Shear Banding Phenomenon Research Articles

Macroscopic Pipe Flow of Micellar Solutions Investigated by Ultrasound Doppler Velocimetry

Abstract Macroscopic flow properties of viscoelastic surfactant solution are investigated in pressure driven pipe flow condition. We focus on an equimolar aqueous solution of cetylpyridinium chloride – sodium salicylate, which in simple shear flow exhibits a shear thinning, and at higher shear rates, a pronounced shear-thickening behavior associated with the formation of shear bands [1–6]. An ultrasound Doppler velocimetry method is used to detect these shear bands in pipe flow. The emitted ultrasonic beam is scattered by the moving sample and the time delay between emitted pulse and received echoes as well as the frequency shift is determined. This Doppler shift is related to the speed and the direction of the moving scatters and with this information, the velocity profile across the pipe is calculated [7]. The shape of the obtained velocity profile is used to determine the flow properties of the sample and the formation of shear bands at the tube's wall or within the bulk phase. For the investigated solution we do not observe shear band phenomena. This is contrary to previous investigations [5, 6, 8] where shear bands in the order of few tenth of a millimeter were found. Our results suggesting that the banded region is not detectable by the utilized UVP technique.

Nonmonotonic Models are Not Necessary to Obtain Shear Banding Phenomena in Entangled Polymer Solutions

Recent experiments on entangled polymer solutions may indicate a constitutive instability, and have led some to question the validity of existing constitutive models. We use a modern constitutive model, the Rolie-Poly model plus a solvent viscosity, and show that (i) this simple class of models captures instability, (ii) shear banding phenomena is observable for weakly stable fluids in flow geometries with sufficiently inhomogeneous total stress, and (iii) transient phenomena exhibit inhomogeneities similar to shear banding, even for weakly stable fluids.

On the modeling of confined buckling of force chains

Buckling of force chains, laterally confined by weak network particles, has long been held as the underpinning mechanism for key instabilities arising in dense, cohesionless granular assemblies, e.g. shear banding and slip-stick phenomena. Despite the demonstrated significance of this mechanism from numerous experimental and discrete element studies, there is as yet no model for the confined buckling of force chains. We present herein the first structural mechanical model of this mechanism. Good agreement is found between model predictions and confined force chain buckling events in discrete element simulations. A complete parametric analysis is undertaken to determine the effect of various particle-scale properties on the stability and failure of force chains. Transparency across scales is achieved, as the mechanisms on the microscopic and mesoscopic domains, which drive well-known macroscopic trends in biaxial compression tests, are elucidated.

Temperature increases caused by shear banding in as-cast and relaxed Zr-based bulk metallic glasses under compression

Using an infrared camera, the temperature evolution of as-cast and relaxed bulk metallic glasses during compression was measured. Substantial variations in the temperatures of both glasses during plastic deformation were observed, which are conjectured to result at least partially from shear-banding phenomena. The relaxed glass has a larger temperature rise than the as-cast glass, which can be attributed to a reduction in the free volume. The larger temperature increase in the relaxed glass may be responsible for the observed work softening. The relaxed glass also has a higher maximum temperature than the as-cast, which can be attributed to a stronger strain-rate dependence of the temperature rise rate, and a shorter dissipation time scale for the heat due to conduction. The experimental data follow the well-known model behavior, and suggest the possibility of a statistical correlation between the fluctuations of strain rates and the rates of the temperature variation.

Shear-banding phenomena and dynamical behavior in a Laponite suspension

Shear localization in an aqueous clay suspension of Laponite is investigated through dynamic light scattering, which provides access both to the dynamics of the system (homodyne mode) and to the local velocity profile (heterodyne mode). When shear bands form, a relaxation of the dynamics typical of a gel phase is observed in both bands soon after the flow stops. Periodic oscillations of the flow behavior, typical of a stick-slip phenomenon, are also observed when shear localization occurs. Both results are discussed in the light of various theoretical models for soft glassy gels.

Rheo NMR and shear banding

The phenomenon of shear banding in complex fluids has been investigated using NMR velocimetry and NMR spectroscopy, mostly in wormlike micelle systems, but more recently in colloidal systems and multilayer vesicles. A particular advantage of NMR is the ability to simultaneously investigate structural ordering and to compare such ordering with local strain rates. In this paper, we describe the basics of Rheo-NMR and summarise its recent application to the study of shear banding.

Evidence for three-dimensional unstable flows in shear-banding wormlike micelles

We report on an experimental study of the shear-banding phenomenon in the concentrated wormlike micellar system CTAB at 20wt.% in D2O . Time-resolved velocity profiles are recorded using ultrasonic velocimetry simultaneously to global rheological data. Our results confirm the studies performed previously by Fischer and Callaghan [Phys. Rev. E 64, 011501 (2001)]. Time averaged velocity profiles display an unsheared "nematic gel." In the range of applied shear rate, the flow field exhibits very fast temporal fluctuations. Suspicions for the presence of three-dimensional flow are evidenced and possible causes for a three-dimensional instability are discussed together with the coupling of wall slip to bulk dynamic.

Deformation Structure and Texture Transformations in Twinned Fcc Metals: Critical Role of Micro- and Macro- Scale Shear Bands

Microstructure and texture development in twinned fcc metals is investigated in order to characterize the influence of micro- and macro-scale brass-type shear bands (SB) on structural and textural changes at large deformations. TEM and SEM analyses are focused on bands developed by plane strain compression in twinned C{112}<111> oriented single crystals. The proposed crystallographic model of the shear banding phenomenon refers to the idea of local lattice reorientation within narrow areas. Most of these rotations occur around the TD||<110> axis with significant further rotations about <112> poles. These two rotations explain the influence of SB’s on the formation of Goss{110}<001> and brass{110}<112>-S{123}<634> texture components clearly observed in highly deformed low SFE metals. At high deformations symmetrically equivalent crystal lattice rotations inside narrow areas lead to the formation of positive and negative macroscopic SBs.

Effect of Low Temperature Rolling on Microstructure and Properties of ECAE Processed Copper

The changes in the tensile properties, in relation to the phenomenon of shear banding are investigated in copper, rolled at liquid nitrogen temperature and then recrystallized, after initial processing by Equal-Channel Angular Extrusion (ECAE) at room temperature. Increases in ductility and strength up to the fourth pass of ECAE processing were noted, then a decrease of both properties was observed. The decrease was accompanied by twinning and shear banding. In rolled samples, pre-cooled down to the temperature of liquid nitrogen and initially recrystallized, the twinning and shear banding mechanisms were the most probable mechanisms responsible for lowering the mechanical properties.

Analytical and geometrical representation of localization in granular materials

Attempts to understand the phenomenon of shear banding through mathematical analysis required exclusive use of the fundamental principles of mechanics. The feasibility of capturing localized deformation using analytical and numerical methods has been demonstrated by a number of investigators. However, most of the formulations have been developed to deal with classical continuum mechanics approaches. In order to describe correctly localization phenomena, a continuum model with microstructure or Cosserat continuum have been formulated and implemented. The main purpose of this paper is to describe and simulate the localization geometrically and analytically for both classical and Cosserat media. Similarities and differences of the two approaches will be summarized. The importance of description of kinematics and statics of soil media with microstructure has been investigated. The nonsymmetric Cosserat formulation has been implemented for analytical and geometrical localization analysis.

Model for estimation of critical packing density in polydisperse hard-disk packings

We introduce a geometric model for unjamming the polydisperse hard-disk packing. The unjamming corresponds to a critical packing density which is assumed to happen uniformly throughout the packing. However, this model can be used for prediction of local dilation in packings. Molecular dynamics (MD) simulations are also performed to create random packings of polydisperse hard disks. In MD simulations, a densification scheme is applied to the event-driven algorithm in which the size of particles increases with controlled rates. The packing densities upon the onset of the critical state are estimated in a series of bidisperse packings by feeding the textural information of the mixtures from MD simulations into the model. These results are relevant for studies of unjamming and shear banding phenomena in granular materials, colloids, metallic glasses and similar systems.

Anchoring-induced texture & shear banding of nematic polymers in shear cells

We numerically explore texture (resolved by the second-moment of the orientational distribution) and shear banding of nematic polymers in shear cells, allowing for one-dimensional morphology in the gap between par- allel plates. We solve the coupled Navier-Stokes and Doi-Marrucci-Greco orientation tensor model, considering both confined orientation in the plane of shear and full orientation tensor degrees of freedom, and both primary flow and vorticity (in the full tensor model) components. This formulation makes contact with a large literature on analytical and numerical (cf. the review [41]) as well as experimental (cf. the review [45]) studies of nematic polymer texture and flow feedback. <em>Here we focus on remarkable sensitivity of texture & shear band phenomena to plate anchoring conditions on the orientational distribution.</em> We first explore steady in-plane flow-nematic states at low Peclet (<em>Pe</em>) and Ericksen (<em>Er</em>) numbers, where asymptotic analysis provides exact texture scaling properties [18, 6]. We illustrate that in-plane steady states co-exist with, and are unstable to, out-of-plane steady states, yet the structures and their scaling properties are not dramatically different. Non-Newtonian shear bands arise through orientational stresses. They are explored first for steady states, where we show the strength and gap location of shear bands can be tuned with anchoring conditions. Next, unsteady flow-texture transitions associated with the Ericksen number cascade are explored. We show the critical <em>Er</em> of the steady-to-unsteady transition, and qualitative features of the space-time attractor, are again strongly dependent on wall anchoring conditions. Other simulations highlight unsteady flow-nematic structures over 3 decades of the Ericksen number, comparisons of shear banding and texture features for in-plane and out-of-plane models, and vorticity generation in out-of-plane attractors.

Development of a heterogeneous microstructurally based finite element model for the prediction of forming limit diagram for sheet material

A heterogeneous finite element model with randomly distributed inhomogeneities has been developed for the determination of the forming limit diagram (FLD) for thin aluminum sheet material based on the prediction of localized necking. The strength difference between the inhomogeneities and the matrix is ascertained either from the fluctuation of the experimental stress-strain curve or from a micromechanical analysis that uses a representative particle field. By changing the specimen geometry and friction conditions, different stress states (or strain paths) are achieved. A plot of the critical Oyane fracture parameter is used to identify the limit strain state. Also, a plot of equivalent plastic strain rate is used to distinguish the boundary of intense shear bands and hence to identify where to take the measurement point. Both a plane stress model and a three-dimensional (3-D) model are adopted to predict the shear banding phenomenon and hence the FLD. The predicted FLD agrees well with the measurements from a recent round robin experimental FLD involving several independent research laboratories. The Taguchi method is applied to assess how the various parameters involved in the heterogeneous model affect the calculated forming limit strain.

A Workability Criterion for the Transformed Adiabatic Shear Band Phenomena during Cold Heading of 1038 Steel

A criterion for predicting the workability limits for internal britde failure was developed for cold heading of 1038 steel. The criterion considers internal defects caused by microstructural changes generated by adiabatic shear. This transformation is termed the transformed adiabatic shear band (TASB) phenomena. The defect that develops is the formation ofbritde martensite as a result ofthe temperature rise and fall inside the adiabatic shear band (ASB). In this work, the material is considered to have a TASB defect when the temperature inside the ASB exceeds the phase transformation temperature (AC3). The empirical formulas provided by Andrews[1] were used to determine transformation temperatures. Microhardness testing and etching with 2% Nital and Le Pera etchants were performed on the sectioned specimens to locate and study the TASB. In order to simulate the cold heading process, a drop weight compression test was used and modeled with finite-element analysis (implemented within ABAQUS/Explicit).

Orientation Imaging in Scanning Electron and Transmission Electron Microscopy for Characterization of the Shear Banding Phenomenon

The texture evolution during deformation of high purity fcc single crystals with initial (112) [11\(\bar{1}\)] orientation has been characterised in detail by transmission (TEM) and scanning (SEM–FEG) electron microscopes. The channel-die deformed samples up to reduction of about 1–1.5, first developing strongly anisotropic layers of elongated cells or twin-matrix plates and then compact clusters of SB. Substantial progress in understanding the mechanism of the SB formation was possible thanks to systematic local orientation measurements (orientation mapping) using SEM and TEM. These two techniques of local orientation measurements have been compared with respect to their applicability for the study of shear banding phenomenon and for characterization of the specific nanostructure of SB in metals with fcc lattice. It was shown that well-developed SB exhibit large orientation spreads up to 35–40° with respect to the adjacent areas outside the band. Most of these misorientations occur by rotations about the TD‖〈110〉 axis with significant further rotations about 〈112〉 poles. This ultimately leads to the formation of the texture components whose occurrence cannot be explained by models homogeneous deformation.

Simulations of complex fluids by mixed lattice Boltzmann—finite difference methods

We present the numerical results of simulations of complex fluids under shear flow. We employ a mixed approach which combines the lattice Boltzmann method for solving the Navier–Stokes equation and a finite difference scheme for the convection–diffusion equation. The evolution in time of shear banding phenomenon is studied. This is allowed by the presented numerical model which takes into account the evolution of local structures and their effect on fluid flow.

Instability-induced ordering, universal unfolding and the role of gravity in granular Couette flow

Linear stability theory and bifurcation analysis are used to investigate the role of gravity in shear-band formation in granular Couette flow, considering a kinetic-theory rheological model. We show that the only possible state, at low shear rates, corresponds to a ‘plug’ near the bottom wall, in which the particles are densely packed and the shear rate is close to zero, and a uniformly sheared dilute region above it. The origin of such plugged states is shown to be tied to the spontaneous symmetry-breaking instabilities of the gravity-free uniform shear flow, leading to the formation of ordered bands of alternating dilute and dense regions in the transverse direction, via an infinite hierarchy of pitchfork bifurcations. Gravity plays the role of an ‘imperfection’, thus destroying the ‘perfect’ bifurcation structure of uniform shear. The present bifurcation problem admits universal unfolding of pitchfork bifurcations which subsequently leads to the formation of a sequence of a countably infinite number of ‘isolas’, with the solution structures being a modulated version of their gravity-free counterpart. While the solution with a plug near the bottom wall looks remarkably similar to the shear-banding phenomenon in dense slow granular Couette flows, a ‘floating’ plug near the top wall is also a solution of these equations at high shear rates. A two-dimensional linear stability analysis suggests that these floating plugged states are unstable to long-wave travelling disturbances.The unique solution having a bottom plug can also be unstable to long waves, but remains stable at sufficiently low shear rates. The implications and realizability of the present results are discussed in the light of shear-cell experiments under ‘microgravity’ conditions.

Identification of the Material Parameters of a Micropolar Model for Granular Materials

AbstractGranular frictional materials show a complex stress‐strain behaviour depending on the stress state and the load history. Furthermore, biaxial experiments exhibit the occurrence of shear band phenomena as the result of the localization of plastic strains. It is well known that the onset of shear bands is associated with microrotations of the granular microstructure, which has a significant influence on the macroscopic behaviour. Consequently, the macroscopic material must result in a micropolar model, which incorporates rotational degrees of freedom. After the formulation of the constitutive equations and the numerical implementation, it is necessary to determine all required material parameters. (© 2004 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Shear banding phenomena in ultrasoft colloidal glasses

We explore the nonlinear rheological response of a soft gel formed by a crowded colloidal star polymer and focus on the occurrence of a stress plateau, marked hysteresis, and yield stress in its flow curve. With the aid of nuclear magnetic resonance velocimetry we find evidence for fluctuations in the flow behavior across the gap of the concentric cylindrical Couette device, in association with a degree of apparent slip at the inner wall. The time scale of the these fluctuations appears rapid (with respect to the measurement time per shear rate in the flow curve), on the order of tens to hundreds of milliseconds, with the speed of fluctuations associated with the flow history of the sample. Our velocity profile analysis suggests a qualitative model in which intermittent changes due to jamming/unjamming transitions occur, analogous to cage dynamics in colloidal glasses.

Simulations of shear-induced melting in two dimensions

We report on nonequilibrium molecular-dynamics simulations of shear-induced melting for a two-dimensional crystal under either constant shear or constant stress. In both cases, dissipation of heat was accounted for by a configurational thermostat which does not exert any constraint on the flow profile. Results from both types of simulation only differ at low shear stress. While melting is always observed in simulations under constant shear, simulations under constant stress reveal the existence of a yield stress. For stresses above the yield stress, both types of simulation exhibit a complex sequence of phase transitions [crystal$\ensuremath{\rightarrow}$hexatic$\ensuremath{\rightarrow}$(coexisting liquid $+$ hexatic)$\ensuremath{\rightarrow}$liquid] with increasing shear. The regime where liquid and hexatic phases coexist is reminiscent of the shear-banding phenomenon, in which bands characterized by different local orders and different local shear rates coexist.