Quantifying the Features of an Amorphous Solid's Local Yield Surface

Abstract

In two-dimensional Lennard-Jones glasses, mechanical probing reveals that local yield surfaces are dominated by regions with a positive second derivative of the yield stress with respect to the loading angle. Each feature corresponds to a shear transformation zone and a characteristic non-affine displacement field at yield. Most features are well described by a combined Schmid-Mohr-Coulomb criterion parameterized by a weak-plane orientation, a critical stress, and a pressure sensitivity. The resulting parameter statistics clarify how the onset of plastic flow is governed by the population of discrete yielding features encoded in the amorphous structure.

Figures (4)

• Figure 1: Top: Critical stress as a function of shear angle, defining a local yield surface. Symbols and lines correspond, respectively, to the atomistic data and their fit (Eq. \ref{['Eq:STZsegment']}); colors indicate the volumetric-strain conditions. Bottom: Similarity metric (Eq. \ref{['eq:dispcomparison']}) quantifying the alignment of plastic non-affine displacement fields; regions along the diagonal are labeled A--G.
• Figure 2: Distributions of the intrinsic critical stresses $\tau_0$ and pressure dependencies, $\phi$, collected from $4$ different glasses. The values are colored by quench rate. Each distribution is shifted for clarity. The mean value of $\tau_0$ shifts higher as the cooling rate decreases, while $\phi$ shows a shift towards lower values at slower cooling rates. See Table \ref{['tab:params']} for more detail. Quench rate dependencies of the mean values of $\tau_0$ and $\phi$ are provided in Figure S1 of the Supplementary Materials.
• Figure 3: Plastic displacement fields shown for the regions labeled A-G in Fig. \ref{['fig:combined']}(bottom), with their scaling factor in the bottom left. The fields can be easily clustered by direction through similarity using Eq. \ref{['eq:dispcomparison']}. From Fig. \ref{['fig:combined']}(top), each distinct deformation mode can be consistently associated with positive curvature regions throughout its angular domain.
• Figure S1: (a) Mean intrinsic critical stress $\tau_0$ versus cooling rate. (b) Mean pressure sensitivity $\phi$ versus cooling rate. Shaded regions indicate 95% confidence intervals.