As a new kind of inhomogeneous composite, functionally graded materials (FGMs) generally consist of a gradual change in the volume fraction of constituents from one location to the other in a component. When FGMs are used as coatings or interfacial materials, appropriate gradual variation of their elastic modulus may significantly reduce mismatching stresses and improve surface properties around the indenter, and even leads to suppression of Hertzian cracking at the edge of the contact region (Suresh et al.,1997: 1307-1321). Functionally graded materials are extensively used in turbine blades, wear-resistant coating, cutting edges, rocket engine components, high speed train, space vehicles, micro-electronics, heat exchanger tubes, etc. In the past two decades, researchers kept their concern the contact mechanics of FGMs because of the potential application to resist the contact deformation and damage. Purpose: The purpose of this study is to solve a continuous contact problem of a functionally graded layer resting on rigid foundation and loaded by a rigid circular punch. Method: An inhomogeneous functionally graded elastic layer of finite thickness h extending infinitely in the x-direction is in contact with a rigid foundation. The graded layer is modeled as an inhomogenous medium with a constant Poisson’ ratio and exponentially varying shear modulus and mass density. It is assumed that contact between all surfaces is frictionless, the effect of functionally graded layer’s body force is taken in consideration, and only compressive stress is transferred along the contact surfaces. Where applicable, the germane quantities are reckoned per unit length in the z-direction. Using theory of elasticity and integral transform techniques, the problem is converted into the solution of a Cauchy-type singular integral equation in which the contact stress under rigid circular punch and half contact width are the unknowns. This singular integral equation is solved numerically using the Gauss–Chebyshev integration formula and an iterative scheme is employed to obtain the correct half contact width that satisfies the equilibrium condition. Findings: The effects of the inhomogeneity parameters (stiffness and density parameters) of the functionally graded layer and the radius of the punch profile on the contact stress distribution under rigid punch, half contact width between functionally graded layer and rigid circular punch, the initial separation load and the initial separation distance between the functionally graded layer and the rigid foundation have been determined. Conclusion: It has been concluded after this study that half contact width between functionally graded layer and rigid circular punch increases with increasing of punch radius. Contact stress distribution under rigid punch is symmetrical, its maximum value occurs at the symmetry axis, its value is zero at the end points of contact and it decreases as the punch radius increases. Results show that with increasing values of inhomogeneity parameters (stiffness and density parameters), the initial separation load between functionally graded layer and rigid foundation decreases. Otherwise, the initial separation distance between functionally graded layer and rigid foundation increases as the inhomogeneity parameter (stiffness parameter) increases and it is not affected by the change in another inhomogeneity parameter (density parameter).
Anahtar Kelimeler: Continuous Contact, Functionally Graded Layer, Rigid Punch
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