Heat Source Modeling in Selective Laser Melting

Abstract

Selective laser melting (SLM) is an emerging additive manufacturing (AM) technology for metals. Intricate three-dimensional parts can be generated from the powder bed by selectively melting the desired location of the powders. The process is repeated for each layer until the part is built. The necessary heat is provided by a laser. Temperature magnitude and history during SLM directly determine the molten pool dimensions, thermal stress, residual stress, balling effect, and dimensional accuracy. Laser-matter interaction is a crucial physical phenomenon in the SLM process. In this paper, five different heat source models are introduced to predict the three-dimensional temperature field analytically. These models are known as steady state moving point heat source, transient moving point heat source, semi-elliptical moving heat source, double elliptical moving heat source, and uniform moving heat source. The analytical temperature model for all of the heat source models is solved using three-dimensional differential equations of heat conduction with different approaches. The steady state and transient moving heat source are solved using a separation of variables approach. However, the rest of the models are solved by employing Green’s functions. Due to the high temperature in the presence of the laser, the temperature gradient is usually high which has a substantial impact on thermal material properties. Consequently, the temperature field is predicted by considering the temperature sensitivity thermal material properties. Moreover, due to the repeated heating and cooling, the part usually undergoes several melting and solidification cycles, and this physical phenomenon is considered by modifying the heat capacity using latent heat of melting. Furthermore, the multi-layer aspect of the metal AM process is considered by incorporating the temperature history from the previous layer since the interaction of the layers have an impact on heat transfer mechanisms. The proposed temperature field models based on different heat source approaches are validated using experimental measurement of melt pool geometry from independent experimentations. A detailed explanation of the comparison of models is also provided. Moreover, the effect of process parameters on the balling effect is also discussed.

Analytical Modeling of Residual Stress in Laser Powder Bed Fusion Considering Part’s Boundary Condition

“…where P is the laser power, α represents absorption coefficient, K is the thermal conductivity, R = x 2 + y 2 + z 2 is the radial distance from heat source, V is the laser speed, D = K ρC is the thermal diffusivity, ρ is the density, C is the specific heat, A is the area of the heat sink, h is convection coefficient, ε is the emissivity, σ is the Stefan-Boltzmann constant, n is the number of heat sinks, i is the index of each heat sink, and T 0 is the initial temperature. More explanation about the heat source solution can be obtained from the previous work of the authors [20][21][22][23]. strength of the part.…”

Analytical Modeling of Residual Stress in Laser Powder Bed Fusion

“…where is the laser power, represents absorption coefficient, is the thermal conductivity, = √ 2 + 2 + 2 is the radial distance from heat source, is the laser speed, = is the thermal diffusivity, is density, is the specific heat, is the area of the heat sink, ℎ is convection coefficient, is emissivity, is Stefan-Boltzmann constant, is the number of heat sinks, is the index of each heat sink, and 0 is the initial temperature. More explanation about the heat source solution can be obtained from the previous work of these authors in [22][23][24][25].…”

Heat Conduction Simulation of 2D Moving Heat Source Problems Using a Moving Mesh Method

“…The most important physical quantity of interest for such practical applications is the temperature field of the medium, which is usually modeled by the heat conduction equation with time-dependent localized source terms for moving heat sources. Once the temperature field is obtained, many other thermophysical properties of material, including metallurgical microstructures, thermal stress, residual stress, and part distortion, could be subsequently determined [6][7][8][9][10]. It is therefore particularly important to precisely and efficiently predict the dynamic variation of the temperature field around the moving heat sources during these engineering processes.…”