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The paper proposes methods to predict the reliability of a multilayered coating based on a model with independently (sequentially) degrading layers. For the mathematical description of the process of crack penetration into the depth of a layered solid body from the free surface with certain roughness, the propagation of a crack tip into a layer adjacent to the free boundary of the coating is considered. This stochastic process is described through the specification of all multipoint probability distributions (densities), and it represents a Markov process. A mathematical model, described by equations of the parabolic type, is proposed to describe the above-mentioned process. Based on the above model, graphs are constructed to describe the change in the time of the crack propagation through a layer depending on the surface roughness and the ultimate strength (ductility) of the coating. The crack growth rate will be in the range from 10-6 mm/s (when the surface roughness is low) to 10-4 mm/s (when the surface roughness is high). [ABSTRACT FROM AUTHOR]

The article proposes a model of the ultimate stress state of the material of the coated tool cutter. It is found that with an increase in the fracture toughness of a tool in connection with the material ductility the machining accuracy deteriorates due to arising elastic-plastic vibrations of the tool cutter. In case when no ultimate stress state is reached, that is, a tool operates in the elastic region, then an alternating stress distribution diagram is realized for the tool cutter at the beam approximation. Therefore, in addition to the frictional vibrations, arising from the interaction between the tool cutter and a workpiece, the elastic vibrations can arise, which affects the machining accuracy and the service life of the coated tool cutter. The use of coatings makes it possible not only to increase the wear resistance of cutting tools, but also to transform the stress distribution diagrams of the normal σN and tangential τγ contact stresses acting on the rake face of the cutting tool. In particular, it is possible to control the length of the total contact area between the chips and the tool rake face. [ABSTRACT FROM AUTHOR]