A semianalytical and finite-element solution to the unbonded contact between a frictionless layer and an FGM-coated half-plane

Abstract

In this work, we examine the receding contact between a homogeneous elastic layer and a half-plane substrate reinforced by a functionally graded coating. The material properties of the coating are allowed to vary exponentially along its thickness. A distributed traction load applied over a finite segment of the layer surface presses the layer and the coated substrate against each other. It is further assumed that the receding contact between the layer and the coated substrate is frictionless. In the absence of body forces, Fourier integral transforms are used to convert the governing equations and boundary conditions of the plane receding contact problem into a singular integral equation with the contact pressure and contact size as unknowns. Gauss–Chebyshev quadrature is subsequently employed to discretize both the singular integral equation and the force equilibrium condition at the contact interface. An iterative algorithm based on the method of steepest descent has been proposed to numerically solve the system of algebraic equations, which is linear for the contact pressure but nonlinear for the contact size. Extensive case studies are performed with respect to the coating inhomogeneity parameter, geometric parameters, material properties, and the extent of the indentation load. As a result of the indentation, the elastic layer remains in contact with the coated substrate over only a finite interval. Exterior to this region, the layer and the coated substrate lose contact. Nonetheless, the receding contact size is always larger than that of the indentation traction. To validate the theoretical solution, we have also developed a finite-element model to solve the same receding contact problem. Numerical results of finite-element modeling and theoretical development are compared in detail for a number of parametric studies and are found to agree very well with each other.

Flamant solution of a half-plane with surface flexural resistibility and its applications to nanocontact mechanics

“…In this work, they were numerically integrated by non-dimensionalizing the integrands, dividing the semi-infinite interval into a larger number of subintervals, separated at the zeros of the sine function, and adding up each pair of neighboring positive and negative contributions. Each of the subintegrals was evaluated with the help of Gauss-Legendre quadrature [44][45][46][47]. To accelerate the convergence, an Euler transformation algorithm was implemented on the resultant alternate series [48].…”

Investigation of indentation response of bi-directional functionally graded materials

“…The gradation of Young's modulus along the coating thickness was assumed to follow exponential and power law functions. Yan et al 33 studied numerically and analytically the frictionless receding contact problem of an elastic layer and an FGM coated half-plane. In all these studies, good agreement between CHFEs and analytical results was found but the simulations of an FGM component using CHFEs are generally computationally expensive.…”

Modeling and analysis of the nonlinear indentation problems of functionally graded elastic layered solids

“…34 Yan et al. 35 considered the frictionless double contact problem involving an FGM coated-homogeneous elastic layer resting on a homogeneous elastic half-plane and indented by a rigid punch. Chidlow and Teodorescu 36,37 derived a semi-analytical model to estimate the stress and displacement fields induced within a layered material including a coating-FGM layer-substrate through frictional contact with another object.…”

“…Considering the receding contact problems, El-Borgi and Ç o¨mez 33 studied analytically the receding frictional contact between an FGM layer and a homogeneous half-plane, which were pressed against each other by a rigid stamp. The frictional receding contact problem for two FGM layers pressed by a rigid punch was analyzed using SIE approach and FEM by Yilmaz et al 34 Yan et al 35 considered the frictionless double contact problem involving an FGM coated-homogeneous elastic layer resting on a homogeneous elastic halfplane and indented by a rigid punch. Chidlow and Teodorescu 36,37 derived a semi-analytical model to estimate the stress and displacement fields induced within a layered material including a coating-FGM layer-substrate through frictional contact with another object.…”