Numerical analysis of fluid structure interaction in water jet incremental sheet forming process using coupled Eulerian–Lagrangian approach

A coupled Eulerian–Lagrangian approach was used to simulate the whole deformation process of a water jet incremental sheet metal forming of a conical part by three dimensional finite element method. The Eulerian elements were used to model the water jet whereas the sheet and tools were simulated by the Lagrangian elements. The geometry of the work piece, thickness distribution,and surface pressure distribution, volume fraction of water in the Eulerian elements and the vectors of the water jet flow were studied by the finite element method. In addition, the relationship between bulging height, pump pressure and inclination angle of a deformed conical copper part by water jet incremental forming was approximated by an analytical method proposed by other researchers with a plane strain formulation and momentum theory of hydrodynamics. To verify the accuracy of the calculated results, the experiment of a water jet incremental sheet metal forming of an annealed copper sheet was carried out. It was shown that the numerical and also analytical results are generally in good agreement with experimental ones. In addition, It was found that the most of the thinning occurs in the former stage of water jet incremental forming and near the first path of the defined water jet trajectory, furthermore surface pressure is higher in the stagnation point whereas it is smaller than water pressure before injection from the nozzle of water jet.