A geometrical model of the kinematics of incremental sheet forming for the prediction of membrane strains and sheet thickness

The sine law is a simple geometrical model for incremental sheet metal forming (ISF). It is based on the assumption that the deformation is a projection of the undeformed sheet onto the surface of the final part. The sine law provides approximations of sheet thinning for shear spinning and ISF at negligible computational cost, but as a plane strain model it can be applied only when plane strain deformation prevails. In this paper, a new model for the process kinematics of ISF is presented that is more general than the sine law. The model treats ISF as an evolution of a surface from the undeformed sheet to the final shape. It computes trajectories of surface points based on idealized intermediate shapes, assuming that the deformation between intermediate shapes proceeds by displacements along the surface normal of the current shape. For 2D and axisymmetrical problems, an analytical solution of the model is developed, which is useful for visualizing and discussing the kinematics of ISF. In order to use the new model with arbitrary parts, it was cast into a computer program that calculates membrane strains and the sheet thickness on a triangular mesh. For a benchmark shape, the model is compared to the sine law and experimental results. It is shown that the new model yields better thickness estimates than the sine law, especially in non-flat part areas where strains parallel to the direction of tool motion are significant.