Parametric study of the deformation of transversely isotropic discs under diametral compression

Christos F Markides,Stavros K Kourkoulis

doi:10.3221/igf-esis.41.51

Abstract

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, indepth 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.

Highlights

The 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 for the estimation of the tensile strength of brittle materials
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 [3,4,5,6,7], the fracture load recorded by such an experiment can be used to determine the material tensile strength, assuming that fracture starts from the disc center
The specific loading scheme is very close to the actual distribution of radial stresses [15, 16] developed along the disc-jaw contact arcs, when an intact isotropic disc is compressed between the curved jaws of the device suggested by the International Society for Rock Mechanics (ISRM) [1], in which case the length of these arcs is not constant but rather it is a function of the load level imposed and the relative stiffness of the disc and jaws materials, as it is expressed by the ratio of the respective elastic moduli [17]

Summary

INTRODUCTION

The 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. 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 [3,4,5,6,7], 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 At this point, it is emphatically underlined that the analytic solutions, which have been used for the derivation of the as above classical formulae, are valid exclusively for linearly-elastic isotropic materials. For the specific purely plane strain configuration, the present study is concerned with a thorough parametric investigation of the displacement and strain fields developed all over the disc cross-section

Guide pin

Shear strain γrθ

Findings

DISCUSSION AND CONCLUDING