Evaluation of the Disorder Temperature and Free-Volume Formalisms via Simulations of Shear Banding in Amorphous Solids

Molecular dynamics simulations of shear band development over 1000% strain in simple shear are used to test whether the local plastic strain rate is proportional to $\exp (-1/\chi )$, where $\chi$ is a dimensionless quantity related to the disorder temperature or free volume that characterizes the structural state of the glass. Scaling is observed under the assumption that $\chi$ is linearly related to the local potential energy per atom. We calculate the potential energy per atom corresponding to absolute zero disorder temperature and the energy needed to create a shear transformation zone.

Figure 1

Stress-strain curves from Quenches I, II, and III tested at a strain rate $0.00002t_0^{-1}$ up to 20% strain. The inset shows strains up to 1000%.

Figure 2

Distributions of plastic deformation in a sample from Quench I (left), Quench II (center), and Quench III (right) at 50% strain. Three strain rates are shown for each: 0.00002 (top), 0.0001 (middle), and $0.0005t_0^{-1}$ (bottom). Black denotes strains in excess of 50% shear strain; white denotes 0% strain.

Figure 3

The strain rate (a) and potential energy per atom (b) as a function of the vertical position in the simulation cell measured at various strains for a sample from Quench I sheared at a strain rate of $0.00002t_0^{-1}$.

Figure 4

The scaled local strain rate as a function of potential energy for all data from Quench I, II, and III. The panes show data from three applied strain rates. Error bars are calculated by averaging over 50 data points. Only data from 200% to 1000% strain are included.