A random critical point separates brittle and ductile yielding transitions in amorphous materials

TL;DR

This paper demonstrates that amorphous materials exhibit two distinct yielding behaviors—brittle and ductile—depending on their preparation, with a critical point separating these regimes, unifying their understanding through initial stability considerations.

Contribution

It introduces a combined analytical and simulation study showing a critical point separates brittle and ductile yielding in amorphous materials based on preparation protocols.

Findings

Well-annealed systems yield discontinuously as a first-order transition.

Poorly annealed systems exhibit smooth, ductile crossover behavior.

A critical point marks the transition between brittle and ductile yielding regimes.

Abstract

We combine an analytically solvable mean-field elasto-plastic model with molecular dynamics simulations of a generic glass-former to demonstrate that, depending on their preparation protocol, amorphous materials can yield in two qualitatively distinct ways. We show that well-annealed systems yield in a discontinuous brittle way, as metallic and molecular glasses do. Yielding corresponds in this case to a first-order nonequilibrium phase transition. As the degree of annealing decreases, the first-order character becomes weaker and the transition terminates in a second-order critical point in the universality class of an Ising model in a random field. For even more poorly annealed systems, yielding becomes a smooth crossover, representative of the ductile rheological behavior generically observed in foams, emulsions, and colloidal glasses. Our results show that the variety of yielding behavior found in amorphous materials does not result from the diversity of particle interactions or microscopic dynamics {\it per se}, but is instead unified by carefully considering the role of the initial stability of the system.