Analytical model of predicting residual stress-process parameter relationship for laser powder bed fusion of Ti6Al4V

An analytical model based on the Rosenthal equation and thermoelastic potential function was established to investigate the mechanism of the residual stress in Ti6Al4V fabricated by laser powder bed fusion (LPBF). Unlike other analytical models that neglected the effect of the process parameters, this analytical model provided a clear physical interpretation of residual stress in relation to process parameters while also considering material properties. The model revealed that the effect of process parameters on residual stress at a specific point is determined by two mechanisms. Firstly, the temperature gradient change rate around the laser center increases as input energy rises, leading to an increase in stress. Secondly, with the increase of the input energy, the distance from the laser center when the temperature drops to 850 °C also increases, leading to a decrease in the temperature gradient change rate and thus a reduction in stress. When the former mechanism dominates, the residual stress rises with input laser energy increasing. Conversely, when the latter mechanism prevails, the residual stress decreases with input laser energy increasing. As a result of the two mechanisms competing, the residual stress fluctuates while the process parameters vary across different ranges. Based on the analytical model calculations, large input energy is more beneficial for achieving low residual stress levels. The developed model can reveal the mechanism behind residual stress variation and predict the relationship between the residual stress and process parameters for the LPBF process.