The standardized Brazilian disc test as a contact problem

Abstract

The standardized Brazilian disc test is revisited considering the disc-jaw complex as a system of two elastic bodies in contact. The aim of the study is to shed light on the conditions at the disc-jaw interface in an effort to quantify the length of the common contact rim developed as the jaw and the disc are compressed against each other. The problem is approached both analytically and experimentally. The analytic solution is based on the complex potentials method introduced by Muskhelishvili and leads to a Mixed Fundamental plane problem of the classic linear elasticity theory. The local displacement field is determined and then the contact length is obtained in closed form in terms of geometrical and material parameters of both the specimen and the loading jaws and also of the externally applied load. Moreover interesting conclusions are drawn concerning the exact variation of the radial pressure along the contact rim. The experimental approach is carried out using the 3D Digital Image Correlation technique which provides a full field representation of the displacement- and strain-fields developed. Taking advantage of the experimental data it was possible to estimate the contact length experimentally. Comparison between analytic and experimental results for the specific quantity is satisfactory.