Dynamics of viscoplastic deformation in amorphous solids

Abstract

We propose a dynamical theory of low-temperature shear deformation in amorphous solids. Our analysis is based on molecular-dynamics simulations of a two-dimensional, two-component noncrystalline system. These numerical simulations reveal behavior typical of metallic glasses and other viscoplastic materials, specifically, reversible elastic deformation at small applied stresses, irreversible plastic deformation at larger stresses, a stress threshold above which unbounded plastic flow occurs, and a strong dependence of the state of the system on the history of past deformations. Microscopic observations suggest that a dynamically complete description of the macroscopic state of this deforming body requires specifying, in addition to stress and strain, certain average features of a population of two-state shear transformation zones. Our introduction of these new state variables into the constitutive equations for this system is an extension of earlier models of creep in metallic glasses. In the treatment presented here, we specialize to temperatures far below the glass transition, and postulate that irreversible motions are governed by local entropic fluctuations in the volumes of the transformation zones. In most respects, our theory is in good quantitative agreement with the rich variety of phenomena seen in the simulations.

The jamming scenario—an introduction and outlook

“…However, at the very least one can say that at the point of instigation, the instability will initially have a very low participation ratio. This is consistent with the observation that when a glass fails due to pressure or shear stress, the failure tends to be highly localized in shear-transformation zones [58,59]. So far, however, it has not been possible to identify sheartransformation zones unless they flip (unless a rearrangement occurs).…”

“…However, the failure often occurs in the form of rather localized rearrangement events rather than via a longrange catastrophic collapse [56,58,59]. Since the system goes unstable when the frequency of a mode reaches zero, it is possible to identify a rearrangement with the lowest-frequency mode just before the rearrangement [113].…”

“…One would expect these modes to shift downwards to zero frequency under the last two circumstances [57] and to give rise to highly heterogeneous deformations in the sample. These could be the underlying mechanism for the localized deformations postulated in the picture of shear transformation zones [58,59].…”

Deblocking of interacting particle assemblies: from pinning to jamming

“…In a few words, a glassy dynamics is associated to the slow structural relaxation which takes place when some parts of the system are trapped by their neighbors and have to surmount large energy barriers to explore further more favorable configurations. Molecular dynamics simulations [104,105,106,107] of glass-forming liquids and polymers have proved of much help in this respect. About the same time, a general "jamming" scenario was also proposed [89] as a common framework to understand the mechanical behavior of a broader class of nonequilibrium physical systems (colloidal suspensions, supercooled liquids, foams, etc.…”

The Development of Structure Model in Metallic Glasses

“…He thought that the "flow event" was not a single isolated event, but a rearrangement of a group of atoms. Falk 78,79 developed the theory of "shear transformation zone (STZ) " according to the molecular dynamics simulation in conjunction with the complete mathematical model. An STZ only appears in response to external stimuli, being undefinable a priori in the static glass structure before deformation 80 .…”