Abstract
The present paper examines the plane strain receding frictionless contact problem of two functionally graded layers indented by a rigid cylindrical punch and with mismatched material properties at the interface. The shear moduli of the layers are assumed to vary in exponential form along the thickness direction and the Poisson’s ratios are taken as constant. With use of the Fourier integral transform, the governing equations are reduced to a system of two singular integral equations, in which the unknowns are the contact pressure and the contact widths. These integral equations are solved numerically using Gauss–Chebychev integration formulas. The main objective of this paper is to study the effect of the material inhomogeneity parameters and interface material property mismatch on the contact pressure and the size of the contact regions.
Similar content being viewed by others
References
Anderson, T.: The boundary element method applied to two-dimensional contact problems with friction. In: Brebbia, C.A. (ed.) Boundary Element Methods, pp. 239–258. Springer, Berlin (1982)
Birinci, A., Erdol, R.: Frictionless contact between a rigid stamp and an elastic layered composite resting on simple supports. Math. Comput. Appl. 4(3), 261–272 (1999)
Civelek, M.B., Erdogan, F.: The axisymmetric double contact problem for a frictionless elastic layer. Int. J. Solids Struct. 10(6), 639–659 (1974)
Comez, I.: Frictional contact problem for a rigid cylindrical stamp and an elastic layer resting on a half plane. Int. J. Solids Struct. 47, 1090–1097 (2010)
Comez, I., Birinci, A., Erdol, R.: Double receding contact problem for a rigid stamp and two elastic layers. Eur. J. Mech. A Solids 23, 301–309 (2004)
Dag, S., Erdogan, F.: A surface crack in a graded medium loaded by a sliding rigid stamp. Eng. Fract. Mech. 69, 1729–1751 (2002)
Dundurs, J.: Properties of elastic bodies in contact. In: de Pater, A.D., Kalker, J.J. (eds.) The Mechanics of the Contact Between Deformable Bodies, pp. 54–66. Delft University Press, Delft (1975)
El-Borgi, S., Abdelmoula, R., Keer, L.: A receding contact plane problem between a functionally graded layer and a homogeneous substrate. Int. J. Solids Struct. 46, 658–674 (2006)
El-Borgi, S., Usman, S., Guler, M.A.: A frictional receding contact plane problem between a functionally graded layer and a homogeneous substrate. Int. J. Solids Struct. 51, 4462–4476 (2014)
Elloumi, R., Kallel-Kamoun, I., El-Borgi, S.: A fully coupled partial slip contact problem in a graded half-plane, mechanics of materials (MoM). Int. J. 42, 417–428 (2010)
Erdogan, F.: Fracture mechanics of functionally graded materials. Compos. Eng. 5, 753–770 (1995)
Erdogan, F., Gupta, G.: On the numerical solutions of singular integral equations. Q. J. Appl. Math. 29, 525–534 (1972)
Garrido, J.A., Foces, A., Paris, F.: B.E.M. applied to receding contact problems with friction. Math. Comput. Model. 15, 143–154 (1991)
Garrido, J.A., Lorenzana, A.: Receding contact problem involving large displacements using the BEM. Eng. Anal. Bound. Elem. 21, 295–303 (1998)
Gecit, M.R.: The axisymmetric double contact problem for a frictionless elastic layer indented by an elastic cylinder. Int. J. Eng. Sci. 24(9), 1571–1584 (1986)
Giannakopoulos, A.E., Pallot, P.: Two-dimensional contact analysis of elastic graded materials. J. Mech. Phys. Solids. 48, 1597–1631 (2000)
Gladwell, G.M.L.: On some unbonded contact problems in plane elasticity theory. J. Appl. Mech. 43, 263–267 (1976)
Graciani, E., Mantic, V., Paris, F., Blazquez, A.: Weak formulation of axisymmetric frictionless contact problems with boundary elements. Appl. Interface Cracks Comput. Struct. 83, 836–855 (2005)
Guler, M.A., Erdogan, F.: Contact mechanics of graded coatings. Int. J. Solids Structs. 41, 3865–3889 (2004)
Holt, J., Koizumi, M., Hirai, T., Munir, Z.A. (eds.): Functionally Gradient Materials, Ceramic Transactions, vol. 34. The American Ceramic Society, Ohio (1992)
Jing, H.-S., Liao, M.-L.: An improved finite element scheme for elastic contact problems with friction. Comput. Struct. 35(5), 571–578 (1990)
Jing, L., Ke, L.-L., Wang, Y.S., Yang, J., Alam, F.: Thermoelastic frictional contact of functionally graded materials with arbitrarily varying properties. Int. J. Mech. Sci. 63, 86–98 (2012)
Jorgensen, O., Giannakopoulos, A.E., Suresh, S.: Spherical indentation of composite laminates with controlled gradients in elastic anisotropy. Int. J. Solids Struct. 35, 5097–5113 (1998)
Keer, L.M., Dundurs, J., Tasi, K.C.: Problems involving a receding contact between a layer and a half-space. J. Appl. Mech. 39, 1115–1120 (1972)
Krenk, S.: On quadrature formulas for singular integral-equations of 1st and 2nd kind. Q. Appl. Math. 33(3), 225–232 (1975)
Krumova, K., Klingshirn, C., Haupet, F., Friedrich, K.: Microhardness studies on functionally graded polymer composites. Compos. Sci. Technol. 61, 557–563 (2001)
Liu, J., Ke, L.-L., Wang, Y.S.: Two-dimensional thermoelastic contact problem of functionally graded materials involving frictional heating. Int. J. Solids Struct. 48, 2536–2548 (2011)
Mao, J.-J., Liu, J., Ke, L.-L., Wang, Y.S.: Thermoelastic contact instability of a functionally graded layer and a homogeneous half-plane. Int. J. Solids Struct. 51, 3962–3972 (2014)
Mao, J.-J., Ke, L.-L., Wang, Y.S.: Thermoelastic instability of a functionally graded layer and a homogeneous layer. Int. J. Mech. Sci. 99, 218–227 (2015)
Paris, F., Blazquez, A., Canas, J.: Contact problems with nonconforming discretizations using boundary element method. Comput. Struct. 57(5), 829–839 (1995)
París, F., Foces, A., Garrido, J.A.: Application of boundary element method to solve three-dimensional elastic contact problems without friction. Comput. Struct. 43(1), 19–30 (1992)
Popov, V.L.: Contact Mechanics and Friction, 8th edn. Springer, Berlin (2010)
Ratwani, M., Erdogan, F.: On the plane contact problem for a frictionless elastic layer. Int. J. Solids Struct. 9(8), 921–936 (1973)
Rhimi, M., El-Borgi, S., Said, W.B., Jemaa, F.B.: A receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate. Int. J. Solids Struct. 46, 3633–3642 (2009)
Rhimi, M., El-Borgi, S., Lajnef, N.: A double receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate. Mech. Mater. 43, 787–798 (2011)
Satish Kumar, K., Dattaguru, B., Ramamurthy, T.S., Raju, K.N.: Elasto-plastic contact stress analysis of joints subjected to cyclic loading. Comput. Struct. 60(6), 1067–1077 (1996)
Suresh, S., Giannakopoulos, A.E., Alcala, J.: Spherical indentation of compositionally graded materials: theory and experiments. Acta Mater. 45, 1307–1321 (1997)
Yan, J., Li, X.: Double receding contact plane problem between a functionally graded layer and an elastic layer. Eur. J. Mech. A Solids 53, 143–150 (2015)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Çömez, İ., El-Borgi, S., Kahya, V. et al. Receding contact problem for two-layer functionally graded media indented by a rigid punch. Acta Mech 227, 2493–2504 (2016). https://doi.org/10.1007/s00707-016-1648-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-016-1648-8