A modified cellular automation model with hybrid simulated annealing and particle swarm optimization procedure for evaluation of the dendritic nucleation and growth during alloys solidification.

摘要

The new 2D algorithm was developed to further accelerate alloys development. A modified cellular automation (CA) model is used to simulate and evaluate competitive dendritic structure evolution and growth during solidification. Classical CA model considers only temperature field. Presented algorithm taking into account solutal, thermal, curvature, kinetic, and pressure undercooling. It allows to evaluate micro-structure development in wider solidification ranges, which will cover fast solidification of the alloy during laser welding, thin wall high pressure structural die casting, and relatively slow solidifying sand castings. Nucleation sites and preferred grain growth orientation are randomly selected when metal reaches an appropriate undercooling temperature. Neighboring computational cells are evaluated in order to determine the best condition for a grain nucleation using swarm optimization approach with the simulated annealing procedure. It improves the accuracy of the traditional probabilistic Monte Carlo approach to a nucleation problem. Implementation of the heuristic algorithms with dynamically adjusted inertia weight parameter was implemented to allow both exploration and exploitation of the computational domain. The position of the newly nucleated grain was adjusted based on a finding of a Pareto optimal solution. Dendrite growth velocity was evaluated based on the KGT (Kurz-Giovanola-Trivedi) model. Finite volume model was coupled with CA model and used to evaluate temperature and solute distribution field in the computational domain. Gaussian distribution model was used in the presented algorithm and covers mold-liquid metal interface, transition zone, and solidification in a bulk metal. The model was coupled with the commercial software FL0W3D®. It allowed increasing the accuracy of the results by including temperature evaluation during the entire manufacturing process, such as; melting during laser welding, or metal flow and solidification during casting processes. Results of the grain size and distribution obtain from modified CA-SA_PSO model was compared with the once obtained experimentally. Numerical results are found to be in good agreement with the experiment.