Hide/Show Apps

Tresca's yield criterion and linearly hardening rotating solid disks having hyperbolic profiles

An analytical solution for the stress distribution in rotating hyperbolic solid disk is obtained under plane stress assumption. The analysis is based on Tresca's yield criterion, its associated flow rule and linear strain hardening material behavior. It is shown that the deformation behavior of the hyperbolic solid disk is different from that of the constant thickness disk. The plastic core consists of three different plastic regions with different mathematical forms of the yield criterion. Accordingly, three different stages of elastic-plastic deformation can be distinguished. The lower and upper bounds of the limit angular velocities for each stage are determined. It is also shown mathematically that in the limiting case the hyperbolic disk solution reduces to the solution of rotating uniform thickness solid disk.