Analytical modeling of post-printing grain size in metal additive manufacturing

Abstract

Metal additive manufacturing technology not only has advantages on geometry complicated components small batch production, but also has the ability to produce the components with specific requirements in properties. However, the properties of the components mainly depend on its microstructure, such as grain size. In this paper, an analytical model for post-printing grain size prediction in metal additive manufacturing is presented. First, the solution of a moving point heat source for the convection-diffusion equation, which is utilized to describe the thermal equilibrium during the additive manufacturing process, is deduced to calculate the temperature distribution in the build part. The thermal stresses due to non-uniform temperature distribution are predicted by the Green's function. Second, the grain size of the build part is obtained from nucleation and growth rate during the additive manufacturing process. The grain growth due to heating is established based on the recrystallized volume fraction of the material during the heating process, which is estimated through Johnson-Mehl-Avrami-Kolmogorov (JMAK) model. Subsequently, the grain refinement due to cooling during additive manufacturing process is established based upon the transformation kinetics, which is predicted by the negative exponential equation. Finally, the proposed model is verified by the literature data of selective laser melting of Ti-45Al-2Cr-5Nb alloy experiment. The predicted temperature distributions in the build parts under different conditions are analyzed. Comparison results show that the predictions are in good agreement with the experimental data under various conditions of laser power 200 W, scan speeds 500 mm/s, 600 mm/s, 700 mm/s, and 800 mm/s. Based on the proposed model, the sensitivity analysis of grain size of the build part with respect to laser power and scan speed is discussed. Results indicate that the temperature at top surface of the build part is not affected by the scan speed, while both the affected zone and peak value of the temperature beneath the surface of the build part increase with the increase of the laser power. The average grain size decreases with the increase of the laser power, while the average grain size decreases with the increase of the scan speed and then increases due to the incomplete melting effect.