Deformation of a plastic wedge by a rigid flat die under the action of a tangential force

Abstract

A slip-line field has been constructed for the deformation of a rigid perfectly-plastic wedge compressed by a flat rigid die and subsequently sheared by a force acting tangentially to the face of the die. An associated velocity field is suggested. Consistency between the slip-line field, the velocity field and the changing profile of the wedge as deformation proceeds is closely, though not exactly, preserved. The progressive deformation has been found, using these fields, by an incremental graphical construction. The deformation and the growth of the area of contact between the wedge and the die face under the action of a constant normal force and increasing tangential force are found to agree well with experiment. The theoretical contact area growth supports Tabor's empirical expression for ‘junction growth’ in the build-up of static friction between metallic surfaces.