Microscopic origin of nonlinear nonaffine deformation in bulk metallic glasses

The atomic theory of elasticity of amorphous solids, based on the nonaffine response formalism, is extended into the nonlinear stress-strain regime by coupling with the underlying irreversible many-body dynamics. The latter is implemented in compact analytical form using a qualitative method for the many-body dynamics. The resulting nonlinear stress-strain (constitutive) relation is very simple, with few fitting parameters, yet contains all the microscopic physics. The theory is successfully tested against experimental data on metallic glasses, and it is able to reproduce the ubiquitous feature of stress-strain overshoot upon varying temperature and shear rate. A clear atomic-level interpretation is provided for the stress overshoot, in terms of the competition between the elastic instability caused by nonaffine deformation of the glassy cage and the stress buildup due to viscous dissipation.

Figure 1

A cage-breaking model: Without shear, the number of particles moving in and out of the cage is equal. In the presence of shear $\gamma$, the number of particles moving out of the cage in the sectors of the local extension axis is higher than in the sectors of the compression axis.

Figure 2

Comparison between theoretical predictions and experimental data from Ref. [18]: Equation (3) with $\dot{\gamma }=0.1{\mathrm{s}}^{-1}$ and $T_g=625$ K for all curves. $K$ and ${\tau }_v$ were chosen to match the experimental data in the elastic and viscous-flow regimes, respectively. List of all parameter values is given in Table 1. The curves are artificially shifted to the right to avoid overlapping.

Figure 3

Comparison between theoretical predictions and experimental data from Ref. [18]: Equation (3) with a constant $T=643$ K and $T_g=625$ K for all curves. $K$ and ${\tau }_v$ were chosen to match the experimental data in the elastic and viscous-flow regimes, respectively. A list of all parameter values is given in Table 1. The curves are artificially shifted to the right to avoid overlapping.