Spatiotemporal dynamics of shear induced bands en route to rheochaos

We show experimentally that the route to rheochaos in shear rate relaxation measurements is via Type-III intermittency and mixed mode oscillations in the shear-thinning wormlike micellar system of cetyltrimethylammonium tosylate in the presence of salt sodium chloride. Depolarised small angle light scattering measurements performed during flow show that scattered intensity temporally follows the shear rate/stress dynamics and portrays the crucial role played by nematic ordering. Direct visualization of the gap of the Couette cell, illuminated by an unpolarised laser sheet, in the (vorticity, velocity gradient) plane shows that the spatiotemporal dynamics of the shear induced structures is closely related to the temporal behaviour of shear rate/stress fluctuations.     

Spatiotemporal rheochaos in nematic hydrodynamics

Motivated by recent observations of rheochaos in sheared wormlike micelles, we study the coupled nonlinear partial differential equations for the hydrodynamic velocity and order-parameter fields in a sheared nematogenic fluid. In a suitable parameter range, we find irregular, dynamic shear banding and establish by decisive numerical tests that the chaos we observe in the model is spatiotemporal in nature.     

A numerical examination of shear banding and simple shear non-coaxial flow rules

Strain localisation and shear band formation is frequently observed during the handling and flow of dense phase particulate materials. However, a complete understanding of how shear bands form and what happens inside shear bands is still lacking. In order to address this problem, discrete particle simulations have been carried out to examine the detailed processes that occur at the grain scale associated with the initiation and development of shear bands. To reliably identify the continuum model applicable within a shear band is difficult due to the small number of particles/contacts involved. However, it is normally accepted that the mode of deformation within a shear band is one of simple shear. Consequently, simple shear simulations have been performed in order to determine the evolution of the stress tensor, dilation rate, and the principal directions of stress and strain-rate. It is demonstrated that the corresponding non-coaxial flow rule is equivalent to that suggested by Tatsuoka et al. (Géotechnique 38 148 (1988)). Furthermore, at fully developed flow when there is no further change in volume, the stress and strain-rate directions are coaxial and the flow rule is that proposed by Hill (The Mathematical Theory of Plasticity (Oxford University Press, 1950) p. 294).     

Two-dimensional perturbations in a scalar model for shear banding

We present an analytical study of a toy model for shear banding, without normal stresses, which uses a piecewise linear approximation to the flow curve (shear stress as a function of shear rate). This model exhibits multiple stationary states, one of which is linearly stable against general two-dimensional perturbations. This is in contrast to analogous results for the Johnson-Segalman model, which includes normal stresses, and which has been reported to be linearly unstable for general two-dimensional perturbations. This strongly suggests that the linear instabilities found in the Johnson-Segalman can be attributed to normal stress effects.     

Multiple shear banding in a computational amorphous alloy model

The strain localized phenomenon, so called shear bands (SBs), in an amorphous alloy have received a lot of attention in recent years. In this study, we microscopically investigated the nature and dynamics of multiple SBs using molecular dynamics model. In the SB region, intense shear-induced structural change occurred, typified by the annihilation of pentagonal short-range order, and significant localized heating accompanied with the SB propagation was observed. Moreover, a large number of fine SBs operated simultaneously at a high strain rate, whereas, only a few SBs appeared and propagated abruptly at a low strain rate. These results were discussed with respect to brittle/ductile deformation of bulk metallic glasses. PACS 31.15.xv; 62.20.F-; 81.05.Kf     

Early stage kinetics in a unified model of shear-induced demixing and mechanical shear banding instabilities

We present a unified model of shear-induced demixing and "mechanical" shear banding instabilities in polymeric and surfactant solutions, by combining a simple flow instability with a two-fluid approach to concentration fluctuations. Within this model, we calculate the "spinodal" limit of stability of initially homogeneous shear states to demixing/banding, and predict the selected length and time scales at which inhomogeneity first emerges after a shear start-up "quench" into the unstable region, finding qualitative agreement with experiment. Our analysis is the counterpart, for this driven phase transition, of the Cahn-Hilliard calculation for unsheared fluid-fluid demixing.     

Complex mixed-mode periodic and chaotic oscillations in a simple three-variable model of nonlinear system

A detailed study of a generic model exhibiting new type of mixed-mode oscillations is presented. Period doubling and various period adding sequences of bifurcations are observed. New type of a family of 1D (one-dimensional) return maps is found. The maps are discontinuous at three points and consist of four branches. They are not invertible. The model describes in a qualitative way mixed-mode oscillations with two types of small amplitude oscillations at local maxima and local minima of large amplitude oscillations, which have been observed recently in the Belousov-Zhabotinsky system. (c) 2000 American Institute of Physics.     

Ideal shear banding in metallic glass

As the most fundamental deformation mechanism in metallic glasses (MGs), the shear banding has attracted a lot of attention and interest over the years. However, the intrinsic properties of the shear band are affected and even substantially changed by the influence of non-rigid testing machine that cannot be completely removed in real compression tests. In particular, the duration of the shear banding event is prolonged due to the recovery of the stressed compliant frame of testing machine and therefore the temperature rise at the operating shear band is, more or less, underestimated in previous literatures. In this study, we propose a model for the ‘ideal’ shear banding in metallic glass. The compliance of the testing machine is eliminated, and the intrinsic shear banding process is extracted and investigated. Two important physical parameters, the sliding speed and the temperature of shear band, are calculated and analysed on the basis of the thermo-mechanical coupling. Strain-rate hardening is proposed to compensate thermal softening and stabilise the shear band. The maximum value of the sliding speed is found to be on the order of 10 m/s at least, and the critical temperature at which strain-rate hardening begins to take effect should reach as high as 0.9T_g (T_g is the glass transition temperature) for a stable shear banding event in metallic glass according to the early experimental data. This model can help to understand and control the shear banding and therefore the deformation in MGs.     

Yielding and shear banding in soft glassy materials

Yield stress fluids have proven difficult to characterize, and a reproducible determination of the yield stress is difficult. We study two types of yield stress fluids (YSF) in a single system: simple and thixotropic ones. This allows us to show that simple YSF are simply a special case of thixotropic ones, and to pinpoint the difference between static and dynamic yield stresses, one of the major problems in the field. The thixotropic systems show a strong time dependence of the viscosity due to the existence of an internal percolated structure that confers the yield stress to the material. Using loaded emulsions to control the thixotropy, we show that the transition to flow at the yield stress is discontinuous for thixotropic materials, and continuous for ideal ones. The discontinuity leads to a critical shear rate below which no steady flows can be observed, accounting for the ubiquitous shear banding observed in these materials.     

Age-dependent transient shear banding in soft glasses

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.     

Softening caused by profuse shear banding in a bulk metallic glass

By controlling the specimen aspect ratio and strain rate, compressive strains as high as 80% were obtained in an otherwise brittle metallic glass. Physical and mechanical properties were measured after deformation, and a systematic strain-induced softening was observed which contrasts sharply with the hardening typically observed in crystalline metals. If the deformed glass is treated as a composite of hard amorphous grains surrounded by soft shear-band boundaries, analogous to nanocrystalline materials that exhibit inverse Hall-Petch behavior, the correct functional form for the dependence of hardness on shear-band spacing is obtained. Deformation-induced softening leads naturally to shear localization and brittle fracture.     

Onset of shear thickening in a simple fluid

We report on nonequilibrium molecular-dynamics simulations of the shear-thickening transition in a simple fluid under shear. We relate the shear-thickening transition to the onset of instabilities in the flow profile and to that of dramatic variations in normal stress differences. The dependence of the critical shear rate, which indicates the onset of shear thickening, on density and temperature is rationalized by introducing a ratio between two characteristic times, quantifying the short-time mobility of a particle and the deformation imposed by the applied shear rate, respectively. The shear-thickening transition is shown to occur at a constant value for this ratio for all state points studied. From a structural point of view, this transition is accompanied by the formation of clusters as recently observed in experiments on complex fluids.Received: 26 July 2004, Published online: 21 September 2004PACS: 83.60.Rs Shear rate-dependent structure (shear thinning and shear thickening) - 47.50. + d Non-Newtonian fluid flows - 83.10.Mj Molecular dynamics, Brownian dynamics     

Isothermal sustained oscillations in a very simple surface reaction

A simple model is used to illustrate that a bimolecular Langmuir—Hinshelwood surface reaction with two empty sites in its reaction step, non-equilibrium in the adsorption steps, and coverage independent parameters may lead to sustained oscillatory reaction rates. The two empty sites in the reaction step play an essential role in the establishment of these oscillations. Numerical simulation is used to demonstrate the periodic behavior predicted by the model. Several similar surface reaction models with coverage independent parameters can also yield oscillations. A mechanism with one vacant site in the adsorption steps, two vacant sites in the reaction step and only two dimensionless non-zero parameters may lead to sustained oscillations.     

Aging, yielding, and shear banding in soft colloidal glasses

Soft colloidal interactions in colloidal glasses are modeled using suspensions of multiarm star polymers. Using a preshearing protocol that ensures a reproducible initial state ("rejuvenation" of the system), we report here the evolution of the flow curve from monotonically increasing to one dominated by a stress plateau, demonstrating a corresponding shear-banded state. Phenomenological understanding is provided through a scalar model that describes the free-energy landscape.     

Kinetics of shear banding in a bulk metallic glass monitored by acoustic emission measurements

Detailed acoustic emission (AE) and surface microscopy investigations of the kinetics of shear banding in bulk Zr_52.5Ti₅Cu_17.9Ni_14.6Al₁₀ metallic glass at room temperature are presented. The shear band propagates in a jump-like mode as reflected by numerous AE bursts. The time distribution and cluster statistical analysis of AE time series revealed, firstly, that there are two shear banding processes notably different in their spatial scales and, secondly, that formation of shear bands at large strains can be correlated in time and space. Independence of the AE characteristics on the current stress magnitude implies that shear band propagation could not be interpreted as a shear front motion in a viscous Newtonian-like medium. The AE response to shear banding is to a certain extent similar to that of a moving dislocation pile-up escaping to a free surface. It is emphasized that AE and microscopic features of shear banding in the bulk metallic glass are very nearly the same as those found earlier for melt-spun ribbon glasses, indicating that the change in the quenching rate by about four orders of magnitude does not cause the kinetics of shear band nucleation and propagation to vary considerably.     

Vorticity banding during the lamellar-to-onion transition in a lyotropic surfactant solution in shear flow

We report on the rheology of a lyotropic lamellar surfactant solution (SDS/dodecane/pentanol/ water), and identify a discontinuous transition between two shear thinning regimes which correspond to the low-stress lamellar phase and the more viscous shear-induced multilamellar vesicle, or “onion” phase. We study in detail the flow curve, stress as a function of shear rate, during the transition region, and present evidence that the region consists of a shear-banded phase where the material has macroscopically separated into bands of lamellae and onions stacked in the vorticity direction. We infer very slow and irregular transformations from lamellae to onions as the stress is increased through the two-phase region, and identify distinct events consistent with the nucleation of small fractions of onions that coexist with sheared lamellae.     

Spatiotemporal dynamics of wormlike micelles under shear

Velocity profiles in a wormlike micelle solution (cetyl trimethyl ammonium bromide in D2O) are recorded using ultrasound every 2 s during a startup experiment into the shear-banding regime. The stress relaxation occurs over more than 6 h and corresponds to the very slow nucleation and growth of the high-shear band. Moreover, oscillations of the interface position with a period of about 50 s are observed during the growth process. Strong wall slip, metastable states, and transient nucleation of three-band flows are also reported and discussed in light of previous experiments and theoretical models.