Abstract
Currently, various structural components have coatings of different purposes that are multilayer or gradient structures. During operation these elements are often subjected to compressive loads, as a result of which sometimes the upper part of the coating is delaminated. To analyze this process, we use a simplified model of infinite structure, namely, a modified beam approximation that takes into account two coefficients of subgrade reaction similarly to the Pasternak model. The coating is subjected to compressive prestresses. Within the framework of the previously proposed model, delamination of the coating from the elastic base is investigated. We consider a simple case when the coefficients of subgrade reaction in the deamination zone are equal to zero. At the first stage, we conduct nondimensionalization of the model under study; obtain and study transcendental equation to find the critical load; prove the existence of a solution within some region of parameter variation; construct approximate formulas for the critical load; and indicate the correlation with the model parameters. The effect of the second coefficient of subgrade reaction on the critical load value is shown. At the second stage, based on the variational formulation, the problem of infinite coating is reduced to the problem on a finite beam with modified boundary conditions. The results obtained on the basis of a simplified model are compared with a numerical solution of the transcendental equation obtained at the first stage. At the final third stage, the problem on the supercritical behavior of the coating is investigated by minimizing the non-quadratic potential energy functional. Using the Ritz method and setting power-exponential functions corresponding to an infinite coating as coordinate, a solution of the problem on supercritical deformation is constructed. A study of the solution depending on the coefficients of subgrade reaction is carried out.
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This study was supported by the Russian Science Foundation, project no. 18-11-00069
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Translated by A. A. Borimova
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Vatulyan, A.O., Morozov, K.L. Investigation of Delamination from an Elastic Base Using a Model with Two Coefficients of Subgrade Reaction. Mech. Solids 55, 207–217 (2020). https://doi.org/10.3103/S002565442002017X
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DOI: https://doi.org/10.3103/S002565442002017X