Limit Analysis of Hollow Disk Forging—Part 2: Lower Bound

A lower bound for hollow disk forging is presented. The hollow disk is separated into several regions by permissible surfaces of stress discontinuity. The friction stress in each zone is assumed to be either variable or constant; the overall friction stress distribution has characteristics similar to experimentally determined distributions. A statically admissible stress field describes the stress distribution within each deforming zone. The dependence of the relative average pressure, the friction stress distribution and the neutral radius upon friction and ring geometry is given. It is found that only for thin rings is the friction stress constant over most of the interface. Finally, it is proposed that friction factors being measured by use of the mathematically calibrated ring compression test may be somewhat high.