On the Speeds of Instability of a Rotating Hollow, Anisotropic Cylinder

Abstract

Hill’s theory of plastic anisotropy is used to investigate the effect of the parameters of anisotropy on the speeds at which long, hollow cylinders rotating about their longitudinal axes reach their maximum load carrying ability. Taking the principal axes of anisotropy to coincide with the principal stress directions and considering true stresses and logarithmic strains a relationship between the tangential strain at the bore and the rotational speed is derived and the rotational speed at which fracture due to instability may begin is noted. It is found that decreasing yield strength in the axial direction results in increased load carrying capacity.