Multiphysics modeling of particle spattering and induced defect formation mechanism in Inconel 718 laser powder bed fusion

Abstract

Powder particle spattering induced by the metal vapor jetting and vortex flow near the melt pool significantly influences the porosity of final product. In this work, a high-fidelity multiphysics model is developed at powder-scale that unidirectionally couples the powder spattering and laser welding simulation to study the spattering and porosity formation mechanism in laser powder bed fusion process. Vapor pressure from single-track laser welding simulation is applied as a moving boundary condition in a discrete element model to simulate particle spattering. Then, coupling simulation between the mass particles and laser welding is performed to study the interaction between melt pool and spattering particles. Two porosity formation mechanisms are observed in experiments and simulation. The first one is the spattering particles falling into melt pool directly and leaving un-melted or partially melted pores to the final product. The second mechanism is the particles near the melt track that are dragged to the melt pool bead and partially melted due to heat conduction. These partially melted particles can be observed as well in the bead region of depositions.

Appendix

The model for spattering particle re-distribution is developed by the Flow-3D discrete element method (DEM) module. A moving velocity boundary condition is applied to the bottom of power bed along the laser scan track. An upward vertical speed of 150 m/s is applied to model the moving vapor jet that blows up the particle near the melt track and leads to denudation. This moving velocity boundary condition is a poor man’s approach to model the complicated particle ejection and denudation which are caused by the complex interaction between powder particles, metal vapor jet and gas flow near the melt pool. To accurately modeling this phenomenon requires multiphysics models which consider the heat and mass transfer and fluid dynamics inside the melt pool. The scope of this paper is to study the interaction between melt pool and particles falling down which are previously blown up by the vapor jet. This spattering particle re-distribution model aims at finding the speed of falling particles with different size. Therefore, we developed this poor-man’s approach to get the speed for the next step laser welding simulation while saving the computation cost. The unidirectional DEM coupling model, as shown in Fig. 11, is briefly discussed as follows:

• A moving jet hole with a radius of 80 μm is in the middle of the substrate underneath the powder bed generated by powder settling and spreading simulation.

• The moving speed of the jet hole equals to the laser scan speed of 1 m/s.

• The boundary condition for the moving jet hole is a velocity boundary condition and the vertical speed is set as 150 m/s corresponding to the vapor coming out the depression zone.

Fig. 11

Schematic of spattering model developed by discrete element method

Spherical powder particles are used in the DEM model. The governing equations for the translational and rotational motions of individual powder particles are:

$${\mathrm{m}}_{\mathrm{i}}\frac{{\mathrm{d}}^{2}{\mathbf{r}}_{\mathrm{i}}}{{\mathrm{dt}}^{2}}={\mathrm{m}}_{\mathrm{i}}\mathbf{g}+ \sum_{\mathrm{j}}\left({\mathbf{F}}_{\mathrm{n},\mathrm{ij}}+{\mathbf{F}}_{\mathrm{t},\mathrm{ij}}+{\mathbf{F}}_{\mathrm{c},\mathrm{ij}}\right)$$

(5)

$${\mathrm{I}}_{\mathrm{i}}\frac{{\mathrm{d}}^{2}{{\varvec{\uptheta}}}_{\mathrm{i}}}{{\mathrm{dt}}^{2}}=\sum_{\mathrm{j}}{\mathbf{T}}_{\mathrm{ij}}=\sum_{\mathrm{j}}{\mathbf{R}}_{\mathrm{i}}\times {\mathbf{F}}_{\mathrm{t},\mathrm{ij}}$$

(6)

where ${\mathrm{m}}_{\mathrm{i}}$ is the mass of the powder particle, ${\mathbf{r}}_{\mathrm{i}}$ is the position vector, ${{\varvec{\uptheta}}}_{\mathrm{i}}$ is the angular displacement, ${\mathbf{R}}_{\mathrm{i}}$ is the radius of particle. ${\mathrm{I}}_{\mathrm{i}}$ is the moment if inertial, ${\mathbf{F}}_{\mathrm{n},\mathrm{ij}}$ and ${\mathbf{F}}_{\mathrm{t},\mathrm{ij}}$ are the contact force along normal and tangential direction. ${\mathbf{F}}_{\mathrm{c},\mathrm{ij}}$ is the cohesion force. ${\mathbf{T}}_{\mathrm{ij}}$ is the moment caused by particle $j$. Hertz-Mindlin contact model [19] is employed to compute the contact force ${\mathbf{F}}_{\mathrm{n},\mathrm{ij}}$ and ${\mathbf{F}}_{\mathrm{t},\mathrm{ij}}$, while JKR cohesion model [20] is used to compute the cohesion force ${\mathbf{F}}_{\mathrm{c},\mathrm{ij}}$. More details can be found in [21].

In the simulation, the powder bed generated by powder settling and spreading before spattering simulation has a mean layer thickness of 80 μm and is densely packed with a packing density of 53%. The powder particles after the jet hole moving along the center line of the powder bed with a scan speed of 1.0 m/s and flow speed of 150 m/s become scattered and the powder bed becomes spread out. There are a large number of particles coming back to the denudation zone with a transverse (along y direction) or vertical (along z direction) speed which indicates a potential pore formation mechanism due to these particles.