A physics-based analytical model is proposed in order to predict the temperature profile during metal additive manufacturing (AM) processes, by considering the effects of temperature history in each layer, temperature-sensitivity of material properties and latent heat. The moving heat source analysis is used in order to predict the temperature distribution inside a semi-infinite solid material. The laser thermal energy deposited into a control volume is absorbed by the material thermodynamic latent heat and conducted through the contacting solid boundaries. The analytical model takes in to account the typical multi-layer aspect of additive manufacturing processes for the first time. The modeling of the problem involving multiple layers is of great importance because the thermal interactions of successive layers affect the temperature gradients, which govern the heat transfer and thermal stress development mechanisms. The temperature profile is calculated for isotropic and homogeneous material. The proposed model can be used to predict the temperature in laser-based metal additive manufacturing configurations of either direct metal deposition or selective laser melting. A numerical analysis is also conducted to simulate the temperature profile in metal AM. These two models are compared with experimental results. The proposed model also well captured the melt pool geometry as it is compared to experimental values. In order to emphasize the importance of solving the problem considering multiple layers, the peak temperature considering the layer addition and peak temperature not considering the layer addition are compared. The results show that considering the layer addition aspect of metal additive manufacturing can help to better predict the surface temperature and melt pool geometry. An analysis is conducted to show the importance of considering the temperature sensitivity of material properties in predicting temperature. A comparison of the computational time is also provided for analytical and numerical modeling. Based on the obtained results, it appears that the proposed analytical method provides an effective and accurate method to predict the temperature in metal AM.

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.

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