Anomalous softness in amorphous matter in the reversible plastic regime

Abstract

We study an integer automaton elasto-plastic model of an amorphous solid subject to cyclic shear of amplitude $\Gamma$. We focus on the reversible plastic regime at intermediate ${\Gamma }_0<\Gamma <{\Gamma }_y$, where, after a transient, the system settles into a periodic limit cycle with hysteretic, dissipative plastic events which repeat after an integer number of cycles. We study the plastic strain rate, $\frac{d\epsilon }{d\gamma }$, (where $\gamma$ is the applied strain and $\epsilon$ is the plastic strain) during the terminal limit cycles and show that it consists of a creeping regime at low $\gamma$ with very low $\frac{d\epsilon }{d\gamma }$ followed by a sharp transition at a characteristic strain, ${\gamma }_{\ast }$, and stress, ${\sigma }_{\ast }$, to a flowing regime with higher $\frac{d\epsilon }{d\gamma }$. We show that while increasing $\Gamma$ above ${\Gamma }_0$ results in lower terminal ground state energy, $U_{\text{min}}$, and a correspondingly narrower distribution of stresses, it, surprisingly, results in lower ${\gamma }_{\ast }$, and ${\sigma }_{\ast }$. The stress distribution, $P(\sigma )$, also becomes skewed for $\Gamma >{\Gamma }_0$. That is, the systems in the RPR are anomalously soft and mechanically polarized. We relate this to an emergent characteristic feature in the stress distribution, $P(\sigma )$, at a value, ${\sigma }_0$, which is independent of $\Gamma$ and show that ${\sigma }_0$ implies a relation between the $\Gamma$ dependence of ${\sigma }_{\ast }$, ${\gamma }_{\ast }$, and the amplitude of plastic strain, ${\epsilon }_p$. We show that the onset of hysteresis is characterized by a power-law scaling, indicative of a second order transition with ${\epsilon }_p\propto (\Gamma -{\Gamma }_0{)}^{1.2\pm 0.1}$. We argue that ${\sigma }_0$ and, correspondingly, the onset of the RPR at $\Gamma ={\Gamma }_0$, is simply set by the so-called Eshelby-stress. Furthermore, we show that cycling at ${\Gamma }_0$ results in a maximally hardened state.

Cited by in corpus (1)

• Fatigue failure of amorphous alloys under cyclic shear deformation