Contents lists available at ScienceDirect International Journal of Mechanical Sciences journal homepage: www.elsevier.com/locate/ijmecsci On the analytical and finite element solution of plane contact problem of a rigid cylindrical punch sliding over a functionally graded orthotropic medium M.A. Güler a, ⁎ , A. Kucuksucu a,b , K.B. Yilmaz b , B. Yildirim b a Department of Mechanical Engineering, TOBB University of Economics and Technology, 06560 Ankara, Turkey b Department of Mechanical Engineering, Hacettepe University, 06800 Ankara, Turkey ARTICLE INFO Keywords: Contact mechanics Sliding contact Singular integral equations FGM Friction Finite element analysis ABSTRACT This study investigates the plane frictional contact problem of a cylindrical punch on a functionally graded orthotropic medium (FGOM). Both analytical and computational methods are developed to obtain the contact stresses. The elastic modulus is assumed to vary exponentially and the principal axes of orthotropy are assumed to be aligned with the global coordinates. In the analytical formulation, plane elasticity equations are converted to Cauchy-type singular integral equation of the second type by using Fourier Transform technique. The resulting integral equations are then solved numerically to obtain the contact stresses throughout the medium for plane stress condition. In the computational model, the elastic modulus of each finite element is specified at its centroid by using the predefined functional variation. The results obtained from the finite element analysis is verified by comparing the results obtained using the analytical formulation. The results of this study can guide tribology engineers in determining the contact stresses that have a great effect on the wear resistance of mating components. 1. Introduction Contact mechanics is a key subject in designing machine elements such as brakes, clutches, internal combustion engines, bush and ball bearings, hinges, gaskets and is of major interest in modern manu- facturing methods [45]. The motivation for using graded materials goes back to the time when Japanese blacksmiths used a graded transition from a hardened edge to a softer core [50]. Because of their smooth transition in elastic and thermal material properties, Funtionally Graded Materials (FGMs) have attracted attraction as wear resistant or thermal barrier coatings in applications such as diesel engine piston heads, heteroepitaxial multilayers used in semiconductor devices, quantum wells and light-emitting diodes. An important study on the wear resistance capability of FGMs was conducted by Suresh [53] who concluded that graded materials suppress indentation cracks during normal and frictional sliding. The research on the mechanics of FGMs was started in the mid- 1980 s with a space craft project in Japan to alleviate the shortcomings of conventional and homogeneous composite materials. The aim of the project was to develop super heat resistant materials that can with- stand high temperature gradients observed in aerospace applications [38]. Since then the application and utilization of FGMs has expanded to applications such as; functionally graded cemented carbide tool [39], nanostructured and functionally graded cathodes for solid-oxide fuel cells [35], biomedical applications [44] and piezoelectric bending devices [51]. FGMs are also used to attenuate problems resulting from fatigue, corrosion and fracture and to improve the tribological perfor- mance of contacting mating parts in an assembly such as strongly adherent super hard amorphous carbon films [52], to improve fracture toughness, biaxial bending strength, and wear resistance in joint prostheses Mishina et al. [36], to improve the adhesion of DLC films to silicone substrates [26], functionally graded diamond-like carbon coatings [8] and to improve wear resistance [57,58]. It has been shown in the literature that FGMs can suppress the formation of herringbone cracks under sliding frictional contact [54] and can eliminate conical cracking resulting from Hertzian indentation [27,42,43]. Because of the processing methods used in the manufacturing of graded coatings, FGMs engender a highly anisotropic structure (e.g. lamellar microstructure with cleavage planes parallel to the boundary when the plasma spraying technique is used [46,49] and a columnar structure with cleavage planes perpendicular to the boundary when the physical vapor deposition technique is used [28,48]). There are significant studies on the contact mechanics of graded isotropic coatings or graded half-planes. Suresh and his co-workers http://dx.doi.org/10.1016/j.ijmecsci.2016.11.004 Received 17 July 2016; Received in revised form 12 October 2016; Accepted 3 November 2016 ⁎ Corresponding author. E-mail addresses: mguler@etu.edu.tr, prof.guler@gmail.com (M.A. Güler). International Journal of Mechanical Sciences 120 (2017) 12–29 0020-7403/ © 2016 Elsevier Ltd. All rights reserved. Available online 12 November 2016 crossmark