Frictional contact of a rigid punch on an arbitrarily oriented gradient half-plane

Frictional contact of a rigid punch on a half-plane with shear modulus varying according to an exponential gradient in an arbitrary direction is investigated in this paper. Fourier integral transform method is employed to reduce the current sliding contact problem to a Cauchy-type singular integral equation of the second kind. The contact pressure and the in-plane stress, as well as the stress singularity and the stress intensity factor near both contact edges are obtained, which are further analyzed for different friction coefficients, non-homogeneity parameters and gradient orientation angles. The moment in order to keep the punch moving perpendicularly to the contact surface is also evaluated. All the present results should be helpful for the design of surfaces with strong wear resistance and understanding the mechanical mechanism of graded materials in nature.