Velocity Gradients and the Evolution of Material Properties in a Narrow Layer near Surfaces of High Friction in Metal Forming Processes

Abstract

Theoretical solutions for several rigid plastic models used to describe plastic flow in metal forming processes are singular in the vicinity of maximum friction surfaces. In particular, velocity gradients and the equivalent strain rate approach infinity near such surfaces. Such singular behavior can be excluded from consideration by choosing another friction law or material model. However, a different approach is proposed in the present paper. The starting point of this approach is that many experiments show that velocity gradients are very high in the vicinity of surfaces of high friction and that a narrow material layer is formed near such surfaces whose properties are very different from the properties in the bulk. Taking into account that the equivalent strain rate has a significant effect on the evolution of material properties, this experimental fact suggests that a theory based on the singular plastic solutions can be developed to describe the formation of the aforementioned material layer. In the present paper such a theory is proposed to describe the evolution of grain size. It is assumed that, in addition to the equivalent strain rate, the material spin has an effect of the evolution of grain size. It is then shown that the solutions for the material spin are singular as well. The interrelation between the present theory and strain gradient theories of plasticity is discussed. It is shown that it is necessary to account for the strain rate gradient to propose a more adequate theory to deal with the material flow near surfaces of high friction. Some experimental results on the formation of the narrow layer of ultra-fine grains in the vicinity of the fraction surface in extrusion are presented. An illustrative example to relate these experimental results and the new theory is given.