The paper presents the results of an analysis of the mechanics of contact between a rigid sphere and an elastic rigidly plastic two-layer half-space that imitates a surface covered with a hard strengthening coating. Analytical dependences are derived which relate the surface hardness to the base and coating hard¬nesses within the whole possible range of the coating thickness. A new physical interpretation of the mechanism of the deformation of a layered solid is proposed for the range of the indentation depth that commonly characterizes the domain of the existence of the composite hardness. The obtained theoretical solutions are used to determine the ranges of the thicknesses within which the composite and real hardnesses of a hardened surface exist.

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Abstract-The mechanics of a rigid sphere contact interaction with the top composite surface of elastic rigid-plastic solids is analyzed. Analytic dependencies are obtained describing both the character of load changing on rigid pyramidal and spherical indenters versus the depth of indentation in a topcomposite and elastic and plastic properties of layered system components.