Boundary element stress analysis for copper-based dies in pressure die casting

It has recently been demonstrated that, for pressure die casting, high rates of heat extraction are possible with the use copper–alloyed dies suitably protected with a thermally sprayed steel layer. The structural integrity of dies of this type is paramount as the thermally sprayed layer has the potential to de-bond necessitating repair or retirement of the dies.In this paper, an efficient three-dimensional elastostatic stress model for the pressure die casting process is described. The collocation based boundary element method is used for the prediction of transient stress fields over a thermally stabilised casting cycle. A peculiar feature of the pressure die casting process is that transient thermal penetration into the die is limited to regions close to the surface of the die cavity and nozzle. The presence of a transient thermal field necessitates the evaluation of domain integrals in the boundary element stress formulation. Two methods for evaluating these integrals are presented in the paper: (i) a simplex method on a mesh local to the cavity surface; (ii) a modified reciprocity method utilising Gaussian radial-basis functions, interpolating on a perturbed thermal field. The simplex method is shown to be superior, providing high accuracy, stability and computational efficiency. The dies present a multi-domain environment for stress predictions making it necessary to utilise a suitably constructed coarse preconditioner to enhance numerical stability and provide for efficient computation. A multiplicative Schwarz method is presented that enables parameter matrix accelerated GMRES to be applied on each domain. Numerical experiments are performed to demonstrate the computational effectiveness of the approach. Predicted strain fields are compared with strain gauge measurements obtained on a purpose built rig designed to be representative of the casting process.