**4. Multiscale modeling technique**

As mentioned earlier, spattering mechanism is difficult to model using traditional simulation approach due to its multi-phase nature and complexity in physics. This applies to the overall additive manufacturing or metal printing process as well. Molecular Dynamics (MD) can be an option in this area, considering only the atomic motion without any other information such as thermal conductivity or specific heat of the material. But, due to its nanoscopic nature, available computational capacity of today falls way behind the complexity of any feasible MD model. Some experimental techniques can be used as demonstrate in [43] to understand he metallurgical defects in PBF parts. But investigate generation of defects due to the process itself is significantly difficult. Computational Fluid Dynamics (CFD) modeling can be applied to simulate sintering process involved in L-PBF, as this can demonstrate the molten pool dynamics. But the fact that solid metal powders can only be stationary in CFD models, can limit the scope of complete simulation of AM process to understand the process-structure– property relationships. On the other hand, a simple meso-scale simulation using finite

element analysis can help to correlate the build part defects (such as, deformation, buckling, holes, staircase effect etc.) with AM process parameters. This in turn initiates the idea of a multi-scale modeling scheme for overall understanding of the AM process.

A CFD modeling tool can correlate the process parameters (laser power, scanner speed etc.) to the defect generation mode or phenomenon (e.g., keyhole and spattering). Finite element simulation can predict temperature distribution over each layer with appropriate beam size and diameter, using material properties of the metal powder and subsequent build. The complexity of simulation depends on the available physics on the modeling scheme. However, these computational studies and any other experimental observations are not sufficient enough to create a comprehensive design and optimization method. To obtain a generalized process parameter optimization technique, a surrogate model is desirable to alleviate the overbearing requirements of frequent experiments/ simulations.

An alternative solution of this impasse is application of machine learning (ML) model. A supervised machine learning algorithm would be able to create an artificial neural network intelligent enough to predict the defect generation and hence recommend suitable combination of process parameters to generate flawless/ near- flawless printed parts. But performance of such algorithm depends on a well training program with appropriate input–output data. This data would come from numerical simulation and/or experimental testing. The multiscale modeling with different level of simulation will add to the experimental data that can be obtained in a real-time laser powder bed setting.

This multiscale modeling work is divided into three major steps:


#### **4.1 CFD analysis**

A commercially available CFD software named *FLOW-3D* specializing in 3D transient flows with free surfaces is used in this study. It follows Volume of Fluid (VoF) method and TruVOF algorithm. The physics behind general welding and laser melting in PBF is similar, hence it is used in the CFD modeling scheme. Key factors involved here are laser beam motion, shield gas pressure, laser heat flux profile distribution, evaporation pressure and multiple laser reflections.

With the input of material properties of metal powder, powder size, bed size, the first step of the simulation is powder bed preparation. After the bed spreading is simulated, we can input the process parameters such as laser power, beam diameter etc. for the designed geometry and it will subsequently complete the laser melting simulation. **Figure 3** the laser melting of metal and subsequent melt pool formation with temperature distribution [44]. Keyhole-induced porosity formation is observed in **Figure 4** [45].

Understanding the evolution of melt pool depending on varying process parameters can provide information on temperature distribution and porosity formation as shown in **Figure 5** [44]. This is a crucial information for the multiscale-surrogate model. Rise in recoil pressure at the bottom of keyhole and increased surface tension *Multiscale Modeling Framework for Defect Generation in Metal Powder Bed Fusion Process… DOI: http://dx.doi.org/10.5772/intechopen.104493*

#### **Figure 3.** *Laser keyhole welding modeling using CFD.*

### **Figure 4.**

*Keyhole induced porosity formation in L-PBF process.*

at the upper region generates an irregular pore. The pore is then pushed to the back of melt pool by string downward flow and then it gets trapped by the advancing solidification front. Using this aforementioned CFD model, we can accurately represent the fluid flow at the melt pool at 1–10 μm length scale [44]. It also demonstrates defective design space and melt pool geometries, predicts compositional segregation and phase nucleation and growth.
