Reliability Calculation for a Multilayered Coating Based on a Model with Independently (Sequentially) Degrading Layers

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).