# Multi-Resolution SPH Simulation of a Laser Powder Bed Fusion Additive Manufacturing Process
## 1 Introduction  
Laser Powder Bed Fusion (LPBF), also known as Laser Beam Melting (LBM), is an Additive Manufacturing (AM) technique used for fabricating metallic parts with complex shapes. LPBF falls into the Powder Bed Fusion (PBF) category, where a small focus spot laser is employed to melt and fuse metallic powders. Recently, LPBF-fabricated parts can feature an almost full density (>99.5%) with mechanical properties comparable to conventionally manufactured metals, according to several review papers published within the last decade, e.g., [1, 2]. More indicatively, [PERSON] et al. [3] claimed in 2016 that densities greater than 99.9% referred to the pure metal can be obtained through optimized PBF processes. The LPBF technology is being used in a wide range of industry applications, most notably in the aerospace [4, 5] and medical [6, 7] domains. Parallel to this rapid growth of AM in industry, understanding the interplay between process parameters and part properties is necessary to design and operate LPBF processes. Modeling and simulation of the LPBF process can help explain the experimental observations and optimize the PBF fabrication systems. An LPBF process is inherently a multi-scale problem that involves a variety of complex phenomena such as laser-powder interactions, material phase transitions, and violent free-surface flows. Figure 1 illustrates some physical challenges of LPBF at the powder scale. In an early effort to simulate this thermally driven process, [PERSON] and [PERSON] [8] used the Finite Element Method (FEM) in a thermo-mechanically coupled analysis to study the heat impact on residual stresses and structural deformations of T-bar cantilever specimens after multiple tracks. The numerical approach they undertook, however, was based on a homogeneous powder-bed model with several simplifications such as modeling a 20\(\times\)thicker powder layer to reduce the required simulation time. [PERSON] et al. [9] addressed this issue by introducing a 2D fine-scale model of the selective beam melting process using a Lattice-Boltzmann approach. They found good agreement with experimental data and predicted the melting behavior as a function of process parameters like the scan speed and powder properties. While the physical model incorporated into [9] was fairly advanced, some crucial phenomena like the Marangoni effect and recoil pressure were still lacking. Many research studies have repeatedly confirmed that these effects play a key role in the melt pool dynamics (e.g., see in [2; 10]). In an extension to the work of [PERSON] et al. [9], [PERSON] and his colleagues [11] followed a similar approach and generalized the analysis of melting and re-solidification of powder to 3D space for the first time. The numerical results suffer from low resolution, and their model does not account for some governing physical phenomena such as surface heat loss and thermo-capillary effects either. In 2014, a particularly robust numerical simulation of LPBF was developed by [PERSON] and [PERSON] [12]. The authors made use of a massively parallel code to simulate a single-track LPBF process in 3D using a hybrid finite element and finite volume formulation, through which they modeled a fully resolved particle bed geometry. This hybrid FEM-FVM approach, however, relies on a crude surface tension model, neglecting the effects of wetting, thermal gradients, and so on. The importance of surface tension effects in melt pool dynamics was highlighted in this paper, concluding that these effects are, in fact, the driving forces in the LPBF process. In another attempt to obtain more efficiency, [PERSON] and [PERSON] [13] used the Volume of Fluid method (VOF) method with a mesh size of 3 \(\upmu\)m and examined the influence of process parameters on the bed geometry and formation of balling defects. No experimental validation of the LPBF simulation is performed in this work, however.