A reaction–diffusion model for grayscale digital light processing 3D printing

Abstract

Digital light processing (DLP) 3D printing is an additive manufacturing process that utilizes light patterns to photopolymerize a liquid resin into a solid. Due to the accuracy of modern digital micromirror devices (DMD) and recent advances in resin chemistry, it is now possible to create functionally graded structures using different light intensity values, also known as grayscale DLP (g-DLP). Different intensities of light lead to differences in the polymer crosslinking density after curing, which ultimately produces a part with gradients of material properties. However, g-DLP is a complicated process. First, the DLP printing is a highly coupled chemical and physical process that involves light propagation, chemical reactions, species diffusion, heat transfer, volume shrinkage, and changes in mechanical behaviors of the curing resin. Second, in g-DLP, light gradients create strong in plane gradients of chemical species concentrations in the curing liquid resin due to the strong dependence of light intensity on the rate of monomer crosslinking. Furthermore, light gradients through the depth create concentration gradients due to the degree of cure dependent light absorption and the use of photoabsorbers. These complex physical features of the printing process must be understood in order to properly control printing parameters such as light exposure time, printing speed, and grayscale variations to achieve accurate mechanical properties. In this paper, a photopolymerization reaction–diffusion model is developed and used in conjunction with experiments to investigate the coupled effects of light propagation, chemical reaction rates, and species diffusion during g-DLP 3D printing. The model is implemented numerically utilizing the finite difference method and simulation results are compared to experimental findings of simple printed structures. The agreement between experimental and model predictions of simple quantities of interest, such as geometric feature sizes, shows that the model can capture the overcure due to free-radical and other species diffusion during printing when grayscale patterns are employed. This model lays the groundwork for future extensions that can incorporate more complex coupled physics such as heat transfer, volume shrinkage, and material property evolution, which are critically important in utilizing g-DLP 3D printing for the fabrication of high-performance parts which excellent geometric and material property tolerances.