Rheology of Hard Glassy Materials

TL;DR

This paper compares two models of cage relaxation in glassy solids, showing that the slowest relaxation process controls deformation in hard glasses, explaining their yielding and rate-dependent properties.

Contribution

It introduces a new model assuming the slowest relaxation controls deformation, contrasting with the traditional fastest relaxation model, to better describe hard glassy materials.

Findings

The slowest relaxation process governs deformation in hard glasses.

The new model explains key features like yielding and rate-stiffening.

It provides a way to distinguish soft and hard glasses based on shear-rate dependence.

Abstract

Glassy solids may undergo a fluidization (yielding) transition upon deformation whereby the material starts to flow plastically. It has been a matter of debate whether this process is controlled by a specific time scale, from among different competing relaxation/kinetic processes. Here, two constitutive models of cage relaxation are examined within the microscopic model of nonaffine elasto-plasticity. One (widely used) constitutive model implies that the overall relaxation rate is dominated by the fastest between the structural ($\alpha$) relaxation rate and the shear-induced relaxation rate. A different model is formulated here which, instead, assumes that the slowest (global) relaxation process controls the overall relaxation. We show that the first model is not compatible with the existence of finite elastic shear modulus for quasistatic (low-frequency) deformation, while the second model is able to describe all key features of deformation of `hard' glassy solids, including the yielding transition, the nonaffine-to-affine plateau crossover, and the rate-stiffening of the modulus. The proposed framework provides an operational way to distinguish between `soft' glasses and `hard' glasses based on the shear-rate dependence of the structural relaxation time.