Spannungszustand im Rohlingflansch beim Tiefziehen eines komplizierten Werkstücks

A two-dimensional stress state occurs during stamping in the flange of a blank, a characteristic feature of which is that one of the main stresses is compression, the other tension. Under such conditions the equations which determine the stress state of an ideally plastic metal coincide with the equations relating to a two-dimensional deformed state. A system of equations of the hyperbolic type is obtained, which has two families of real characteristics, both of which coincide with the trajectories of the maxiumum tangential stresses and have the property of orthogonality. Using the method of characteristics, it is possible to construct the optimal contour of the blank which will ensure that there is no displacement along a contour of the die. The described method of determining the stress state in the flange of the blank during extrusion can also be used in cases when the shape of the clamping surface is not two-dimensional and the contour of the inside of the die has an arbitrary configuration. If the clamping surface is a complicated one, the surface must be developed onto a plane in order to construct the trajectories of the maximum tangential stresses