Analytical and numerical study of the stress field in a circular semi- ring under combined diametral compression and bending

Abstract

The stress field developed in a circular semi-ring under the com­bined action of diametral compression and bending is explored both analytically and num­erically. The analytic solution is implemented by means of the complex potentials technique as it was formulated by Muskhe­lishvili, while for the nu­m­eri­cal study a finite element model, properly validated based on expe­ri­mental data, is used. The ana­lytic solution provided closed formulae for the stress field along strategic loci of the specimen, while the nu­m­eri­cal model permitted thor­ough parametric investigation of the de­pend­ence of critical quantities on geometrical and loading factors. The idea behind the study is to assess the potentialities of the circular semi-ring as a possible substitute of the familiar Brazilian disc, in the direction of curing drawbacks of the latter. It was concluded that a circular semi-ring subjected to eccentric diametral com­pression provides reliable data for the tensile strength of very brittle materials, relieved from ambiguities char­acterizing the standardized Brazilian-disc test.