Issue 41

Ch. F. Markides et alii, Frattura ed Integrità Strutturale, 41 (2017) 396-411; DOI: 10.3221/IGF-ESIS.41.51 396 Parametric study of the deformation of transversely isotropic discs under diametral compression Christos F. Markides, Stavros K. Kourkoulis 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 stakkour@central.ntua.gr A BSTRACT . The displacement field in a circular disc made of a transversely isotropic material is explored in a parametric manner. The disc is assumed to be loaded by a parabolic distribution of compressive radial stresses along two finite arcs of its periphery in the absence of any tangential (frictional) stresses. Advantage is here taken of a recently introduced closed-form analytic solution for the displacement field developed in an orthotropic disc under diametral compression which was achieved adopting the complex potentials technique for rectilinear anisotropic materials as it was formulated in the pioneering work of S.G. Lekhnitskii. The analytic nature of this solution permits thorough, in- depth exploration of the influence of some crucial parameters on the qualitative and quantitative characteristics of the deformation of transversely isotropic circular discs compressed between the jaws of the devise suggested by the International Society for Rock Mechanics for the standardized implementation of the Brazilian-disc test. The parameters considered include the anisotropy ratio (i.e., the ratio of the two elastic moduli characterizing the disc material), the angle between the loading axis and the planes of transverse isotropy and the length of the loaded arcs. Strongly non-linear relationships between these parameters and the components of the displacement field are revealed. K EYWORDS . Rectilinearly anisotropic materials; Transverse isotropy; Aniso- tropy ratio; Brazilian-disc test; Displacement field. Citation: Markides, Ch.F., Kourkoulis, S.K., Parametric study of the deformation of trans- versely isotropic discs under diametral com- pression, Frattura ed Integrità Strutturale, 41 (2017) 396-411. Received: 21.05.2017 Accepted: 31.05.2017 Published: 01.07.2017 Copyright: © 2017 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 configuration of a circular disc squeezed between two either plane or curved jaws is quite familiar to engineers, since it is widely used in practical applications (in the standardized form of the Brazilian-disc test [1, 2]) for the estimation of the tensile strength of brittle materials. Although the stress and displacement fields developed in a circular disc under the as above loading scheme are quite complicated and by no means uniaxial, it is widely accepted that, under specific restrictions and limitations [3-7], the fracture load recorded by such an experiment can be used to determine the material tensile strength (according to the simplified formulae proposed by Carneiro [8], Akazawa [9] and Hondros [10]), assuming that fracture starts from the disc center. T