The Brazilian disc under non-uniform distribution of radial pressure and friction

Abstract

The stress field developed in an intact Brazilian disc is determined assuming that the externally imposed radial pressure is not uniform but rather it varies according to a sinusoidal law along the loaded rims of its periphery. In addition it is considered that friction forces are developed at the loading platen–disc interface. The problem is solved using the complex potential method adopting the theory of holomorphic functions. The solution obtained is believed to be closer to the experimental evidence either the tests are realized using plane platens or the ISRM suggested device. Comparing the results of the present solution with the respective ones obtained for a disc exclusively under uniform radial pressure it is concluded that there are no significant differences at the center of the disc. On the contrary significant discrepancies appear in the vicinity of the load application area. The presence of friction amplifies the phenomenon and the discrepancies become higher. It is concluded that the stress field obtained is relieved from some of the drawbacks of solutions adopting uniform pressure, like for example the unnatural stress gradients developed at the end-points of the externally applied load.