Finite element simulation of three-dimensional casting, extrusion and forming processes

Abstract

An iterative penalty finite element model is developed for the analysis of three-dimensional coupled incompressible fluid flow and heat transfer problems. The pressure is calculated by solving the momentum equation using known values of velocities, velocity gradients, and flow stresses from previous iteration. An iterative solution algorithm which employs the element-by-element data structure of the finite element equations is used to solve large systems of algebraic equations resulting from finite element models of real world problems. Three different iterative methods (ORTHOMIN, ORTHORES and GMRES) are implemented and tested to determine the efficiency of each algorithm terms of CPU time and storage requirements. Jacobi/Diagonal preconditioning is used to scale the system of equations and improve the convergence of the iterative solvers.

The developed iterative penalty finite element model is extended to analyse three-dimensional manufacturing processes such as casting, extrusion and forming of metals. For numerical simulation of extrusion and forming, flow formulation is used since these operations involve large deformations. The viscosity of the metal at elevated temperatures is calculated from the flow stress. The formulation uses the enthalpy method to account for the transfer of latent heat during phase change. The fluid inside the mushy region (between liquid and solid regions) is assumed to obey D’Arcy’s law for flow through porous materials. The permeability of the material is determined as a function of liquid fraction. This forces the velocities in the solid region to zero. In the finite element model, the effects of convection during phase change of the material are included.

A method for calculation of the movement of liquid metal-air interface during mold filling process is presented. The developed model predicts the location of the interface (defined by a pseudo-concentration value) by solving for its movement due to forced convection. Also during filling analysis, only the filled and interface elements are used for flow field calculations.