An alternative analytic approach to the Brazilian disc test with friction at the disc-jaw interface

The role of the tangential (friction) stresses developed at the disc-jaw interface during the standardized realization of the Brazilian disc test is quantified. Sinusoidal variation of both the radial pressure and the friction stresses is considered. The pressure is maximized at the symmetry axis of the load distribution while friction is maximized at the mid-point of the contact semi-arc. Both load distributions (radial and frictional) are exerted along the actual contact length as it is developed during the loading procedure. The stress field all over the disc due to friction stresses is determined in closed form using the complex potentials technique. The solution obtained is applied for two materials both of brittle nature and of different relative deformability compared to steel (i.e. the material of the jaw). The stress field due to friction is compared for both materials with that due to radial pressure, and then, the two solutions are superimposed in order to quantify the total stress field. It is concluded that as one approaches the loading platens, non-ignorable tensile stresses are developed that could lead the disc to premature failure far from the disc’s center. The magnitude of these stresses strongly depends among others on the relative deformability of the disc’s and jaw’s materials since the latter dictates the extent of the loading rim.