Issue 50

Ch. F. Markides, Frattura ed Integrità Strutturale, 50 (2019) 451-470; DOI: 10.3221/IGF-ESIS.50.38 451 Focused on the research activities of the Greek Society of Experimental Mechanics of Materials Double initial and caustic curves in diametrically compressed transparent discs - Application to the contact length Christos F. Markides National Technical University of Athens, School of Applied Mathematical and Physical Sciences, Department of Mechanics, 5 Heroes of Polytechnion Avenue, Theocaris Bld., Zografou Campus, 157 73 Athens, Greece markidih@mail.ntua.gr A BSTRACT . 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 para- meters, 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 Inter- national Society for Rock Mechanics suggested device for the execution of the Brazilian-disc test. The experimental method of caustics can provide the con- tact length quite accurately, even in the case of double curves which seem that are not always a consequence of a wide contact region. K EYWORDS . Double initial and caustic curves; Compressed discs; Contact length Citation: Markides, Ch. F., Double initial and caustic curves in diametrically compressed transparent discs - Application to the contact length, Frattura ed Integrità Strutturale, 50 (2019) 451-470. Received: 12.01.2019 Accepted: 28.05.2019 Published: 01.10.2019 Copyright: © 2019 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. I NTRODUCTION he experimental method of caustics is now 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. It is based on the high sensitivity of light in the slightest change taking place in the surfaces as well as within the thickness of an elastic plate. At first, in the case of an opaque highly polished elastic plate, recording the path of the impinging light after reflection on its distorted surface, significant results can be drawn regarding the response on externally applied loads and constrains in conjunction with the existence or not of geometrical discontinuities. The same is true in the case of a transparent highly polished elastic plate where one has to record the paths of the impinging light after reflection on both (front and rear) surfaces of the plate. In the case of the plane elastic problem the method was first introduced by Manogg [1–4] for the case of Transmitted Caustics and then it was broadened by Theocaris [5, 6] who included the method of Reflected Caustics, to be used soon after on numerus applications [7] keeping used uninterruptedly up to nowadays . In this context, a wide variety of problems has been confronted by the method of caustics, as, the description of the stress intensity in T