Induced Stress Fields in Isotropic Elastic Discs Due to Contact Shear Stresses and Their Implications for Brazilian Test Strength Characterization

Tensile strength characterization of brittle materials by means of uniaxial tensile tests is often unfeasible, as most samples form chips during specimen preparation, leading to unacceptable geometric deviations. For this reason, the disc specimens used in Brazilian tests to determine indirect tensile strength are preferred. Despite its influence on the induced stress field and the location of the failure initiation point, the actual stress distribution along the contact is still under debate. In the present work, the complex variable method is used to develop a new analytical formulation based on the simplest possible shear stress distribution along the disc boundary that fulfils elastic equilibrium. Based on this formulation, an integration method is used to obtain the stress field generated inside specimens—elastic discs—that are subjected to distributed shear forces on their contact rims. An application of this method to the Brazilian test case is performed, proving that shear and frictional forces can be considered simultaneously. Furthermore, a mathematical procedure to simultaneously consider radial and shear stress distributions along the loaded boundary is developed to determine any possible stress field for relevant practical applications. The results confirm that shearing significantly increases stress in the vicinity of the contact area, which may explain the wedge failure pattern sometimes observed in real test specimens. Additionally, the proposed formulation guarantees that if failure is initiated in the centre of the specimen, the applied shear stress distribution no longer influences the indirect tensile strength of the material, although it influences the final test output if failure is initiated at any other point along the vertical diameter.