PSI - Issue 72

Liubomyr Ropyak et al. / Procedia Structural Integrity 72 (2025) 20–25

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3.2. Critical equilibrium

The strength of each of the layers is estimated by the von Mises criterion. Thus, the strength condition for a plane deformed composite functionally gradient coating will be:

[ ] 2 2           xy x y y x eq y y y y . 3 ) (1 2() 2 ()) ( ))( (1 ( ) 2 2 2

Here eq  is the von Mises equivalent stress, [ ]  is the allowable stresses for non-homogeneous coating materials ( n Y / [ ]    , where ( ) y Y  is a yield strength, and n is a safety factor). The results obtained make it possible to determine the value of the allowable load and safety margin, depending on the mechanical and geometric characteristics of the functionally gradient coating. 3.3. Example For the practical simulation of the behavior of ceramic Al2O3 coatings, a linear approximation of the mechanical characteristics distribution over the thickness of the hard part of the coating ( H = 250 μ m) was used. In case of the ceramic layer obtained by plasma electrolytic oxidation of the duralumin alloy D16T of thickness h = 1000 μm , a thin layer of annealed aluminum of thickness b = 50 μm appears under the oxide layer in the alloy. So for the characteristics of the soft heterogeneous substrate, we used piecewise constant functions. Distributions of mechanical characteristics over the thickness of the coating are shown in Fig. 2.

Fig. 2. Distribution of the mechanical characteristics over the thickness of the functionally gradient coating

As we can see in Figs. 3 and 4, the stress state is concentrated in the vicinity of the line of application of the local load, and the highest level of the equivalent stresses is observed in case of fixed abrasive. Since we have a nonhomogeneous coating, we should also take into account the spatial distribution of strength characteristics. Therefore, a more correct determination of the limit state of a functionally gradient layered coatings