A numerical solution for the axisymmetric flow of a plastic tube on a rigid fibre

Abstract

In the case of rigid perfectly plastic material the strain rate intensity factor appears in the vicinity of maximum friction surfaces. This factor controls the magnitude of the equivalent strain rate in a narrow region near the surface. On the other hand, the equivalent strain rate controls the evolution of material surfaces. Therefore, the existence of the strain rate intensity factor in theoretical solutions are in qualitative agreement with experimental observations that demonstrate that a narrow layer with drastically modified microstructure is often generated in the vicinity of frictional interfaces in machining and deformation processes. In order to use the strain rate intensity factor for describing such material behaviour, it is necessary to develop an efficient numerical method for calculating the strain rate intensity factor. Since this factor is involved in a singular series expansion, it is evident that commercial finite element packages are not capable of calculating the strain rate intensity factor. In the case of Tresca’s solids the theory of characteristics can be used for the development of the method in question. This paper presents a first step in this direction