Solution of the problem of sheet bending by the slip line field method

Abstract

One of the limitations imposed on this process of bending is the possibility of cracking on the surface of the sheet during bending. To predict this type of metal destruction, information is needed on the plastic properties of the material and the stress state in the deformation zone during the bending process. The solution of the problem of sheet bending under conditions of a flat-strained state by graphical construction of the slip line field using a rigid cylindrical mandrel has been analyzed. The material model is a perfectly plastic body. The stresses in the deformation zone and accumulated strains have been determined. The bending process is characterized as unidirectional and monotonous. It has been determined that the mean stress on the outer surface of the sheet during bending equals to 1, and it does not depend on the sheet thickness and the radius of the rigid cylindrical mandrel. Verification of the accuracy of the graphical solution is made. The resulting solution can be used as the basis for an experimental method for testing the plastic properties of metals.