10.1515/tvsb-2017-0034 109 Transactions of the VŠB – Technical University of Ostrava Civil Engineering Series, Vol. 17, No. 2, 2017 paper #34 Ivan SHATSKYI 1 , Mykola MAKOVIICHUK 2 , Lubomyr ROPYAK 3 ANALYTICAL ESTIMATIONS OF STRENGTH OF TWO LAYER COATING LOADED ALONG A LINE Abstract The engineering calculation procedure of the stress-strain state of the two-layer coating under the load localized along a line is proposed. The plane coupled problem of the plate equilibrium has been formulated. The analytical solutions of the problem have been obtained and compared with previous results for the uncoupled problem. The analytical estimations of strength of the composite coating have been given. Keywords Two-layer coating, Winkler foundation, local load, stress distribution, strength. 1 INTRODUCTION Workability of machines, mechanisms and equipment subjected to contact loads and to interaction with aggressive or abrasive media is mainly controlled by the state and structure of the surface layers of their critical components. Conventional procedure of surface hardening of machine parts implies deposition of functionally gradient coatings whose integral parts have different functions. Such heterogeneous structures include, in particular, two-layered coatings of the ceramics- aluminum system, which cover the surface of steel [1] or aluminium [2] parts. The external (oxide) layer exhibits a high hardness and ensures the protection from mechanical wear, while the subsurface (aluminum) layer provides the necessary bond with the base metal (steel) and protects the latter from hydrogen saturation in aggressive media. Similar problems rise also in civil engineering within interaction of building walls and base plates on soil bodies. The available literature in this domain [3–7] provides insufficient insight into the effect of structure and mechanical properties of the two-layer coating components on the limit load values. Especially, this is vital for localized spatial loads. Study [6] describes the approach to analytical calculation of local stresses in a two-layer coating treated as a plate lying on the Winkler bed and provides the assessment of the limit load transferred from the tool applied during the finishing mechanical treatment of the coated part. The procedure for design optimization of a two-layer coating for particular local loading conditions is considered in the article [7]. The aim of the present study is elaboration of the technique [6, 7] in the case of taking into consideration interconnection of the membrane and bending fields in coating. 1 Prof., Ivan Shatskyi, DSc., Department of modelling of damping systems, Ivano-Frankivsk Branch of Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NAS of Ukraine, Mykytunetska str., 3; 76002, Ivano-Frankivsk, Ukraine, phone: (+380) 99 4444 967, e-mail: ipshatsky@gmail.com 2 Assoc. Prof., Mykola Makoviichuk, PhD., Department of modelling of damping systems, Ivano-Frankivsk Branch of Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NAS of Ukraine, Mykytunetska str., 3; 76002, Ivano-Frankivsk, Ukraine, phone: (+380) 50 7832 439, e-mail: makoviy@ua.fm 3 Assoc. Prof., Lubomyr Ropyak, PhD, Department of Computer Engineering Manufacturing, Ivano-Frankivsk National Technical University of Oil and Gas, Karpatska Str., 15, Ivano-Frankivsk, 76019, Ukraine, phone: (+380) 50 5408 007, e-mail: l_ropjak@ukr.net