Temperature field in the vicinity of maximum friction surfaces in viscoplasticity
The velocity field is singular in the vicinity of maximum friction surfaces for several rigid plastic solids. In particular, the quadratic invariant of the strain rate tensor approaches infinity in the vicinity of such surfaces and the strain rate intensity factor controls the magnitude of the second invariant of the strain rate tensor in a narrow region near the friction surface. Moreover, the strain rate intensity factor controls the magnitude of the plastic work rate in this narrow region near frictional interfaces and thus affects the temperature field in this region. However, numerical modeling of corresponding boundary value problems by means of standard finite element methods is impossible since the velocity field is singular. Therefore, an asymptotic representation of the temperature field in the vicinity of maximum friction surfaces is derived in the present paper adopting a viscoplastic material model with a saturation stress. An applied aspect of the present study is that a narrow layer with drastically modified properties is generated in the vicinity of frictional interfaces in deformation processes. This layer affects the quality of final products. It is known that the generation of this layer is controlled by plastic deformation and temperature. There are models that account for the effect of plastic deformation on the generation of the layer with drastically modified properties by means of the strain rate intensity factor. The results of the present study can be used to extend these models to account for the effect of temperature on the generation of the layer with drastically modified properties near frictional interfaces.