Strain Localization and Percolation of Stable Structure in Amorphous Solids

Spontaneous strain localization occurs during mechanical tests of a model amorphous solid simulated using molecular dynamics. The degree of localization depends upon the extent of structural relaxation prior to mechanical testing. In the most rapidly quenched samples higher strain rates lead to increased localization, while the more gradually quenched samples exhibit the opposite strain rate dependence. This transition coincides with the $k$-core percolation of atoms with quasi-crystal-like short range order. The authors infer the existence of a related microstructural length scale.

Figure 1

Averaged stress-strain curves with strain rates of $1\times {10}^{-6}{t}_0^{-1}$ for, from bottom to top, instantaneously quenched samples (schedule 1), quickly quenched samples (schedule 5), and slowly quenched samples (schedule 9), respectively.

Figure 2

DPR at 5% strain in uniaxial tension tests for strain rates of $2\times {10}^{-4}{t}_0^{-1}$, $2\times {10}^{-5}{t}_0^{-1}$, and $2\times {10}^{-6}{t}_0^{-1}$ as function of the average potential energy per atom of the samples prior to testing. Each point represents a particular quenching schedule from Table .

Figure 3

The spatial distribution of deviatoric strain in three samples produced by quenching schedules 1 (a), 5 (b), and 9 (c), loaded to 5% nominal strain at a strain rate of ${10}^{-6}(1/t_0)$. The DPRs for these three samples are 0.48, 0.36, and 0.20, respectively. Black corresponds to 10% strain; gray is 0% strain. The scale bar in the upper right of the image is $20{\sigma }_{SL}\approx 6\mathrm{nm}$.

Figure 4

Data points with error bars represent $m$, the strain rate sensitivity of DPR, as a function of potential energy of the samples prior to testing. The solid line is a fit to this data. The other lines show the fraction of the specimens tested that exhibited $k$-core percolation of the SRO (dashed line, circles) and bond percolation of the SRO (dot-dashed line) as a function of potential energy.