An upper bound analysis of a process-induced side- surface defect in forgings Part 1: The velocity fields and power terms

摘要

An upper bound analysis for anaxisymmetric forging with a double ram action hasbeen developed. The results of the analysis provide thegeometric and processing conditions that can be usedto avoid the development of unacceptable side-surfacecracks. Kinematically admissible velocity fields thatsatisfy the incompressibility condition and the velocityboundary conditions have been determined and thecorresponding upper bound solution for the flowpattern has been developed. To determine theconditions under which the process-induced surfacecracks would occur, a kinematically admissiblevelocity field for defective flow was developed andanalyzed by the upper bound approach. An extra powerterm that accounts for the power dissipated duringcrack formation has been added to the upper bound power for defective flow.This first paper in a two-part series presents thevelocity fields and the individual power terms thatwere derived based upon these flow patterns, whilst thesecond paper shows the characteristics of the upperbound solution for this forging process. The secondpaper also presents the criteria for the prevention of theside-surface defects that were determined based upon the upper bound solution.