PSI - Issue 72

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

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electrochemical chrome-nickel plating in an electrolyte (Protsenko et al. (2018), Kukhar et al. (2021), Lavrinenko et al. (2021)), plasma-electrolytic oxidation (Student et al. (2019), Simchen et al. (2020), Ropyak et al. (2023a, 2023b)), electrospark alloying (Tarelnyk et al. (2020)), laser shock action (Munther et al (2000), Rajčić et al. (2021)) and ion-plasma method (Klimenko et al. (2014)). Based on theoretical approaches at the stage of choosing the composition of materials (Prysyazhnyuk et al. (2015)) and taking into account the technological heredity in manufacturing (Dai et al. (2019), Kusyi et al. (2022)), it is possible to ensure the functioning of products during the life cycle (Kopei et al. (2020)). Functionally gradient composite coatings with ultrafine nano- or microstructure components are most often used to improve the surface of parts (Mellor (2006), Liu et al. (2022)). The effect of thin flexible and composite coatings on the limiting state of damaged plate (Shatskii (1989), Mohammadi et al. (2020)) and shell (Ahmed and Mourad (2013), Shatskyi et al. (2018, 2020), Dutkiewicz et al. (2021)) structures also was studied. Jeremić et al. (2018) investigated the cracking of carbide coatings. In those cases, where a sufficiently rigid laminated coating is separated from the part by a pliable layer, it is possible to reduce the dimension of the continuum, applying the theory of plates resting on a Winkler’s foundation to describe the equilibrium of the coating. Thanks to this approach, approximate analytical results can be achieved. This idea is the motivation for our study aimed at developing a one-dimensional model for calculating the stress state and limit equilibrium of a contrast functionally gradient composite coating under arbitrarily oriented local load, caused by the interaction with fixed or unfixed abrasive. Here we develop the results obtained by Shatskyi et al. (2023) for a non-uniform coating under normal local loading. 2. Material and methods Let us consider a rigid structure element (a foundation) covered by a thin coating, consisting of an outer, hard functionally gradient layer and a relatively soft non-homogeneous substrate as it is shown in Fig.1. Mechanical contact between layers is considered as perfect. From a mechanical point of view, the hard outer layer is considered as a non- uniform elastic plate working for tension and bending, and the soft inner layer is subject to Winkler’s hypothesis of the stress and displacement proportionality. The structure is loaded by a vertical force P (N/m) and a horizontal friction force fP , uniformly distributed along a the z-axis deep into the drawing, that simulates a contact with a sliding abrasive particle. In the presented model, large values of the friction coefficient f correspond to the sliding of the fixed abrasive in the micro-cutting process; small values of f correspond to the sliding of the unfixed abrasive with possible rolling. We assume also that the structure is under plane strain conditions ( 0   z ). The distribution of stresses in the non-homogeneous coating and its strength should be studied.

Fig. 1. Scheme of the functionally gradient coating under local load.