A Self-Consistent Scheme for the Relaxation Behavior of Metals

We identify in this paper that stress relaxation in metals is a “strain-free” process. The corresponding self-consistent relations between the strain, and stress variations of a grain and of its aggregate are derived from Eshelby’s solution of an ellipsoidal inclusion. It is shown that, under such a process, the strain in a more favorably oriented grain continues to rise and that its stress decreases more drastically than that of the aggregate; conversely, for a less favorably oriented grain, its strain decreases and its stress relaxes less. The self-consistent relations are supplemented with a temperature-dependent, physically consistent constitutive equation for the slip system. Such an equation enables us to determine the single crystal constants at one temperature from the polycrystal data at another temperature; it also makes the self-consistent scheme applicable to the varying-temperature environment. The established theory was finally applied to predict the relaxation behavior of an RR-59 aluminum alloy under combined stress; the results showed reasonably good agreement with the experimental data.