A Mechanism of the Oscillating Variation with Time in Yield Strength of Cu Alloys during Low Temperature Annealing

A mechanism was proposed to account for time dependent decaying oscillations in yield strength of prestrained α-Cu alloys subjected to low temperature annealing. A set of nonlinear simultaneous differential equations with two variables (mobile dislocation density, ρm, and thermally surmountable obstacle dislocation density, ρs) was established as a constitutive equation, based on the idea that the strength variation during annealing is controlled by the following two opposite factors and a negative feedback effect : Softening caused by the decrease in ρs by recovery, hardening by the increase in ρs formed by combination reactions among mobile dislocations and a negative feedback effect where newly increased thermally surmountable obstacles block further increase in ρm originated from the dislocations introduced during prestraining and trapped by thermally surmountable obstacles. Linearized stability analyses and numerical calculations of the constitutive equation revealed that the time dependent decaying oscillation in ρs was observed for particuler sets of parameters in the equation, and that both the period and amplitude of the oscillation were shown to decrease with increasing annealing temperature. Assuming that both increase in ρm and decrease in ρs are controlled by thermal activation, a maximum in a plot of the equilibrium ρs against annealing temperature was predicted mathematically, and the behavior of the plot well coincided with the hardness maximum observed in α-Cu-Al and α-Cu-Zn. The comparisons between these experimental and theoretical data showed that the activation energies obtained for the increase process of ρm were close to the activation energy for the vacancy migration along dislocations, and the activation energies for the decrease process were close to the value for the solute atom diffusion in Cu.