The incorporation of work hardening and redundant work in rod-drawing analyses

Abstract

With few exceptions, metal deformation analyses employ a constant yield stress (rigid, perfectly plastic metal) which ignores strain hardening, or a “mean” yield stress which attempts to accommodate strain hardening in a simplified manner. Since strain hardening is of interest here, little reference will be made to a rigid, plastic type of behavior. The first part of this paper demonstrates that the use of a mean yield stress underestimates the working loads (or stresses) needed to draw metal through conical dies as compared to those loads predicted by more “exact” analyses. In this context “exact” refers to those solutions obtained by incorporating the strain hardening relationship in the governing “force balance” differential equations prior to the integration of the said equations. It is shown, however, that the error introduced by the use of a mean yield stress is no more than some 8 per cent for conditions that typify actual practice. Since analyses of other metal-working processes, such as rolling and extrusion, employ the same sort of differential equation, it is felt that these results are applicable there also. The second part of this paper shows that redundant work in rod drawing may be approached either from considerations of the mechanical properties that result after the metal is drawn or from considerations of the stress necessary to draw down the rod. Contrary to what is implied in the literature, it is shown that these two approaches lead to different interpretations of the “redundant work factor”. Relationships are given between the two for metals that are assumed to strain harden in certain simple ways.