Fracture of glass in tensile and bending tests

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I.

INTRODUCTION

THE experimental determination of strength in brittle materials is a highly complex problem, t',21 For example, in tension tests, a major difficulty lies in mounting the specimen in the machine. Fixtures used for tensile testing of ductile materials cannot be used, because they rely on plastic deformation of the specimen ends to assure gripping. If used on a brittle material, they cause fractures before any significant plastic deformation occurs. On the other hand, dog-bone grips or others for gripping button-ended specimens require careful adjustment to attain the near perfect alignment required to eliminate spurious bending stresses. Therefore, in brittle materials of relatively large size, it is easier, and more usual, to measure mechanical strength using bending tests. In the case of material samples such as optical fibers, having small transverse dimensions (micrometers) combined with high flexibility, a tensile test can be performed quite easily using a capstan-drive grip system.t31 By contrast, in these materials, the conventional bending test is nearly impossible to perform, because the high flexibility demands such a small spacing between knife edge supports. An alternative test in this case is to wrap the fiber around a mandrel to attain a specific radius of curvature. In studying the mechanical behavior of optical fibers, both bending and tension tests are used. Generally, the so-called dynamic fatigue strength t4.5] is measured using a tension test, while the static fatigue strength ]6J is more conveniently measured in bending. However, difficulties may arise when comparing results from the different tests, for instance, interpretation of the proof testing experiments generally used as a guarantee of mechanical strength for optical fibers. Proof testing may be conducted either by tension tT] or by bending tsj tests, and ORESTES E. ALARCON, Professor, is with LABMAT, Univ. Fed. S. Catarina, CP 476 88040-970, Florianrpolis, SC, Brazil. RICARDO E. MEDRANO, Emeritus Professor, is with the Faculdade de Engenharia Mechnica, UNICAMP, CP 6122 13081-970, Campinas, SP, Brazil. PETER P. GILLIS, Professor, is with the Department of Materials Science and Engineering, University of Kentucky, Lexington, KY 40506-0046. Manuscript submitted May 17, 1993. METALLURGICALAND MATERIALSTRANSACTIONSA

there are definite problems in trying to establish an appropriate correlation between the two. Two assumptions commonly made in analyses of fracture in brittle materials are that some distribution of flaws exists initially in the material and that the fracture process consists of the propagation of a single crack from that flaw which is most highly stressed in relation to its size. Consequently, compressive stresses are usually ignored and some sort of "weakest link" model is adopted to describe the material. Although other distributions have also been used, Weibull statistics r9.1o1are used most often because they fit a great many data sets. II.

THEORY

Compare the central span of a cylindrical specimen underg