Solute strengthening at high temperatures
The high temperature behavior of solute strengthening has previously been treated approximately using various scaling arguments, resulting in logarithmic and power-law scalings for the stress-dependent energy barrier Delta E(tau) versus stress tau. Here, a parameter-free solute strengthening model is extended to high temperatures/low stresses without any a priori assumptions on the functional form of Delta E(tau). The new model predicts that the well-established low-temperature, with energy barrier Delta E-b and zero temperature flow stress tau(y0), transitions to a near-logarithmic form for stresses in the regime 0.2 < tau/tau(y0) <= 0.5 and then transitions to a power-law form at even lower stresses tau/tau(y0) < 0.03. Delta E-b and tau(y0) remains as the reference energy and stress scales over the entire range of stresses. The model is applied to literature data on solution strengthening in Cu alloys and captures the experimental results quantitatively and qualitatively. Most importantly, the model accurately captures the transition in strength from the low-temperature to intermediate-temperature and the associated transition for the activation volume. Overall, the present analysis unifies the different qualitative models in the literature and, when coupled with the previous parameter-free solute strengthening model, provides a single predictive model for solute strengthening as a function of composition, temperature, and strain rate over the full range of practical utility.