This article was contributed by Y.S. Lee 1,2 and W. Zhang 1
1 Welding Engineering Program, Department of Materials Science and Engineering, The Ohio State University, Columbus, OH
2 Currently, Oak Ridge National Laboratory, Oak Ridge, TN
Heat transfer and fluid flow modeling
Laser-powder bed fusion (L-PBF) additive manufacturing involves complex physical processes. Particularly, the absorbed laser beam energy melts the particles and forms a molten pool where a strong fluid flow occurs driven primarily by surface tension gradient (or Marangoni shear stress). The heat transfer and fluid flow are significantly affected by local arrangement of powder particles in the powder bed that can vary from location to location. Because of the highly transient fluid flow, the shape of the molten pool surface (a free surface) is constantly evolving, affecting the final surface quality.
Numerical modeling approach
To quantitatively understand the effect of powder packing characteristics, process parameters, and molten pool dynamics on the surface quality, the present study uses two models in sequence. The first model is a powder particle packing model developed based on Yade, an open source discrete element method (DEM) code. It provides the particle stack-up information (e.g., locations and radii of individual particles). Such information is then input into the second model, a 3D transient molten pool model based on FLOW-3D. Details of the two models are available in the literature . Salient features of the molten pool model based on FLOW-3D are summarized below.
The transient fluid flow simulation is performed in a 3D computational domain with dimensions of 1000 μm (length), 270 μm (width) and 190 μm (height), as shown in Fig. 1. The domain comprises a 50-μm-thick layer of powder particles laid on a 90-μm-thick substrate. The reminder of the domain is initially filled with void. The powder layer geometry is initialized using the results from the DEM simulation. To maximize spatial resolution while reducing the total number of cells, biased meshing is utilized where the mesh size reduces continuously from 9 μm to 3 μm in the substrate toward the substrate/powder layer interface. The mesh size is kept constant 3 μm in the powder layer and the void above it. The total number of cells is 1.43 million.
For boundary conditions, a prescribed heat flux based on Gaussian distribution is imposed on the top surface of the powder layer to represent the heat input from laser which is moving along the X-direction. The temperature dependent surface tension is included using the improved surface tension model available in FLOW-3D. For other thermo-physical properties, the data for IN718 alloy available in the FLOW-3D database is used.
The transient simulation of about 600-microseconds-long L-PBF takes approximately 40 hours clock time to finish in a moderately powerful workstation with Intel® Xeon® Processor E5335 and 4 GB RAM.
Result and discussion
Figure 2 plots the longitudinal section view (i.e., a section parallel to the laser travel direction) of temperature isosurface and velocity vectors in the molten pool at time = 55 μs. The molten pool boundary is represented by the isotherm at 1608.15 K, which is the liquidus temperature of IN718. As shown to the right side of this figure, a particle is partially melted into the molten pool. Near the molten pool surface, the molten metal is pulled from the center location directly underneath the laser beam to the rear end of the pool. Such backward flow of molten metal near the pool surface produces a surface profile that is depressed underneath the laser beam while it forms a hump toward the rear end of the pool. As discussed in the following, the humped shape can lead to the formation of balling defect.
Balling is a defect that can occur when the molten pool becomes discontinuous and breaks into separated islands, as illustrated in Fig. 3. As shown in this figure, the molten pool directly underneath the laser beam is not stable and the rear end quickly breaks apart from the front to form a separate island. The separation initiates from a void in the middle of the molten pool, as shown in Fig. 3(c). This void expands as the laser continues to travel forward, eventually breaking the molten pool into two parts, as shown in Figs. 3(e) and (f). The formation of void and its expansion are likely caused by the strong backward flow driven by the surface tension gradient (Marangoni effect).
The 3D transient simulation of heat transfer and fluid flow in L-PBF is conducted to provide a quantitative understanding the formation of balling defect. Although only a simple linear track is simulated, the present model shows the importance of powder level simulation in studying the molten pool surface profile and formation of balling defect, which are important attributes of the final build quality.
This material is based upon research supported by, or in part by, the U. S. Office of Naval Research (ONR) under award number N00014-14-1-0688.
 Y.S. Lee and W. Zhang, Mesoscopic Simulation of Heat Transfer and Fluid Flow in Laser Powder Bed Additive Manufacturing, In: 2015 Annual International Solid Freeform Fabrication Symposium, Austin, TX, pp. 1154-1165, August 2015.