Analytical prediction of keyhole porosity in laser powder bed fusion

Porosity is a common process-induced defect in laser powder bed fusion (LPBF) metal additive manufacturing, which will have detrimental effects on the mechanical performance of the fabricated products. In this study, an analytical modeling method with closed-form solutions is developed for the prediction of keyhole-induced porosity in LPBF. A two-dimensional model which considers the keyhole pores formation and trapping is employed to calculate the keyhole porosity, with the molten pool geometries, average pore size, velocity of melt flow, and frequency of pore formation as inputs. An analytical temperature prediction model is used to compute the temperature distribution in LPBF. The molten pool shapes and dimensions are determined by comparing the predicted temperature profiles with melting temperature. The relationship between average pore size and laser power energy density is obtained by regression analysis. The velocity of melt flow and frequency of keyhole pore formation are adapted from the literature. To validate the model, the predictions of keyhole porosity under various process conditions are compared with experimental measurements of Ti6Al4V in LPBF. The predicted results are in good agreement with experimental data, which demonstrates the acceptable predictive accuracy of the proposed model. Also, the analytical modeling method does not include any iteration-based numerical calculations, which makes it computationally efficient. Thus, the proposed model can be an acceptable tool for the fast prediction of keyhole porosity and can also help the researchers understand the physics behind the formation of part porosity.