Shear-induced crystallization of an amorphous system

The influence of a stationary shear flow on the crystallization in a glassy system is studied by means of molecular dynamics simulations and subsequent cluster analysis. The results reveal two opposite effects of the shear flow on the processes of topological ordering in the system. Shear promotes the formation of separated crystallites and suppresses the appearance of the large clusters. The shear-induced ordering proceeds in two stages, where the first stage is related mainly to the growth of crystallites and the second stage is due to an adjustment of the created clusters and a progressive alignment of their lattice directions. The influence of strain and shear rate on the crystallization is also investigated. In particular, we find two plausible phenomenological relations between the shear rate and the characteristic time scale needed for ordering of the amorphous system under shear.

Figure 1

(Color online) Snapshot of the simulation cell. Two parallel amorphous walls (dark particles) restrict the sheared system. The particles of the top wall are removed with the velocity proportional to the distance between the walls $L_y$, which is variable with the time due to the normal pressure $P_{yy}$. The particles of the bottom wall are fixed.

Figure 2

(Color online) Evolution of the global orientational order parameter ${\mathcal{Q}}_6$ at the various shear rates $\dot{\gamma }$ as a function of time. The shear rate increases from bottom to top. The full lines are linear fits to the data. The arrow indicates the value of ${\mathcal{Q}}_6$ for a perfect fcc structure.

Figure 3

Structural characteristics of the sample under shear (at the shear rate $\dot{\gamma }=0.001{\tau }^{-1}$). (a) Radial distribution function at the different times after starting the shear flow: $t=0$, 250, 500, 750, 1500, and $2500\tau$ (from bottom to top). The curves are shifted upward for clarity. (b) Density profiles for two different times as averaged over a time window of $10\tau$.

Figure 4

(Color online) Main: Strain dependence of the global orientational order parameter ${\mathcal{Q}}_6$ at the different shear rates $\dot{\gamma }=0.0001$, 0.0005, 0.001, 0.005, and $0.01{\tau }^{-1}$ (from left to right). The correspondence between curves and shear rates is the same as in Fig. 2. The dashed line is the linear interpolation, indicating the steady behavior (plateau) in the strain dependence of order parameter. Inset: Shear rate dependence of the strain ${\gamma }_m$, at which the order parameter reaches the plateau value. Errors are defined by the change of slope in ${\mathcal{Q}}_6\left(\gamma \right)$. The solid and dotted curves are the logarithmic and power-law approximations, respectively (see text).

Figure 5

(Color online) Rescaled velocity profile as a function of distance from the bottom (unmoved) wall. Main: Shear with $\dot{\gamma }=U_{\text{wall}}/L_y=0.01{\tau }^{-1}$ at different points of the strain $\gamma$ above ${\gamma }_m=3$. The broken line corresponds to $u/U_{\text{wall}}=0.36$. Inset: Shear rate $\dot{\gamma }=0.001{\tau }^{-1}$ at two different strains above ${\gamma }_m$. Results are averaged over the time window $t=\Delta \gamma /\dot{\gamma }$, where $\Delta \gamma =0.01$ is the strain scale. All runs exhibit a similar behavior.

Figure 6

Connected empty circles: Shear stress vs strain rate in the sheared part of the velocity profiles shown in Fig. 5. Connected full circles: Stress as a function of the average shear rate in the sample. These curves are indicative of a coexistence between a rapidly flowing shear band and a nonflowing solid below its yield stress.

Figure 7

Different characteristics vs strain at the shear rate $\dot{\gamma }=0.001{\tau }^{-1}$ after a single run: (a) Number of solidlike particles in a whole system (connected full circles) and potential energy per particle (solid line). (b) Number of crystallites (connected open circles). The dashed line corresponds to the value 415.

Figure 8

(Color online) Main: Cluster size distribution at the different shear rates $\dot{\gamma }=0.01$, 0.001, and $0.0001{\tau }^{-1}$ (dashed, thin, and thick lines, respectively) and for a strain of 400%, where the system is characterized by the order parameter ${\mathcal{Q}}_6\approx 0.37$ for all shear rates (see Fig. 4). Each histogram is averaged over different runs. Inset: The same distribution in log-log representation. The solid line is the interpolation of the tail of the distribution at $\dot{\gamma }=0.01{\tau }^{-1}$ by a power-law dependence.