The plastic forming of metals is a branch of technology, in which great progress has been achieved mainly by collecting practical data resulting from long-time experience. The contribution of theoretical analysis to this progress is not significant. The common argument was, that such an analysis is too difficult and often even impossible. However, the constantly increasing significance of coldwork processing in industrial practice and the progress in the automatic control of these processes, demanding a broad knowledge of the influence of various parameters, and also the need to improve the mechanical behaviour of coldworked elements have proved beyond doubt that better understanding of the theory of plastic forming processes is necessary. This general trend has become evident in several recent publications in recent years, even though these represent only the engineering, approximate approach to theoretical analysis. Recent significant progress in the mathematical theory of plasticity allows to build an analysis of plastic forming processes on a more sound basis. In particular there have been developed graphical methods by means of which slip-line and hodograph meshes are constructed for plane strain and axially symmetric problems. These graphical methods yield not only the required forces but also the. mode of plastic deformation, even for very complex problems. Numerical procedures also give good results if the digital computer technique is employed.

The plastic forming of metals is a branch of technology, in which great progress has been achieved mainly by collecting practical data resulting from long-time experience. The contribution of theoretical analysis to this progress is not significant. The common argument was, that such an analysis is too difficult and often even impossible. However, the constantly increasing significance of coldwork processing in industrial practice and the progress in the automatic control of these processes, demanding a broad knowledge of the influence of various parameters, and also the need to improve the mechanical behaviour of coldworked elements have proved beyond doubt that better understanding of the theory of plastic forming processes is necessary. This general trend has become evident in several recent publications in recent years, even though these represent only the engineering, approximate approach to theoretical analysis. Recent significant progress in the mathematical theory of plasticity allows to build an analysis of plastic forming processes on a more sound basis. In particular there have been developed graphical methods by means of which slip-line and hodograph meshes are constructed for plane strain and axially symmetric problems. These graphical methods yield not only the required forces but also the. mode of plastic deformation, even for very complex problems. Numerical procedures also give good results if the digital computer technique is employed.