Papers by Keyword: Strain Rate Intensity Factor

Abstract: Solutions for many rigid/plastic models are singular in the vicinity of maximum friction surfaces. In particular, the magnitude of the equivalent strain rate near such surfaces is controlled by the strain rate intensity factor. This factor is the coefficient of the leading singular term is a series expansion of the equivalent strain rate in the vicinity of maximum friction surfaces. Since the equivalent strain rate has a great effect of material properties, it is of important to reveal the dependence of the strain rate intensity factor on parameters characterizing material models. In the present paper, quite a general model of anisotropic plasticity under plane strain conditions is adopted. Then, using an analytic solution for instantaneous compression of a layer of plastic material between two parallel plates the effect of the shape of the yield locus on the asymptotic behavior of the equivalent strain rate in the vicinity of the friction surface is demonstrated.

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.

Abstract: The present paper concerns with the concept of the strain rate intensity factor in rigid plastic solids. The strain rate intensity factor is the coefficient of the principal singular term in the expansion of the equivalent strain rate in a series in the vicinity of maximum friction surfaces. Such singular velocity fields appear in solutions based on several rigid plastic models. Because of this singularity in the velocity field, many conventional evolution equations for material properties are not compatible with such rigid plastic solutions. On the other hand, qualitative behaviour of the singular rigid plastic solutions in the vicinity of maximum friction surfaces is in agreement with a number of experimental results. Therefore, the primary objective of research in this direction is to develop an approach to relate parameters of the singular velocity fields and parameters characterizing material properties. The approaches proposed in previous works are based on the strain rate intensity factor. In the case of analytical and semi-analytical solutions the strain rate intensity factor can be found by means of an asymptotic analysis of the solutions. A number of such solutions obtained by inverse methods are reviewed in the present paper and the strain rate intensity factor is found. An effect of process parameters on its magnitude is shown and discussed.