Analytic Solution for Axial Point Load Strength Test on Solid Circular Cylinders

Abstract

This paper presents a new analytic solution for the stresses within an elastic solid finite cylinder subjected to the axial point load strength test (PLST). The “displacement potential approach” is used to uncouple the equations of equilibrium; then the contact stresses on the end surfaces induced by the point load indentors are expanded in terms of a Fourier-Bessel expansion to yield the unknown constants of the appropriate form of the displacement potential. Our solution shows that a zone of higher tensile stress is developed in the vicinity of the applied point loads, compared with the roughly uniform tensile stress in the central portion of the line between the two point loads. This peak tensile stress within the cylinder decreases with increasing Poisson's ratio and the size of the loading area, and it increases with increasing Young's modulus. The tensile stress distributions along the axis of symmetry in a cylinder under the axial PLST are remarkably similar to that observed in a sphere under the diametral PLST. Our solution also demonstrates both size and shape effects on the point load strength index (PLSI) that we observed in our experiments. In particular, for a fixed length-to-diameter ratio, the larger the specimen, the smaller the PLSI, whereas for a fixed diameter, the longer the specimen the smaller the PLSI.