# Roles of Modeling and Artificial Intelligence in LPBF Metal Print Defect Detection: Critical Review
## 3 Advances in Numerical Modeling Techniques for LPBF Defect Detection
### Melt Pool Defect Modeling
#### 3.1.1 Thermo-Mechanical Simulations of LPBF Defects Using FEM
The stress formation was attributed to the cooled material inhibiting the thermal expansion of the previously scanned track. Compressive stress in the neighboring region was generated by the thermal expansion occurring in the area surrounding the melt pool. A numerical model that implemented non-equilibrium equations for phase formation, microstructure evolution, and the dissolution of Ti6 Al4V in SLM using ABAQUS [33] was developed. The results of the validated model support the idea that sharper thermalgradients will indicatively lead to more residual stresses. An FE framework for numerically simulating the heat transfer process in the LPBF of Ti6 Al4V using COMET was created [34]. According to the results, the heat dissipation rate through the powder bed and the definition of the power input were identified as the most sensitive mechanisms to assess the simulation accuracy. A continuous-mesoscale level set model of the LPBF process to evaluate the Ti6 Al4V melt pool and track development during building was developed using an in-house FEM code [35]. The pressure force formed as a result of metallic vaporization causes the molten liquid surface to become inwardly concave, allowing the laser beam to go deeper. A capillary digging phenomenon was observed for the Ti6 Al4V, which led to keyhole pores in the solidified melt pool. An FE model was tested to understand the dynamic behavior and stability at keyhole thresholds of Ti6 Al4V during LPBF printing using COMSOL [36]. It was observed that a complex interaction between molten liquid hydrodynamics and ray optics characterizes the development of pores. The action of the melt pool pressure determines the depth and energy balance of the melt pool shape. An evident correlation exists between the keyhole depth and the melt pool absorptivity. An investigation was performed to understand the temperature contour plots of LPBF-printed Ti6 Al4V (Amnovis, Aarschot, Belgium) powder using ANSYS, showing that the maximum temperature on each node throughout the entire build time can help predict the melt pool shape and, hence, the quality of the part [37]. Another study analyzed the residual stress formation occurring during two scanning strategies (alternating and unidirectional) of LPBF printing of Ti6 Al4V using AdhoC++ [38]. The alternating scan strategy reduced the residual stresses at the end of the scan vectors. A numerical study that implemented a 2D model by a phase field using FEM for Ti6 Al4V using COMSOL was reported [39]. The results of the simulation showed that liquidity can strangely alter the surface wettability of the unmelted particles and enhance gas to release and form bubbles inside the pool. Also, porosity can be effectively eliminated during the remelting process to allow the parts to self-clean impurities. A profound balling phenomenon was noticed for low levels of laser beam energy and speed. LOF defects were investigated by simulating melt pool behavior using ABAQUS [40]. The influence of deposited thickness was reported to affect the profile of the liquid pool extensively, and an analytical solution cannot represent this influence. A thermal model was developed to simulate the LPBF process of Ti6 Al4V using COMSOL [41], capable of predicting the thickness of the molten pool by relating absorbed energy through the laser level of energy and beam velocity and using a multiplication coefficient to calculate the depth of energy stored by the part. The mixing and associated convective transport effect within the melt pool were seen. A study numerically assessed the impact of scan lengths on the thermal, microstructural, and mechanical behaviors of  
Figure 4: Snapshots of almost-solidified 4-track-layer thermo-mechanical FEM simulation of the LPBF melt pool showing detected LOF pores in (**a**) the top view (top) and transversal direction (bottom); and (**b**) the longitudinal direction [35]. the LPBF process of Ti6 Al4V using ABAQUS [42]. It was revealed that shortening the scan lengths can result in a more rapid cooling rate.