Double initial and caustic curves in diametrically compressed transparent discs - Application to the contact length

Christos Markides

doi:10.3221/igf-esis.50.38

Abstract

General formulae for double initial and caustic curves (reflected and transmitted) are obtained in the case of smooth contact of two cylindrical elastic bodies of arbitrary radii. Namely, based on the method of reflected and transmitted caustics, the conditions for the development of double initial and contact caustic curves are established as functions of six independent parameters, while easy-to-use closed-form expressions are given for obtaining the contact length. An experimental protocol is then implemented in the case a thin cylindrical transparent disc is compressed between the jaws of the International Society for Rock Mechanics suggested device for the execution of the Brazilian-disc test. The experimental method of caustics can provide the contact length quite accurately, even in the case of double curves which seem that are not always a consequence of a wide contact region.

Highlights

The experimental method of caustics is a more than fifty years old method
Based on the method of reflected and transmitted caustics, the conditions for the development of double initial and contact caustic curves are established as functions of six independent parameters, while easy-to-use closed-form expressions are given for obtaining the contact length
An effort was undertaken to describe the nature of double initial and caustic curves, generated in the contact region realized between two cylindrical bodies when compressed against each other, and based on the above description to extend/complete existing formulae [26] for obtaining the contact length

Summary

INTRODUCTION

The experimental method of caustics is a more than fifty years old method. It is a powerful technique for the study of various issues related to the mechanical behaviour of elastic bodies. The general formulae for the contact initial curves on the disc’s front and rear faces Consider the ordinary set-up of the experimental method of caustics shown in Fig.. In this context, keeping Pframe, RJ, Zo,f, and Zi constant, equal to the respective values of the reference set-up, Fig.5a shows the variations of Ff, Fr and Ft against the modulus of elasticity E; the Ff,r,t=1 line is shown as the critical value below which a double initial curve appears. The equation of the line E+t L+f (in both cases of Fig.(8a,b), which is of the form Yf,t=αXf,t+β, with α the slope, and β the ordinate of the point the line E+t L+f intersects Yf,t -axis, is given as:

L f α X E t

EXPERIMENTAL PROCEDURE

Findings

CONCLUSIONS