Surface shear-transformation zones in amorphous solids

We perform a systematic study of the characteristics of shear transformation zones (STZs) that nucleate at free surfaces of two-dimensional amorphous solids subject to tensile loading using two different atomistic simulation methods, the standard athermal, quasistatic (AQ) approach and our recently developed self-learning metabasin escape (SLME) method, to account for the finite temperature and strain-rate effects. In the AQ, or strain-driven limit, the nonaffine displacement fields of surface STZs decay exponentially away from their centers at similar decay rates as their bulk counterparts, though the direction of maximum nonaffine displacement is tilted away from the tensile axis due to surface effects. Using the SLME method at room temperature and at the high strain rates that are seen in classical molecular dynamics simulations, the characteristics for both bulk and surface STZs are found to be identical to those seen in the AQ simulations. However, using the SLME method at room temperature and experimentally relevant strain rates, we find a transition in the surface STZ characteristics where a loss in the characteristic angular tensile-compression symmetry is observed. Finally, the thermally activated surface STZs exhibit a slower decay rate in the nonaffine displacement field than do strain-driven surface STZs, which is characterized by a larger drop in potential energy resulting from STZ nucleation that is enabled by the relative compliance of the surface as compared to the bulk.

Figure 1

Representative nonaffine displacement field $\delta \mathbf{u}$ for (a) bulk STZ and (c) surface STZ nucleation. von Mises local shear strain $\eta$ for (b) bulk STZ and (d) surface STZ nucleation. All cases for AQ loading conditions, where the arrows indicate the direction of tensile loading.

Figure 2

Representative radial ($\delta {\mathbf{u}}_r$) projection of the AQ nonaffine displacement field $\delta \mathbf{u}$ for (a) bulk and (c) surface STZs. Representative tangential ($\delta {\mathbf{u}}_t$) projection of the AQ nonaffine displacement field for (b) bulk and (d) surface STZs.

Figure 3

Normalized angle resolved radial [$\delta {\mathbf{u}}_r\left(\theta \right)$] projections of the AQS nonaffine displacement field $\delta \mathbf{u}$ for (a) bulk and (c) surface STZs. Normalized angle-resolved tangential [$\delta {\mathbf{u}}_t\left(\theta \right)$] projections of the AQS nonaffine displacement field for (b) bulk and (d) surface STZs. Filled symbols are raw data of 20 independent AQ simulations, which were averaged to obtain the bulk and surface radial and tangential projections.

Figure 4

Schematic plots of the ellipsoidal geometry of (a) bulk and (b) surface STZs. Ellipsoidal characteristics obtained by averaging over the results of 20 independent AQ simulations.

Figure 5

Angularly averaged nonaffine displacement magnitudes ${\langle \left|\delta \mathbf{u}\right|\rangle }_{\theta }$ as a function of distance $d$ from the STZ center for both bulk and surface STZs. Gray filled and open symbols are raw data of 20 independent AQ simulations, which were averaged to obtain the bulk and surface STZ curves.

Figure 6

Representative nonaffine displacement field $\delta \mathbf{u}$ for (a) bulk STZ and (c) surface STZ nucleation at a strain rate of $\dot{\epsilon }=1\times {10}^{-5}$. Representative nonaffine displacement $\delta u$ for (b) bulk STZ and (d) surface STZ nucleation at a strain rate of $\dot{\epsilon }=1\times {10}^{-18}$.

Figure 7

Representative Mises local shear strain $\eta$ for bulk STZ at strain rates of (a) $\dot{\epsilon }=1\times {10}^{-5}$ and (b) $\dot{\epsilon }=1\times {10}^{-18}$. Representative von Mises local shear strain $\eta$ for surface STZ at strain rates of (c) $\dot{\epsilon }=1\times {10}^{-5}$ and (d) $\dot{\epsilon }=1\times {10}^{-18}$.

Figure 8

Nonaffine displacement magnitude decay rate for bulk STZs at a strain rate of (a) $1\times {10}^{-5}$; (b) $1\times {10}^{-18}$ (right) at $T=0.33T_g$. Open symbols are raw data of 20 independent SLME simulations while the filled symbols are the average values. The solid lines represent fitting functions.

Figure 9

Nonaffine displacement magnitude decay rate for surface STZs at a strain rate of (a) $1\times {10}^{-5}$; (b) $1\times {10}^{-18}$ (right) at $T=0.33T_g$. Open symbols are raw data of 20 independent SLME simulations while the filled symbols are the average values. The solid lines represent fitting functions.

Figure 10

Representative potential energy versus tensile strain curves for (a) strain-driven and thermally activated surface STZs and (b) thermally activated bulk and surface STZs.