Modeling stress relaxation at high temperatures involving delayed elasticity

Deformation in a material at any temperature is known to consist of two major components - a reversible (elastic) part and an irreversible part (often called plastic). What is not universally known is the fact that at high temperatures greater than about 0.4Tm, where Tm, is the melting point in Kelvin, the reversible part includes not only elastic but also a delayed elastic (recoverable but time dependent) component. A very simple computational model is presented here for a constant-strain stress relaxation test (SRT) on the basis of a three-component constant-stress rheological equation derived from strain relaxation and recovery test (SRRT) data. It is shown that the rapid stress reduction during the early periods of relaxation when the stresses are high is governed primarily by delayed elasticity irrespective of the imposed strain level. This is in contradiction to the popular concept prevailing today. The asymptotic approach to a quasi-stable stress rate at longer times and lower stresses is, however, controlled by viscous flow (power-law creep). The validity of the theory is examined by comparing the predictions with experimental results obtained for a titanium-base alloy Ti-6246 at 0.45Tm.