Dynamical theory of shear bands in structural glasses

Abstract

The heterogeneous elastoplastic deformation of structural glasses is explored using the framework of the random first-order transition theory of the glass transition along with an extended mode-coupling theory that includes activated events. The theory involves coupling the continuum elastic theory of strain transport with mobility generation and transport as described in the theory of glass aging and rejuvenation. Fluctuations that arise from the generation and transport of mobility, fictive temperature, and stress are treated explicitly. We examine the nonlinear flow of a glass under deformation at finite strain rate. The interplay among the fluctuating fields leads to the spatially heterogeneous dislocation of the particles in the glass, i.e., the appearance of shear bands of the type observed in metallic glasses deforming under mechanical stress.glass transition | mode-coupling theory | strength of materials | shear bands W hether and how glasses flow have been fascinating questions for a long time. In the absence of stress, a glass seems to be static on human timescales, the molecules being arranged like a frozen snapshot of the liquid state. In fact, molecules in the glass are constantly moving and the glass itself is not in a state of equilibrium. Even without applied stress, molecules do change their locations through rare, activated events. These events occur at a rate that is both spatially and temporally heterogeneous. Glasses therefore continue to evolve, albeit slowly, as they approach equilibrium and age (1). These activated events are accelerated by applied stresses and typically will act to reduce the stress so that under sufficient stress the glass will not just deform elastically but visibly flow and possibly break. The deformations caused by stress are not uniform in the glass, but appear to concentrate in shear bands (2-4). In this work, we show how shear bands arise dynamically by the coupling of the activated dynamics of configurationally rearranging regions with elastic strain transport. The heterogeneous activated dynamics of glasses under mechanical deformation are described using a first-principle framework based on the random first-order transition (RFOT) theory along with an extended mode-coupling theory that describes how activated events are coupled in space and time (5-10).The random first-order transition theory of glasses is a microscopic theory that has already provided a unified quantitative description of large number of aspects of the behavior of supercooled liquids and structural glasses (11). The theory brings together two seemingly disparate aspects of glass formation: the breaking of replica symmetry that occurs in mean-field models and a theory of the activated events that tend to locally restore replica symmetry in systems with short-range interactions (7,8,(12)(13)(14). In mean-field models, there is a special temperature T d at which a dynamical transition to immobility occurs discontinuously. Above this temperature the system is well described by ordinary mode-coupli...

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