Deformation assisted precipitation in binary alloys: A competition of time-scales

We consider the process of precipitation in binary alloys in the presence of mechanical deformation. It is commonly observed that mechanical deformation prior to or during precipitation leads to microstructure with excess defects, which allows for enhanced precipitate nucleation and growth rates \cite{Weiss1979,Okaguchi1992,Deschamps2003}. To investigate this phenomenon, we employ a two-dimensional phase-field crystal alloy model endowed with a temperature dependent mobility, making it capable of recovering isothermal transformation (TTT) diagrams with a characteristic inflection point (nose) about a critical temperature. We examine the variation in the time-scale of precipitation and its connection to the time-scale of the applied deformation, focusing on the roles of atomic defects in the processes involved. Our results indicate that precipitation is initially delayed through application of a deformation until a critical strain is achieved, beyond which precipitation proceeds more rapidly, assisted by plastic deformation such as grain boundary serration or dislocation nucleation. We show that the evolution of the precipitated fraction, $f(t)$, departs from classical Avrami behaviour. Specifically, $df/dt$ develops two peaks indicative of a ``plateau"-like inflection in $f(t)$, signalling the transition to defect assisted precipitate nucleation. We analyze these plateaus as a function of the deformation rate and demonstrate that the they exhibit a discontinuous bifurcation as the time-scale of applied deformation is increased. These findings are compared to and found to be consistent with experiments.