Closed-Form Solution for the Stresses in Brazilian Disc Tests Under Vertical Uniform Loads

Loading arcs, which create a definite contact range and have a radius equal to the test specimen, have been recently introduced into Brazilian disc tests, which are common indirect tensile strength tests. Inspired by the testing apparatus, a new kind of loading pattern acting on the disc is assumed: the vertical uniform load. This load can be resolved into radial and tangential surface forces on the loaded rims of the specimen. Under the assumptions of isotropic, linear-elastic, and homogenous disc materials, the explicit closed-form expressions for the full-field stresses in the disc are derived by the complex variable method. The analytical solutions satisfy the stress boundary condition, and the analytical results are in good agreement with the numerical simulations. Based on the closed-form solutions, it is analytically proven that the maximum tensile stress occurs at the disc center. Then, the suggested formula for the tensile strength, which is related to the contact range, the external load, and the size of specimen, is provided.