A multilayer approach is developed to solve the moving Hertzian contact problem involving a circular punch and a functionally graded multiferroic coating. The mathematical model constructed consists of arbitrary numbers of multiferroic layers and elastic interlayers, and a half -plane substrate. The formulation is based on wave equations of plane elastodynamics and Maxwell's equations. The problem is reduced to a singular integral equation by applying Galilean and Fourier transformations. The integral equation is solved numerically through an expansion -collocation technique. A convergence analysis is performed to determine the number of homogeneous multiferroic layers required to simulate the behavior of functionally graded coatings. Presented parametric analyses illustrate the influences of coating type, punch speed, kinetic friction coefficient, and coating thickness upon contact stresses, electric displacement, magnetic induction, and the required contact force. Magnetoelectricity of the system is shown to be significantly coupled with mechanical parameters such as the kinetic friction coefficient and coating thickness.

This article presents analytical solution procedures for moving Hertzian contact problems involving multi-layer and functionally graded coatings. A frictional circular punch is assumed to slide down the surface of the coating with a specified velocity. Formulation is based on wave equations of plane elasticity, and reduced to a singular integral equation by Galilean and Fourier transformations. Developed procedures are verified through comparisons to the findings available in the literature. Numerical results illustrate influences of factors such as dimensionless punch speed, coefficient of kinetic friction, property variation profile, and contact length-to-thickness ratio upon the contact stresses, and the required contact force.

This paper presents a multi-layer model for moving contact problems of functionally graded coatings whose physical properties have general spatial variations. The coating is assumed to be composed of an arbitrary number of layers and perfectly bonded to an elastic substrate. Wave equations for the layers and the substrate are derived in accordance with the plane theory of elastodynamics. The equations are solved by the application of Galilean and Fourier transformations. Flat and triangular punch profiles are considered, and the formulation is reduced to a singular integral equation of the second kind in both cases. The integral equations are solved by means of Jacobi expansion and collocation techniques. Proposed procedures are verified through comparisons to the results available for a special case in the literature. Parametric analyses are carried out for functionally graded coatings possessing ceramic-rich, metal-rich, and linear profiles. The results presented demonstrate the influences of factors such as punch speed, coefficient of friction, material property variation profile, and contact-length-to-thickness ratio on contact stresses, punch stress intensity factors, and required contact force. It is shown that the multi-layer model is required to account for general property distributions in a functionally graded coating subject to moving contact.

This article presents analytical methods for analysis of an inclined surface crack in an orthotropic medium subjected to contact loading. Governing partial differential equations are derived in accordance with plane theory of orthotropic elasticity. Contact and crack problems are formulated separately utilizing Fourier transformation techniques. The contact problem consists of a rigid flat punch pressing upon an orthotropic half-plane, and is reduced to a singular integral equation of the second kind. The surface crack is assumed to be tilted at an arbitrary angle with respect to the normal of the half-plane surface. Three different crack configurations are considered, which are completely closed, partially-closed, and fully-open cracks. Frictional contact between the crack faces is implemented in the cases of completely closed, and partially-closed cracks. A single singular integral equation is derived for the completely closed crack, whereas each of the problems of partially- and fully-open cracks requires derivation of a set of two singular integral equations. The contact problem and each of the crack problems are solved numerically by means of the expansion-collocation technique. A flowchart is developed and implemented to detect the type of crack closure configuration under a given contact loading. The parametric analyses carried out illustrate the influences of factors such as crack inclination angle, crack face and contact surface friction coefficients, material orthotropy, and relative punch location on crack face contact stresses, degree of crack closure, and mode I and II stress intensity factors.