1 Introduction

Laser powder bed fusion (L-PBF), one of the most popular metal additive manufacturing (AM) techniques, has gained unprecedented attention from both industry and academia owing to its capability of producing components with complex geometry and intricate internal structures. L-PBF has been widely used for automobile, aerospace, and biomedical applications to produce components that are difficult or even impossible to be fabricated by conventional manufacturing process, as well as reduce part number and simplify assembly process. However, spattering particles, particle ejected away from the hot laser spot, could oxidize during in-flight cooling, contaminate the powder bed, lead to process defects, and affect the mechanical performance of as-built part. For example, in a phenomenon called “laser shadowing”, particle agglomerates emitted from the melt pool may partially or completely block the laser beam from powder bed, leading to shallow melt pool or leaving un-melted area inside the building part [1]. Moreover, spatter particle redeposition will change the local layer thickness of the original powder bed and lead to lack-of-fusion pores [2]. There are two types of spatters identified by high-speed camera: (1) micro-droplet spattering, also called “incandescent spatter”, caused by tearing of molten metal, and (2) cold powder particle spatter driven by the vortex flow near melt pool [3]. This incomplete melting of spatter particles brings inclusions and pores in the parts [3]. It was also reported that spatters could also increase the powder bed heterogeneity [4] and oxide inclusion [5].

Understanding better the underlying mechanism of spattering will help improve process design to stabilize the laser scanning process, decrease instabilities, and deliver parts with higher reliability. Various defect mechanisms due to spatter particles such as laser expulsion, self-replication, and laser shadowing have been revealed by the Lawrence Livermore National Laboratory (LLNL) through simulation and experiments [1]. Tang et al. [6] revealed the droplet spatter formation mechanism in the SLM process of 316L stainless steel through simulation. A viscous shear force acting on the keyhole wall drives the backward molten flow which forms a liquid column in the rear subsequently. The liquid column begins to neck and then is pinched off and emitted outside the melt pool as a droplet spatter. Ly et al. [7] revealed that the dominant mechanism leading to micro-droplet ejection is the vapor driven entrainment of micro-particles by ambient gas flow. Chen and Yan [8] also elaborated that vapor jetting and the consequent vortex flows are dominant in the spattering and denudation phenomena by a multiphase flow model that bi-directionally couples discrete particles and laser welding simulation. Pauzon et al. [2] studied the significant effect of using helium as the protected gas on incandescent spatter reduction.

Porosity inside the as-built part is one of the common process-induced defects which could deteriorate the mechanical performance of L-PBF part such as fatigue life. There are pore formation mechanisms that remain unclear in the L-PBF process due to the complex physics involved. Hojjatzadeh et al. [9] reported six pore formation mechanisms observed in L-PBF through high-speed camera. Zhao et al. [10] found correlation between keyhole tip instability and trapped pore in the solidification front. Process-induced pores such as lack-of-fusion pores and keyhole pores due to trapped gas have also been studied extensively [11,12,13,14,15]. Porosity also could come from both raw and used powder particles [16]. Hojjatzadeh et al. [17] also proposed a pore elimination approach utilizing the thermocapillary force induced by the high temperature gradient in melt region to achieve pore-free metal fabrication.

In this paper, the interaction between cold spatter particles and the melt track is studied through numerical simulations and experiments. The porosity formation mechanism associated with cold spatter particles is then revealed. The remaining content of this paper is organized as follows. In Sect. 2, the experimental details on single and multiple track depositions are presented. Section 3 presents the multiphysics modeling for laser welding process. Section 4 reports the experimental and simulation results. Section 5 gives the conclusions. The particle re-distribution simulation is presented in the Appendix.

2 Experimental details

In the printing experiment, two single tracks were deposited under the power of 285 W and scan speed of 0.96 m/s on one 80-μm-thick layer of Inconel 718 powders by the EOS M290 DMLS system. The powder size distribution is summarized in Table 1. The distance between two single tracks is set to be 0.25 mm, 0.50 mm, 0.75 mm, and 1.0 mm in the building process. All the single tracks were scanned by the EOS M290 DMLS system using an Ytterbium fiber laser with a maximum power of 400 W, a wavelength of 1060–1100 nm and focus diameter of 100 μm. The focal length is 410 mm. Spattering particles from the first deposited single track can also influence the second track. Therefore, more spattering particles are expected when depositing the second track which increases the chance of interaction between the melt track and falling particles. All the as-built specimens were cross-sectioned in the middle by electrical discharge machine along the plane perpendicular to the laser scanning direction. The samples were mounted and grounded to 1200 grit, followed by vibrator polishing, then etched in a solution of 15 parts acetic acid, 10 parts nitric acid, and 10 parts hydrochloric.

Table 1 The distribution of IN718 powder particles used from the vendor
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3 Multiphysics models

In this work, three different models are developed and coupled to simulate spattering phenomenon during L-PBF process and study the porosity formation mechanisms. The workflow of the proposed modeling work is presented in Fig. 1. In step 1, the powder spreading process is simulated by Flow-3D DEM module to generate the powder bed with a mean layer thickness of 80 μm. The size distribution of powder particles from the vendor in Table 1 is used in this simulation. In step 2, a moving pressure boundary condition is applied along the center line of the powder bed to induce spattering. In step 3, a model that couples laser welding and falling solid spattering particles is developed by Flow-3D welding module.

Fig. 1
figure 1

Flowchart of the proposed spattering modeling

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3.1 Laser welding model calibration

To calibrate the simulation setup including absorptivity, evaporation model and boundary conditions, the melt pool cross sections from simulation for single-track deposition on powder bed with a layer thickness of 80 μm and triple-track deposition in S-pattern on powder bed with a layer thickness of 40 μm are compared to experimental ex situ measurements.

The comparison of melt pool cross section for single-track deposition between simulation and experiment is presented in Fig. 2. In the experiment, we spread a layer of powder with a layer thickness of 80 μm. It can be found that melt pool bead height is around 80 μm in both simulation and experiment. The melt pool width in simulation is 8.28% larger than experiment, while the melt pool width is 8.37% smaller than experiment. The difference of melt pool dimensions between simulation and experiment is attributed to the variation of powder bed layer thickness. In ex situ cross section, two sphere particles are found to have attached to the melt pool bead on the right and left side, respectively. This is caused by the particle entrapment due to molten flow during the laser scanning process.

Fig. 2
figure 2

Melt pool cross section comparison between simulation and experiment for single track

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Calibration for the triple-track deposition simulation is performed as well. The comparison of melt pool cross section between simulation and experiment is presented in Fig. 3. It can be found that the melt pool depth increases from the first track to the third track (from left to right) in both simulation and ex situ measurement, which is attributed to the residual heat. The absorptivity value is set to 0.28, and the simulation is performed on a bare plate without powder particles. In the experiment, we spread a layer of powder with a layer thickness of 40 μm. However, the purging took half an hour, and most the spread particles were blown away. It can be found that the melt pool depths have a good agreement with experimental measurements. The top region of the melt pools in simulation is similar to the experiment measurement as well.

Fig. 3
figure 3

Melt pool cross section comparison between simulation and experiment for triple tracks

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3.2 Laser welding model coupled with mass particles

A coupling simulation is developed to study the interaction between spattering particles and laser welding track and reveal the pore formation mechanism associated with the entrainment of mass particles into unsolidified melt pool. Three particle sources are added into the single-track laser welding simulation. The mass particles with initial velocity coming out of each particle source are shown in Fig. 4. The laser power is 285 W, scan speed is 1.0 m/s, and the powder bed before spattering is used.

Fig. 4
figure 4

Setup for simulation model that couples DEM and laser welding

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The molten metal flow is taken as Newtonian and incompressible in the simulation. Mass continuity, momentum, and energy conservations in Eqs. (1)–(3) are solved:

$$\nabla\cdot\overset\rightharpoonup{v}=0$$
(1)
$$\frac{\partial\overset\rightharpoonup{v} }{\partial \mathrm{t}}+\left(\overset\rightharpoonup{v}\cdot \nabla \right)\overset\rightharpoonup{v}=-\frac{1}{\uprho }\nabla\overset\rightharpoonup{P} +\upmu {\nabla }^{2}\overset\rightharpoonup{v}+\overset\rightharpoonup{g}\left[1- \alpha \left(T-{T}_{m}\right)\right]$$
(2)
$$\frac{\partial h}{\partial t}+ \left(\overset\rightharpoonup{v}\cdot \nabla \right)h=\frac{1}{\rho }\left(\nabla \cdot k\nabla T\right)$$
(3)

where \(\overset\rightharpoonup{v}\) is the velocity vector, \(\overset\rightharpoonup P\) is the pressure, \(\upmu\) is the viscosity, \(\overset\rightharpoonup{g}\) is the gravity vector, \(\mathrm{\alpha }\) is the thermal expansion coefficient, \(\rho\) is the density, \(h\) is the specific enthalpy, and \(k\) is the thermal conductivity.

The location of melt pool free surface is tracked by the volume of fluid (VOF) method, in which the volume fraction of fluid occupying each mesh in the computation domain is defined by the fluid fraction F:

$$\frac{\partial F}{\partial \mathrm{t}}+\nabla \cdot \left(F\right)=0$$
(4)

where \(0\le F\le 1\). For a reasonable and precise description of the L-PBF process, the physical model is customized based on the process conditions and accounts for buoyant flow, Marangoni convection, vapor recoil pressure, and heat radiation in the simulation. The thermal properties of the IN718 alloy and the coefficients used in the simulation can be found in Ref. [18].

4 Results and discussion

A coupling simulation is developed to study the interaction between spattering particles and laser welding track and reveal the pore formation mechanism associated with the entrainment of mass particles into unsolidified melt pool. Three particle sources are added into the single-track laser welding simulation. The laser power is 285 W, scan speed is 1.0 m/s, and the powder bed before spattering is used. Snapshots of interaction between falling particles and laser welding are presented in Fig. 10. It can be observed that the particles falling into the melt pool are melted due to the heat transfer between molten flow and particles, while particles falling on the powder bed near melt track are heated up but not melted.

Figure 5 shows the snapshots of the simulation coupling laser welding and falling mass particles. At 0.61 ms, the first falling particle right above the melt track (as indicated by the white arrow) has a temperature 80 °C. At 0.63–0.67 ms, this particle enters into the depression zone caused by vapor evaporation pressure. This particle is then melted by the molten flow and cannot be tracked anymore at 0.68 ms. At 0.67 ms, there is another particle falling on the power bed near the laser melt track as indicated by the black arrow. At 0.68 ms, this particle contacts with a few particles on the powder bed. Due to the heat conduction between falling particle and power bed, the particle temperature rises to around 300 °C at 0.71 ms.

Fig. 5
figure 5

Snapshots of coupling simulation between mass particles and laser welding

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The cross section where the falling mass particles are attached to the melt region is shown in Fig. 6. Mass particles falling on the powder bed near the melt track are heated up. In the real building process, these falling particles will change the local powder bed morphology, and large particles can also lead to lack of fusion in the neighboring track or subsequent layers. These particles attached to melt pool bead are not completely melted and increase the porosity of the as-built part. Moreover, these particles also serve as origin of pores in the subsequent layers.

Fig. 6
figure 6

Cross section where mass particles attached to melt region

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Attachment of powder particles to melt pool is also observed in the ex situ melt pool cross section measurement as shown in Fig. 7. These melt pools in Fig. 7 all have one particle with different diameter attached to the melt pool bead surface. The left melt pool has a very small attachment which is caused by the falling small particles while the middle melt pool has a larger particle that connects the neighboring powder bed and melt pool bead and leaves a void. The right melt pool has a particle in circular shape which may not be completely melted by laser scanning in neighboring tracks or subsequent layers.

Fig. 7
figure 7

Cross section where mass particles attached to melt region

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The coupling between falling mass particles and melt pool is presented in Fig. 8a. The moving laser melts the powder bed and forms a melt pool first. Then, particles with a falling speed of − 10 m/s enters into the molten pool. Some particles are in contact with the melt pool surface and then are ejected away due to the pressure inside the melt pool. There are also some particles fall into the melt pool and then are melted by the molten flow due to heat transfer. Among these particles, some of the large particles cannot be completely melted by the molten pool, and a pore may be formed due to this partial melting after melt pool solidification. These particles which are ejected away from the melt pool have a speed around ~ 10 m/s and will fall elsewhere on the powder bed and leads to local layer thickness variation. In the cross-section measurement, unmelted particles inside the melt pool are also observed as shown in Fig. 8b.

Fig. 8
figure 8

Cross section where mass particles attached to melt region. a Simulation result; b experiment result

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Compared to the experimental measurement on single track deposition under the same laser power and scan speed on bare plate without any particles as shown in Fig. 9. In contrast to the two large pores inside the melt pool as shown in Fig. 8b, the melt pool deposited on the bare plate under the same laser power and scan speed does not have any pores inside. This is a circumstantial evidence to the proposed porosity formation mechanisms that ejected particles fall into the melt pool and are not fully melted.

Fig. 9
figure 9

Cross section of melt pool on bare plate without powder particles

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Figure 10 shows a schematic of melt pool arrangement in two consecutive layers in the L-PBF process to illustrate the likelihood of pore formation due to the above spattering mechanism. Note that there is a shift of 55 μm (half of the hatch spacing) along horizontal direction between these two layers. Suppose that once the first layer deposition is done, there are three melt pools and two pores formed. The pore attached to melt pool bead is indicated by the orange dot while the pore due to falling solid particle entrainment is indicated by the black dot. The pore attached on melt pool bead will be completely removed during the second layer deposition. The blue melt pool on the left side will fully cover this pore, implying that it will likely be melted and eliminated. However, the pore near the melt pool bottom due to solid particle entrainment cannot be re-melted. When depositing the second layer, these melt pools in the middle are not able to re-melt this pore because of the spatial location. This pore will be left inside the part as a permanent defect and may lead to degraded fatigue performance.

Fig. 10
figure 10

Schematic of melt pool overlaps within two layers and pore elimination

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5 Conclusion

In this paper, a modeling approach that couples the mass particle with laser welding process is proposed to study the interaction between spatter particles and melt track and the defect formation mechanism associated with spattering. Multiphysics models were developed and calibrated by ex situ cross-sectional measurements. The major conclusions are presented as follows:

  • A unidirectional coupling model was developed by Flow-3D DEM to simulate the powder particle movement during the deposition process. A moving pressure boundary condition was applied along the melt track to represent the recoil pressure that blows away the neighboring solid particles;

  • Laser welding model that considers the falling spatter particle was developed by Flow-3D to study the interaction between solid spatter particle and the melt track. It was found that depending on the location, these falling particles could be completely melted, partially melted or re-deposited on the neighboring powder bed.

  • Powder particle attachment to melt pool bead is observed in both simulation and single-track deposition experiment. Particles near the melt track may not be completely melted during the deposition process. It was revealed that pores caused by particle attachment can be eliminated by the subsequent layer building;

  • Another pore formation mechanism is the solid particle falls into the melt pool and cannot be completely melted by the molten flow. This pore usually cannot be eliminated by the subsequent layer printing since it locates near the bottom of melt pool.