The Stress Field Induced by a Twisting Sphere

Abstract

Analytical solutions are presented for the stress field induced in an elastic half space by a sphere pressed normally into its surface, and twisted. It is found that the stresses decay rapidly with depth, and that the severest stress state occurs in the surface. Cases of both partial slip, i.e., where there is a central disk where no relative rotation occurs, surrounded by a slip annulus, and full slip where the disk degenerates to a point, are considered. The largest tensile stress, associated with brittle fracture and cracking, occurs on the edge of the contact circle, while the greatest tendency to yield, by von Mises criterion, occurs somewhere within the slip annulus, depending on the coefficient of friction. Twisting has a first order effect on the strength of contact as measured by each of these criteria.