Dynamic frictional contact mechanics between a functionally graded orthotropic medium and a moving flat punch

Abstract

The present study establishes a general theory for dynamic frictional contact mechanics between an orthotropic graded half-plane and a moving rigid punch of a flat profile. The rigid punch moves over the orthotropic graded half-plane at a constant subsonic speed. Analytical method is developed for the contact mechanics problem based on two-dimensional elastodynamics. Stresses in the orthotropic graded medium are determined considering plane elasticity. Governing partial differential equations are solved analytically by the use of Galilean and Fourier transformations. The unknown functions appearing in the displacement components are determined considering the surface boundary conditions. The mixed boundary value problem is then reduced to a singular integral equation of the second kind which is solved numerically using an appropriate expansion-collocation technique. The contact stress results of the present analytical study are compared to those generated through a finite element analysis regarding the elastostatic case. Moreover, the contact stress results obtained in the elastodynamic case are also verified using some analytical results available in the literature. Successful agreement is attained in all the comparative analyses. Normal contact stress, lateral contact stress and punch stress intensity factors are calculated for various values of punch speed, coefficient of friction, in-homogeneity constant and orthotropic elastic constants. Results of the present study clearly indicates that the utilization of elastodynamic theory is crucial to get more realizable and accurate estimations of contact stresses especially in high speed sliding conditions.