Mesoscopic simulation of selective beam melting processes

Modeling of Ti-W Solidification Microstructures Under Additive Manufacturing Conditions

“…The inclusion of temperature-dependent force terms for effects such as capillarity, wetting, or buoyancy allows the coupling of the energy evolution equations into those for fluid. [7,85] Use of the thermal Lattice Boltzmann method with a second set of distribution functions to model the internal energy density has been shown to agree with analytical solutions for natural convection, lid-driven convection in square cavities, and other benchmark fluid dynamics problems. [78,82,85,86] Though the present work is focused on microstructure evolution and not the process-scale melt pool dynamics, we are exploring such a model for consideration of the coupled fluid flow and heat transport problem at the appropriate scale.…”

“…The thermal Lattice Boltzmann method for coupled heat and incompressible fluid flow fields has been used previously to simulate convection problems [29,[82][83][84] and been coupled to cellular automata (CA) to simulate the solidliquid phase change for pure materials. [7,31,32,36,79] If it is assumed that the fluid is incompressible, viscous heat dissipation is negligible, and no work is done by the external pressure, an additional set of distribution functions can be introduced to the model for heat transport. These are analogous to those for solute (the heat is advected as a passive scalar), but include a heat diffusivity, internal energy density, and a heat source term in place of solute diffusivity, concentration, and the solute source term, respectively.…”

“…Heat transport through various modes in solid, liquid, and gas are important in determining the temperature field and molten pool dimensions. [7] Owing to the inherent asymmetry of the beam melting problem (particularly when beam motion is accounted for), there will be a significant location dependence of the thermal gradient and cooling rate; these temperature fields play a large role in initial microstructure formation and thus on the properties of the final part. Much of our detailed understanding of these fields come from applications of the finite element method (FEM), which has been used extensively to model them.…”

“…Another approach has been based on the use of the Lattice Boltzmann method (LB), which is an attractive method for solving this particular fluid transport problem (relative to NavierStokes algorithms) because of its ease of handling complex geometries, [29,30] ease of modeling the changing boundary conditions found in solidification [31,32] and its ability to model coupled fluid, heat, and solute transport problems. [7,31,33] Additionally, the method is computationally efficient and easily parallelized. [34,35] Ko¨rner et al [7,36] used a thermal Lattice Boltzmann model for the combined heat transport, fluid flow, and phase change problem, for Ti-6Al-4V in a powder bed-based AM process.…”

“…[7,31,33] Additionally, the method is computationally efficient and easily parallelized. [34,35] Ko¨rner et al [7,36] used a thermal Lattice Boltzmann model for the combined heat transport, fluid flow, and phase change problem, for Ti-6Al-4V in a powder bed-based AM process.…”