Using rheology experiments to predict the spreading of extruded beads undergoing transient solidification for material extrusion additive manufacturing

A successful Material Extrusion (MEX) ink must solidify soon after being deposited to (i) retain the bead’s as-deposited shape, (ii) to enable patterning of high-resolution features, and (iii) enable printing of subsequent layers. Currently, no analytical models exist that predict the time-dependent spreading of inks undergoing transient solidification. As a result, the development of new inks and selection of printing parameters requires time-consuming “trial and error” printing to select an ink formulation and process parameters that produce an acceptable amount of spreading. In this paper, an analytical model that uses experimental rheology data to predict the time-dependent spreading of an ink is presented. Importantly, this model accounts for inks undergoing transient solidification, such as the resolidification of yield-stress inks and photocuring of photopolymer inks. Accurate predictions of time-dependent spreading ultimately enable evaluation of an ink’s suitability for MEX printing and informs the selection of process parameters. The developed model considers the capillary and gravitational forces contributing to bead spreading and the viscous force opposing bead spreading. Summing the forces acting on the bead yields a first order differential equation that is solved numerically for bead profile over time. Further, an algorithm is presented to continuously update the governing differential equation with the measured transient rheological properties of the ink to make predictions of an ink undergoing transient solidification. This algorithm enables understanding of how different curing conditions, process parameters, and ink formulations affect spreading, ultimately informing the optimal parameters for successful MEX printing. To validate this model, we demonstrate its ability to accurately predict spreading of two photocurable inks and a yield-stress ink. Close agreement was observed between the predicted model and experimental data for the 10:1 photocurable ink ( R 2 = 0.82 ), the 1:1 photocurable ink ( R 2 = 0.92 ), and the silicone ink ( R 2 = 0.99 ). Additionally, we demonstrate how the model predicts spreading for different UV processing conditions, including varying the time between deposition and UV exposure and varying UV irradiance.