Abstract—
The problem of loading a textured two-layer elastic foundation with a rigid smooth indenter is considered. At the interface between the textured layer and the half-space, the conditions for complete adhesion are specified. Relief elements are elastic cylinders, characterized by height and radius, located on the surface of the base with a given period. The one-dimensional Winkler model is used to describe the mechanical properties of relief elements. The contact problem is solved using the boundary element method. Pressure, displacements, and also the shape of the indenter are approximated by piecewise constant functions. The influence coefficients are constructed using a method based on double integral Fourier transforms. The analysis of the influence of the texture elements arrangement density and their compliance on the distribution of the contact pressure is carried out. It was found that in most cases contact is made only with the elements of the texture. For a relatively stiff textured layer, the combined effect of layer curvature and additional pliability imparted by texture elements is important. For relatively stiff and pliable textured layers, load-penetration curves were obtained depending on the texture period. Within the framework of the proposed setting, the limiting case of contact of an indenter with a Winkler layer completely covering the surface of a two-layer elastic half-space is also considered. Load-penetration curves are obtained and analyzed for an indenter in the form of a Berkovich pyramid.
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REFERENCES
E. A. Kuznetsov and G. A. Gorokhovsky, “On actual contact pressure,” Probl. Treniya Iznashyvaniya, No. 12, 10–15 (1977).
I. G. Goryacheva, Mechanics of Friction Interaction (Nauka, Moscow, 2001) [in Russian].
J. R. Barber, Contact Mechanics (Springer, 2017).
I. G. Goryacheva, N. I. Malanchuk, and R. M. Martynyak, “Contact interaction of bodies with a periodic relief during partial slip,” J. Appl. Math. Mech. 76 (5), 695–709 (2012). https://doi.org/10.1016/j.jappmathmech.2012.11.002
I. Y. Tsukanov, “Effects of shape and scale in mechanics of elastic interaction of regular wavy surfaces,” Proc. Inst. Mech. Eng., Part J. 231 (3), 332–340 (2017). https://doi.org/10.1177/1350650116657699
I. A. Soldatenkov, “Contact deformation of an elastic composition of a half-plane and a strip of variable width,” J. Appl. Math. Mech. 65 (1), 145–153 (2001). https://doi.org/10.1016/S0021-8928(01)00016-8
I. G. Goryacheva, E. V. Torskaya, F.I. Stepanov, et al., “Simulation of deformation of the textured layer under conditions of contact interaction,” Tren. Iznos 38 (6), 526–531 (2017) [in Russian].
E. Torskaya, “Study of roughness effect on elastic indentation of coated bodies,” Proc. Inst. Mech. Eng., Part C. 230 (9), 1392–1397 (2016). https://doi.org/10.1177/0954406215622498
V. S. Nikishin and G. S. Shapiro, Space Problems of the Elasticity Theory for Multilayered Media (VTs AN SSSR, Moscow, 1970) [in Russian].
T. Liskiewicz, K. Kubiak, and T. Comyn, “Nano-indentation mapping of fretting-induced surface layers,” Tribol. Int. 108, 186–193 (2017). https://doi.org/10.1016/j.triboint.2016.10.018
M. M. Gubenko, A. M. Mezrin, O. O. Shcherbakova, et al., “Analysis of changes in the mechanical properties of the surface layers of aluminum alloys under the conditions of sliding friction,” J. Frict. Wear 38, 407–410 (2017). https://doi.org/10.3103/S1068366617050038
E. V. Torskaya, T. I. Muravyeva, and J. C. Sánchez-López, “Study of TiC/a-C(:H) Coatings before and after friction by nanoindentation,” in Proceedings of the 4th International Conference on Industrial Engineering. ICIE 2018. Lecture Notes in Mechanical Engineering. (Springer, Cham, 2019), pp. 1011–1018.
F. I. Stepanov and E. V. Torskaya, “Modeling of indentation of hard coatings by an arbitrarily shaped indenter,” J. Frict. Wear 40, 326–331 (2019). https://doi.org/10.3103/S1068366619040147
E. Torskaya, S. Siroezkin, and S. Chizhik, “The method of elastic coatings diagnostics from indentation data,” in Advanced Tribology, Ed. by J. Luo, Y. Meng, T. Shao, and Q. Zhao (Springer, Berlin, 2009), pp. 705–706. https://doi.org/10.1007/978-3-642-03653-8_229
Funding
This work was supported by the Russian Foundation for Basic Research, grant no. 19-01-00231 (contact of textured surfaces) and grant no. 20-58-00007 (indentation of thin films).
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Translated by M. K. Katuev.
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Stepanov, F.I., Torskaya, E.V. CONTACT BETWEEN A SMOOTH INDENTER AND A TWO-LAYER ELASTIC HALF-SPACE WITH COMPLICATED CONDITIONS ON THE SURFACE. Mech. Solids 57, 49–56 (2022). https://doi.org/10.3103/S0025654422010034
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DOI: https://doi.org/10.3103/S0025654422010034