The Stress Field in the Flattened Brazilian Disc and the Critical Role of the Actual Boundary Conditions

Abstract This is the final part of a project nearing completion, aiming to provide an analytical solution for the stress field in the Flattened Brazilian Disc. Its innovative aspect, besides providing full-field solution for the stresses, is that it describes realistically the boundary conditions that prevail along the disc-loading platens contact area during the laboratory implementation of the homonymous test, without ignoring the friction stresses. The problem is solved in two discrete steps. Initially, the distributions of stresses (normal and frictional ones) along the contact area are obtained by solving the respective disc-loading platen contact problem. It is indicated that the contact length increases with increasing load, generating, thus, additional contact stresses. The above distributions are, then, employed as boundary conditions for the formulation of the respective first fundamental problem for the isolated Flattened Brazilian Disc. Solving this problem, analytical, full-field expressions for the stress field developed are obtained. Exploration of this field reveals the dependence of the outcomes of the test on the actual disc-platens contact conditions, and the diversity between the Flattened and the classical Brazilian Disc Test. Finally, nomograms are provided, correlating the outcomes of the present solution, and those of existing ones, to the respective outcomes of the standardized Brazilian Disc Test, in the direction of facilitating and standardizing the procedure for the determination of the indirect tensile strength of brittle materials.