Quasi-amorphous crystal

Abstract

Brittle plastic yielding is a salient feature of well-annealed glassy materials. Here we show that the same behavior is characteristic of perfect crystals after they experience mechanically driven elastic instability leading to massive nucleation of dislocations. We argue that such 'preparation' effectively converts an atomic configuration from crystalline to quasi-amorphous. To understand the nature of the subsequent mechanical response, which is reminiscent of quasi-brittle yielding we study an athermal model 2D crystal subjected to quasistatic loading. We show that the intermittent pre- and post-yield dislocation avalanches exhibit power law statistics with matching exponents. The computed value of these exponents is indicative of marginal stability.

Figures (7)

• Figure 1: $GL(2, \mathbb{Z})$-induced tessellation of the configuration space of metric tensors $C_{11}, C_{22},C_{12}$ with $\det \mathbf{C}=1$ stereographically projected on the Poincaré disk $p^2 + q^2 < 1$ where $p = t(C_{11} - C_{22})/2$, $q = tC_{12}$, and $t = 2/(2 + C_{11} + C_{22})$. The highlighted domain $\mathscr{D}$ is the fundamental (minimal periodicity) domain.
• Figure 2: Energy landscape in the space of metric tensors (Poincaré) disk shown in Fig. \ref{['fig:atlas0']}. Color indicates the energy level with only the lowest energy levels shown. The deepest energy wells correspond to equivalent representations of the same square lattice.
• Figure 3: Dislocated configuration emerging after a homogeneous lattice is mechanically driven to the threshold of elastic instability. Colors indicate the level of the shear component of the Cauchy stress tensor $\sigma_{xy}$. The highest stress levels of both signs correspond to the location of dislocation cores.
• Figure 4: (a) Stress-strain response of a quasi-amorphous crystal shown in Fig. \ref{['fig:22']}. (b) Dislocated configuration in a typical pre-yield state characterizing the stage of 'microplasticity'. (c,d) Dislocated configuration characterizing different stages of unfolding of the quasi-brittle system size event. Colors indicate the level of the shear component of the Cauchy stress tensor $\sigma_{xy}$.
• Figure 5: The micro-configuration configuration corresponding to the state $C$ marked in Fig. \ref{['fig:2']}. Colors indicate the magnitude of strain-energy density. The inset shows a single grain and details the dislocation structure of the grain boundaries.