Contact mechanics of the functionally graded monoclinic layer. (English) Zbl 1473.74102

Çömez, İsa

Eur. J. Mech., A, Solids 83, Article ID 104018, 11 p. (2020).

Summary: In this study, the frictional contact problem of a functionally graded (FG) monoclinic layer was addressed based on the linear elasticity theory. The FG monoclinic layer was loaded by a rigid cylindrical punch that transmits both normal and tangential concentrated loads. It was assumed that the elastic stiffness coefficients varied exponentially through the thickness of the layer. The contact area was assumed to be under Coulomb friction conditions that relate the tangential traction to the normal component. The general expressions of the stress and displacement for the FG monoclinic layer were obtained by applying the integral transform technique. Using the boundary conditions of the problem, a second kind singular integral equation was obtained, and it was solved numerically by applying the Gauss-Jacobi integration formulas. The effect of the fiber angle, the material inhomogeneity, the friction coefficient, the punch radius, material type and the external load on the contact width, contact stress, and in-plane stress were given. This is the first study that investigates the effect of inhomogeneity on the contact problem of monoclinic materials.

MSC:

74M15	Contact in solid mechanics
74M10	Friction in solid mechanics
74E05	Inhomogeneity in solid mechanics
74B05	Classical linear elasticity

Keywords:

monoclinic linear elastic material; friction coefficient; singular integral equation; Gauss-Jacobi integration formula

References:

[1]	Alinia, Y.; Güler, M. A., On the fully coupled partial slip contact problems of orthotropic materials loaded by flat and cylindrical indenters, Mech. Mater., 114, 119-133 (2017)
[2]	Alinia, Y.; Zakerhaghighi, H.; Adibnazari, S.; Güler, M. A., Rolling contact problem for an orthotropic medium, Acta Mech., 228, 2, 447-464 (2017) · Zbl 1381.70016
[3]	Alinia, Y.; Hosseini-nasab, M.; Güler, M. A., The sliding contact problem for an orthotropic coating bonded to an isotropic substrate, Eur. J. Mech. Solid., 70, 156-171 (2018) · Zbl 1406.74515
[4]	Altenbach, H.; Altenbach, J.; Kissing, W., Mechanics of Composite Structural Elements (2004), Springer-Verlag: Springer-Verlag Berlin
[5]	Arslan, O.; Dag, S., Contact mechanics problem between an orthotropic graded coating and a rigid punch of an arbitrary profile, Int. J. Mech. Sci., 135, 541-554 (2018)
[6]	Bagault, C.; Nelias, D.; Baietto, M. C.; Ovaert, T. C., Contact analyses for anisotropic half-space coated with an anisotropic layer: effect of the anisotropy on the pressure distribution and contact area, Int. J. Solid Struct., 50, 5, 743-754 (2013)
[7]	Binienda, W. K.; Pindera, M. J., Frictionless contact of layered metal-matrix and polymer-matrix composite half planes, Compos. Sci. Technol., 50, 1, 119-128 (1994)
[8]	Chaudhuri, P. K.; Ray, S., Receding contact between an orthotropic layer and an orthotropic half-space, Arch. Mech., 50, 4, 743-755 (1998) · Zbl 0956.74032
[9]	Choi, H. J.; Thangjitham, S., Stress analysis of multilayered anisotropic elastic media, J. Appl. Mech., 58, 2, 382-387 (1991) · Zbl 0825.73069
[10]	Çömez, I., Frictional moving contact problem of an orthotropic layer indented by a rigid cylindrical punch, Mech. Mater., 133, 120-127 (2019)
[11]	Çömez, İ.; Yilmaz, K. B., Mechanics of frictional contact for an arbitrary oriented orthotropic material, ZAMM-J. Appl. Math. Mech./Z. für Ange. Math. Mech., Article e201800084 pp. (2019)
[12]	Comez, I.; Yilmaz, K. B.; Güler, M. A.; Yildirim, B., On the plane frictional contact problem of a homogeneous orthotropic layer loaded by a rigid cylindrical stamp, Arch. Appl. Mech., 1-17 (2019)
[13]	Dong, X. Q.; Zhou, Y. T.; Wang, L. M.; Ding, S. H.; Park, J. B., Stress state of two collinear stamps over the surface of orthotropic materials, Arch. Appl. Mech., 84, 5, 639-656 (2014) · Zbl 1344.74046
[14]	Erdogan, F., Mixed Boundary Value Problems. Mechanics Today, vol. 4, 1-86 (2013), S. Nemat-Nasser
[15]	Erdogan, F.; Gupta, G. D.A.; Cook, T. S., Numerical solution of singular integral equations, (Methods of Analysis and Solutions of Crack Problems (1973), Springer: Springer Dordrecht), 368-425
[16]	Fukumasu, N. K.; Souza, R. M., Numerical analysis of the contact stresses developed during the indentation of coated systems with substrates with orthotropic properties, Surf. Coating. Technol., 201, 7, 4294-4299 (2006)
[17]	Guler, M. A., Closed-form solution of the two-dimensional sliding frictional contact problem for an orthotropic medium, Int. J. Mech. Sci., 87, 72-88 (2014)
[18]	Güler, M. A.; Kucuksucu, A.; Yilmaz, K. B.; Yildirim, B., On the analytical and finite element solution of plane contact problem of a rigid cylindrical punch sliding over a functionally graded orthotropic medium, Int. J. Mech. Sci., 120, 12-29 (2017)
[19]	Hou, P. F.; Zhang, W. H.; Chen, J. Y., Three-dimensional exact solutions of homogeneous transversely isotropic coated structures under spherical contact, Int. J. Solid Struct., 161, 136-173 (2019)
[20]	Hou, P. F.; Zhang, W. H.; Chen, J. Y., Three-dimensional exact solutions of transversely isotropic coated structures under tilted circular flat punch contact, Int. J. Mech. Sci., 151, 471-497 (2019)
[21]	Kahya, V.; Ozsahin, T. S.; Birinci, A.; Erdol, R., A receding contact problem for an anisotropic elastic medium consisting of a layer and a half plane, Int. J. Solid Struct., 44, 17, 5695-5710 (2007) · Zbl 1125.74036
[22]	Krenk, S., On quadrature formulas for singular integral equations of the first and the second kind, Q. Appl. Math., 33, 3, 225-232 (1975) · Zbl 0322.45022
[23]	Krenk, S., On the elastic constants of plane orthotropic elasticity, J. Compos. Mater., 13, 2, 108-116 (1979)
[24]	Kucuksucu, A.; Guler, M. A., Analytical solution of the frictional contact problem of a semi-circular punch sliding over a homogeneous orthotropic half-plane, Hittite J. Sci. Eng., 3, 2 (2016)
[25]	Kucuksucu, A.; Guler, M. A.; Avci, A., Mechanics of sliding frictional contact for a graded orthotropic half-plane, Acta Mech., 226, 10, 3333-3374 (2015) · Zbl 1323.74057
[26]	Kuo, C. H.; Keer, L. M., Contact stress analysis of a layered transversely isotropic half-space, J. Tribol., 114, 2, 253-261 (1992)
[27]	Lekhnitskii, S. G., Theory of Elasticity of an Anisotropic Body (1963), Holden Day Inc., San Fransisco: Holden Day Inc., San Fransisco Berlin · Zbl 0119.19004
[28]	Lin, R. L., Punch problem for planar anisotropic elastic half-plane, J. Mech., 27, 2, 215-226 (2011)
[29]	Mokhtari, M.; Schipper, D. J.; Vleugels, N.; Noordermeer, J. W., Transversely isotropic viscoelastic materials: contact mechanics and friction, Tribol. Int., 97, 116-123 (2016)
[30]	Patra, R.; Barik, S. P.; Chadhuri, P. K., Frictionless contact of a rigid punch indenting a transversely isotropic elastic layer, Int. J. Adv. Appl. Math. Mech., 3, 100-111 (2016) · Zbl 1367.74045
[31]	Patra, R.; Barik, S. P.; Chaudhuri, P. K., Frictionless contact between a rigid indenter and a transversely isotropic functionally graded layer, Int. J. Appl. Mech. Eng., 23, 3, 655-671 (2018)
[32]	Pindera, M. J.; Lane, M. S., Frictionless contact of layered half-planes, part I: analysis, J. Appl. Mech., 60, 3, 633-639 (1993) · Zbl 0795.73066
[33]	Pindera, M. J.; Lane, M. S., Frictionless contact of layered half-planes, Part II: numerical results, J. Appl. Mech., 60, 3, 640-645 (1993) · Zbl 0795.73066
[34]	Sneddon, I. N., The Use of Integral Transforms (1972), Me Graw-Hill Book Company: Me Graw-Hill Book Company New York · Zbl 0237.44001
[35]	Yilmaz, K. B.; Çömez, İ.; Güler, M. A.; Yildirim, B., Analytical and finite element solution of the sliding frictional contact problem for a homogeneous orthotropic coating‐isotropic substrate system, ZAMM-J. Appl. Math. Mech./Z. für Ange. Math. Mech., Article e201800117 pp. (2019)
[36]	Zhou, Y. T.; Lee, K. Y.; Jang, Y. H., Explicit solution of the frictional contact problem of anisotropic materials indented by a moving stamp with a triangular or parabolic profile, J. Appl. Math. Phys., 64, 3, 831-861 (2013) · Zbl 1457.74156
[37]	Zhou, Y. T.; Lee, K. Y.; Jang, Y. H., Influences of the moving velocity and material property on frictionless contact problem of orthotropic materials indented by a moving punch, Arch. Mech., 65, 3, 195-217 (2013) · Zbl 1291.74145
[38]	Zhou, Y. T.; Lee, K. Y.; Jang, Y. H., Indentation theory on orthotropic materials subjected to a frictional moving punch, Arch. Mech., 66, 2, 71-94 (2014) · Zbl 1298.74185