Effect of mushy zone constant in Voller-Prakash model on keyholing behaviour in laser powder bed fusion simulation

Abstract

This paper is a study of the model constant of the Voller-Prakash model: the mushy zone constant (C), which determines the flow resistance in the mushy zone during metal solidification. A drag force-liquid fraction relation was derived, assuming that the dynamic and static pressures were equal. The C values for the three morphologies were estimated by analytically calculating the morphological parameters of the Kozeny-Carman equation, which was the basis of the Voller-Prakash model. As a result, much smaller values of C were obtained compared to the commonly used range of C>105. This was due to the drag force model included a parameter related to the grid size of the simulation. Based on previous studies of the scale of the dendrite structure and the grid size widely used in simulations, we concluded that the rectangular morphology was reasonable. To evaluate the effect of C value on keyholing behaviour, a series of the multiphysics CFD simulations was performed varying C, including the C for rectangular morphology and the commonly-used C from past studies. The flow resistance force in the mushy zone increased with larger C values, resulting in significant restriction of pore displacement. Consequently, pores formed with smaller C values were immobilised farther away from the laser position. For larger values of C, the flow resistance force had a significant effect, causing the mushy zone to behave like a solid. The pores that formed were trapped by the solid-like mushy zone before they could reach a stable shape and size.

Keywords

• Laser powder bed fusion
• Mushy zone flow resistance
• Voller-Prakash model
• Multiphysics CFD simulation
• Keyhole pore formation