Plane Strain Forging—A Lower Upper Bound Approach

Abstract

A general kinematically admissible velocity field applicable to forging of a rectangular strip of a incompressible material is presented. Generalized shape of any dead zone, if assumed, can be obtained in terms of process parameters from this velocity field. Two different upper bound solutions for average forging pressure are obtained from simple velocity fields which are special cases of proposed general velocity field. Numerical results of the solutions show improvement over previous upper bound solutions published in literature over a certain range of process parameters.

A variational upper-bound method for analysis of upset forging of rings

“…In several past investigations, such as in Refs. [14,[18][19][20][21]26], solutions were determined without taking account for such a natural boundary condition. However, the advantage of the natural boundary condition can be in better understanding with the results to be discussed in a subsequent section.…”

“…Although such a problem has been widely investigated on the basis of upperbound theorem [18][19][20][21][22][23][24], the method we employed, also based on the upper-bound theorem, is significantly distinguishable. Specifically, an arbitrary function, which governs the velocity field in deforming material at each step of the upsetting process, is associated with the upper-bound theorem to formulate the total forming energy rate equation.…”