Apparent activation energy and stress exponent in materials with a high Peierls stress

Abstract

Equations are derived for the apparent stress exponent and activation energy in materials whose deformation is controlled by double kink nucleation and propagation on dislocations. The apparent activation energy (determined from Arrhenius plots of creep rate against inverse temperature) can easily be 10–20% lower than the true activation energy, depending on the stress. The apparent stress exponent (determined from the strain rate dependence of the stress or the stress dependence of the creep rate) is shown to be strongly dependent on stress, and therefore on temperature, and can decrease from values greater than 10 at low temperatures to unity at high temperatures, even though a single mechanism is controlling. Reasonable agreement has been found between the experimental and theoretical values of the stress exponent for yielding in single crystals of sapphire, spinel, Ni 3Al and NiAl, except that the calculated high temperature values tend to be somewhat lower than the observed values. The analysis should apply to yielding in many ceramics and intermetallics in single crystal form (or large grain polycrystals) where the double kink mechanism is rate-controlling.