The failure of glass cylinders in diametral compression
Abstract
This paper considers the failure mechanism of diametrically-compressed glass cylinders. Examination of failed specimens shows that fracture always initiates at the contact surface, and not within the cylinder as predicted by conventional theory. A tentative explanation for this phenomenon is given in terms of the three-dimensional stress system in the contact region and also of the frictional effects at the interface; in this connection, an analytical solution is given to the problem of adhesive contact between normally-loaded dissimilar elastic cylinders. The results have some relevance to the application of the well-known indirect tensile test for materials such as concrete and rock, and also to the general design of roller bearings.
References (29)
- H.D. Conway et al.
Inf. J. Mech. Sci.
(1969) - J. Gramberg
Engng Geol.
(1965) - R. Khadem et al.
Int. J. Engng Sci.
(1969) - E. Addinall et al.
Civ. Engng publ. Wks Rev.
(1964) - J.J. Bikerman et al.
Phil. Mag.
(1939) - F.P. Bowden et al.
The friction and lubrication of solids
- E.T. Brown et al.
Rock Mech. Engng Geol.
(1967) - P.S.B. Colback
- D.F. Cornelius et al.
RRL Rep. LR 260
(1969) - Hawkes, I. and Mellor, M. 1970 Private...
Aust. J. appl. Sci.
Br. J. appl. Phys.
Cited by (48)
The incurved Brazilian disc as an alternative to the standardized Brazilian disc test
2023, Theoretical and Applied Fracture MechanicsA modified configuration of the standardized Brazilian disc is proposed here, namely the incurved Brazilian disc, aiming to address the main drawback of the traditional indirect tensile test introduced by Carneiro and Akazawa (broadly known as the Brazilian disc test), namely the onset of fracture from the disc-jaw contact region rather than from the center of the disc. In this context, the disc is circularly truncated in the vicinity of the disc-jaw contact area, leading, in fact, to a wide, and as it is seen predefined contact length. The wide extent of the contact arc ensures small stress concentrations, while its predefined length ensures independence of the outcomes of the tests from material and geometry. The incurved Brazilian disc is compressed between the flat loading platens with the aid of two semicircular indenters, which will completely fit into the cavities of the disc under load. The analytical solution of the described configuration is obtained using Muskhelishvili’s complex potentials method. Comparison of the results of the present analysis concerning the stress and displacement fields with the respective ones due to existing solutions for the traditional Brazilian disc as well as with those of the flattened Brazilian disc, reveals interesting aspects of the modified configuration proposed, enlightening some advantages, concerning mainly the intensity of the stress field in the disc-jaw contact area.
The actual boundary conditions in the Flattened Brazilian Disc test
2023, Materials Today: ProceedingsIn the present study an attempt is made to assess a recently presented analytical approach to the problem of the contact stresses developed along the Flattened Brazilian Disc (FBD) – loading platen interface, during the implementation of the homonymous test. In this direction, a finite element model was constructed, resembling both the FBD and the platen, using the commercially available software ABAQUS. As it is seen, the predictions of the numerical analysis for the stresses induced at the interface and inside FBD are in a satisfactory agreement with the analytical ones, justifying the proposed analytic approach for the FBD configuration. In this context, it is concluded that FBD does significantly reduce the stress severity at contact region, however, the end points of the flat edges of the FBD now become points of increased stress magnitudes so that care should be taken during the preparation of the specimens regarding the cutting process at these points.
Griffith-based analysis of crack initiation location in a Brazilian test
2022, International Journal of Rock Mechanics and Mining SciencesThe Brazilian test has been extremely popular while prompting significant debate. The main source of controversy is rooted in its indirect nature; the material tensile strength is inferred upon assuming that cracking initiates at the centre of the sample. Here, we use the Griffith criterion and finite element analysis to map the conditions (jaws geometry and material properties) that result in the nucleation of a centre crack. Unlike previous studies, we do not restrict ourselves to evaluating the stress state at the disk centre; the failure envelope of the generalised Griffith criterion is used to establish the crack nucleation location. We find that the range of conditions where the Brazilian test is valid is much narrower than previously assumed, with current practices and standards being inappropriate for a wide range of rock-like materials. The results obtained are used to develop a protocol that experimentalists can follow to obtain a valid estimate of the material tensile strength. This is showcased with specific case studies and examples of valid and invalid tests from the literature. Furthermore, the uptake of this protocol is facilitated by providing a MATLAB App that determines the validity of the experiment for arbitrary test conditions.
The circularly truncated Brazilian disc
2022, Procedia Structural IntegrityThe Circularly Truncated Brazilian Disc test is here proposed, as an alternative to the classical Brazilian Disc test, in order to confront the premature fracture often observed at the disc-loading platen contact area, which undermines the validity of the results of the test. Using the configuration proposed, a predefined contact length is achieved, which is long enough to reduce the intensity of the stress field at the disc's periphery and ensuring valid outcomes of the test independently of the materials involved.
Revisiting the flattened Brazilian disc configuration - Part I: The actual boundary conditions
2022, Procedia Structural IntegrityIn a recently presented analytic solution for the Flattened Brazilian Disc (FBD), it was shown that under the usually adopted assumption of uniform pressure on the flat edges of the FBD these edges turn to appear bent after deformation. Taking into account the high rigidity and flatness of the loading platens this bent sounds somehow unnatural. In the present study an attempt is undertaken to confront this unnatural bent by considering alternative non-uniform stress distributions on the flat edges of the FBD. In this context, the present paper, which is the first part of an ongoing research project, deals with the 1st fundamental problem for a FBD when it is compressed between two rigid flat stamps of the same length with the flat edge of the FBD. The distribution of the normal compressive stresses, and that of the respective frictional ones, imposed to the flat edge of the FBD are adopted from the approach of Muskhelishvili for the contact problem of a rigid flat stamp compressed against an elastic half plane, here the FBD in question. After obtaining the complex potentials for this 1st fundamental problem for the FBD, the stresses and the displacements are calculated in closed form everywhere on the FBD’s cross section. For the assessment of the analytic solution, a numerical model is also developed, with the aid of the Finite Element Method. The agreement between the theoretical and numerical analyses is satisfactory.
Mathematical formulation of an analytic approach to the stress field in a flattened Brazilian disc
2020, Procedia Structural IntegrityAlthough more than fifteen years have passed since the flattened Brazilian disc test was introduced, analytic studies on the respective stress field are scarce, mainly due to difficulties related to the shape of its boundary. In this context, an alternative mathematical formulation, providing a full-field solution for the distribution of stresses in the flattened Brazilian disc, is here proposed, based on the configuration of an intact circular disc, under a large number of equal point forces, arranged at equal distances along two symmetric parallel chords of the disc. Considering each point force as the resultant of stresses acting on an eliminated hole, a great number of such forces implies the introduction of a large number of small holes, dividing the uniform disc into three distinct parts; the one between the two chords is to stand as the flattened disc under uniform compression. This particular problem for the uniform disc is here solved with the aid of Muskhelishvili’s complex potential technique, providing a closed-form, full-field solution for the stresses on the as above “truncated” disc, and thus, in a first approximation, on the flattened Brazilian disc. The analysis, apart from highlighting the advantage of the flattened against the classical intact Brazilian disc (regarding the reduction of stress concentration along the disc-loading platen contact region), revealed, also, that the pressure on the flat edges of the flattened disc should be non-uniform in order to better approximate the experimental reality. In this direction, a numerical model was developed, indicating the proper non-uniform distribution of pressure that should be applied along the flat edges of the flattened Brazilian disc, in order for these edges to remain plane after deformation, in accordance to the laboratory implementation of the experiment.