New analytic solution for the diametral point load strength test on finite solid circular cylinders

This paper presents an exact analytic solution for a finite isotropic circular cylinder of diameter D and length 2L subjected to the diametral point load strength test (PLST). Two displacement functions are introduced to uncouple the equations of equilibrium, and two new series expressions for these functions are proposed in terms of the Bessel and modified Bessel functions of the first kind, the trigonometric functions and the hyperbolic functions. The contact stresses between the curved surface of the cylinder and the spherical heads of the indentors are expanded into double Fourier series expansion in order to match the limiting values of the stress field on the boundary. Our numerical results show that tensile stress concentrations are developed near the point loads, compared to the roughly uniform tensile stress at the central portion of the line between the two point loads. The pattern of tensile stress distribution along this line resembles that obtained for a sphere under the diametral PLST and a cylinder under the axial PLST. The maximum tensile stress decreases with the increase of Poisson's ratio, the contact area, the radius of the spherical heads of the indentors, but increases with the diameter of the cylinder. It also decreases drastically with the increase of L/D for short cylinders (say L/D<0.4), but remains roughly constant when L/D is long enough (say L/D>0.7). Both the predicted size and shape effects of specimens on the diametral PLST agree with our experimental observations.