New dislocation velocity-based rate equation for thermally activated flow in face-centered cubic metals

In the classic strain-rate equation for thermally activated dislocation intersection, the applied shear stress, τ, was introduced into the probability of thermal activation in response to the imposed shear strain rate, γ˙. The chemical model assumed that the pre-exponential term was comprised of the total number of activation sites times the frequency of attempts. The formulation did not explicitly address the experimental insensitivity of flow stress, σ, to strain-rate magnitude, ε˙. Devolution of the pre-exponential term indicates that the change in magnitude response is in the frequency term. The +rate of doing work, τγ˙ and in turn γ˙ must arise from the operative velocity of dislocation segments. The modified strain-rate relation becomes γ˙=B0(τm∗+2)γ0e−(ΔGo−τνkT), analogous to Orowan, wherein B0 converts dislocation velocity to stress, γ0 is the number of sites times incremental strain areasΔν,G0 is free energy change due to dislocation intersection, ν, is activation volume, and kT is thermal energy. Constant strain rate is maintained by the decrease of m*, and the integral strain rate sensitivity, minteg, slope of log(σ-σ0) versus log(ε˙)|T, where σ0 is a yield stress, may increase with strain whereas the differential one, mdif = ∂ln(σ-σ0)/∂ln(ε˙)|T, remains constant, because change in τν is equally offset by change in ΔG0. The correlation of m* to mdif shows that the experimentally determined activation volume is twice the theoretical one, meaning the pre-exponential term is proportional to the strain rate. Moreover, the derivation of m* as a function of τ predicts a linear relation of log(υ) to log(τ) as validated by experiment.