Solute segregation kinetics and dislocation depinning in a binary alloy

Static strain aging, a phenomenon caused by diffusion of solute atoms to dislocations, is an important contributor to the strength of substitutional alloys. Accurate modeling of this complex process requires both atomic spatial resolution and diffusional time scales, which is very challenging to achieve with commonly used atomistic computational methods. In this paper, we use the recently developed “diffusive molecular dynamics” (DMD) method that is capable of describing the kinetics of the solute segregation process at the atomic level while operating on diffusive time scales in a computationally efficient way. We study static strain aging in the Al-Mg system and calculate the depinning shear stress between edge and screw dislocations and their solute atmospheres formed for various waiting times with different solute content and for a range of temperatures. A simple phenomenological model is also proposed that describes the observed behavior of the critical shear stress as a function of segregation level.

Figure 1

(Top) Snapshots of the equilibrium solute distribution near the split (a) edge and (b) screw dislocation cores in Al-2.5at%Mg at $T=600$ K from DMD calculation. (Bottom) Concentration profiles along the $X$ direction at different $Y$ levels labeled by the numbers from 1 to 8 (color variation from green to blue), where data below and above the glide plane are shown by filled and empty symbols, respectively.

Figure 2

Disregistry profile (top) and its derivative (bottom) calculated across the slip plane and along the $X$ direction for edge components of the split (a) edge and (b) screw dislocations in Al-2.5at%Mg at $T=600\mathrm{K}$. DMD relaxation results and fitted curves are shown by symbols and solid lines, respectively.

Figure 3

Contour plots of the equilibrium solute concentration near the split edge (left) and screw (right) dislocations from (a) DMD calculation, (b) Eq. (3) using the DMD hydrostatic pressure field existing prior to segregation and (c) Eq. (3) using the continuum model expression for the pressure given in Eq. (4) for $c_0=2.5\%$ at $T=600\mathrm{K}$.

Figure 4

Binding energy difference with respect to initial equilibrium structure per unit length (top) and force converted to shear stress (bottom) between the split (a) edge, (b) screw dislocations, and equilibrium solute cloud as a function of distance between them from the DMD calculation (symbols) and continuum model (solid red line) for $c_0=2.5\%$ and $T=600\mathrm{K}$.

Figure 5

Time evolution of the excess solute concentration (left) and its log-log representation (right) given by DMD calculations for the split (a) edge $\left(R_c=18\AA \right)$ and (b) screw $\left(R_c=13\AA \right)$ dislocations. The inset shows a magnification of the crossover regime between cross-core and bulk diffusion. The characteristic time unit $\tau$ is listed for the considered range of temperatures in Table 2.

Figure 6

Total DMD free energy per unit length with respect to initial equilibrium structure (top) and shear stress $\mathrm{\Delta }\tau$ (bottom) exerted on the split (a) edge and (b) screw dislocations that interact with the equilibrium solute cloud as a function of the applied shear strain $\gamma$ at $T=600\mathrm{K}$.

Figure 7

Critical resolved shear stress needed to depin a solute cloud from the dislocation core in the Al-Mg alloy with (a) $c_0=2.5\%$ and (b) $c_0=5\%$ as a function of segregation time: actual computed values (left) and normalized by the depinning stress from equilibrium solute atmosphere (right). DMD results are shown by symbols, while solid and dashed lines correspond to the model predictions (see text). The characteristic time unit $\tau$ is listed for the considered range of temperatures in Table 2.

Figure 8

Graphs show the cross-core component $\mathrm{\Delta }{\tau }_c$ and bulk diffusion component $\mathrm{\Delta }{\tau }_b$ that comprise the total depinning stress $\mathrm{\Delta }\tau$ for the split (a) edge and (b) screw dislocations for $c_0=2.5\%$ at $T=600\mathrm{K}$. The characteristic time unit $\tau$ is listed for the considered range of temperatures in Table 2.