All different production processes have one thing in common: in each case a workpiece with characteristic material behavior, stress, strain, self-hardening and temperature will be produced by a tool with special geometry and individual kinematic conditions, with a wide range of energy in a designed machine tool which is working along programmed lines. For the workpiece material, it is not important from which machine the energy is coming. To be able to predict more accurate values of the production process, it will be necessary to focus more on the complex and difficult process mechanics. The result must have a strong physical base and be in good agreement with practical results To solve these problems, we have to uncover all previous simplification assumptions for the existing models. This leads in a first step to a new fundament in process mechanics, which is only based on mathematics, physics and material behavior with friction conditions, and resulting temperatures during metal plastic flow. The new mathematical equations developed for yield shear stress and strain rate will be presented and discussed in this paper. The plastic deformation is the only parameter that will not disappear after completing the operation. Therefore, this will be the base to compare the developed theoretical deformation with the experimental results for two operations: cutting and grinding. In addition, it could be shown that yield shear stress and corresponding strain rate versus temperatures have an interdependent relationship, which creates the opportunity to determine the temperatures during metal plastic flow.