Modeling, analysis, and simulation for aqueous-based ceramic pastes in freeze-form extrusion fabrication process

During the freeze-form extrusion fabrication process, both the extrusion and freezing processes are complex due to the aqueous-based ceramic pastes' non-Newtonian behavior, large latent heat of the water contained in the paste, and the small temperature difference between the ambient and the paste. In this study, the steady-state relationship between plunger velocity and extrusion force is developed based on a modified Herschel-Bulkley viscosity model and the Navier-Stokes equations, and the dynamic response of the extrusion force is described by a first-order nonlinear equation when plunger velocity is taken as an input. It is shown that the extrusion response time depends on the amount of air inside the extruder and the magnitude of the extrusion force. Air bubble release and pre-loading are then analyzed based on the developed constitutive model. The freezing process is modeled by a simplified one-dimensional heat transfer model and a lumped method. As the layer number increases, the paste freezing time increases and finally reaches a steady state. A non-dimensional analytical solution for the freezing time of parts with large numbers of layers was obtained using the lumped method. The effects of both non-dimensional and dimensional factors on the critical freezing time were studied. The critical freezing time is the time when the steady-state freezing time equals the total time between layers, which is the sum of the deposition time for the current layer and the dwell time between the current and next layers. A series of simulations and experiments were conducted to validate the predictive capabilities of the constitutive model for the extrusion force and the critical freezing time for parts with large numbers of layers. Good agreements between the simulation and experimental results were obtained.