Probing the Degree of Heterogeneity within a Shear Band of a Model Glass

Recent experiments provide evidence for density variations along shear bands in metallic glasses with a length scale of a few hundred nanometers. Via molecular dynamics simulations of a generic binary glass model, here we show that this is strongly correlated with variations of composition, coordination number, viscosity, and heat generation. Individual shear events along the shear band path show a mean distance of a few nanometers, comparable to recent experimental findings on medium range order. The aforementioned variations result from these localized perturbations, mediated by elasticity.

Figure 1

(a) System averaged shear stress versus overall strain of the sheared glass in the athermal limit. Capital letters ($A$, $B$, $C$, $D$) indicate stress states for which the strain field is shown in the right panel. (b) Color coded atomic strain in the shear ($xz$) plane for different stress states depicted as full red spheres in the left panel. Strain is evaluated using particle displacements within finite time intervals corresponding to 1% global deformation. It contains both affine and nonaffine contributions.

Figure 2

(a) A typical zigzag type path of the shear band along the sample. White (black) dashed lines correspond to descending (ascending) segments. Note that the aspect ratio is not $1:1$ but, to better highlight the wavy character of the SB path, the image is vertically enlarged. (b) Spatial variations of the relative density differences $[\mathrm{\Delta }\rho (x)/{\rho }_M]$ along the SB path.

Figure 3

Spatial correlations between fluctuations of $\mathrm{\Delta }\rho (x)$ ($\mathrm{\Delta }\rho (x)\equiv {\rho }_{\mathrm{SB}}(x)-{\rho }_M=\mathrm{density}$ difference between the shear band and the matrix) and those of other properties such as (a) the deflection angle, (b) the coordination number, (c) the composition or percentage (%) of $A$ particles in $A_x{B}_{100-x}$, (d) the excess volume [4, 47], (e) the $D_{\min }^2$ parameter [46], (f) the dynamic viscosity, and (g) energy dissipation rate. In order to highlight whether a given quantity is positively or negatively correlated with density, the obtained correlation function is divided by the absolute value of the first (leftmost) data point. In the case of positive (negative) correlations, the data thus start with a value equal to $+1$ ($-1$). The main question here is then whether or not the data remain positive (negative) within the entire shear band. This is the case for all the quantities shown here (see Supplemental Material, Figs. S3–S9 [38]).

Figure 4

(a) Scaled displacement vectors $\overrightarrow{u}$ colored by their nonaffine component $u_z$. (b) Enlargement of two adjacent STZs of the SB. (c) The region between the two STZs shows the vortex structure of the displacement vectors (black). The vortex in gold is the continuum mechanics solution for the displacement vector field generated by two adjacent localized shear perturbations color coded in panel (d). The schematic drawing of the contraction and dilation axes in (c) serves to highlight the alternating sign of ${ϵ}_{xz}$ between two adjacent STZs (see Supplemental Material, Fig. S1 [38]).

Figure 5

(a) Distribution of the distance between two adjacent STZs along the shear band (reduced LJ units).