The influence of jaw's curvature on the results of the Brazilian disc test

The general contact problem of a disc squeezed between jaws of arbitrary curvature is considered employing Muskhelishvili's complex potentials. Taking advantage of the general solution introduced, the closed-form expressions for the stresses along strategic loci (loaded rim, loaded diameter, disc's center) are obtained, in terms of the ratio ρ of the disc's to the jaw's curvature. Then, the effect of ρ (as well as that of the relative stiffness of the disc's and jaw's materials dictating the contact arc) on the stress distribution along these loci is explored. It is concluded that, for both smooth contact (zero friction) and contact with friction, the role of the jaw's curvature is significant not only along the disc-jaw contact arc (as it could be expected), but also all along the loaded diameter. On the other hand, it is indicated that the stress field at the disc's center is more or less insensitive to the jaw's curvature assuming that ρ lies within the range (0, 0.67) or in other words within the limits defined by the two standardized suggestions, i.e. that of American Society for Testing and Materials (ASTM) (plane loading platens with ρ = 0) and that of International Society for Rock Mechanics (ISRM) (curved jaws with ρ = 0.67). The upper limit of this range is a kind of compromise between the need to make the stress field at the disc's center independent of the boundary conditions while keeping at the same time the contact angle large enough to reduce the stress concentration and the risk for premature fracture initiation far from the disc's center. For jaws with radius of curvature exceeded by that suggested by ISRM, the stress field at the disc's center is significantly influenced. Especially for jaws with radius approaching that of the disc, the stress field at the disc's center is dramatically distorted rendering Hondros' formula inapplicable and the test results erroneous.