Aluminum and Aluminum Alloys - The Effect of Thermal-mechanical History on the Strain Hardening of Metals (Metals Tech., Sept. 1948, TP 2445)

Introduction The concept that the flow stress for plastic deformation of metals in the work hardening range is a function of the instantaneous values of the strain, strain rate and test temperature was promulgated by Ludwick' many years ago. This thought has been more or less a guiding principle throughout the immediate period of development and growth of mechanical metallurgy. It has been tacitly assumed or knowingly applied to many investigations on the plastic behavior of metals. Spurred by the theoretical interest and practical importance of the plastic behavior of metals, many investigators have attempted to determine empirical, semi-empirical, and theoretical equations2-l8 relating the flow stress with the strain, strain rate, and temperature. Although the applications of such equations have been extensive, the experimental verification of the existence of a mechanical equation of state is weak. Furthermore, some of the available evidence on plastic flow appears to suggest that no simple functional relation between stress, strain-rate, strain and temperature can exist. The mechanical equation of state demands that Where a = true stress = loadlinstantaneous area e = true strain _ Instantaneous gauge length ~ initial gauge length i = true strain rate T = temperature This formulation implies that da is an exact differential. Therefore the flow stress (a) is a function of the instantaneous values of the strain (c) the strain rate (i) and the temperature (T), independent of the previous mechanical or thermal history. Having reached a certain strain, strain rate, and temperature, by any path whatsoever, a definite and fixed value of the flow stress should be obtained. One check on the validity of the mechanical equation of state is easily obtained. Consider the following three tests on the stress-strain curve at constant temperature: A. Strain at rate :I B. Strain at rate it C. Strain at rate 11 to el and continue test at &. A graphical representation of possible results of such tests are shown in Fig I. If, for strains greater than el, test (C) data coincide exactly with the data from test (B), as shown in Fig ra, a limited verification of the mechanical equation of state is obtained for the range of strain rates from il to iz. But if the data from test (C) differ from those of (g) beyond strain t\ where the strain rate is changed from il to k2, the mechanical equation of state is not