Towards the Integration of Phase Change Behavior in Topology Optimization Problems - Bi-material mold optimization for improved solidification front propagation using FEniCS

Abstract

Phase change processes between liquid and solid are widely used in industry for the mass production of parts using molds. Casting and injection molding allow for geometrically complex parts to be produced at scale for metals and plastics respectively. Due to the inherent physics at play during solidification, defects tend to occur at the last place to change phase, causing solidification shrinkage and porosity. Currently proposed techniques to deal with improper solidification front propagation and shrinkage inside the mold are based on the addition of material to guide the front, which leads to added weight and decreased performance. Current efforts in casting related topology optimization integrate casting constraints and proper front propagation by modifying the shape of the part. This master’s thesis studies the topology optimization of a multi material mold solution for which the part is left unmodified. Instead, the distribution of the material inside the mold is optimized in order to passively control the front propagation through the use of materials with different heat conductivity. Heat transfer inside the mold is modeled as an unsteady heat diffusion using the finite element method. The temperature distribution is solved at each time step using the Python interface of FEniCS. The latent heat of fusion of the molten material is modeled using the apparent heat capacity method. The material properties of the two mold materials are chosen with either high or low conductivity. The distribution is optimized using GCMMA, the gradients are computed automatically using the adjoint method with the dolfin adjoint package in order to compute the sensitivity analysis. Two molds are optimized using different initial sequences, with an improved front propagation by up to 42%, and an imposed location of last solidification improved by up to 87%.