Vacancy concentration in strain ageing of substitutional f c c alloys

Abstract

The relation between vacancy concentration, C v and tensile plastic strain, ɛ, has been constantly expressed as C v ∞ ɛ m . To take into account the grain-size effect, we have recently proposed that C∞ ɛβv ∞ϱm, where ϱm is the mobile dislocation density. With the conventional expression that ϱm d −n , where d is the average grain size, the strain and grain-size dependence of vacancy concentration appears to be C v ∞ ɛβγ d -nγ. This equation has proved effective in rationalizing the onset strain, ɛc, and stress amplitude, Δσ, of flow instability associated with the Portevin-LeChatelier effect of substitutional f c c alloys, where ɛc and Δσ are described by $$\dot \varepsilon \propto \varepsilon _c^{\beta (1/2 + \gamma )} d^{ - n(1/2 + \gamma )} T^{ - 1} exp( - Q/kT)$$ and $$\Delta \sigma \propto \left[ {\dot \varepsilon ^{ - 1} \varepsilon _c^{\beta (1/2 + \gamma )} d^{ - n(1/2 + \gamma )} T^{ - 1} exp( - Q/kT)} \right]^{2/3} $$ in which $$\Delta \sigma \gamma \propto \left[ {\varepsilon ^{\beta \gamma } d^{ - n\gamma } t_a T^{ - 1} exp( - Q/kT)} \right]^{2/3} $$ , T, Q and k are the strain rate, temperature, Boltzmann constant and activation energy for solute migration, respectively. Using the same concept, we have obtained $$\Delta \sigma \gamma \propto \left[ {\varepsilon ^{\beta \gamma } d^{ - n\gamma } t_a T^{ - 1} exp( - Q/kT)} \right]^{2/3} $$ to rationalize the increment of stress drop, Δσγ, observed at the instant of reloading after a static ageing time of t a. By adopting the above three equations, the strain-ageing data of two Al-Mg alloys in this study reveal that the vacancy concentration which is responsible for strain ageing is lower than the reported data from electrical resistivity measurements. This result is in agreement with the idea of migration of a vacancy-solute complex which has been proposed in the literature.