Viscoplastic deformation of rotating thin-walled disks

Abstract

It is assumed, that the total strain rate can be decomposed additively into a purely elastic and an inelastic part. The evolution of the inelastic strain rate tensor is governed by a viscoplastic constitutive model with internal state variables. A rotating disk of uniform thickness is considered. It is presupposed that the thickness is much smaller than the outer diameter of the disk. Then a state of plane stress can be assumed and a quasianalytical solution is derived which contains parameter integrals of functions of the inelastic strain rates. The inelastic constitutive model poses an initial value problem. Since the governing ordinary differential equations are not only highly nonlinear but also mathematically stiff special consideration has to be given to time integration. Therefore, an implicit time integration algorithm is presented which is unconditionally stable. A numerical solution is computed using Hart's model and it is compared with a finite element solution. Deviations between the quasianalytical and the finite element solution are discussed.