On the receding contact between a graded and a homogeneous layer due to a flat-ended indenter

Abstract

This paper solves the frictionless receding contact problem between a graded and a homogeneous elastic layer due to a flat-ended rigid indenter. Although its Poisson’s ratio is kept as a constant, the shear modulus in the graded layer is assumed to exponentially vary along the thickness direction. The primary goal of this study is to investigate the functional dependence of both contact pressures and the extent of receding contact on the mechanical and geometric properties. For verification and validation purposes, both theoretical analysis and finite element modelings are conducted. In the analytical formulation, governing equations and boundary conditions of the double contact problem are converted into dual singular integral equations of Cauchy type with the help of Fourier integral transforms. In view of the drastically different singularity behavior of the stationary and receding contact pressures, Gauss–Chebyshev quadratures and collocations of both the first and the second kinds have to be jointly used to transform the dual singular integral equations into an algebraic system. As the resultant algebraic equations are nonlinear with respect to the extent of receding contact, an iterative algorithm based on the method of steepest descent is further developed. The semianalytical results are extensively verified and validated with those obtained from the graded finite element method, whose implementation details are also given for easy reference. Results from both approaches reveal that the property gradation, indenter width, and thickness ratio all play significant roles in the determination of both contact pressures and the receding contact extent. An appropriate combination of these parameters is able to tailor the double contact properties as desired.

Effects of a tilted flat-ended punch on the receding contact between a graded and a homogeneous layer

“…Prior to investigating the effects of eccentricity, material, and geometric parameters on the contact properties of the double-contact model, verification and validation are conducted for the proposed solution method and the numerical algorithm of the dual singular integral equations. For this purpose, the symmetric frictionless indentation of the same double-layer structure due to a rigid flat-ended punch studied by Cao and Mi [25] is used as a benchmark. To make the results comparable, the eccentricity is set to zero ( e = 0 ) .…”

“…To develop a numerical solution scheme, let us now replace the dimensionless contact pressures (u 1 (s 1 ), u 2 (s 2 )) with equation (25). Since the singularity behavior of the receding contact interface is not affected, the weighting function (27a) remains valid for g 1 (s 1 ).…”

“…As indicated by the above-reviewed references, most literature studies employed either traction loads or smooth punches to indent the layer-substrate receding structure. Nonetheless, rigid indenters with a flat-ended contour are also widely used in engineering practice [23][24][25]. The use of rigid flat-ended punches introduces additional complexes that must be carefully addressed.…”

“…Figure 2. Validation of the (a) upper and (b) lower contact pressures with literature results[25] for the case of zero eccentricity (a=h 1 = 1,h 2 =h 1 = 1, e=h 1 = 0).…”

Receding Contact Problem of Multi-Layered Elastic Structures Involving Functionally Graded Materials

“…Ozsahin and TaskJner [41] investigated an elastic layer on an elastic half plane loaded by three rigid flat indenters. A recent study [42] solved for the frictional receding contact between an FG layer and an orthotropic substrate under the indentation of a rigid flat-ended indenter, and Cao and Mi [43] investigated the receding contact between a graded and a homogeneous layer.…”