Structural rearrangements are an essential property of atomic and molecular glasses; they are critical in controlling resistance to flow and are central to the evolution of many properties of glasses, such as their heat capacity and dielectric constant. Despite their importance, these rearrangements cannot directly be visualized in atomic glasses. We used a colloidal glass to obtain direct three-dimensional images of thermally induced structural rearrangements in the presence of an applied shear. We identified localized irreversible shear transformation zones and determined their formation energy and topology. A transformation favored successive ones in its vicinity. Using continuum models, we elucidated the interplay between applied strain and thermal fluctuations that governs the formation of these zones in both colloidal and molecular glasses.

http://absimage.aps.org/image/MAR11/MWS_MAR11-2010-008328.pdf

Structural rearrangements that govern flow in colloidal glasses

The development of new glassy materials is key for addressing major global challenges in energy, medicine, and advanced communications systems. For example, thin, flexible, and large-area glass substrates will play an enabling role in the development of flexible displays, roll-to-roll processing of solar cells, next-generation touch-screen devices, and encapsulation of organic semiconductors. The main drawback of glass and its limitation for these applications is its brittle fracture behavior, especially in the presence of surface flaws, which can significantly reduce the practical strength of a glass product. Hence, the design of new ultrastrong glassy materials and strengthening techniques is of crucial importance. The main issues regarding glass strength are discussed, with an emphasis on the underlying microscopic mechanisms that are responsible for mechanical properties. The relationship among elastic properties and fracture behavior is also addressed, focusing on both oxide and metallic glasses. From a theoretical perspective, atomistic modeling of mechanical properties of glassy materials is considered. The topological origin of these properties is also discussed, including its relation to structural and chemical heterogeneities. Finally, comments are given on several toughening strategies for increasing the damage resistance of glass products.

Towards Ultrastrong Glasses

We review the recent literature on the simulation of the structure and deformation of amorphous solids, including oxide and metallic glasses. We consider simulations at different length scale and time scale. At the nanometer scale, we review studies based on atomistic simulations, with a particular emphasis on the role of the potential energy landscape and of the temperature. At the micrometer scale, we present the different mesoscopic models of amorphous plasticity and show the relation between shear banding and the type of disorder and correlations (e.g. elastic) included in the models. At the macroscopic range, we review the different constitutive laws used in finite-element simulations. We end with a critical discussion on the opportunities and challenges offered by multiscale modeling and information transfer between scales to study amorphous plasticity.

http://ilm-perso.univ-lyon1.fr/~drodney/dr_articles/2011_MSMSE%5BRodney_Tanguy_Vandembroucq_topical%5D.pdf

Modeling the mechanics of amorphous solids at different length scale and time scale

The deformation and flow of disordered solids, such as metallic glasses and concentrated emulsions, involves swift localized rearrangements of particles that induce a long-range deformation field. To describe these heterogeneous processes, elastoplastic models handle the material as a collection of 'mesoscopic' blocks alternating between an elastic behavior and plastic relaxation, when they are too loaded. Plastic relaxation events redistribute stresses in the system in a very anisotropic way. We review not only the physical insight provided by these models into practical issues such as strain localization, creep and steady-state rheology, but also the fundamental questions that they address with respect to criticality at the yielding point and the statistics of avalanches of plastic events. Furthermore, we discuss connections with concurrent mean-field approaches and with related problems such as the plasticity of crystals and the depinning of an elastic line.

/pdf/deformation-and-flow-of-amorphous-solids-insights-from-31hhogb2t0.pdf

Deformation and flow of amorphous solids: Insights from elastoplastic models

We review the recent literature on the simulation of the structure and deformation of amorphous glasses, including oxide and metallic glasses. We consider simulations at different length and time scales. At the nanometer scale, we review studies based on atomistic simulations, with a particular emphasis on the role of the potential energy landscape and of the temperature. At the micrometer scale, we present the different mesoscopic models of amorphous plasticity and show the relation between shear banding and the type of disorder and correlations (e.g. elastic) included in the models. At the macroscopic range, we review the different constitutive laws used in finite element simulations. We end the review by a critical discussion on the opportunities and challenges offered by multiscale modeling and transfer of information between scales to study amorphous plasticity.

Modeling the mechanics of amorphous solids at different length and time scales

We study theoretically the onset of shear banding in the three most common time-dependent rheological protocols: step stress, finite strain ramp (a limit of which gives a step strain), and shear startup. By means of a linear stability analysis we provide a fluid-universal criterion for the onset of banding for each protocol, which depends only on the shape of the experimentally measured time-dependent rheological response function, independent of the constitutive law and internal state variables of the particular fluid in question. Our predictions thus have the same highly general status, in these time-dependent flows, as the widely known criterion for banding in steady state (of negatively sloping shear stress vs shear rate). We illustrate them with simulations of the Rolie-Poly model of polymer flows, and the soft glassy rheology model of disordered soft solids.

/pdf/criteria-for-shear-banding-in-time-dependent-flows-of-495jcxva5i.pdf

Criteria for Shear Banding in Time-Dependent Flows of Complex Fluids

We study numerically the formation of long-lived transient shear bands during shear startup within two models of soft glasses (a simple fluidity model and an adapted ``soft glassy rheology'' model). The degree and duration of banding depends strongly on the applied shear rate, and on sample age before shearing. In both models the ultimate steady flow state is homogeneous at all shear rates, consistent with the underlying constitutive curve being monotonic. However, particularly in the soft glassy rheology case, the transient bands can be extremely long lived. The banding instability is neither ``purely viscous'' nor ``purely elastic'' in origin, but is closely associated with stress overshoot in startup flow.

Age-Dependent Transient Shear Banding in Soft Glasses

We study theoretically the formation of shear bands in time-dependent flows of polymeric and wormlike micellar surfactant fluids, focussing on the protocols of step shear stress, step shear strain (or in practice a rapid strain ramp), and shear startup, which are commonly studied experimentally. For each protocol we perform a linear stability analysis to provide a fluid-universal criterion for the onset of shear banding, following our recent letter [Moorcroft and Fielding, Phys. Rev. Lett. 110, 086001 (2013)]. In each case this criterion depends only on the shape of the experimentally measured rheological response function for that protocol, independent of the constitutive properties of the material in question (Therefore our criteria in fact concern all complex fluids and not just the polymeric ones of interest here.). An important prediction is that pronounced banding can arise transiently in each of these protocols, even in fluids for which the underlying constitutive curve of stress as a function of strain-rate is monotonic and a steadily flowing state is accordingly unbanded. For each protocol we provide numerical results in the rolie-poly and Giesekus models that support our predictions. We comment on the ability of the rolie-poly model to capture the observed experimental phenomenology and on the failure of the Giesekus model.

/pdf/shear-banding-in-time-dependent-flows-of-polymers-and-316qdina3x.pdf

Shear banding in time-dependent flows of polymers and wormlike micelles

We study numerically the formation of long-lived transient shear bands during shear startup within two models of soft glasses (a simple fluidity model and an adapted \"soft glassy rheology\" model). The degree and duration of banding depends strongly on the applied shear rate, and on sample age before shearing. In both models the ultimate steady flow state is homogeneous at all shear rates, consistent with the underlying constitutive curve being monotonic. However, particularly in the soft glassy rheology case, the transient bands can be extremely long lived. The banding instability is neither \"purely viscous\" nor \"purely elastic\" in origin, but is closely associated with stress overshoot in startup flow.

Erratum: Age-Dependent Transient Shear Banding in Soft Glasses [Phys. Rev. Lett. 106, 055502 (2011)]

Glassy polymers show “strain hardening”: at constant extensional load, their flow first accelerates, then arrests. Recent experiments under such loading have found this to be accompanied by a striking dip in the segmental relaxation time. This can be explained by a minimal nonfactorable model combining flow-induced melting of a glass with the buildup of stress carried by strained polymers. Within this model, liquefaction of segmental motion permits strong flow that creates polymer-borne stress, slowing the deformation enough for the segmental (or solvent) modes then to re-vitrify. Here, we present new results for the corresponding behavior under step-stress shear loading, to which very similar physics applies. To explain the unloading behavior in the extensional case requires introduction of a “crinkle factor” describing a rapid loss of segmental ordering. We discuss in more detail here the physics of this, which we argue involves non-entropic contributions to the polymer stress, and which might lead to some important differences between shear and elongation. We also discuss some fundamental and possibly testable issues concerning the physical meaning of entropic elasticity in vitrified polymers. Finally, we present new results for the startup of steady shear flow, addressing the possible role of transient shear banding.

/pdf/modeling-the-relaxation-of-polymer-glasses-under-shear-and-2jsxxkpoc1.pdf

Robyn L. Moorcroft

Papers

Criteria for Shear Banding in Time-Dependent Flows of Complex Fluids

Age-Dependent Transient Shear Banding in Soft Glasses

Shear banding in time-dependent flows of polymers and wormlike micelles

Erratum: Age-Dependent Transient Shear Banding in Soft Glasses [Phys. Rev. Lett. 106, 055502 (2011)]

Modeling the relaxation of polymer glasses under shear and elongational loads