and solidification, including rapid changes in heat flux and temperature [1, 4] that affect the final mechanical properties of the part as well as its quality and shape. The processes of formation and production in FDM involve all mechanics of heat transfer: radiation, convention, and conduction. Radiation plays a significant role at the high temperature regions, specifically during the first phases of material deposition and forming. In addition, a highly concentrated heat source that initiates melt pool formation where energy transport by convection in the fluid region may be dominant [8–10]. From the heat transfer perspective, properly modeling conduction, radiation, and convection for temperature dependent material property and boundary conditions is rather complex. To realize the modeling of FDM, radiation, transient conditions, as well as natural/force convection need to be incorporated together with moving boundaries and conditions. 6.2 Methodology Because of the complex multiphysics involved in FDM and the need for reliable simulations, we are developing 3D thermal models to study FDM by combining modeling and experimentation. Our efforts to model FDM in 3D begins by first considering a 1D thermal problem. In this case, a cylindrical domain of finite radius is selected where material is incrementally deposited layer-by-layer in one dimension along the vertical direction. The radius of the domain is selected such as the ratio of convection and conduction effects, i.e., Biot number, satisfies lumped model conditions. Fig. 6.1 Representative image of additive manufacturing by layer deposition that includes multiscale and multiphysics investigations [4, 6] Fig. 6.2 Schematic of layerby-layer deposition by FDM (1-Extruder, 2-deposited layers, 3-Platform) [7]. Deposition takes place in three orthogonal directions 46 K. Pooladvand and C. Furlong
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