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

Abstract

This paper considers the receding contact problem between an exponentially graded layer and a homogeneous layer under the indentation of a tilted rigid flat-ended punch. In the presence of an offset load deviated from the symmetry axis of the rigid punch, the contact pressures both under the rigid punch and along the receding contact interface between the layers lose symmetry. Depending on the magnitude of eccentricity, either complete or incomplete contact may take place under the rigid flat-ended punch, whereas a receding type of contact always occurs along the interface separating the graded and the homogeneous layers. Fourier integral transforms help to convert the governing equations and mixed boundary conditions of the double-contact problem into dual Fredholm integral equations of the second kind with Cauchy-type singular kernels. Gauss–Chebyshev and Gauss–Jacobi numerical quadratures are subsequently employed to discretize and collocate the dual singular integral equations, together with the four force and moment equilibrium equations, for the complete and incomplete contact, as well as the transitional status corresponding to the critical load eccentricity. Extensive parametric studies indicate that the critical load eccentricity depends on the property gradation of the graded layer and the layer-thickness ratio, but not on the magnitude of the indentation load. The extent of contact both under the rigid flat-ended punch and along the receding contact interface is also independent of the magnitude of the indentation load. The results suggest reasonable departures from the contact properties of a homogeneous half-plane under a tilted rigid flat-ended punch, indicating the valuable information on optimizing the double-contact properties in terms of the property gradation and layer-thickness ratio under a given eccentricity.