The small displacement elastic solution to the ball-on-ring testing method

The ball-on-ring experiment is used for testing of the biaxial strength of ceramics. In this work the solution for the stress distribution and displacements of the disc specimen in the ball-on-ring experiment are determined on closed form. The solution comprises the displacement field and its derivatives, the shear force distribution, the bending moments distribution for the entire specimen. From these the stress distributions are obtained. Solutions for this problem already exist in the literature, but these are incorrect and they have been shown to deviate from both experiments and finite element solutions. The correctness of the solution in this work is validated with more than 3000 finite element simulations for a large range of geometric parameters of the experimental setup. It is shown that the solution is accurate and only deviates in limiting cases.

► The stress field in a ball-on-ring test specimen is obtained analytically.
► Radial, tangential and shear stresses for the entire specimen are obtained.
► The elastic modulus can be found from the determined vertical displacement field.
► The solution is found accurate by comparison to finite element models.