Ductile and brittle yielding in thermal and athermal amorphous materials

TL;DR

This paper theoretically investigates how initial sample annealing influences the transition from ductile to brittle yielding in amorphous materials, revealing a continuum of behaviors in thermal systems and a consistent brittle response in athermal systems.

Contribution

It introduces a unified theoretical framework explaining the transition from ductile to brittle yielding based on annealing and shear rate effects in amorphous materials.

Findings

Thermal systems show a gradual transition from ductile to brittle yielding with increased annealing.

Athermal systems exhibit brittle yielding at low shear rates regardless of annealing.

The overshoot in stress-strain curves drives shear banding instability in thermal systems.

Abstract

We study theoretically the yielding of sheared amorphous materials as a function of increasing levels of initial sample annealing prior to shear, in three widely used constitutive models and three widely studied annealing protocols. In thermal systems we find a gradual progression, with increasing annealing, from smoothly "ductile" yielding, in which the sample remains homogeneous, to abruptly "brittle" yielding, in which it becomes strongly shear banded. This progression arises from an increase with annealing in the size of an overshoot in the underlying stress-strain curve for homogeneous shear, which causes a shear banding instability that becomes more severe with increasing annealing. "Ductile" and "brittle" yielding thereby emerge as two limiting cases of a continuum of yielding transitions, from gradual to catastrophic. In contrast, athermal systems with a stress overshoot always show brittle yielding at low shear rates, however small the overshoot.