Analytical modeling of 3D temperature distribution in selective laser melting of Ti-6Al-4V considering part boundary conditions

Abstract Selective laser melting (SLM) is widely used in metallic additive manufacturing to create geometrically complex parts, in which temperature distribution directly affects thermal stress and residual stress states of the build. Finite element models were developed by researchers to predict temperature distribution of the build part with a finite volume, but they were computationally expensive. Analytical models were developed based on a semi-infinite medium assumption because a closed-form solution has not been provided to apply the boundary conditions. In this work, an original physics-based analytical model is presented to predict 3D temperature distribution in SLM with consideration of heat transfer boundary conditions so that the effects of build edges and geometries can be considered in the context of a closed-form solution. Heat input from a laser heat source is calculated using point moving heat source solution. Heat loss at part boundaries due to heat conduction, convection, and radiation is calculated by modifying the heat source solution with equivalent power loss and using zero moving velocity. The temperature distribution is obtained based upon linear heat source solution and linear heat loss solution using the superposition principle. Ti-6Al-4 V is chosen to demonstrate the capability of the presented model. Molten pool dimensions are determined by comparing predicted temperatures to material melting temperature, and then validated with documented values in references. Close agreements were observed upon validation. The presented analytical model predicts the 3D temperature distribution in SLM with boundary conditions solved by a closed-form solution for the first time.