Modelling the pressure die casting process using boundary and finite element methods

This paper is concerned with an investigation into the benefits and problems of modelling the pressure die casting process using a finite element solidification model for the casting and a boundary element model for the die. Linking boundary and finite element methods is beset with difficulties with each method requiring different mesh, time-step and other requirements for accurate results. The numerical models described in this paper have been specifically developed to overcome these problems. In particular, novel finite element solidification and transient thermal boundary element formulations have been developed. Moreover, iterative solution procedures have been formulated and implemented to enable the efficient solution of the coupled systems of non-linear equations. The latent energy released during solidification is calculated using a swept volume formulation which has shown itself to be highly stable and accurate, even for relatively course meshes and large time-steps. The domain integrals generated by the boundary element method have been avoided by developing a source based approximation procedure. The iterative schemes developed for solving the systems of equations are based on new and classical methods. The use of iterative schemes allows the boundary and finite element meshes and time-steps to be decoupled so that accuracy can be maintained. This decoupling is required because although the new solidification formulation allows for relatively course meshes and time-steps it is still unable to compete with the boundary element method in this regard, The predictions made by the model are compared against experimental results to demonstrate the accuracy of this approach.