Effect of Plastic Anisotropy on the Size of Elastic-Plastic Boundary in a Rotating Disk Problem

Abstract

The problem of dependence of stress distribution and size of elastic-plastic boundary on the angular velocity, material anisotropy, boundary conditions and geometric parameters in rotating disks is of great importance due to a large number of applications. In particular, all of these parameters can have a significant effect on the development of plastic zones in such disks. The elastic stress distribution in rotating anisotropic disks with constant and variable thickness is well known. However, there are only a few studies incorporating plastic stress analysis for anisotropic materials. Considering the case of a single elastic perfectly-plastic annular rotating disk, subjected to typical stress boundary conditions, the influence of the leading design parameters - material anisotropy coefficients - on the size of elastic-plastic boundary arising due to the action of centrifugal forces is investigated. An axisymmetric problem is formulated assuming that the principal axes of anisotropy coincide with the radial and tangential directions in the plane of the disk. The Hill’s quadratic yield criterion is adopted in the plastic zone, and material properties in the elastic zone are considered to be isotropic obeying the general Hooke’s law. All stresses are assumed to be continuous across the elastic-plastic boundary. Three different characteristic values of rotational speed are chosen in numerical calculations. It is demonstrated that the size of the plastic zone is very sensitive both to the change in material anisotropy coefficients and the magnitude of angular velocity.