PSI - Issue 42

Christos F. Markides et al. / Procedia Structural Integrity 42 (2022) 202–209 Stavros K. Kourkoulis and Christos F. Markides et al. / Structural Integrity Procedia 00 (2022) 000 – 000

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material tested or their results depend on the geometry of the specimen and the relative stiffness of the disc and jaw (or loading platens) materials , which obviously should not be the case when defining a mechanical property of a material. In this context, an alternative configuration is here introduced, denoted as the Circularly Truncated Brazilian Disc (CTBD), in an attempt to ensure, as much as possible, central splitting of the disc and, also, independence of the test results of the relative stiffness of the disc-jaw pair of materials and the geometry of the specimens used. The CTBD is essentially a BD of radius R and thickness t , bearing two symmetric cavities of radius R 1 at a distance h from the disc’s center (Fig.1a). Two semi-circular indenters of slightly smaller radius R 2 ( R 2 < R 1 ) are placed into these cavities transferring the compressive load ( P frame ) from the loading platens to the specimen (Fig. 1b). In this way, a predefined contact length is achieved during loading, since the whole of the cavity ’s rim comes in contact with the indenter, thus removing the influence of the relative stiffness of the disc’s and platens materials. In addition, the contact length (the whole rim of the cavity) is quite longer, compared to the respective lengths achieved when using the classical BD configuration, reducing, thus, significantly the severity of the contact stress field at the midpoint of the contact length. Moreover, these stresses are bounded or even zero at the ends of the contact rim, due to the concave shape of the indenter (contrary to convex indenters, often used in tests between the classical BD and the flat platens, triggering high stress concentration-penetration at the ends of the loaded rim).

frame P

me

1 R

1 R

Indenter

Semicircular indenter

Semicircular indenter

2 R

2 R

Platen

t

R

R

Circularly truncated Brazilian disc (CTBD)

R

h

h

CTBD

(Undeformed state)

(Undeformed stat

(a) (b) Fig. 1. The configuration of the specimens and the experimental setup according to the CTBD.

The problem concerning the stress distribution in the CTBD is here solved analytically in two steps; first the contact stresses are obtained from the CTBD-indenter contact problem. Then these stresses are used as the boundary values of stresses in solving the problem of the isolated CTBD. Under the assumption of linear elastic, isotropic and homogeneous materials, Muskhelishvili’s complex potentials technique is used (Muskhelishvili 1963). According to the solution proposed, stresses and displacements are obtained everywhere on the CTBD. Tables for the maximum contact, and the hoop stresses at the center of the disc (standing for the tensile strength of the material) are then given comparatively for the CTBD, the BD test according to the ASTM standard, the BD test according to the ISRM standard, and the FBD test for non-uniformly distributed boundary stresses (Markides & Kourkoulis 2022). It is re vealed that the CTBD configuration provides results closely approaching the respective ones provided by Hondros’ formula (Hondros 1965) for the tensile strength of the disc’s material, independently of the geometry and the rela tive stiffness of the materials the disc and the loading device are made of. The comparison reveals, also, the relative ly low contact stress severity through the whole contact rim of the CTBD, which reduces significantly the possibil ities of premature fracture in this area in favor of a successful centrally splitting test. It is to be mentioned, however, that an extensive experimental protocol needs to be implemented, in order to evaluate and validate the theoretical approach described here, before drawing any final conclusions concerning the efficiency of the proposed setup.