The use of Hertzian contact in determining coating thickness

摘要

The elastic response between cylindrical bodies in contact was first described by Hertz in his classic papers [I], and expanded upon over the ensuing years [2,3]. The nature of the elastic response between curved bodies is readily modified to describe that of a curved body and a planar one, simply by allowing the radius of curvature of one body to become infinitely large; this is the form of Hertz's solutions which is commonly applied to the situation of a spherical indenter impinging on a flat substrate (see Fig. 1). On application of a normal force (P), a circular region of contact is produced. The diameter of the contact area, 2a, is dependent upon the magnitude of the indentation load, and the elastic properties of the indenter and substrate. The relation originally described by Hertz is given in a slightly modified form specific to this application by: