The process mechanics phenomena play an important role in all metal cutting processes. Conditions are changing progressively not only to high velocities and deformation, but also to the interfacial friction between two different materials — tool and workpiece, and inside the same material, as a result of material flow with high temperatures. It will be shown, that during the ploughing effect in the interface between tool and chips there are two different kinds of friction, external and internal friction. All the existent models ignore this reality. Therefore, an alternative must be found to model the real phenomena during metal plastic flow in a more appropriate manner. In this study, we will consider the cutting process in fundamental terms based only on mathematics and physics. In connection with this fundamental development a question arises, “Which parameters are the best for characterizing the cutting process and can the equations be proven after processing, because nearly each parameter will disappear, such as stress, strain, friction or temperatures etc.”? It might be that only the plastic material deformation in connection with the external and internal friction can be identified and visualized after the cutting process for comparing the developed theoretical result with the experimental result of the chip formation region. That leads to the fact that, as long as agreement between theoretical and experimental result can be demonstrated, there is evidence that stress and strain, as well as friction and temperatures are correctly estimated. Therefore, this paper is focused on the plastic deformation ds in the plastic region during the cutting process. This plastic deformation will be expressed for the non-stationary, dynamic cutting process with non-uniform feed (toolworkpiece contact evolving from rubbing to material separation) and chip flow. This process behavior is relevant for the milling operation of metals as well as for carbon composites with glass fibers. For carbon composites with glass fibers, additional environmental and human safety aspects will arise, as described in this paper.