Effect of Particle Spreading Dynamics on Powder Bed Quality in Metal Additive Manufacturing

Abstract

Powder spreading precedes creation of every new layer in powder bed additive manufacturing (AM). The powder spreading process can lead to powder layer defects such as porosity, poor surface roughness and particle segregation. Therefore, the creation of homogeneous layers is the first task for optimal part printing. Discrete element methods (DEM) powder spreading simulations are typically limited to a single layer and/or small number of particles. Therefore, results from such model configurations may not be generalized to multiple layer processes. In this study, a computationally efficient multi-layer powder spreading DEM simulation model is proposed. The model is calibrated experimentally using static Angle of Repose measurements. The adhesion model parameter, cohesive energy density is related to adhesive surface energy and strain energy release rate parameters. The model results show that interaction between particle and the powder spreading rake leads to noticeable variation in packing density, surface roughness, dynamic angle of repose (AOR), particle size distribution, and particle segregation. The powder model is experimentally validated using a recoater spreading rig to measure the dynamic AOR at spreading speeds consistent with recoating speeds and layer heights used in AM processes.

Introduction

Metal powder bed additive manufacturing (AM) including laser, electron beam powder bed fusion, and binder jetting has revolutionized the way of designing and manufacturing products [1]. AM provides exceptional design flexibility, which is not achievable in the traditional subtractive manufacturing processes. The AM technologies excel in minimization of machining time, material waste, lead time, shipping time and physical storage space [2].

Powder-based AM processes consist of two key steps of object construction. The first is the powder spreading in which powder is distributed evenly over the entire bed surface including; a previous powder layer or recently layered part. The second step is the powder fusion or binding wherein the powder particles are melted and solidified by a heat source or bound together by fluidic binders. Most researchers in metal powder bed AM have focused on the melting/solidification stage assuming random or some idealized powder packing and spreading [3,4,5,6]. However, the final AM fabricated part properties are affected by all processing steps. Figure 1 shows the categories of the AM process parameters that influence the final part properties; (1) feedstock material, (2) thermal signature, and (3) execution of machine.

Fig. 1
figure1

Process parameters affecting the final AM fabricated part properties organized in three categories; 1 Feedstock material, 2 thermal profile/distribution and 3 execution of machine

Metal powder particle properties vary between powder manufacturers due to powder specification [7] or due to the powder recycling and manipulation during AM processes, which consequently influences melt pool physics (e.g., melting temperature, fluid convection, solidification and microstructure). The powder spreading step can lead to spatial inhomogeneity in the particle size distribution (PSD) and powder bed density and as a result, uneven surface and porosity can be formed during the melting/solidification stage. Thus, the powder spreading process in powder bed AM has a significant impact on the powder bed uniformity and final part quality [8, 9]. Much of the recent research in the powder bed AM is focused on controlling the melt pool physics and thermal signatures. The former is the primary factor determining the part properties and the latter is an intuitive measure of the process. Optimization of process parameters such as melting source configuration and movement is an effective and promising method to minimize part imperfections. The material thermal history is also dependent on powder bed quality affecting melting and cooling physics. The last variation factor outlined in Fig. 1 is the machine execution. The method of loading and unloading powders or environmental conditions cause uncertainty in operating conditions and can lead to inconsistent final part quality.

In practice, the powder spreading process is challenging and is often the main culprit for powder layer defects (i.e. porosity, high surface roughness and particle segregation). Nandwana et al. [7] investigated the effect of different powder feedstocks for variation on final part porosity and variation in mechanical properties in electron beam melting (EBM) process. They showed that two different powders with similar apparent packing densities of 2.61 g/ml and 2.60 g/ml can lead to significant differences in porosity level, i.e. 20–30 pores per layer and 100 pores per layer. The authors hypothesized that the difference can be attributed to the difference in particle size distribution (PSD). Muniz-Lerma et al. [10] assessed the quality of powder feedstock and powder bed using various characterization techniques in laser powder bed fusion (L-PBF) process. They observed particle segregation across the powder bed in a single 50 µm thickness layer. The particle segregation potentially leads to local variation in powder bed structure and consequently changes the heating and melting signature during printing. Hence, finding the optimal size balance is important to improve printability of the process. Mindt et al. [11] also observed the occurrence of particle segregation using discrete element method (DEM) for L-PBF process. They showed that the number of finer particles decreases as the particle spreading progresses across the bed and coarser particles remain at the end of the spreading process. The segregation occurs because of spreading action and the tendency increases as the spreading process repeats. Recently, the particle spreading dynamics in AM were observed through in-situ x-ray imaging by Escano et al. [12]. Evolution of dynamic angle of repose (AOR), slope surface roughness and dynamics of powder clusters with two different PSD were investigated at the front of the powder pile. The coarser particles (= 67 µm in average diameter) showed a larger dynamic AOR of 45° compared to the finer particles of 36° (= 23 µm in average diameter). They concluded that the particle size is a crucial factor influencing powder spreading dynamics and segregation.

Discrete element method (DEM) has been used to simulate interaction between the powder particles and recoater systems in AM processes. Parteli and Pöschel [13] developed a powder spreading simulation for AM applications with particles of complex shapes. They found that roller spreader velocity was an important factor to improve powder bed quality. Higher roller velocity and larger PSD lead to lower packing density and inferior powder bed surface roughness. Haeri et al. [9] have performed parametric studies to characterize the powder spreading process with non-spherical composite powders. They reported that lower translational velocities achieved better powder bed quality, and that particles can be segregated during the spreading process. Although the packing density can be increased by manipulating particle shape, the particle distribution may not be uniform across layers. Dynamic AOR and mass flow rate during powder spreading process were investigated and quantified using DEM simulations and a digital camera by Chen et al. [14]. They found that as a particle radius increased (from 30 to 135 μm), the value of dynamic AOR increased by approximately 3° indicating the reduction of powder spreadability. Nan and Chadiri [15] investigated the effects of the gap height (between the blade and plate) and the spreading velocity on particle mass flow using DEM. A shear band formed locally around the blade such that the position of the band was sensitive to the blade velocity and gap height. They observed that the flow rate increased with the gap height. Recently, Meier et al. [16, 17] focused on the modeling of inter-particle cohesion in DEM simulation. The DEM model was calibrated by fitting simulated AOR values to the AOR experiments. They showed that the cohesive force should be considered to achieve accurate model of AOR. The following research by the same authors showed that increase cohesiveness and decrease of particle size results in significant decrease of powder bed quality in terms of packing density and surface roughness.

Powder spreading simulation using DEM typically requires a large number of particles. Most powder spreading simulations reported in the literature were limited to single layer with a small number of particles of 8000–16,000 [8, 15, 18, 19]. Such model configurations may not be extrapolated to simulations of multiple layer deposition, which is a characteristic feature of the AM process. In this work, we describe an efficient multi-layer powder spreading simulation using approximately 315,000 particles in this work. Our model was calibrated and validated with the measurement of AOR and dynamic AOR. The influence of interaction between particle and recoater system was analyzed in terms of powder bed quality (i.e. packing density, surface roughness and PSD).

In this paper, the effect of particle spreading on powder bed quality was studied with a developed model for multi-layer deposition. The experimental section describes a static and dynamic AOR measurement used for model calibration and validation. The methodology section proposes the method for a computationally efficient multi-layer spreading model. In the last section, the interaction between particle and powder spreading rake was addressed using the developed multi-layer model. The effect of the particle-rake interaction on powder bed quality was investigated; where powder bed quality was defined by the bed packing density, surface roughness, static and dynamic angle of repose (AOR), particle size distribution, and observed particle segregation. The main contribution of this work is to provide a framework to fully quantify the various powder bed properties related to bed quality.

Experiments

Measurement of Particle Size Distribution

The size and distribution of Co–Cr particles were measured using a Microtrac S3500 laser light diffraction particle size analyzer. The particle size range was between 25 and 105 µm. The measured D10, D50 and D90 are 29.84 µm, 52.08 µm and 86.11 µm, respectively. The measured PSD values were converted into LIGGGHTS simulation [20] based on the D10 ~ D95 values. Figure 2 shows (a) the measured particle size in cumulative size frequency and inset for size frequency in radius, and (b) converted particles used in the DEM simulation.

Fig. 2
figure2

a Measured particle size in cumulative size frequency and size frequency in radius (inset) and b converted particles used in DEM simulation

Static Angle of Repose

The experimental setup for static AOR measurements is presented in Fig. 3. The dimension of the box in Fig. 4a is 40 mm (L) × 30 mm (W) × 35 mm (H). Initially, the powder is scooped with a spatula and fills about 50% of the box, Fig. 3b. Once the powder is loaded, the bottom plate of the measurement system slides to the left and the powder falls into the bottom reservoir. As a result, the remaining particles on the bottom plate in Fig. 3c create a slope toward the bottom. The disk behind the powder is rotated until the visual lines align with the angle of the powder pile, thus measuring the static AOR. The experimentally measured AOR for this lot of Co–Cr powder is 33°.

Fig. 3
figure3

Experimental setup for AOR a empty box and b half-filled particles before the experiment performed, and c the slit is sliced out and the particles form the angle. The measured values of AOR was 33.0°

Fig. 4
figure4

Powder spreading setups

Powder Spreading System

A powder bed test rig was designed and built to evaluate powder spreading onto a bed. To do this, we opted to utilize a moving stage and a stationary blade such that the dynamic AOR can be measured using a stationary camera perpendicular to the stage and aligned with the recoater blade, as shown in Fig. 4. The recoater blade is a Concept Laser hard recoater fixed to a stationary stand. Powder is dropped onto the test platform from above the plate and then spread at a fixed speed (2.54 cm/s, 5.08 cm/s or 12.7 cm/s) dictated by the speed of the moving stage. The blade can be adjusted to accommodate powder layer thicknesses in increments of 102–127 µm after an initial bed of 1 mm is placed onto the stage.

Table 1 presents the different layer thicknesses achieved for the 2.54 cm/s recoating experiments. Initially, the powder bed was charged with 1 mm of powder to create a base layer. Then, the bed recoater coats a 100 µm thick powder layer while the camera is used to capture the dynamic AOR resulting in the interaction between the powder being deposited onto the bed with the existing 1 mm base layer on the moving stage.

Table 1 Layer thickness used in the experiment

In-Situ Measurement of Powder Flow

During each powder spreading experiment the images were captured using a Point Grey GS3-U3-50S5M-C camera. An initial calibration image was used to determine the length scale on the center plane of the recoater blade, Fig. 5a. The focus is maintained on this plane throughout the experiments.

Fig. 5
figure5

a calibration at the focus plane at the center along the recoater blade, b example of the dynamic AOR, θ, measured during the spreading event

Image post-processing was performed to determine the dynamic AOR the powder makes with the existing powder bed, θ, for each image captured during the experiment, Fig. 5b. Image analysis was done using image analysis software Clemex, Inc. Vision. A program was written that sequentially processed the images beginning with the start of spreading each layer. Each image in the layer would be enhanced for sharpness to brighten the image and make it easier to discern the angle of the powder. The area of powder angle was identified, and an angle tool was used to align and measure an apparent angle of the loose powder. This angle was recorded as the dynamic AOR.

Physical and Numerical Model

Discrete Element Method

In the powder DEM simulations, particles are modeled as discrete elastic entities of prescribed shapes (e.g., spheres). Their motion is governed by the field (e.g., gravitational) and inter-particle (contact) forces. Particle movement is evolved in a time increment based on the forces acting on them. Then, the DEM’s solution process determines the overlap between particles and between the particles and other objects and calculates contact forces based on contact constitutive law (e.g., Hertzian contact). Spherical shape idealization is a reasonable approximation for metal particles since they are typically spherical and elastic at a given small particle size range (e.g., in the order of 10 µm) and low forces involved in AM powder manipulation. The contact force is decomposed into contact normal and contact tangential components with respect to the contact plane. Several adhesive forces may be present between particles, such as electrostatic, capillary, and Van der Waals forces. These adhesive forces might contribute to reduction of packing density due to cohesion-induced particle clustering [16, 17]. For the metallic particles, electrostatic forces are negligible with the particle size greater than 1 µm [16, 17, 19]. Van der Waals forces are only effective at a very short-range (~ 1 nm). Furthermore, metallic bonding in the short-range might be much stronger than the Van der Waals forces. Powder spreading in AM typically happens in atmospheric environmental conditions, potentially resulting in oxidation, contamination and moisturization [12, 16, 17]. Moisture increases the cohesion whereas the oxidation layer can lower the adhesive force between particles. In practice, the surface asperity/roughness makes the measurements of inter-particle forces difficult because the values of adhesive forces drastically vary with the effective distance between particles. Under these uncertainties, the parameters for the adhesion model are commonly used as calibration parameters for the DEM models. The Johnson–Kendall–Roberts (JKR) theory [21] is the core of the contemporary contact mechanics. It incorporates the classical Herzian elastic contact model and the adhesive forces between the particles. The simplified Johnson–Kendall–Roberts (SJKR) adhesion model [19, 22, 23] is commonly used in DEM simulations. It assumes the inter-particle contact is immediately broken when the normal overlap becomes negative. Adhesive normal force between spherical particles in SJRK model is calculated using Eq. (1):

$$ F_{\text{c}} = \kappa \alpha $$
(1)

where κ is the termed cohesion energy density and α is the effective contact area between spheres, which in our model is estimated as an area of undeformed sphere to sphere intersection, A. The relation between the cohesive energy density and more commonly used surface energy parameters such as surface energy density and strain energy release rate are given in Appendix.

The particles were modeled as perfect spheres. Total force acting on a particle is a sum of contact normal force, contact shearing force, gravitational force and cohesion force. The contact shear force is tangential to the sphere surface and causes the rotational momentum on the particle. In between two particles, the momentum leads to relative rotation and consequently generates rolling resistance. The total force and momentum force acting on the particles are used to calculate the translational and rotational acceleration using equations of (2) and (3):

$$ F_{\text{tot}} = F_{\text{cn}} + F_{\text{cs}} + F_{\text{g}} + F_{\text{c}} = m\ddot{x} $$
(2)
$$ M_{\text{tot}} = M_{\text{cs}} + M_{\text{r}} = I\ddot{\omega } $$
(3)

where Ftot is total force acting on a particle, Fcn is contact normal force, Fcs is contact shear force, Fg is gravitational force, \( m \) is particle mass, \( \ddot{x} \) is acceleration velocity of particle, Mtot is total momentum acting on a particle, Mcs is momentum caused by shear force, Mr is rolling resistance, I is inertial of a particle and \( \ddot{\omega } \) is angular acceleration of a particle.

These translational and rotational accelerations are used to calculate the translational and rotational velocities in each time increment. Finally, the position of individual particles (i.e. x, y and z coordinates) is calculated at the end of each time step. Detailed description of the DEM algorithm can be found in the literature [13, 16, 17, 19, 24], and is beyond the scope of this paper.

The properties for Co–Cr particles used in the simulations that follow are given in Table 2. The Young’s modulus and Poisson’s ratio of the particle are used to determine the elastic Hertz contact solution. The friction coefficient is used to describe the relative sliding motion between two contacting particles using Coulomb law of friction. The shear force can lead to rotational momentum acting on two contacting particles which causing relative rotation between the particles. The rolling friction coefficient is used to describe the resistance momentum occurring during rolling. A local non-viscous damping force is commonly used in DEM simulation to improve numerical convergence when solving the equation of motion [25]. The restitution coefficient is used to add a braking force to the direction of particle linear movement when the particle velocity is positive. Strictly speaking, all the particle properties used in the DEM simulation should be obtained from the corresponding experiments. However, obtaining all the properties was not practical due to uncertainty in experimental adhesive forces and surface energies. The cohesion energy density and correspondingly adhesive surface energy between particles and particle-system is not only difficult to measure but also may vary by orders of magnitude due to surface roughness, contamination, and oxidation [16, 17]. The particle property values in Table 2 are used as base values for calibration and validation of the DEM model. Young’s modulus used in the simulation was approximately one order lower than the real value to avoid extremely long computation time stemming from considerably small-time step, i.e. the modulus is scaled by 1/10 from the its original value. This Young’s modulus scaling method has commonly used in DEM simulation to reduce the computation cost since the numerical results are not sensitive to wide range of the value change [14].

Table 2 Particle properties of Co–Cr used in DEM simulation

Model Setup

AOR tests are often used to calibrate and validate the DEM models [16, 26]. The computation domain for the AOR simulation was set within the dimensions of 6 mm (L) × 3 mm (W) × 1.8 mm (H) in Fig. 6. 105,000 particles are inserted into the rectangular box using raindrop method, and approximately half-filled. 10 × 10 × 10 mm reservoir was placed beneath the rectangular box to collect the fallen particles. Particle size was in the range of approximately 14–50 µm in radius. The bottom plate slides out to the left side of the system to allow particle-drop under the action of gravity.

Fig. 6
figure6

Simulation setup for AOR prediction, 105,000 particles are filled with half of the box and fall as the bottom plate slides out

Long range particle spreading and interaction between the recoater and the particles differentiate the DEM simulations of powder bed AM from typical particle packing simulations. These processes strongly influence the quality of the powder bed [8]. Figure 7 shows the geometry of the powder spreading simulation before adding the particles. The simulation domain has dimensions of 18.9 mm (L) × 3 mm (W) × 1.8 mm (H) for the spreading plate. The recoater thickness is 0.5 mm and has an angle of 10° at the bottom edge. The particles are inserted in front of the rake at every layer deposition step. The spacing between rake and the plate was set to be 102 µm or 508 µm depending on the experimental setting.

Fig. 7
figure7

Computation domain for powder spreading simulation

Workflow for Multiple Layer Spreading Simulation

In our model, the multi-layer spreading simulation consists of two main steps: (1) generation of initial particle pileup and (2) spreading the particles using recoater. The workflow to simulate multiple layer spreading process is given in Fig. 8. Initial particle pile in Fig. 8a was generated using the raindrop method driven by gravity. After the particle pile is stabilized, the information about the individual particles location and radius was exported from the particle generating model and imported into actual spreading system with rake in Fig. 8b. This is a reasonable simplification because the shape of the particle pileups is similar between the layers. This approach significantly reduces the total computation time as it avoids repeated particle deposition and settlement. The insertion of initial particle pile is shown in Fig. 8b, d. The creation of the first and the second layer are shown in Fig. 8c, e. Total of 321,000 particles were used in the simulation of multi-layer spreading.

Fig. 8
figure8

Workflow to model the layer deposition process. The initial particle stacks shown in (a) are inserted at every beginning of the deposition (b, d). This method significantly reduces the total computation time. The spreading steps are shown in (c) for the first and (e) for the second layer

Results and Discussion

Modeling and Calibration of Static Angle of Repose

Static AOR and powder spreadability depend on the interactions between the particles and between the particles and the walls in the system. The effect of friction and rolling coefficient on AOR was investigated and reported in Fig. 9. The coefficient of static and rolling friction is increased by 1.5 times from the base value and three times, respectively. The AOR is 28.8° in Fig. 9a and 29.0° in Fig. 9b at cohesion energy density of 3.2 × 107 erg/cm3 (≈ adhesive surface energy of 5.35 × 10−2 mJ/m2). Derivation of the formulas for the conversion is given in Appendix. Our simulations show low sensitivity of the AOR for both parameters.

Fig. 9
figure9

Effect of static friction and rolling coefficient on AOR. Both coefficients showed little influence on the change of AOR

On the other hand, the cohesion force has a strong influence on AOR [16]. We varied cohesion energy density from 3.0 × 107 to 3.6 × 107 erg/cm3. Figure 10 shows that AOR increases from 28.9° to 32.1° as the cohesion energy density increases from 3.0 × 107 to 3.6 × 107 erg/cm3. Notice that the predicted AOR is 32.1° at cohesion energy density of 3.6 × 107 erg/cm3 which is close to the experimentally measured AOR of 33.0°.

Fig. 10
figure10

Predicted AOR with particle cohesion energy a 3.0 × 107 erg/cm3, b 3.2 × 107 erg/cm3, c 3.5 × 107 erg/cm3, and d 3.6 × 107 erg/cm3 that shows the best match with the measured value of 33.0°

Formation of Deposit Layers

The powder bed thickness varied with the layer sequence as described in Table 1. The gap spacing between rake and spreading plate was adjusted for every layer in the correspondence to the specified bed height in the experiment. The predicted and experimentally measured bed height were compared at every layer in Fig. 11. The predicted and measured results agreed within 1% error range.

Fig. 11
figure11

Validation of the predicted powder bed height. The bed height matches well with the experiment. The predicted bed height matches with the measured height (in Table 1) within 1% error range

Dynamic Angle of Repose

In powder bed AM processes, particles with good spreadability are beneficial for forming defect-free layers. Static AOR may be insufficient to describe the dynamics of particles during spreading as it captures the slope angle for static equilibrium state. The dynamic AOR accounts for dynamic interactions between the particles and recoating system. Figure 12 shows the evolution of the dynamic AOR at rake velocity of 2.54 cm/s and pile geometry with time at the third layer. In Fig. 12a, the dynamic AOR is almost constant overall in both the experiment and the simulation. Fluctuations are present due to dynamics of particle motion. Note an abrupt increase of the angle at the beginning of the spreading in the experiment. It indicates an initial resistance against forward motion. Then, when the weak bonds between the particles are broken by the rake, the angle becomes relatively constant. A possible explanation is that the experiment was carried out in atmospheric condition which contains moisture that was not accounted for in the model [27]. After the initial cohesive bond breakage, the model predicts the variation of the dynamic AOR reasonably well. Figure 12b–d shows the characteristic shape of powder piles from the results of both simulation and experiments. The volume of pile progressively decreases as the powder pile is moved by the rake from (d) right to (b) left region of the plate. Plateau region appears at the top of the powder pile in both simulation and experiment in Fig. 12d and disappears as the particles are spread in Fig. 12b. The DEM simulation captures the appearance and disappearance of the plateau region.

Fig. 12
figure12

Comparison of dynamic AOR with experiment. a Evolution of dynamic AOR with time and bd characteristic geometry of powder pile compared with experimental images

Smaller dynamic AOR indicates better spreadability of powder particles during layering stage [14]. Figure 13 shows the predicted evolution of the dynamic AOR with rake velocity. Rake velocity was increased by 2× and 5× times from the initial rake velocity of 2.54 cm/s. In general, the dynamic AOR increases with increasing rake velocity from 27.3°, 29.6° to 38.3°. Also, a higher gradient of the angle variation was observed with an increase of the rake velocity. These increases imply that higher rake velocity decreases the spreadability of particles. Consequently, an inferior quality of powder bed can be developed at high rake velocity (e.g., irregular surface and lower packing density).

Fig. 13
figure13

Evolution of dynamic AOR with rake velocity. High velocity increases the dynamic AOR and the gradient of angle variation

Influence of Rake Velocity on Powder Bed Quality

Variation of Packing Density

Packing density is one of the critical indicators of powder bed quality. It is reported that a higher packing density is favorable to producing denser parts with better surface finish [28]. Two kind of packing density can be used to compare the variations. One is the “apparent” packing density, which is defined by the ratio of total volume of particles to total volume of the box enclosure. The second is the “voxel” packing density, a theoretical quantity, is defined by the ratio of the total volume of particles in an imaginary reference volume inside the packed particles to the total particle volume in the volume. Since the voxel is not subjected to the wall effect, it leads to higher packing density than the apparent packing density. The voxel and apparent packing densities can represent the upper and lower bounds of the actual packing density, respectively. In this work, the apparent packing density is used to investigate the influence of the rake velocity on the packing density, which is marked in black solid box in Fig. 14b. Figure 14a shows the variation of packing density with the change of rake velocity at the first layer. The density was decreased by about 5% as the rake velocity increases by five times. Figure 14b shows the change of surface quality at different rake velocities. The nominal velocity produces fairly uniform surface while the 5× velocity results in an unfilled and non-uniform surface at the left side of powder bed. Our results indicate that higher rake velocity may produce poor surface finish.

Fig. 14
figure14

Variation of a packing density and b surface roughness with rake velocity

Particle Segregation

Figure 15 shows the predicted PSD (a) before the spreading, and (b) during deposition. Particles are color coded based on their size where larger particles are red and smaller particles are blue. The particles are uniformly mixed at the initial particle pile while more large particles are observed in the particle pile in front of the rake during deposition. Prevalence of red color indicates larger particles in the pile in Fig. 15b. Comparison of the measured PSD with the predicted PSD before and during spreading is shown in Fig. 16. The shift of size frequency before and during spreading was compared in the volume of green-dashed box in Fig. 15. The PSD before spreading corresponds to the measurements. As the rake moves the particles to the end of the plate, the PSD shifts to the right (= coarser region). This indicates that particle segregation occurs by the interaction between particle and rake system. The particle segregation was recently reported in the AM experimental literature [10, 11, 29]. The authors hypothesized that dynamic particle-recoater interaction can lead to particle segregation during the powder spreading stage. The segregation can cause inhomogeneous packing density in the powder bed. Consequently, it also increases the propensity for generating defects during the powder melting process.

Fig. 15
figure15

Particle segregation on the top surface of the powder stack front

Fig. 16
figure16

Comparison of the measured PSD with the predicted PSD at before and during spreading in the volume of green-dashed box in Fig. 15

Figure 17 shows the variation of the simulated PSD at the first layer as a function of rake velocity where the PSD reported is for the population in the first half of the recoating layer. We explore the PSD as a function of rake velocity and find that the PSD shifts to finer particle sizes with increasing rake velocity. As has already been discussed we also find that the coarse particles are segregated to the front of the moving pile (Figs. 15, 16). This may drive PSD shift to coarser particle region at lower rake velocity. These seemingly contradictory observations may be explained by particle mixing. In other words, higher rake velocity leads to stronger particle mixing and therefore deposits on the bed a population of particles that more closely represents the original PSD. This suggests that particle segregation may be controlled by manipulating the rake velocity.

Fig. 17
figure17

Shift of PSD as a function of rake velocity. Higher rake velocity drives PSD shift to finer region

Summary and Conclusions

We propose a new modeling approach for investigation of the powder spreading process in power bed AM processes. The influence of particle spreading dynamics on powder bed quality was analyzed using DEM simulations. The modeling results showed that the rake velocity leads to noticeable variation in packing density, surface roughness, dynamic AOR, PSD and particle segregation. The key findings from the present study are summarized as follows:

  1. 1.

    An effective multi-layer powder spreading simulation was developed using DEM based on read and restart option.

  2. 2.

    The particle’s static and dynamic models were in a good agreement with the experiments.

  3. 3.

    Packing density decreases with increasing rake velocity. Also, excessive rake velocity can result in an unfilled and non-uniform bed surface.

  4. 4.

    Dynamic AOR increases with rake velocity at the beginning of the spreading step.

  5. 5.

    PSD shift was driven by interaction between particle and rake. Higher rake velocity leads to larger shift in PSD toward finer region.

  6. 6.

    The SJRK adhesive model parameter, cohesive energy density is related to adhesive surface energy and stain energy release rate.

The proposed modeling approach simplifies modeling of the interactions between particles and recoater system (e.g., effect of layer thickness, binder and part geometry on part quality). Also, the newly developed modeling approach minimizes/eliminates a particle stacking step at every layer which may consume approximately 50% of total computation time. Furthermore, this method allows more than 314 K particles with minimum number of processor cores, which is approximately 20–40 times larger number of particles commonly found in the standard DEM literature [8, 15, 18, 19]. Since newly developed algorithm requires a relatively smaller number of processor cores for multiple layer simulation, it enables the AM manufacturing industries to optimize their systems without high-performance computing investment. The developed work is a part of a broader computational modeling framework under development that will enable end-to-end simulation of powder-bed based additive processes to support virtual process design and certification.

References

  1. 1.

    Babu SS, Love L, Dehoff R, Peter W, Watkins TR, Pannala S (2015) Additive manufacturing of materials: opportunities and challenges. MRS Bull 40(12):1154–1161

    Article  Google Scholar 

  2. 2.

    Körner C (2016) Additive manufacturing of metallic components by selective electron beam melting—a review. Int Mater Rev 61(5):361–377

    Article  Google Scholar 

  3. 3.

    Gürtler F-J, Karg M, Leitz K-H, Schmidt M (2013) Simulation of laser beam melting of steel powders using the three-dimensional volume of fluid method. Physi Proc 41:881–886

    Article  Google Scholar 

  4. 4.

    Khairallah SA, Anderson A (2014) Mesoscopic simulation model of selective laser melting of stainless steel powder. J Mater Process Technol 214(11):2627–2636

    CAS  Article  Google Scholar 

  5. 5.

    Khairallah SA, Anderson AT, Rubenchik A, King WE (2016) Laser powder-bed fusion additive manufacturing: physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones. Acta Mater 108:36–45

    CAS  Article  Google Scholar 

  6. 6.

    Körner C, Attar E, Heinl P (2011) Mesoscopic simulation of selective beam melting processes. J Mater Process Technol 211(6):978–987

    Article  Google Scholar 

  7. 7.

    Nandwana P, Kirka MM, Paquit VC, Yoder S, Dehoff RR (2018) Correlations between powder feedstock quality, in situ porosity detection, and fatigue behavior of Ti–6Al–4 V fabricated by powder bed electron beam melting: a step towards qualification. JOM 70(9):1686–1691

    CAS  Article  Google Scholar 

  8. 8.

    Haeri S (2017) Optimisation of blade type spreaders for powder bed preparation in additive manufacturing using DEM simulations. Powder Technol 321:94–104

    CAS  Article  Google Scholar 

  9. 9.

    Haeri S, Wang Y, Ghita O, Sun J (2016) Discrete element simulation and experimental study of powder spreading process in additive manufacturing. Powder Technol 306:45–54

    Article  Google Scholar 

  10. 10.

    Muñiz-Lerma J, Nommeots-Nomm A, Waters K, Brochu M (2018) A comprehensive approach to powder feedstock characterization for powder bed fusion additive manufacturing: a case study on AlSi7Mg. Materials 11(12):2386

    Article  Google Scholar 

  11. 11.

    Mindt HW, Megahed M, Lavery NP, Holmes MA, Brown SGR (2016) Powder bed layer characteristics: the overseen first-order process input. Metall Mater Trans A 47(8):3811–3822

    CAS  Article  Google Scholar 

  12. 12.

    Escano LI, Parab ND, Xiong L, Guo Q, Zhao C, Fezzaa K, Everhart W, Sun T, Chen L (2018) Revealing particle-scale powder spreading dynamics in powder-bed-based additive manufacturing process by high-speed x-ray imaging. Sci Rep 8(1):15079

    Article  Google Scholar 

  13. 13.

    Parteli EJ, Pöschel T (2016) Particle-based simulation of powder application in additive manufacturing. Powder Technol 288:96–102

    CAS  Article  Google Scholar 

  14. 14.

    Chen H, Wei Q, Wen S, Li Z, Shi Y (2017) Flow behavior of powder particles in layering process of selective laser melting: numerical modeling and experimental verification based on discrete element method. Int J Mach Tools Manuf 123:146–159

    Article  Google Scholar 

  15. 15.

    Nan W, Ghadiri M (2019) Numerical simulation of powder flow during spreading in additive manufacturing. Powder Technol 342:801–807

    CAS  Article  Google Scholar 

  16. 16.

    Meier C, Weissbach R, Weinberg J, Wall WA, Hart AJ (2019) Modeling and characterization of cohesion in fine metal powders with a focus on additive manufacturing process simulations. Powder Technol 343:855–866

    CAS  Article  Google Scholar 

  17. 17.

    Meier C, Weissbach R, Weinberg J, Wall WA, Hart AJ (2019) Critical influences of particle size and adhesion on the powder layer uniformity in metal additive manufacturing. J Mater Process Technol 266:484–501

    CAS  Article  Google Scholar 

  18. 18.

    Herbold E, Walton O, Homel M (2015) Simulation of powder layer deposition in additive manufacturing processes using the discrete element method. Lawrence Livermore National Lab (LLNL), Livermore, CA (United States)

  19. 19.

    Lee Y, Nandwana P, Zhang W (2018) Dynamic simulation of powder packing structure for powder bed additive manufacturing. Int J Adv Manuf Technol 96(1–4):1507–1520

    Article  Google Scholar 

  20. 20.

    Kloss C, Goniva C, Hager A, Amberger S, Pirker S (2012) Models, algorithms and validation for opensource DEM and CFD–DEM. Progr Comput Fluid Dyn Int J 12(2–3):140–152

    Article  Google Scholar 

  21. 21.

    Johnson KL, Kendall K, Roberts A (1971) Surface energy and the contact of elastic solids. Proc R Soc Lond A Math Phys Sci 324(1558):301–313

    CAS  Google Scholar 

  22. 22.

    Hærvig J, Kleinhans U, Wieland C, Spliethoff H, Jensen AL, Sørensen K, Condra TJ (2017) On the adhesive JKR contact and rolling models for reduced particle stiffness discrete element simulations. Powder Technol 319:472–482

    Article  Google Scholar 

  23. 23.

    Parteli EJ, Schmidt J, Blümel C, Wirth K-E, Peukert W, Pöschel T (2014) Attractive particle interaction forces and packing density of fine glass powders. Sci Rep 4:6227

    CAS  Article  Google Scholar 

  24. 24.

    Stershic A, Simunovic S, Nanda J (2015) Modeling the evolution of lithium-ion particle contact distributions using a fabric tensor approach. J Power Sources 297:540–550

    CAS  Article  Google Scholar 

  25. 25.

    P.A. Cundall, O.D. Strack, A discrete numerical model for granular assemblies, geotechnique 29(1) (1979) 47-65

  26. 26.

    Coetzee C, Els D (2009) Calibration of granular material parameters for DEM modelling and numerical verification by blade–granular material interaction. J Terramech 46(1):15–26

    Article  Google Scholar 

  27. 27.

    Mitarai N, Nori F (2006) Wet granular materials. Adv Phys 55(1–2):1–45

    CAS  Article  Google Scholar 

  28. 28.

    Lee Y, Zhang W (2015) Mesoscopic simulation of heat transfer and fluid flow in laser powder bed additive manufacturing. In: International solid free form fabrication symposium, Austin, pp 1154–1165

  29. 29.

    Zielinski J, Vervoort S, Mindt H-W, Megahed M (2017) Influence of powder bed characteristics on material quality in additive manufacturing. BHM Berg- Huettenmaenn Monatsh 162(5):192–198

    Article  Google Scholar 

  30. 30.

    Barthel E (2008) Adhesive elastic contacts: JKR and more. J Phys D Appl Phys 41(16):163001

    Article  Google Scholar 

  31. 31.

    Packham D (1996) Work of adhesion: contact angles and contact mechanics. Int J Adhes Adhes 16(2):121–128

    CAS  Article  Google Scholar 

  32. 32.

    Maugis D, Barquins M (1980) Fracture mechanics and adherence of viscoelastic solids. In: Adhesion and adsorption of polymers. Springer, pp 203–277

Download references

Acknowledgements

This research was supported by the High-Performance Computing for Manufacturing Project Program (HPC4Mfg), managed by the U.S. Department of Energy Advanced Manufacturing Office within the Energy Efficiency and Renewable Energy Office. This research used resources of the Compute and Data Environment for Science (CADES) at the Oak Ridge National Laboratory. The authors thank Dr. John Turner for support in preparation of this manuscript.

Funding

This research is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Yousub Lee.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Appendix

Appendix

Simplified Johnson–Kendall–Roberts (SJKR) adhesion model is derived by simplification of its original JKR form for contact of elastic spheres with adhesion [21, 30]. It is applicable for modeling weak interaction between surfaces in contact which in our case describes a multitude of possible interaction mechanisms that result in a weak cementation between the particles. A general form of the SJKR model describes the force, Fc, resisting separation between particles as:

$$ F_{\text{c}} = \kappa \cdot \alpha $$
(4)

where \( \kappa \) is an effective cohesive stress, termed cohesion energy in SJKR model, and α is an effective contact area between the particles. Different selection of \( \kappa \) and α result in variations of the model. In principle, parameter \( \kappa \) can be related to the cohesive surface energy between the particles, \( \Delta \gamma \), which is more commonly used in the continuum mechanics problems for modeling strong and weak interactions. The critical contact surface radius, acr, and pull out force, Fcr, in the original JKR model are:

$$ a_{\text{cr}}^{3} = \frac{{9 R^{*2} \Delta \gamma \pi }}{{8 E^{*} }} $$
(5)
$$ F_{\text{cr}} = \frac{3}{2} \Delta \gamma \pi R^{*} $$
(6)

where R* denotes the effective particle radius of the contact of two particles, and E* denotes the effective elastic contact modulus, as:

$$ \frac{1}{{R^{*} }} = \frac{1}{{R_{1} }} + \frac{1}{{R_{2} }} $$
(7)
$$ \frac{1}{{E^{*} }} = \frac{{1 - \upsilon_{1}^{2} }}{{E_{1} }} + \frac{{1 - \upsilon_{2}^{2} }}{{E_{2} }} $$
(8)

Symbols Ri, Ei and νi denote radius, elastic modulus and Poisson’s ratio of particle i, respectively. Selecting the effective contact surface α as the area of the critical contact surface for the pull-out force, Fcr,

$$ \kappa = \frac{{F_{\text{cr}} }}{{a_{\text{cr}}^{2} \pi }} $$
(9)

we have Eq. (10) after substitution of acr and Fcr from Eq. (5) and (6) into Eq. (9):

$$ \kappa = \sqrt[3]{{\frac{{8 E^{*2} }}{{3 R^{*} \pi^{2} }}}}\sqrt[3]{\Delta \gamma } $$
(10)

or equivalently

$$ \Delta \gamma = \frac{3}{8}\frac{{R^{*} \pi^{2} }}{{E^{*2} }}\kappa^{3} $$
(11)

relate the two adhesive contact parameters κ and \( \Delta \gamma \).

Using Eq. (11), the nominal value of the cohesive energy density, κ, value of 3.6 × 106 J/m3 (= 3.6 × 107 erg/cm3) used in our model is converted to the adhesive surface energy, \( \Delta \gamma \), value of 5.35 × 10−2 mJ/m2. The calculated value for \( \Delta \gamma \) is fairly close to the value of 0.02 mJ/m2 for AOR = 29° and 0.06 mJ/m2 for AOR = 34° found in the literature for Ti–6Al–4V powder [16]. The value can be compared to the measured adhesive surface energy of 20–40 mJ/m2 in polymer materials [31].

An alternative theory for adhesion of particle was given by Maguis and Barquins [32]. Unloading of the spheres in contact was modeled as a crack propagation at the contact interface and the strain energy release rate for adhesion

$$ G = \frac{{\left( {\frac{{4a^{3} E^{*} }}{{ 3 R^{*} }} - F_{\text{cr}} } \right)^{2} }}{{8 \pi a^{3} E^{*} }} $$
(12)

Substituting acr and Fcr from Eqs. (5) and (6) into Eq. (12) for contact radius, a, and contact force, F, the cohesive energy density, κ, can be converted to the strain energy release. The cohesive energy density, κ, value of 3.6 × 106 J/m3 is converted to G value of 5.93 × 10−3 mJ/m2 that is in the one order of magnitude lower as the adhesive surface energy converted value above, 5.35 × 10−2 mJ/m2.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Lee, Y., Gurnon, A.K., Bodner, D. et al. Effect of Particle Spreading Dynamics on Powder Bed Quality in Metal Additive Manufacturing. Integr Mater Manuf Innov 9, 410–422 (2020). https://doi.org/10.1007/s40192-020-00193-1

Download citation

Keywords

  • Powder bed additive manufacturing
  • Powder spreading
  • Powder bed quality
  • Multi-layer deposition
  • Discrete element methods (DEM)
  • Cohesive energy density