On elastic contact problems of micro-periodic slant layered composite pressed by a rigid punch with a parabolic or rectangular shape

• Autorzy: Sebastianiuk Piotr , Perkowski Dariusz M. , Kulchytsky-Zhyhailo Roman

Identyfikatory

DOI

10.24425/bpasts.2021.138091

• Języki publikacji: EN

Abstrakty

EN

The paper presents an analysis of the influence of the shape of the rigid body pressed into the micro-periodic composite half-space on the examples of two punch shapes – parabolic and rectangular. The presented material is a layered body that consists of infinitely many thin alternately arranged homogenous layers. Layers of the presented composite are oblique to the boundary surface. Two cases of punch tip shape are examined – parabolic and rectangular. The presented problem has been formulated within the framework of a homogenized model with microlocal parameters and solved using the elastic potentials method and averaged boundary condition. Fourier integral transform method has been used to obtain the solution and the inverse integrals have been calculated numerically. Solutions in terms of contact pressure and maximum pressure characteristics were shown in the form of graphs.

Słowa kluczowe

EN

contact problem; microperiodic composites; punch shape

PL

problem kontaktu; kompozyty mikroperiodyczne

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2021
• Tom: Vol. 69, nr 6
• Strony: art. no. e138091
• Opis fizyczny: Bibliogr. 26 poz., il.

Twórcy

autor

Sebastianiuk Piotr

• Faculty of Mechanical Engineering, Białystok University of Technology, ul. Wiejska 45C, 15-351 Białystok, Poland

autor

Perkowski Dariusz M.

• Faculty of Mechanical Engineering, Białystok University of Technology, ul. Wiejska 45C, 15-351 Białystok, Poland

autor

Kulchytsky-Zhyhailo Roman

• Faculty of Mechanical Engineering, Białystok University of Technology, ul. Wiejska 45C, 15-351 Białystok, Poland

Bibliografia

• [1] G.M.L. Gladwell, Contact Problems in the Classical Theory of Elasticity. Springer Netherlands, 1980. [Online]. Available: https://books.google.pl/books?id=Y3-Ju0WQ6msC.
• [2] J.R. Barber, „Hertzian Contact”, in Solid Mechanics and its Applications, vol. 250, Springer Verlag, 2018, pp. 29-41, doi: 10.1007/978-3-319-70939-0_3.
• [3] A. Sackfield and D.A. Hills, „Some useful results in the classical hertz contact problem”, J. Strain Anal. Eng. Des., vol. 18, no. 2, pp. 101-105, 1983, doi: 10.1243/03093247V182101.
• [4] S.J. Childow and M. Teodorescu, „Two-dimensional contact mechanics problems involving inhomogenously elastic solid split into three distinct layers”, Int. J. Eng. Sci., vol. 70, pp. 102-123, 2013, doi: 10.1016/j.ijengsci.2013.05.004.
• [5] D. Pączka, „Elastic contact problem with Coulomb friction and normal compliance in Orlicz spaces”, Nonlinear Anal. Real World Appl., vol. 45, pp. 97-115, Feb. 2019, doi: 10.1016/J.NONRWA.2018.06.009.
• [6] C. Peijian, C. Shaohua, and P. Juan, „Sliding Contact Between a Cylindrical Punch and a Graded Half-Plane With an Arbitary Gradient Direction”, J. Appl. Mech., vol. 82, no. 4, pp. 41008-41009, Apr. 2015, doi: 10.1115/1.4029781.
• [7] K.B. Yilmaz, I. Comez, B. Yildirim, M.A. Güler, and S. El-Borgi, “Frictional receding contact problem for a graded bilayer system indented by a rigid punch”, Int. J. Mech. Sci., vol. 141, pp. 127–142, 2018, doi: 10.1016/j.ijmecsci.2018.03.041.
• [8] D.M. Perkowski, R. Kulchytsky-Zhyhailo, and W. Kołodziejczyk, “On axisymmetric heat conduction problem for multilayer graded coated half-space”, J. Theor. Appl. Mech., vol. 56, no. 1, pp. 147–156, 2018, doi: 10.15632/jtam-pl.56.1.147.
• [9] O. Arslan and S. Dag, “Contact mechanics problem between an orthotropic graded coating and a rigid punch of an arbitrary profile”, Int. J. Mech. Sci., vol. 135, pp. 541–554, 2018, doi: 10.1016/j.ijmecsci.2017.12.017.
• [10] T.-J. Liu, Y.-S. Wang, and Y.-M. Xing, “The axisymmetric partial slip contact problem of a graded coating”, Meccanica, vol. 47, no. 7, pp. 1673–1693, 2012, doi: 10.1007/s11012-012-9547-0.
• [11] M. Kot, J. Lackner, and L. Major, “Microscale interpretation of tribological phenomena in Ti/TiN soft-hard multilayer coatings on soft austenite steel substrates”, Bull. Pol. Acad. Sci. Tech. Sci., vol. 59, no. 3, pp. 343–355, 2011, doi: 10.2478/v10175-011-0042-x.
• [12] R. Kulchytsky-Zhyhailo, S.J. Matysiak, and D.M. Perkowski, “On displacements and stresses in a semi-infinite laminated layer: Comparative results”, Meccanica, vol. 42, no. 2, pp. 117–126, Mar. 2007, doi: 10.1007/s11012-006-9026-6.
• [13] D.M. Perkowski, S.J. Matysiak, and R. Kulchytsky-Zhyhailo, “On contact problem of an elastic laminated half-plane with a boundary normal to layering”, Compos. Sci. Technol., vol. 67, no. 13, pp. 2683–2690, Oct. 2007, doi: 10.1016/j.compscitech.2007.02.013.
• [14] M.-J. Pindera and M.S. Lane, “Frictionless Contact of Layered Half-Planes, Part II: Numerical Results”, J. Appl. Mech., vol. 60, no. 3, pp. 640–645, 1993, doi: 10.1115/1.2900852.
• [15] C. Woźniak, “A nonstandard method of modelling of thermoelastic periodic composites”, Int. J. Eng. Sci., vol. 25, no. 5, pp. 483–498, Jan. 1987, doi: 10.1016/0020-7225%2887%2990102-9.
• [16] S. Timoshenko, “Goodier. JN, Theory of Elasticity”, New. York McGraw—Hil1, vol. 970, no. 4, pp. 279–291, 1970.
• [17] S.J. Matysiak and C.Z. Woźniak, “Micromorphic effects in a modelling of periodic multilayered elastic composites”, Int. J. Eng. Sci., vol. 25, no. 5, pp. 549–559, Jan. 1987, doi: 10.1016/0020-7225%2887%2990106-6.
• [18] A. Kaczyński and S.J. Matysiak, “Plane contact problems for a periodic two-layered elastic composite”, Ingenieur-Archiv, vol. 58, no. 2, pp. 137–147, Mar. 1988, doi: 10.1007/BF00536233.
• [19] I.N. Sneddon, “Integral transform methods”, in Methods of analysis and solutions of crack problems: Recent developments in fracture mechanics Theory and methods of solving crack problems, G.C. Sih, Ed. Dordrecht: Springer Netherlands, 1973, pp. 315–367, doi: 10.1007/978-94-017-2260-5_6.
• [20] R. Kulchytsky-Zhyhailo and W. Kolodziejczyk, “On axisymmetrical contact problem of pressure of a rigid sphere into a periodically two-layered semi-space”, Int. J. Mech. Sci., vol. 49, no. 6, pp. 704–711 2007, doi: 10.1016/j.ijmecsci.2006.10.007.
• [21] P. Sebestianiuk, D.M. Perkowski, and R. Kulchytsky- Zhyhailo, “On Contact problem for the microperiodic composite half-plane with slant layering”, Int. J. Mech. Sci., vol. 182, p. 1057342020, doi: 10.1016/j.ijmecsci.2020.105734.
• [22] P. Sebestianiuk, D.M. Perkowski, and R. Kulchytsky-Zhyhailo, “On stress analysis of load for microperiodic composite halfplane with slant lamination”, Meccanica, vol. 54, pp. 573–593 2019, doi: 10.1007/s11012-019-00970-z.
• [23] I.Y. Shtaerman, “Contact Problems of the Theory of Elasticity (FTD-MT-24-61-70)”, vol. 55, no. 6, pp. 887–901, 1970.
• [24] M. Sadowsky, “Zweidimensionale Probleme der Elastizitätstheorie”, ZAMM – J. Appl. Math. Mech./Zeitschrift für Angew. Math. und Mech., vol. 8, no. 2, pp. 107–121, 1928, doi: 10.1002/zamm.19280080203.
• [25] L.A. Galin, Contact Problems in the Theory of Elasticity. Department of Mathematics, School of Physical Sciences and Applied Mathematics, North Carolina State College, 1961. [Online]. Available: https://books.google.pl/books?id=9F-4QgAACAAJ.
• [26] I.S. Gradshteyn, I.M. Ryzhik, and R.H. Romer, “Tables of Integrals, Series, and Products”, Am. J. Phys., vol. 56, p. 958, 1988, doi: 10.1119/1.15756.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).