A solution methodology for contacting domains in pressure die casting

Multi-domain elastostatic problems can often be efficiently solved using coupled single domain iterative techniques. A particular difficulty however is the decrease in convergence rate associated with the increase in number of solution domains. Further convergence difficulties are encountered for multi-domain problems where contacting domains suffer variable contact conditions. Problems of this type are evident in pressure die casting with die blocks coupled together prior and subsequent to thermal loading. Particular interest in this paper is the development of an efficient solution methodology for prediction of gaps at block interfaces in pressure die casting.The methodology developed incorporates a coarse preconditioner designed to enhance the overall system stability. The governing equations across domains are coupled by means of a multiplicative-Schwarz method for non-overlapping domains, as focus is on the use of serial processing. The coarse preconditioner is obtained from a crude representation of the global system of equations although high accuracy is generally required at the contacting interfaces. Attention is restricted to thermo-elastostatic problems arising in pressure die casting with domains connected through spring interfaces. The effect of lowering and increasing the interfacial stiffness coefficients between domains is investigated. In addition, it is demonstrated how variable contact arising through thermally induced distortion is accounted for by the removal and attachment of interface springs. The coarse preconditioner is shown to be particularly beneficial to variable contact problems providing stability to the overall assembly. Computation times are determined for the iterative procedures and for elimination techniques indicating the relative benefits for problems of this nature. In addition, predictions are compared against experiment results to demonstrate the practical worth of the method for predicting gaps at die interfaces and the consequential flashing that can often result.