Numerical modelling and experimental verification of the formation of 2D and 3D brazed joints

This paper addresses the issue of determining the joint shape formed after molten metal re-solidification at the peak brazing temperature. A theoretic al approach for modelling two- and three-dimensional joint shapes in situat ions where the mating surfaces are neither plane nor orthogonal is presente d. The approach is based on a variational principle involving the minimizat ion of the potential energy of the molten metal liquid just prior to the on set of solidification. The numerical solution of the variational problem is obtained by employing a parametric finite element method in conjunction wi th a direct optimization algorithm. The results from the theory are verifie d by comparison with experimental data obtained from a set of controlled at mosphere brazing tests of aluminium alloys. The results obtained from the t heory are in good agreement with the experimental data and empirical eviden ce. An analysis of the influence of geometry, configuration and orientation of mating surfaces on both two- and three-dimensional brazed joint shapes is presented in an accompanying paper.