Because metal forming produces elastic and plastic deformations in the workpiece material and elastic deformations in the dies, an in-depth study of the metal forming process will require the determination of stresses and strains in the workpiece and the tooling. In addition, one needs to know some basic topics from the theory of elasticity and plasticity. In this chapter, a short introduction to this theory is therefore given. Because of the rather shallow treatment here, readers who are unfamiliar with this theory are referred to other textbooks for a more profound study.

Stresses

During metal forming the workpiece is deformed plastically by forces transferred from the die to the workpiece. A successful forming operation requires that there be plastic deformations in the workpiece, so that it changes shape permanently and conforms to the geometry of the die, while the die remains in the elastic state. If the die material becomes plasticized, the situation is one of overloading of the tooling, and the die geometry will gradually change because of the excessive forming loads. This means that the correct geometry of the formed component no longer can be maintained, so to continue appropriate metal forming, the dies must be replaced by new dies that can work the material while remaining in the elastic state.

The Stress Concept

Stress is defined as force per unit of area and refers to a particular point in a material.