Effects of Couple Stresses on Stress Distributions in a Disc Specimen Subjected to Diametral Compression

Abstract

The present paper is concerned with the effects of couple stresses on the stress distribution in a disc subjected to diametral compression. An analytic solution was obtained by the Fourier-Bessel expansion method. Results are as follows. (1) The effect of couple stresses is remarkable. The larger the material parameter l for bending rigidity becomes, the more the magnitude of stresses on the diametral plane in the loading direction is reduced, especially in tension. In the case, for instance, where the ratio of the material parameter l to the radius of the disc a, i.e. l/a, is 0.2, the tensile and the compressive stresses at the center are respectively reduced to about 50 percent and 80 percent of those obtained by the classical theory of elasticity. The stresses on the diametral plane perpendicular to the loading direction develop more uniformly with an increase of the ratio l/a. (2) The effect of the loading width on the stress distribution is limited near the loaded boundary. As the loading width increases, the turning point of the circumferential stress from tensile to compressive is shifted toward the center and the radial compressive stress becomes more uniform. The influence of the loading width is less dominant in the couple stress theory. (3) As the Poisson's ratio increases, the magnitude of both compressive and tensile stresses generally increases. The effect of the Poisson's ratio, however, is not very predominant.