Disk and Strip Forging with Side-surface Foldover—Part 1: Velocity Field and Upper-Bound Analysis

With the assumptions of a Mises’ rigid, perfectly-plastic material and constant shear stress friction prevailing between the forge platens and deforming solid, the upper-bound analysis technique was applied to the upset forging of rectangular strip and solid cylindrical disks in an effort to incorporate the combined phenomena of bluge and fold. A two-zone velocity field was proposed for each geometry with Zone I occupying the interior volume and Zone II, the region near the free-surface periphery. The velocity field in Zone I was chosen as the exponential cusp-type used successfully in several previous analyses. Zone II was represented by a velocity field compatible with a foldover phenomenon and kinematically admissible with respect to boundary conditions and compatibility with Zone I. Solutions based on the above assumptions provide the forging pressure as a function of specimen geometry, interface friction, material strength, rate of bulge formation and relative size of Zone II. Minimization with respect to the last two variables provides the optimum rate of barreling or bulging and determines the degree of foldover expected.