, 𝜌𝑎𝑝𝑝. Table 5 summarizes the masses of powder required for different runs of the

experiment.

𝑀𝑎𝑠𝑠 =𝐴𝑝𝑙𝑎𝑡𝑒∗𝑡∗𝐹

𝜌𝑎𝑝𝑝 [11]

Table 5. Required mass of powder for different treatment conditions of the experiment.

Layer

Thickness

Percent of

Build Plate

Volume of

Powder Mass of Powder

LPW Al10SiMg 40 um

75% 1.91 cm^3 2.629 g

80 um 3.81 cm^3 5.258 g

Eckhart Al10SiMg 40 um

75% 1.91 cm^3 2.629 g

80 um 3.81 cm^3 5.258 g

The next chapter presents the results of the experimental findings of the experiment

outlined in the current chapter.

64

Chapter 6. RESULTS AND DISCUSSION

This chapter provides the results of the spreadabililty testing experiments. First, the results

of the various powder characterizations performed are given. These results aid in explaining the

results of the 24 experimental design discussed in Section 5.2. Then, preliminary evaluations of

the seven powder spreadability metrics are provided, explaining which metrics warrant further

discussion. Details of promising metrics are discussed, and then final conclusions from the

experiment are given.

6.1 Powder Characterization

As presented in Section 5.2, the two powders used in this experiment are both gas atomized

Al10SiMg alloys. The 10th, 50th, and 90th percentile of a particle size distribution, denoted by the

D10, D50, and D90, are common ways of succinctly conveying the overall trend in a normal or

lognormal distribution. The D10, D50, and D90 for each powder used in this work is given in Table

6.

Table 6. The D10’s, D50’s, and D90’s for each of the powders used in the experiment.

30° 40°

D10 22.5µm 11.9µm

D50 38.4µm 25.5µm

D90 63.8µm 67.5µm

Both powder samples show similar particle size distributions (PSDs) by volume. The D90’s

for each powder are roughly 65µm, indicating that both powders were sieved using a similarly

sized mesh. However, the 40° powder has a slightly wider particle size distribution relative to the

30° powder, which is known to cause poor flowability in powder metallurgy applications [16]. The

65

difference between the D90 and D10 for the 40° powder is 55.7µm, nearly 15µm more than same

metric for the 30° powder.

Figure 49. SEM images of the two powder samples of varying powder quality: (a) is the

30° powder and (b) is the 40° powder.

Morphologically, scanning electron microscopy (SEM) images (see Figure 49) indicate

that the 40° powder contains more irregularly shaped particles than the 30° powder; however,

quantitative analysis using the Malvern Morphologi’s image analysis tools reveals that the two

aluminum powders have similar morphologies with no significant differences between the two

samples according to the circularity, elongation, or convexity metrics. Additionally, the number-

based particle size distributions from image analysis indicate that both powders have D10’s of

roughly 3µm although the D90 for the 30° powder is roughly 12µm larger than the 40° powder’s

28µm D90.

Traditional, bulk characterization of each powder feedstock confirms the findings of the

angle of repose. Using the Hall Flowmeter, only the 30° powder was able to flow; however, the

40° powder was unable to flow through the Hall Flowmeter. Furthermore, by normalizing the

apparent and tapped densities of each powder by the specific density of the material, the apparent

and tapped packing efficiency can be estimated. For both powders, the apparent packing

efficiencies are roughly 54% while the tapped packing efficiencies are approximately 62%.

Rheometric analysis of the two powders, however, shows contrasting findings to the angle

of repose. Two metrics from the basic rheometric analysis from the FT4 are used in this work: (1)

the specific energy, SE, and (2) the flow rate sensitivity, FRI. The specific energy is the work

66

performed by the motor required to spin the propeller of the FT4 at its specified rotational velocity

normalized by the mass of the powder used in this test. Because the volume of powder tested in

the FT4 is constant across all tests, the specific energy allows for comparisons between powders

of different compositions. Similarly, the flow rate sensitivity quantifies a powder’s response to

changes in the flow rate by increasing the velocity of the propeller. Table 7 summarizes the results.

Table 7. Summary of the powder rheology results from the FT4.

30° 40°

SE 3.79 mJ/g 3.06 mJ/g

FRI 1.24 1.20

According to the results of the powder rheometer, the 40° powder should outperform the

30° powder under shear conditions as evidenced by the lower value for the specific energy of the

40° powder. Additionally, the 40° powder should be the most robust against changes in the flow

rate, an analog to the recoating speed, due to its lower FRI value of 1.20.

Dynamic avalanche testing using the REVOLUTION powder analyzer was also performed

on each sample, and three metrics are reported: (1) the avalanche energy, (2) the energy average,

and (3) the average angle. The avalanche energy is determined by the change in potential energy

for each pixel in the field of view before and after avalanching. The energy average is the time

average potential energy of the powder as it is being rotated, and the average angle is the time

average angle relative to horizontal during testing.

Table 8. Summary of the dynamic avalanche results from the REVOLUTION.

30° 40°

Avalanche Average

17 mJ/kg 29 mJ/kg

Energy Average

284 mJ/kg 303 mJ/kg

Angle Average

36° 40°

67

Unlike the rheology results, the dynamic avalanching results indicate that the 30° powder

should exhibit the best flowability and spreadability during testing. The 30° powder has a lower

average avalanching angle, a dynamic analog to the static angle of repose, and a lower average

energy. For all metrics evaluated, the 30° powder outperformed the 40° powder. These findings

are in agreement with the angle of reposes of each powder.

6.2 Metric Evaluation

The generalized model for this experimental design is given by Equation [12] and is

composed of an intercept corresponding to the mean response, 𝛽0, main effect terms, and two-

factor interactions. Each of the different 𝛽’s corresponds to the coefficient estimated from the

ANOVA and can be interpreted as the mean effect from changing the value of each input factor to

its corresponding levels. According to the sparsity of effects principle in experimental design,

higher order interaction terms are often not significant and thus were not considered [65].

To evaluate the suitability of the seven potential powder spreading metrics, the model’s

fitness for predicting the measured responses generated by ANOVA was identified for each

response variable. Table 9 summarizes which of the terms in Equation [12] were considered to be

statistically significant, i.e., with a p-value less than 5%, and the corresponding R-squared values

for the original and reduced order models are given. The statistically relevant terms are denoted

with X’s. The raw model fit refers to the R-squared value when all terms, even those that are not

statistically significant are included in the model. However, it is good practice to reduce the order

of the model by removing those terms that were found to not be statistically relevant. Once those

terms are removed, the R-squared values will drop due to the reduced complexity of the model.

68

Table 9. Summary of statistically relevant terms for each response variable and the

corresponding model fitnesses.

As shown, none of the terms for the microscope layer roughness, the Keyence layer

roughness, or the deposition rate were found to be statistically significant, resulting in a model

fitness of 0%. Additionally, only the powder quality was found to be statistically significant for

the 𝑑𝜃

𝑑𝑡 response variable, resulting in a reduced order model fitness of 36.3%. Figure 50 shows the

model’s predicted response against the actual measured response.

78.1%

dθ/dt X 58.2%

Average

AngleX X

---

Deposition

Rate---

Keyence

Roughness

92.0%

Microscope

Roughness---

Percent

CoverageX X X

Model Fit

Visual

InspectionX X X 90.3%

Main Effects Two Factor InteractionsQuadratic

Effects

A

Layer

Thickness

B

Recoating

Speed

C

Recoater

Material

A

Powder

Quality

AB AC AD BC BD CD DD

69

Figure 50. Predicted response versus measured response for 𝑑𝜃

𝑑𝑡 shows poor correlation,

indicating a poor model fitness.

As shown, the model using statistically significant input variables is unable to accurately

capture the dynamics of the measured response for 𝑑𝜃

𝑑𝑡. In the case of the two layer roughness

metrics and the deposition rate, none of the input factors were statistically significant. The poor

fitness of each of these four metrics indicates that within the context of determining a metric for

powder spreadability, these measurement devices are not suitable. This is not to say that these

techniques will not have value in other forms of powder spreading metrics. For example, the

Keyence profilometer is able to identify macro-level irregularities in the powder bed, such as

streaking due to electrostatic buildup on the recoater blade (see Figure 51). However, for the

purposes of this work, these metrics will not be considered further. The next section gives more

detailed analysis for the four remaining spreadability metrics.

70

Figure 51. Streaking in the powder bed due to electrostatically adhered powder to the

recoating mechanism.

6.3 Influence of Input Factors on Statistically Relevant Metrics

Of the seven originally proposed spreadability metrics, three were considered for further

analysis: (1) visual inspection, (2) percentage of the build plate covered, and (3) average

avalanching angle made during spreading. The visual inspection and percent coverage are analyzed

together due to their conceptual similarity. The average avalanching angle is analyzed separately.

6.3.1 Visual Inspection and Percent Coverage

The reduced order model equations for the visual inspection and the percent coverage are

given by Equations [13] and [14], respectively.

𝑉𝑖𝑠𝑢𝑎𝑙 𝐼𝑛𝑠𝑝𝑒𝑐𝑡𝑖𝑜𝑛 = 2.863 + 0.838𝑥𝐶 − 1.438𝑥𝐷 − 0.513𝑥𝐶𝑥𝐷 [13]

% 𝐶𝑜𝑣𝑒𝑟𝑎𝑔𝑒 = 58.406 + 7.916𝑥𝐶 − 13.583𝑥𝐷 − 3.621𝑥𝐶𝑥𝐷 [14]

Because each of the variables in the experimental analysis were coded, each of the 𝑥𝑖′𝑠

refer to the level (either -1 or +1) for each statistically relevant input factor. For both the visual

inspection and the percent coverage, the recoater blade material (C) and the powder quality (D)

are statistically significant main effects. The recoater blade material has positive effects on the two

response variables, as evidenced by the sign of the estimated coefficients of 𝑥𝐶, indicating that

71

spreading with the tool steel blade resulted in better coverage of the build plate during

experimentation. On average, the experimental runs using the tool steel blade covered 8% more of

the build plate and received almost an entire point more during the visual inspection. Conversely,

the powder quality had a negative influence on the measured spreadability. According to the above

models, the 30° powder covered 13.6% more of the build plate and received 1.44 more points on

a 1-7 qualitative scale on average. Additionally, the interaction term between the recoater blade

material and the powder quality is also statistically significant for both metrics.

Overall, both the visual inspection and percent coverage show exceptional agreement

between the measured responses and the models’ predicted values. The reduced order R2 values

for the visual inspection and percent coverage models are 90.3% and 92.0%, respectively. Figure

52 shows the corresponding model value plotted against the measured responses. The root-mean-

square error of the visual inspection model is 8.8% relative to the maximum value of seven whereas

the root-mean-square error for the percent coverage model is 5.9%. Both models show good

agreement with the measured responses.

Figure 52. Measured response versus the predicted response for both the visual

inspection (a) and the percent coverage (b).

Due to the similarity of the two metrics, a model was generated to estimate the relationship

between the qualitative visual inspection and the quantitative percent coverage. Equation [15]

shows a clear linear relationship between the two metrics with an R2 of roughly 94%. Figure 53

shows this relationship graphically, while corresponding images from the visual inspection and

percent coverage are presented in Figure 54.

72

%𝐶𝑜𝑣𝑒𝑟𝑎𝑔𝑒 = 9.10 ∗ 𝑉𝐼 + 32.35 [15]

Figure 53. The correlation between the qualitative visual inspection and the quantitative

percent coverage is very high at R2 = 93.2%.

Figure 54. Raw and processed overhead images for the 30° powder (a and b) and the 40°

powder (c and d) with the other input variables being equal. The corresponding scores

for the visual inspection and percent coverage are also given.

73

6.3.2 Average Angle

For the average avalanching angle made during powder spreading, both the main effects of

the layer thickness and the powder quality were the only statistically significant input variables.

Equation [16] gives the reduced order model for the average avalanching angle.

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐴𝑛𝑔𝑙𝑒 = 27.341 − 3.446𝑥𝐴 − 5.538𝑥𝐷 [16]

According to the ANOVA, increases in the layer thickness from 40μm to 80μm resulted in an

average decrease in the avalanching angle of 3.446°. Similarly, the higher quality powder with a

lower angle of repose decreases the average avalanching angle. Figures 55 and 56 show

representative avalanche angle data for high- and low-quality powder from Runs #1 and #16,

respectively. For both high- and low-quality powder, the initial angle of the powder avalanche is

roughly 20°. As the spread progressives, the avalanching angle for the 40° powder remains roughly

constant. In contrast, the avalanche angle for the high-quality powder shows a linear increase as

the spread progresses, resulting in a higher average avalanching angle.

Figure 55. Avalanching angle as a function of time for the low-quality powder.

74

Figure 56. Avalanching angle as a function of time for the high-quality powder. As

opposed to the low-quality powder, the angle increases linearly throughout the spread.

Of the three remaining spreadability metrics, the average avalanching angle has the lowest

model fitness with a reduced order R-squared value of 78.1%. Although the lowest value, the

fitness is adequate for a physical experiment. Figure 57 shows the measured average avalanching

angle versus to the model’s predicted values. Residual plots confirming the assumptions of the

ANOVA are found in Appendix A.

75

Figure 57. Measured average avalanching angle versus the model’s predicted value.

6.4 Conclusions from Physical Spreadability Experiments

Of the seven metrics evaluated as potential spreadability metrics, only three were

considered for in depth analysis: (1) the qualitative visual inspection, (2) the percentage of the

build plate covered during the spread, and (3) the average avalanching angle. The other four

metrics, the microscope layer roughness, Keyence layer roughnesses, the deposition rate, and the

rate of change of the avalanching angle, showed no discernable relationship with any of the user-

defined input variables or exhibited poor model fitness and, consequently, were not considered

further. Although the visual inspection did correlate well with the powder quality, the qualitative

nature of this metric makes it sensitive to the judges of the powder. For example, the majority of

the experimental runs received similar scores by all judges, but Run #4 had a standard deviation

of 1.9 out of a possible score of seven, nearly twice the next highest standard deviation value.

Although all judges were given the same scoring criteria, the resulting scores are sensitive both to

the judging criteria and the judges themselves. Instead, the visual inspection can be interpreted as

validation of the quantitative percent coverage metric. As shown in Section 6.3.1, the percent

coverage and visual inspection scores were highly correlated; however, the percent coverage is not

prone to subjectivity of the visual inspection and thus represents a promising candidate as a

spreadability metric. Additionally, the average avalanching angle also showed a statistically

significant relationship with the powder quality in addition to the layer thickness. Both metrics

76

show promise as powder spreadability metrics and warrant further investigations in future

confirmatory studies.

In the next chapter, powder spreading simulations using the discrete element method

(DEM) are used to investigate spreading characteristics that are difficult to measure

experimentally. DEM simulations are introduced followed by results of simulations investigating

the impact of layer height and interparticle cohesion on spread quality.

77

Chapter 7. PBF SPREADING SIMULATIONS USING EDEM

Despite the success of the physical powder spreading experiments in identifying promising

powder spreadability metrics, additional analysis can be performed through simulation. As

Karapatis et al. [43] hypothesized, the interaction between the particle size distribution and the

layer height can impact the success of a spread layer of feedstock. This phenomenon is investigated

in simulation using a commercially available discrete element method (DEM) software, EDEM©.

First, the discrete element method, a simulation technique that models the collective behavior of a

mass of particulate material, is introduced. The algorithmic development is presented as well as

several relevant physics models. Next, the simulation setup for this application is described.

Finally, the effect of layer height and interparticle cohesion on the uniformity of a powder spread

is investigated and correlated to physical results.

7.1 Discrete Element Method (DEM) Background

The closed system architecture found in most commercial PBF systems presents challenges

for experimental investigations into in situ powder spreading dynamics. Limited space and the

harsh environment within the build chamber makes outfitting the requisite sensing technologies

difficult. Although in situ sensing efforts are prevalent within the current literature, most are

related to melt pool sensing and part defect detection [66]. Few target powder spreading failures

specifically. However, a recent surge of interest in modelling powder spreading has come about in

the AM community both to develop powder feedstock requirements and understand spreading-

related processing defects. Whereas finite element analysis (FEA) is traditionally the first-choice

technique for modelling many engineering applications, the computational effort required to model

the size and number of particles found in AM using FEA is too inefficient. Consequently, discrete

element method (DEM) models have been implemented.

Originally created for modeling larger rock granules for the agricultural industry, DEM

models have grown in popularity in recent years for modelling the interactions of smaller particles

and are heavily used in the pharmaceutical industry for modelling and optimization of coating and

mixing processes [67]. In DEM simulations, each particle is modelled individually as a single

sphere, and the kinematic behavior of a single particle is determined by its interactions with

78

surrounding particles and equipment material. Figure 58 outlines the methodology employed in

DEM algorithms.

Figure 58. Architecture of a discrete element method algorithm.

The first step in a DEM model is particle initialization. A population of particles is

generated according to user-specified particle size distributions and physical properties, such as

density, tensile strength, Poisson’s ratio, etc., and is given an initial position and velocity. Next,

all particles’ positions advance according to their initial velocity and the acceleration of gravity.

At the end of each time step, a small search region is explored around every particle looking for

near neighbors. Neighboring particles falling within this region are then tested to see if they overlap

with the current particle according to Equation [17] (see Figure 59). Particle pairs that satisfy this

condition are said to be in contact with one another, and the degree of particle overlap is fed as

input to a contact model, either strain- or displacement-based, which determines the translational

and rotational velocities for the next time step based on Newton’s equations of motion. This

process is repeated for every particle at every timestep until the simulation is complete, and the

final particle positions and velocities are output.

79

𝑟𝑖 + 𝑟𝑗 > 𝛿 [17]

In general, contact mechanics for two colliding particles are broken up into two different

categories: (1) hard contacts and (2) soft contacts [68]. Hard contact models assume that the two

particles are infinitely stiff, resulting in impulsive force loading on the center of mass of each

corresponding particle. In this configuration, the resulting translational and rotational velocities of

the bodies in contact are fully defined by the input velocities, the coefficient of restitution, and the

coefficient of friction. The coefficient of restitution is defined as the ratio of the incoming particle

velocities to the outgoing particle velocities and accounts for inelastic losses during the collision

[69]. In soft contact mechanics, however, the elasticity of the materials is considered, resulting in

a force-displacement relationship that is a function of time. While hard contact mechanics are more

computationally efficient, these models have been found to lack the fidelity to accurately describe

the dynamics of particulate matter flow [68]. Therefore, soft contact mechanics are the primary

contact model of choice for most DEM approaches and will be the primary focus for the remainder

of this discussion.

Figure 59. Definition of particle overlap criteria for determining reactionary forces [68].

Once two particles are determined to be overlapping, there are a variety of contact models

utilized to estimate the resulting normal and tangential forces. These forces are then applied around

the center of mass of each particle to calculate the rotational and translational velocities for the

next time step. Contact models can be as simplistic as a mass-spring-damper system but are often

more complex to capture relevant physics. The contact model used in this work is the Hertz-

80

Mindlin model with J.K.R. cohesion. The Hertz-Mindlin model, originally developed in 1950’s,

is a common contact model used in DEM modelling (CITE). As opposed to the linear spring

models, the reactionary force increases increasing overlap and better approximates the force-

displacement relationship of real contacts between elastic bodies [70]. The addition of cohesive

interactions, such liquid bridging, van der Waals forces, electrostatics, etc., is captured through the

addition of Johnson, Kendall, and Roberts’s cohesion model (see Figure 60). In this formulation,

attractive forces begin affecting particles prior to contact, pulling them closer together and

increasing contact velocity. The degree of attraction is defined by a surface energy parameter, γ,

and is defined as the energy required to create a unit area of a new surface when two bodies are

connected through adhesive forces [71]. As the particles begin to overlap, the cohesive forces

become antagonistic and aid in the repulsion of the two bodies. Inclusion of cohesion into the

contact model allows for investigation into the role of particle cohesion in powder spreading.

Figure 60. Pictorial representation of the difference between the base Hertz-Mindlin

contact model and the modified model with J.K.R. cohesion [72].

For the Hertz-Mindlin model, the required time step for accurate temporal resolution is

defined by Rayleigh wave propagation theory [72] and is a function of the particle radii, R, and

several physical properties of the material, i.e., the density, ρ, the shear modulus, G, and Poisson’s

ratio, υ, according to [18]. As this method is an approximation, it is recommended that the

timesteps taken are no more than 40% of the calculated value of 𝑡𝑐𝑜𝑛𝑡𝑎𝑐𝑡.

81

𝑡𝑐𝑜𝑛𝑡𝑎𝑐𝑡 =𝜋𝑅 √

𝜌

𝐺

0.1631𝑣+0.8766 [18]

A list of equations and symbols for the Hertz-Mindlin contact model with J.K.R. cohesion

can be found in Appendix B. Further details on this model can be found in [72]–[74].

7.2 Simulation Setup

The DEM model utilized in this work is EDEM©, a commercially available software

composed of three components: (1) EDEM Creator, (2) EDEM Simulator, and (3) EDEM Analyst.

The EDEM Creator module is where the physical parameters of the model are defined. Powder

size distributions and material properties are defined and equipment material, such the EOS

recoater blade and build plate used in this work, are also given material properties and initial

velocities. Equipment models can either be generated within EDEM using CAD primitives or more

complicated models can be imported as .STL’s. Equipment can also be given kinematic profiles

to translate and rotate components in the desired configuration. The simulation environment is also

defined within EDEM Creator. Next, the simulation parameters, i.e., the time step, number of

CPU’s, computational cell sizes, etc., are defined in EDEM Simulator. Finally, the simulation is

run within EDEM Simulator, and the results can be analyzed within EDEM Analyst.

Within EDEM Creator, gas atomized Al10SiMg powder is simulated using a Hertz-

Mindlin with J.K.R. cohesion contact model. The powder has a size distribution of 20-65μm by

volume, a density of 2.67g/cm3, a Poisson’s ratio of 0.33, and a shear modulus of 2.65x106. Due

to the time step’s strong dependence on the shear modulus of the material in question, the shear

modulus is often artificially reduced by several orders of magnitude [75]. Reduction in the shear

modulus does not affect the results of the simulation as long as the time step does not become large

enough to dissatisfy the Rayleigh surface wave criterion of the Hertz-Mindlin model (see Figure

61).

82

Figure 61. Effect of reducing the shear modulus on simulation accuracy [75].

In addition to defining the physical properties of the material, all EDEM models require

calibration of contact model coefficients before simulations can be performed, namely, the

coefficient of restitution, the coefficient of static friction, and the coefficient of rolling friction. In

this work, simulations of the angle of repose test are used for model calibration (CITE). A

population of particles is generated according to the user-specified material properties and PSD

inside a two-dimensional cross-section of a Hall Flowmeter. The powders are prevented from

escaping via a small, simulated plug in the bottom orifice of the funnel until all particles have

settled. The plug is then removed from the simulation environment, and the particles are allowed

to fall onto a baseplate under gravity, forming a conical pile of powder (see Figure 62).

Figure 62. Angle of repose calibration simulation (left). The simulation is analyzed as a

2D Hall Flowmeter (right) to reduce computational requirements [76].

Screenshots of the powder pile are collected and analyzed in ImageJ, an open source image

analysis tool (CITE), to determine the simulated angle of repose. A 23 full factorial design with

four center point runs is used to determine the best combination of coefficient values. The run that

produced a simulated angle of repose closest to that of the physical powder is chosen as the

83

calibration values for the simulation study. Table 10 presents the low, medium, and high values

used for each calibration coefficient.

Table 10. Coefficient levels for the DEM calibration procedure.

Low Level (-) Center Point (0) High Level (+)

Coefficient of

Restitution 0.1 0.5 0.9

Coefficient of

Static Friction 0.1 0.5 0.9

Coefficient of

Rolling Friction 0.05 0.1225 0.195

Like the shear modulus, the density also plays a crucial role in defining the time step in

Hertz-Mindlin contact models. Due to the high density of metals, coupled with particle diameters

on the order of microns, the requisite time step to accurately model the reactionary forces in an

individual particle can be less than a microsecond. This resulted in initial simulations in EDEM

with intractably long run times, sometimes several days, despite the reduction in shear modulus.

Thus, all particle diameters, equipment geometry, velocities, and accelerations were scaled

according to the procedure outlined by Feng et al. [77]. Scaling the simulation increases the particle

diameters, increasing the time step and allowing for faster simulation times. To ensure that scaling

did not detrimentally affect the results of the simulation, a scaling study was performed at 1X,

10X, 25X, and 50X using the calibrated model coefficients for Al10SiMg. The simulated angle of

repose was shown to have no response to the scaling (see [76] for more details).

Finally, a Hertz-Mindlin contact model with J.K.R. cohesion is used to model the particle

interactions. Initial simulations are run with no surface energy as a baseline. Powder is spread

using an EOS tool steel recoater blade at 50 mm/s across a 1mm x 250mm simulation domain. The

blade is accelerated at 12.5 mm/s2 for four seconds, resulting in a steady state speed of 50 mm/s

for the remainder of the spread. The simulation time, in total, is 10 seconds. The simulation

environment covers the full length of an EOS build plate and is wide enough to accommodate

approximately 30 powder particles across. Periodic boundary conditions are used at the short ends

of the simulation domain to reduce computational time without sacrificing the fidelity of the model

[72]. Powder spreading simulations are run for layer thicknesses of 30μm to 90μm in 20μm

increments, spanning the range of processing conditions used in the physical spreadability

84

experiments. The simulations are then repeated with surface energies of 10 J/m2 and 20 J/m2 to

assess the simulation’s response to interparticle cohesion. Although physical measurements of the

surface energy of powder particles are challenging, these values represent relevant values used

within the literature [12], [64].

7.3 Results

DEM simulations were used to investigate the effect of the layer thickness on the

spreadability of AM feedstock when the particle size distribution is larger than the layer thickness.

Figure 63 shows the average diameter of the deposited powder particles as a function of the spread

time for simulations without interparticle cohesion. As shown, increasing the layer thickness

during spreading results in an increase in the average diameter of the deposited powder. Note that

for layer thicknesses less than the D90 of the simulated feedstock, i.e., the 30 and 50µm layer

thicknesses, the average particle diameter never exceeds the D50 of the feedstock of 38.4µm.

Figure 63. Average deposited particle diameter for varying layer thicknesses.

15

20

25

30

35

40

45

50

2 3 4 5 6 7 8

Ave

rage

Par

ticl

e D

iam

eter

, μm

Time, sec

Average Particle Diameter vs. Time( 0 J/m2 )

30μm

50μm

70μm

90μm

85

For the 70µm and 90µm layers, however, the average particle diameters rapidly increase

above the D50 at 4.5 seconds and 6.25 seconds, respectively, denoting the time when the powder

feedstock begins to short during deposition. This indicates that larger particles are successfully

able to pass through the gap between the bottom of the recoating mechanism and the top of the

build plate. Furthermore, the steady increase of the average particle diameter for all layer thickness

indicates that smaller particles are preferentially deposited to larger particles during the initial

stages of the spread. Figure 64 displays snapshots of the deposition at various times during the

spread of a 30µm layer with no interparticle cohesion.

Figure 64. Side views of the simulated powder wave without interparticle cohesion at one

second intervals.

86

The introduction of interparticle cohesion through the surface energy parameter

significantly alters the deposition physics. Three levels of the surface energy were used in

simulation: 0 J/m2 representing no interparticle cohesion, 10 J/m2, and 20 J/m2. As shown in Figure

65, the introduction of interparticle cohesion retains the gradual increase of the average particle

diameter through time but leads to a global increase in the average diameter. For example, the

30µm layer simulations show an increase of the average particle diameter with increasing levels

of the surface energy parameter for all times during the simulation except for the last second.

Similarly, the 90µm layers also shows increasing average particle diameters with more

interparticle cohesion, and the addition of cohesive interactions also increases the overall rate of

deposition denoted by the earlier end times of the deposition.

Figure 65. Average deposited powder diameter for 30µm and 90µm layers with

increasing levels of interparticle cohesion.

The earlier deposition times are possibly the result of the smaller particles most affected

by cohesive forces clumping together during deposition. Without the surface energy parameter,

these particles would act individually and would not interact with each other except during

15

20

25

30

35

2 3 4 5 6 7 8

Ave

rage

Par

ticl

e D

iam

eter

, μm

Time, sec

30μm @ 0 J/m^2 30µm @ 10 J/m^2 30µm @ 20 J/m^2

90μm @ 0 J/m^2 90µm @ 10 J/m^2 90µm @ 20 J/m^2

87

collisions. Interparticle cohesion initiates an attraction bond between particles prior to contact,

resulting in clumping of the deposited material (see Figure 66). However, the total number of

spread particles is less in the simulations with cohesion that those without (see Figure 67).

Figure 66. Isometric views of the simulated powder depositions three seconds into the

simulation (a) without interparticle cohesion and (b) with a surface energy of 20 J/m2.

Figure 67. Number of particles deposited for 30µm and 90µm layers with increasing

levels of interparticle cohesion.

0

100

200

300

400

500

600

3 4 5 6 7 8

Nu

mb

er o

f Pa

rtic

les

Time, sec

Number of Particles

30μm @ 0 J/m^2 30µm @ 10 J/m^2 30µm @ 20 J/m^2

90μm @ 0 J/m^2 90µm @ 10 J/m^2 90µm @ 20 J/m^2

88

Assuming that all particles are staying within the simulation environment, the reduction in

the number of deposited particles with increasing particle cohesion creates a conservation of mass

imbalance, implying that some particles, likely smaller particles, are being ejected from the

simulation domain. The introduction of interparticle cohesion also changes the smooth

avalanching behavior exhibited in Figure 64 to a more erratic deposition with localized features in

the powder wave (see Figure 68). This nonuniform wave profile is more representative of the shape

of the powder wave during deposition of the real spreading experiments, indicating that

interparticle cohesion is necessary to accurately capture the physics of powder spreading.

Additionally, the cohesive forces introduce a circulatory eddy motion into the powder wave, which

is more indicative of the behavior seen in the avalanching videos during experimentation.

Figure 68. Side views of the simulated powder wave with interparticle cohesion set at 20

J/m2 at one second intervals.

89

Finally, the simulated avalanching angles during deposition were recorded for the three

levels of the surface energy parameter. The avalanching angle was measured using the same

methodology described in Section 4.2.3 and is represented in Figure 69. As shown, all three surface

energy levels start with a relatively low avalanching angle of roughly 10° and then rapidly increase

to a higher avalanching angle. This region is denoted as the ramp up region. Eventually, the

avalanching angles reach a steady state region in which the avalanching angle increases linearly

throughout the spread. The slope of this linear increase appears robust against changes in

interparticle cohesion, but the addition of cohesive interactions does create an offset between the

free flowing and cohesive particle simulations. Additionally, increasing the surface energy

parameter from 10 J/m2 to 20 J/m2 does not significantly impact the avalanching angle behavior.

Figure 69. Simulated avalanche angle for varying levels of interparticle cohesion.

Discrete element simulations using the commercial software, EDEM, have shown a

correlation between the diameter of deposited particles and the layer thickness during spreading.

Decreasing the layer thickness results in a lower average diameter of deposited material. The

inclusion of interparticle cohesion through the surface energy parameter induces eddy motion

10

20

30

40

50

0 1 2 3 4 5 6 7 8

Ava

lan

chin

g A

ngl

e, ,d

eg

Time, sec

Simulated Avalanche Angle vs. Time

0 J/m^2 10 J/m^2 20 J/m^2

Ramp Up

Region

Steady State

Region

90

within the powder wave as well as clumping of deposited particles. Both of these effects are

representative of the behavior exhibited during physical experimentation and demonstrate the

necessity of modelling powder cohesion of metallic feedstock in PBF spreading applications.

However, interparticle forces also appear to cause a mass imbalance wherein the smaller particles

are ejected from the simulation domain, resulting in an artificial loss of mass and an accelerated

rate of deposition. Further work is needed to understand the root cause of this imbalance.

91

Chapter 8. CONCLUSIONS AND FUTURE WORK

As Seifi et al. [7] note, “determining the properties of the powder used for metal-based AM

… is a necessary condition for the industry to be able to confidently select the powders and produce

consistent parts with known and predictable properties”. Variability of AM feedstock for both

directed energy deposition and powder bed fusion applications represents a source of inconsistency

in part quality and has been shown to affect part density, surface finish, and various mechanical

properties of additively manufactured material. Despite the wealth of powder characterization

literature, no work to date has been done to understand how powder characteristics and AM

processing parameters influence the ability of a powder to spread across a build plate. Instead, the

flowability has been studied extensively through a combination of traditional and novel methods

in an effort to predict powder spreading performance. However, the underlying physics of gravity-

driven free flow are substantially different from the shear-driven recoating process. Furthermore,

the particle size distribution of typical metallic PBF feedstock is on the same order of magnitude

as the layer thickness, challenging many of the assumptions made in traditional bulk

characterization methods.

In this work, a spreadability testing rig was constructed and outfitted with a variety of

sensing equipment. Data collected from these sensors was used to generate six quantitative powder

spreadability metrics in addition to a qualitative visual inspection. The viability of these metrics

for evaluating powder spreadability was tested through a 24 full factorial experimental design with

four input variables: (1) the layer height, (2) recoating speed, (3) recoater blade material, and (4)

the powder quality. As no powder characterization methods currently evaluate powder

spreadability, the static angle of repose, a simple and accessible metric taken from the powder

metallurgy industry, was used as the powder quality indicator. Two powder feedstocks

representing a breadth of angle of repose values were evaluated in the experimental design through

each of the seven proposed metrics.

Four of these metrics, the Keyence layer roughness, the microscope layer roughness, the

deposition rate, and the rate of change of the avalanching angle, did not show statistically

significant correlation with any of the input variables or generated models through ANOVA that

were unable to accurately predict the measured responses. Of the remaining spreadability metrics,

visual inspection is purely qualitative in nature and is sensitive to judging criteria and user

92

subjectivity while the deposition rate did not show a statistically significant correlation with the

powder quality metric. Thus, the percent coverage and average avalanching angle are considered

to be the two most viable powder spreadability metrics as both produce ANOVA models capable

of predicting the measured responses and show statistically significant dependencies on the

powder quality. Of the user-defined processing variables, only the recoater blade material and the

layer height showed statistical significance while the recoating speed failed to influence any of the

powder quality metrics. The recoating speeds tested in this experiment span the range of typical

recoating speeds employed in commercial PBF systems; however, further increases in the

recoating speed may reveal more significant effects.

While the results of the current work are promising, several improvements can be made to

improve experimental reliability. As noted in Section 4.2.3, all frames in the avalanching videos

taken by the DinoLite microscope were manually analyzed in Matlab to determine both the

avalanching angle and the cross-sectional area of the deposition. This method is sensitive to user

bias, and an automated image analysis program could be implemented to better quantify the

measurements. Such efforts were undertaken with the raw video files, but a reflection from the

stepper motor opposing the microscope generated a circular object that obscured the automated

image analysis algorithms. Design improvement to the testing rig could block the reflected light

and allow for edge detection, image segmentation, and morphological analysis algorithms to

robustly determine the avalanching angle and deposition areas for each experimental run.

Figure 70. Reflections from the opposing stepper motor created a large circular object in

the videos, making automated image analysis challenging.

Additionally, the metrics evaluated in this work were relatively simple and do not capture

all of the physics displayed during powder testing. For example, the avalanching angle metrics for

93

Run #13 are unable to capture the transition from low to high avalanching angles displayed during

this run (see Figure 71). Run #13, which used the low quality 40° powder, had an average

avalanching angle of 30.1°, but the average avalanching angle for all other runs using this

feedstock was 22.6°±2.5°, demonstrating a shift in the behavior of the material.

Figure 71. Transition from low to high avalanching angles for the 40° powder was not

captured by the current metrics.

In addition to being detrimental to the developed experimental models, this run displayed

dynamic avalanching that manifested as a change in the recoating behavior of the spread layer.

Estimating the beginning and end of the shift in the avalanching angle as 6.0 and 6.5 seconds into

the spread, the thin band shown on the build plate in Figure 72 corresponds to this shift in

avalanche angle. On the right side of the build plate, a small region of good powder spreading can

be observed that is significantly different than the spreading behavior in the rest of the build plate.

94

Efforts to recreate this phenomenon and establish its origin could help in understanding processing

defects due to recoating failures.

Figure 72. Small region of good powder deposition which potentially corresponds to the

shift in the avalanching behavior displayed in Run #13.

95

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APPENDIX A – SUPPLEMENTAL MATERIAL FOR THE EXPERIMENTAL DESIGN

Table 11. Uncoded experimental design matrix in run order.

Standard

Order

Run

Order Layer Thickness

Recoating

Speed

Recoating

Material

Powder

Quality

Wh

ole

Plo

t 1 4 1 40 μm 50 mm/s Tool Steel 30°

13 2 80 μm 50 mm/s Silicon 30°

22 3 80 μm 150 mm/s Tool Steel 30°

7 4 40 μm 150 mm/s Silicon 30°

Wh

ole

Plo

t 2 12 5 40 μm 150 mm/s Tool Steel 40°

3 6 40 μm 50 mm/s Silicon 40°

18 7 80 μm 50 mm/s Tool Steel 40°

21 8 80 μm 150 mm/s Silicon 40°

Wh

ole

Plo

t 3 10 9 40 μm 150 mm/s Tool Steel 30°

19 10 80 μm 150 mm/s Silicon 30°

16 11 80 μm 50 mm/s Tool Steel 30°

1 12 40 μm 50 mm/s Silicon 30°

Wh

ole

Plo

t 4 5 13 40 μm 50 mm/s Tool Steel 35°

23 14 80 μm 150 mm/s Tool Steel 35°

8 15 40 μm 150 mm/s Silicon 35°

14 16 80 μm 50 mm/s Silicon 35°

Wh

ole

Plo

t 5 2 17 40 μm 50 mm/s Silicon 35°

20 18 80 μm 150 mm/s Silicon 35°

11 19 40 μm 150 mm/s Tool Steel 35°

17 20 80 μm 50 mm/s Tool Steel 35°

Wh

ole

Plo

t 6 15 21 80 μm 50 mm/s Silicon 40°

24 22 80 μm 150 mm/s Tool Steel 40°

9 23 40 μm 150 mm/s Silicon 40°

6 24 40 μm 50 mm/s Tool Steel 40°

104

Response Percent Coverage

Actual by Predicted Plot

Effect Summary

Source LogWorth PValue

Recoating Material 2.117 0.00763

Powder Quality 1.556 0.02777

Recoating Material*Powder Quality 1.218 0.06049

Recoating Speed*Powder Quality 1.075 0.08420

Layer Thickness*Powder Quality 0.640 0.22915

Layer Thickness 0.375 0.42214

Layer Thickness*Recoating Material 0.350 0.44618

Recoating Speed 0.297 0.50418

Layer Thickness*Recoating Speed 0.172 0.67266

Recoating Speed*Recoating Material 0.144 0.71831

Summary of Fit

RSquare 0.981521

RSquare Adj 0.944563

Root Mean Square Error 4.925284

Mean of Response 58.40563

Observations (or Sum Wgts) 16

Parameter Estimates

Term Estimate Std Error DFDen t Ratio Prob>|t|

Intercept 58.405625 2.312149 2 25.26 0.0016*

Layer Thickness[40] -1.141875 1.231321 3 -0.93 0.4221

Recoating Speed[50] 0.931875 1.231321 3 0.76 0.5042

Recoating Material[Tool Steel] 7.915625 1.231321 3 6.43 0.0076*

105

Powder Quality[30] 13.583125 2.312149 2 5.87 0.0278*

Layer Thickness[40]*Recoating Speed[50] 0.574375 1.231321 3 0.47 0.6727

Layer Thickness[40]*Recoating Material[Tool

Steel]

-1.076875 1.231321 3 -0.87 0.4462

Layer Thickness[40]*Powder Quality[30] -1.854375 1.231321 3 -1.51 0.2291

Recoating Speed[50]*Recoating Material[Tool

Steel]

-0.488125 1.231321 3 -0.40 0.7183

Recoating Speed[50]*Powder Quality[30] -3.135625 1.231321 3 -2.55 0.0842

Recoating Material[Tool Steel]*Powder

Quality[30]

3.620625 1.231321 3 2.94 0.0605

REML Variance Component Estimates

Random

Effect

Var Ratio Var

Component

Std Error 95% Lower 95% Upper Pct of Total

Whole Plots 0.6315135 15.319521 21.949954 -27.7016 58.340641 38.707

Residual 24.258423 19.806919 7.7847804 337.24217 61.293

Total 39.577944 26.037617 14.988272 264.3208 100.000

-2 LogLikelihood = 63.152039475

Note: Total is the sum of the positive variance components.

Total including negative estimates = 39.577944

Residual by Predicted Plot

Residual by Row Plot

106

Interaction Profiles

107

Response Microscope Layer Roughness

Actual by Predicted Plot

Effect Summary

Source LogWorth PValue

Layer Thickness*Recoating Material 0.520 0.30188

Recoating Material 0.512 0.30768

Recoating Speed 0.368 0.42868

Layer Thickness*Recoating Speed 0.323 0.47554

Recoating Speed*Recoating Material 0.311 0.48909

Layer Thickness 0.273 0.53351

Recoating Speed*Powder Quality 0.110 0.77700

Layer Thickness*Powder Quality 0.076 0.83956

Recoating Material*Powder Quality 0.042 0.90883

Powder Quality 0.033 0.92584

Summary of Fit

RSquare 0.958276

RSquare Adj 0.819198

Root Mean Square Error 43.64482

Mean of Response 63.05214

Observations (or Sum Wgts) 14

Parameter Estimates

Term Estimate Std Error DFDen t Ratio Prob>|t|

Intercept 74.031678 33.81667 1.871 2.19 0.1687

Layer Thickness[40] -14.90023 17.1666 1.105 -0.87 0.5335

Recoating Speed[50] -17.24543 13.97967 1.033 -1.23 0.4287

Recoating Material[Tool Steel] -30.54773 17.1666 1.105 -1.78 0.3077

108

Powder Quality[30] -3.703523 35.25377 2.019 -0.11 0.9258

Layer Thickness[40]*Recoating Speed[50] 17.778977 17.1666 1.105 1.04 0.4755

Layer Thickness[40]*Recoating Material[Tool

Steel]

26.604178 13.97967 1.033 1.90 0.3019

Layer Thickness[40]*Powder Quality[30] -3.575428 13.97967 1.033 -0.26 0.8396

Recoating Speed[50]*Recoating Material[Tool

Steel]

17.061477 17.1666 1.105 0.99 0.4891

Recoating Speed[50]*Powder Quality[30] 6.1347731 17.1666 1.105 0.36 0.7770

Recoating Material[Tool Steel]*Powder

Quality[30]

-2.002928 13.97967 1.033 -0.14 0.9088

REML Variance Component Estimates

Random

Effect

Var Ratio Var

Component

Std Error 95% Lower 95% Upper Pct of Total

Whole Plots 1.9909722 3792.5439 4779.4488 -5575.004 13160.091 66.566

Residual 1904.8703 2700.2613 118.36931 30654.321 33.434

Total 5697.4142 4867.7154 1762.4582 96485.057 100.000

-2 LogLikelihood = 62.749329695

Note: Total is the sum of the positive variance components.

Total including negative estimates = 5697.4142

Residual by Predicted Plot

Residual by Row Plot

109

Interaction Profiles

110

Response Deposition Rate

Actual by Predicted Plot

Effect Summary

Source LogWorth PValue

Powder Quality 0.954 0.11114

Layer Thickness 0.770 0.16983

Layer Thickness*Powder Quality 0.669 0.21418

Recoating Speed 0.613 0.24362

Recoating Speed*Powder Quality 0.431 0.37072

Recoating Material 0.420 0.38053

Recoating Speed*Recoating Material 0.340 0.45657

Layer Thickness*Recoating Speed 0.199 0.63243

Layer Thickness*Recoating Material 0.120 0.75932

Recoating Material*Powder Quality 0.091 0.81078

Summary of Fit

RSquare 0.894452

RSquare Adj 0.683356

Root Mean Square Error 1.704017

Mean of Response 2.040937

Observations (or Sum Wgts) 16

Parameter Estimates

Term Estimate Std Error DFDen t Ratio Prob>|t|

Intercept 2.0409375 0.652547 2 3.13 0.0888

Layer Thickness[40] -0.766438 0.426004 3 -1.80 0.1698

Recoating Speed[50] -0.616563 0.426004 3 -1.45 0.2436

Recoating Material[Tool Steel] -0.436938 0.426004 3 -1.03 0.3805

111

Powder Quality[30] 1.7903125 0.652547 2 2.74 0.1111

Layer Thickness[40]*Recoating Speed[50] 0.2260625 0.426004 3 0.53 0.6324

Layer Thickness[40]*Recoating Material[Tool

Steel]

0.1429375 0.426004 3 0.34 0.7593

Layer Thickness[40]*Powder Quality[30] -0.669313 0.426004 3 -1.57 0.2142

Recoating Speed[50]*Recoating Material[Tool

Steel]

-0.363187 0.426004 3 -0.85 0.4566

Recoating Speed[50]*Powder Quality[30] -0.447438 0.426004 3 -1.05 0.3707

Recoating Material[Tool Steel]*Powder

Quality[30]

-0.111313 0.426004 3 -0.26 0.8108

REML Variance Component Estimates

Random

Effect

Var Ratio Var

Component

Std Error 95% Lower 95% Upper Pct of Total

Whole Plots 0.3365914 0.9773513 1.80345 -2.557346 4.5120484 25.183

Residual 2.9036727 2.3708389 0.9318188 40.367046 74.817

Total 3.8810241 2.4622896 1.5087939 23.534417 100.000

-2 LogLikelihood = 51.723478478

Note: Total is the sum of the positive variance components.

Total including negative estimates = 3.8810241

Residual by Predicted Plot

Residual by Row Plot

112

Interaction Profiles

113

Response dAngle/dt

Actual by Predicted Plot

Effect Summary

Source LogWorth PValue

Powder Quality 1.539 0.02889

Recoating Speed*Recoating Material 0.612 0.24414

Layer Thickness*Recoating Material 0.526 0.29803

Recoating Speed 0.308 0.49209

Layer Thickness*Powder Quality 0.207 0.62067

Recoating Speed*Powder Quality 0.180 0.66032

Recoating Material 0.178 0.66407

Layer Thickness 0.161 0.69005

Recoating Material*Powder Quality 0.128 0.74506

Layer Thickness*Recoating Speed 0.018 0.95909

Summary of Fit

RSquare 0.710217

RSquare Adj 0.130651

Root Mean Square Error 5.912292

Mean of Response 8.055063

Observations (or Sum Wgts) 16

Parameter Estimates

Term Estimate Std Error DFDen t Ratio Prob>|t|

Intercept 8.0550625 1.015944 2 7.93 0.0155*

Layer Thickness[40] -0.649563 1.478073 3 -0.44 0.6901

Recoating Speed[50] -1.153438 1.478073 3 -0.78 0.4921

114

Recoating Material[Tool Steel] -0.709438 1.478073 3 -0.48 0.6641

Powder Quality[30] 5.8470625 1.015944 2 5.76 0.0289*

Layer Thickness[40]*Recoating Speed[50] -0.082313 1.478073 3 -0.06 0.9591

Layer Thickness[40]*Recoating Material[Tool Steel] 1.8564375 1.478073 3 1.26 0.2980

Layer Thickness[40]*Powder Quality[30] -0.812813 1.478073 3 -0.55 0.6207

Recoating Speed[50]*Recoating Material[Tool Steel] -2.136188 1.478073 3 -1.45 0.2441

Recoating Speed[50]*Powder Quality[30] -0.718188 1.478073 3 -0.49 0.6603

Recoating Material[Tool Steel]*Powder Quality[30] -0.526938 1.478073 3 -0.36 0.7451

REML Variance Component Estimates

Random

Effect

Var Ratio Var

Component

Std Error 95% Lower 95% Upper Pct of Total

Whole Plots -0.13189 -4.610234 8.2435506 -20.7673 11.546828 0.000

Residual 34.955198 28.540799 11.217487 485.94942 100.000

Total 34.955198 28.540799 11.217487 485.94942 100.000

-2 LogLikelihood = 60.958511314

Note: Total is the sum of the positive variance components.

Total including negative estimates = 30.344963

Residual by Predicted Plot

Residual by Row Plot

Interaction Profiles

115

Response Average Angle

116

Actual by Predicted Plot

Effect Summary

Source LogWorth PValue

Powder Quality 1.754 0.01763

Layer Thickness 1.203 0.06261

Layer Thickness*Powder Quality 0.506 0.31156

Recoating Material 0.362 0.43491

Recoating Material*Powder Quality 0.331 0.46632

Recoating Speed*Powder Quality 0.203 0.62719

Layer Thickness*Recoating Material 0.102 0.79034

Layer Thickness*Recoating Speed 0.094 0.80620

Recoating Speed 0.013 0.96995

Recoating Speed*Recoating Material 0.006 0.98632

Summary of Fit

RSquare 0.783002

RSquare Adj 0.349006

Root Mean Square Error 4.756987

Mean of Response 27.34113

Observations (or Sum Wgts) 16

Parameter Estimates

Term Estimate Std Error DFDen t Ratio Prob>|t|

Intercept 27.341125 0.74527 2 36.69 0.0007*

Layer Thickness[40] 3.44625 1.189247 3 2.90 0.0626

Recoating Speed[50] 0.048625 1.189247 3 0.04 0.9700

Recoating Material[Tool Steel] -1.069125 1.189247 3 -0.90 0.4349

Powder Quality[30] 5.53825 0.74527 2 7.43 0.0176*

Layer Thickness[40]*Recoating Speed[50] 0.3185 1.189247 3 0.27 0.8062

117

Layer Thickness[40]*Recoating Material[Tool Steel] -0.3455 1.189247 3 -0.29 0.7903

Layer Thickness[40]*Powder Quality[30] 1.443875 1.189247 3 1.21 0.3116

Recoating Speed[50]*Recoating Material[Tool Steel] 0.022125 1.189247 3 0.02 0.9863

Recoating Speed[50]*Powder Quality[30] 0.64125 1.189247 3 0.54 0.6272

Recoating Material[Tool Steel]*Powder Quality[30] -0.98975 1.189247 3 -0.83 0.4663

REML Variance Component Estimates

Random

Effect

Var Ratio Var

Component

Std Error 95% Lower 95% Upper Pct of Total

Whole Plots -0.15182 -3.435521 5.1256379 -13.48159 6.6105444 0.000

Residual 22.628922 18.476438 7.2618566 314.58874 100.000

Total 22.628922 18.476438 7.2618566 314.58874 100.000

-2 LogLikelihood = 58.414690181

Note: Total is the sum of the positive variance components.

Total including negative estimates = 19.193401

Residual by Predicted Plot

Residual by Row Plot

Interaction Profiles

118

119

Response Visual Inspection

Actual by Predicted Plot

Effect Summary

Source LogWorth PValue

Powder Quality 2.196 0.00637

Recoating Material 2.138 0.00727

Recoating Material*Powder Quality 1.553 0.02799

Layer Thickness 0.957 0.11049

Layer Thickness*Powder Quality 0.708 0.19569

Recoating Speed*Powder Quality 0.621 0.23944

Recoating Speed 0.352 0.44444

Layer Thickness*Recoating Speed 0.265 0.54355

Layer Thickness*Recoating Material 0.181 0.65902

Recoating Speed*Recoating Material 0.032 0.92841

Summary of Fit

RSquare 0.97275

RSquare Adj 0.918249

Root Mean Square Error 0.512348

Mean of Response 2.8625

Observations (or Sum Wgts) 16

Parameter Estimates

Term Estimate Std Error DFDen t Ratio Prob>|t|

Intercept 2.8625 0.115244 2 24.84 0.0016*

Layer Thickness[40] -0.2875 0.128087 3 -2.24 0.1105

Recoating Speed[50] -0.1125 0.128087 3 -0.88 0.4444

Recoating Material[Tool Steel] 0.8375 0.128087 3 6.54 0.0073*

120

Powder Quality[30] 1.4375 0.115244 2 12.47 0.0064*

Layer Thickness[40]*Recoating Speed[50] 0.0875 0.128087 3 0.68 0.5436

Layer Thickness[40]*Recoating Material[Tool Steel] -0.0625 0.128087 3 -0.49 0.6590

Layer Thickness[40]*Powder Quality[30] -0.2125 0.128087 3 -1.66 0.1957

Recoating Speed[50]*Recoating Material[Tool Steel] 0.0125 0.128087 3 0.10 0.9284

Recoating Speed[50]*Powder Quality[30] -0.1875 0.128087 3 -1.46 0.2394

Recoating Material[Tool Steel]*Powder Quality[30] 0.5125 0.128087 3 4.00 0.0280*

REML Variance Component Estimates

Random

Effect

Var Ratio Var

Component

Std Error 95% Lower 95% Upper Pct of Total

Whole Plots -0.047619 -0.0125 0.0754544 -0.160388 0.1353878 0.000

Residual 0.2625 0.2143304 0.084239 3.649292 100.000

Total 0.2625 0.2143304 0.084239 3.649292 100.000

-2 LogLikelihood = 37.577722105

Note: Total is the sum of the positive variance components.

Total including negative estimates = 0.25

Residual by Predicted Plot

Residual by Row Plot

Interaction Profiles

121

Response Keyence Roughness

122

Actual by Predicted Plot

Effect Summary

Source LogWorth PValue

Layer Thickness*Powder Quality 0.862 0.13743

Layer Thickness*Recoating Speed 0.650 0.22408

Recoating Material 0.483 0.32853

Recoating Speed*Powder Quality 0.463 0.34428

Layer Thickness*Recoating Material 0.452 0.35287

Recoating Speed*Recoating Material 0.256 0.55415

Powder Quality 0.152 0.70473

Recoating Material*Powder Quality 0.054 0.88261

Recoating Speed 0.013 0.96970

Layer Thickness 0.006 0.98660

Summary of Fit

RSquare 0.711713

RSquare Adj 0.135139

Root Mean Square Error 12.75479

Mean of Response 26.57322

Observations (or Sum Wgts) 16

Parameter Estimates

Term Estimate Std Error DFDen t Ratio Prob>|t|

Intercept 26.573219 3.469671 2 7.66 0.0166*

Layer Thickness[40] 0.0581437 3.188697 3 0.02 0.9866

Recoating Speed[50] -0.131481 3.188697 3 -0.04 0.9697

Recoating Material[Tool Steel] -3.712131 3.188697 3 -1.16 0.3285

Powder Quality[30] -1.516469 3.469671 2 -0.44 0.7047

Layer Thickness[40]*Recoating Speed[50] 4.8707688 3.188697 3 1.53 0.2241

123

Layer Thickness[40]*Recoating Material[Tool Steel] 3.4974438 3.188697 3 1.10 0.3529

Layer Thickness[40]*Powder Quality[30] 6.4224813 3.188697 3 2.01 0.1374

Recoating Speed[50]*Recoating Material[Tool Steel] 2.1173688 3.188697 3 0.66 0.5541

Recoating Speed[50]*Powder Quality[30] 3.5714563 3.188697 3 1.12 0.3443

Recoating Material[Tool Steel]*Powder Quality[30] -0.512119 3.188697 3 -0.16 0.8826

REML Variance Component Estimates

Random

Effect

Var Ratio Var

Component

Std Error 95% Lower 95% Upper Pct of Total

Whole Plots 0.0459989 7.4833114 58.494552 -107.1639 122.13053 4.398

Residual 162.68457 132.8314 52.207171 2261.6514 95.602

Total 170.16788 110.65126 64.992258 1100.9449 100.000

-2 LogLikelihood = 70.484716782

Note: Total is the sum of the positive variance components.

Total including negative estimates = 170.16788

Residual by Predicted Plot

Residual by Row Plot

Interaction Profiles

124

125

APPENDIX B – EQUATIONS IN THE HERTZ-MINDLIN WITH J.K.R. COHESION

Table 12. List of kinematic variables in EDEM’s simulation models.

Table 13. List of material properties in EDEM’s Hertz-Mindlin with cohesion model.

Variable Name Description Units (SI)

𝑖 index for the ith

particle ---

𝑗 index for the jth

particle ---

𝑅 particle radius m

𝑅∗ equivalent particle radius m

𝑟 particle position m

𝑣𝑛𝑟𝑒𝑙 relative normal velocity m/s

𝑣𝑡𝑟𝑒𝑙 relative tangential velocity m/s

𝜔 rotational velocity rad/s

𝑎 contact/overlap radius m

𝛿𝑛 normal overlap m

𝛿𝑡 tangential overlap m

𝛿�̇� normal overlap velocity m/s

𝛿�̇� tangential overlap velocity m/s

Variable Name Description Units (SI)

𝜌 particle density kg/m^3

𝜈 Poisson’s ratio ---

𝑚 particle mass kg

𝑚∗ equivalent particle mass kg

𝐸 Young’s modulus Pa

𝐸∗ equivalent Young’s modulus Pa

𝐺 shear modulus Pa

𝐺∗ equivalent shear modulus Pa

𝐹𝑛 normal force N

𝐹𝑛𝑑 normal damping force N

𝐹𝑡 tangential force N

𝐹𝑡𝑑 tangential damping force N

𝜏 torque N-m

𝑘 normal spring stiffness N/m

𝑘𝑡 tangential spring stiffness N/m

𝑐 normal damping coefficient N/m-s

𝑐𝑡 tangential damping coefficient N/m-s

𝑒 coefficient of restitution ---

𝜇𝑠 static friction coefficient ---

𝜇𝑟 rolling friction coefficient ---

𝛾 surface energy N/m^2

𝑡𝑐𝑜𝑛𝑡𝑎𝑐𝑡 particle contact time s

126

Equations List

𝐹𝑁 =4

3𝐸∗√𝑅∗𝛿𝑁

3/2

1

𝐸∗=

1 − 𝜈𝑖2

𝐸𝑖+

1 − 𝜈𝑗2

𝐸𝑗

1

𝑅∗=

1

𝑅𝑖+

1

𝑅𝑗

1

𝑚∗=

1

𝑚𝑖+

1

𝑚𝑗

𝐹𝑁𝑑 = −2√

5

6β√𝑆𝑛𝑚∗𝑣𝑛

𝑟𝑒𝑙

𝛽 =ln(𝑒)

√ln2(𝑒) + 𝜋2

𝑆𝑛 = 2𝐸∗√𝑅∗𝛿𝑁

𝐹𝑡 = −𝑆𝑡𝛿𝑡

𝑆𝑡 = 8𝐺∗√𝑅∗𝛿𝑁

𝐺∗ =𝐸∗

2(1 + 𝜈)

𝐹𝑡𝑑 = −2√

5

6β√𝑆𝑡𝑚∗𝑣𝑡

𝑟𝑒𝑙

𝜏𝑖 = −𝜇𝑖𝐹𝑁𝑅𝑖𝜔𝑖

𝐹𝐽𝐾𝑅 = −4√𝜋𝛾𝐸∗𝑎32 +

4𝐸∗

3𝑅∗𝑎3

127

𝛿 =𝑎2

𝑅∗− √

4𝜋𝛾𝑎

𝐸∗

𝐹𝑁 =4

3𝐸∗√𝑅∗𝛿3/2

𝛿𝑐 = −√4𝜋𝛾𝑎𝑐

𝐸∗+

𝑎𝑐2

𝑅∗

𝐹𝑝𝑢𝑙𝑙𝑜𝑢𝑡 = −3

2𝜋𝛾𝑅∗

𝐹𝑝𝑢𝑙𝑙𝑜𝑢𝑡 = 2𝜋𝛾𝑠cos (𝜃)√𝑅𝑖𝑅𝑗

128

APPENDIX C – RAW DATA FROM VARIOUS POWDER CHARACTERIZATIONS

Table 14. Summary of Powder Characterization Results

Al10SiMg

LPW

Al10SiMg

Eckhart Measurement Units

Hall

Flowmeter

Flow Time sec 34.9 No Flow

Apparent Density g/cm^3 1.38 g/cm^3 1.38 g/cm^3

Tapped Density g/cm^3 1.60 g/cm^3 1.67 g/cm^3

Apparent PF 52% 52%

Tapped PF 60% 63%

Hausner Ratio --- 1.16 1.21

Angle of Repose degrees 30 40

Laser

Diffraction

Size, D10 (V) um 22.5 11.9

Size, D50 (V) um 38.4 25.5

Size, D90 (V) um 63.8 67.5

D90-D10 um 41.3 55.7

Malvern

Morphologi

# of Particles --- 4010 5000

Size, D10 (V) um 28.5 17.3

Size, D50 (V) um 46.9 35.3

Size, D90 (V) um 68.6 70.6

Size, D10 (N) um 2.9 3.8

Size, D50 (N) um 9.2 14.0

Size, D90 (N) um 40.7 27.7

Circularity, D10 --- 0.72 0.73

Circularity, D50 --- 0.94 0.96

Circularity, D90 --- 0.98 0.99

Elongation, D10 --- 0.64 0.58

Elongation, D50 --- 0.91 0.87

Elongation, D90 --- 0.99 0.97

Convexity, D10 --- 0.94 0.96

Convexity, D50 --- 0.99 0.99

Convexity, D90 --- 1.00 1.00

Porosimetry

BET Surface Area m^2/g 0.1058 ---

Theoretical SA m^2/g 0.0731 ---

Surface

Roughness --- 0.309 ---

Avalanche

Tester

Avalanche

Average mJ/kg 17.4 29.2

Energy Average mJ/kg 284.2 302.7

Angle Average degrees 35.8 40.0

Powder

Rheometry

BFE mJ 380.4 850.0

SE mJ/g 3.79 3.06

SI --- 1.01 1.04

FRI --- 1.24 1.20

CBD g/cm^3 1.45 4.61

129

Figure 73. SEM image of the 30° powder: Al10SiMg from LPW.

130

Figure 74. SEM image of the 40° powder: Al10SiMg from Eckhart.