PSI - Issue 59

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Ivan Shatskyi et al. / Procedia Structural Integrity 59 (2024) 407–412 Shatskyi et al. / Structural Integrity Procedia 00 (0000) 000 – 000

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corrosion, for example, electrochemical chrome plating in an electrolyte (Protsenko et al. (2018), Merlo and Leonard (2021), Kukhar et al. (2021)), nickel plating (Lavrinenko et al. (2021)) and oxidation (Ropyak et al. (2023)), electrospark alloying (Tarelnyk et al. (2017)), 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 (Kusyi et al. (2022), Dai et al. (2019)), it is possible to ensure the functioning of products during the life cycle (Kopei et al. (2020)). To achieve a multi-purpose result, to improve the surface of a part, functionally gradient, in particular, composite and layered coatings with ultrafine nano- or microstructure components are most often used (Liu et al. (2022)). To date, models and methods of the mechanics of layered coatings have been sufficiently developed taking into account changes in temperature and the diffusion process (Gay (2014)). Approaches to the analysis of the influence of thin flexible and composite coatings on the limit state of damaged plate (Shatsky (1988), Shatskii (1989), Mohammadi et al. (2020)) and shell (Ahmed and Mourad (2013), Shatskyi et al. (2020), Dutkiewicz et al. (2021)) structures also deserve attention. A separate class of problems with a singular stress field is the study of the deformation of layered coatings under a localized load. Loads of this type occur when surfaces interact with an abrasive or with wear and oxidation products, as well as when testing coatings by nano- and microindentation (Milman et al. (1993), Liu, T.-J. (2021)). In those cases where a sufficiently rigid laminated coating is separated from the part by a pliable layer, it is advisable to apply t he theory of plates on a Winkler’s foundation to describe the equilibrium of the coating. This makes it possible to reduce the dimension of the continuum and achieve analytical results. Shatskyi et al. (2016) give examples of such 1D models for a steel part with an Al 2 O 3 coating on an aluminum sublayer and Bembenek et al. (2022)) – for an infrared filter with a silicon coating on a layered Si/SiO structure. If the rigid part in the composition is considered an inhomogeneous plate, and the soft fragment is a compliant interlayer, then the above calculation scheme can claim success. 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 layered coating under local load. 2. Material and methods Let us consider a steel structure element coated with a thin contrast composite coating consisting of outer multilayer part and inner soft monolayer (Fig. 1). From the point of view of mechanics, a packet of rigid layers is considered as a piecewise homogeneous plate working on a bend, and a pliable layer obeys the Winkler hypothesis about the proportionality of normal stresses and elastic transversal displacements. For simplicity, the steel base is assumed absolutely rigid. Mechanical contact between components on mating surfaces is considered ideal. The composition is loaded with a normal force P (N/m), uniformly distributed along a straight-line perpendicular to the plane of the drawing. In addition, we assume the state of plane deformation ( 0  z  ). The distribution of stresses in the layered coating should be studied and the level of allowable local load should be established.

c y soft layer .....................................  hard part of coating с H 1 h N h 2 h P h 

x

N N ν E , 1 1 ν E , 2 2 ν E ,

ν E,

rigid substrate absolutely

y

Fig. 1. Scheme of multilayer contrast coating under local load.