Numerical simulations of die casting with uncertainty quantification and optimization using neural networks

Die casting is one type of metal casting in which liquid metal is solidified in a reusable die. In such a complex process, measuring and controlling the process parameters is difficult. Conventional deterministic simulations are insufficient to completely estimate the effect of stochastic variation in the process parameters on product quality. In this research, a framework to simulate the effect of stochastic variation together with verification, validation, uncertainty quantification and design optimization is proposed. This framework includes high-speed numerical simulations of solidification, micro-structure and mechanical properties prediction models along with experimental inputs for calibration and validation. In order to have a better prediction of product quality, both experimental data and stochastic variations in process parameters with numerical modeling are employed. This enhances the utility of traditional numerical simulations used in die casting. OpenCast, a novel and comprehensive computational framework to simulate solidification problems in materials processing is developed. Heat transfer, solidification and fluid flow due to natural convection are modeled. Empirical relations are used to estimate the microstructure parameters and mechanical properties. The fractional step algorithm is modified to deal with the numerical aspects of solidification by suitably altering the coefficients in the discretized equation to simulate selectively only in the liquid and mushy zones. This brings significant computational speed up as the simulation proceeds. Complex domains are represented by unstructured hexahedral elements. The algebraic multigrid method, blended with a Krylov subspace solver is used to accelerate convergence. Multiple case studies are presented by coupling surrogate models such as polynomial chaos expansion (PCE) and neural network with OpenCast for uncertainty quantification and optimization. The effects of stochasticity in the alloy composition, boundary and initial conditions on the product quality of die casting are analyzed using PCE. Further, a high dimensional stochastic analysis of the natural convection problem is presented to model uncertainty in the material properties and boundary conditions using neural networks. In die casting, heat extraction from molten metal is achieved by cooling lines in the die which impose nonuniform boundary temperatures on the mold wall. This boundary condition along with the initial molten metal temperature affect the product quality quantified in terms of micro-structure parameters and yield strength. Thus, a multi-objective optimization problem is solved to demonstrate a procedure for improvement of product quality and process efficiency