The circular disc under rotational moment and friction: application to the cracked Brazilian disc test

Abstract

Indications from literature suggest that a centrally cracked circular disc subjected to diametral loading exhibits a rigid body rotation tendency due to the inherently asymmetric nature of the displacement field developed (unless the load line is either along the crack or normal to it). In turn, this rotation tendency imposes a counterbalancing distribution of friction stress along the loaded arcs of the disc’s periphery. As a result, parasitic stresses are developed perturbing the stress field developed by the main stimulus (i.e. the diametral compressive load). In this context, a first attempt is described here for the quantification of this perturbation, by considering an intact finite elastic circular disc acted by a central rotational moment and a statically equivalent distribution of counterbalancing friction stresses. The latter are assumed as parabolically distributed along the loaded arcs of the disc’s periphery. Using the complex potentials technique, the parasitic stress field is determined in closed form all over the disc and its main features along strategic loci are explored. This field is then compared to the main stress field produced by the radial pressure, assuming that the disc is compressed between the jaws of the device suggested by the International Society for Rock Mechanics for the standardised implementation of the Brazilian disc test. It is concluded that the perturbation of the main stress field in the vicinity of the disc–jaw interface cannot be neglected: locally, the parasitic stresses are well comparable to the respective ones of the main field. Along this direction, a mixed fundamental problem is then formulated and solved permitting quantification of the central rotational moment by means of the couple of forces produced by the displacement field along the lips of a central crack in a disc radially loaded by uniform pressure.