Steady shear banding in complex fluids

Shear banding (SB) is manifested by the abrupt “demixing” of the flow into regions of high and low shear rate. In this paper, we first relate analytically the rheological parameters of the fluid with the range of shear rates and stresses of SB occurrence. For this, we accept that the origin of shear banding is constitutive, and adopt a non-linear viscoelastic expression able to accommodate the double-valuedness of the stress with flow intensity, under certain conditions. We then implement the model for the case of pressure driven flow through a cylindrical pipe; we derive approximate expressions for the velocity profile in the two-banded regions (core and outer annular), the overall throughput in the presence or absence of “spurt”, and the radial location limits of the shear rate discontinuity.     

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.     

Recent experimental probes of shear banding

Recent experimental techniques used to investigate shear banding are reviewed. After recalling the rheological signature of shear-banded flows, we summarize the various tools for measuring locally the microstructure and the velocity field under shear. Local velocity measurements using dynamic light scattering and ultrasound are emphasized. A few results are extracted from current works to illustrate open questions and directions for future research.

Distinguishing shear banding from shear thinning in flows with a shear stress gradient

Shear banding occurs in complex fluids that exhibit a non-monotonic constitutive instability, such as wormlike micelles, and potentially also in polymeric fluids with presumably monotonic constitutive behavior. However, velocity profiles for shear thinning fluids in geometries possessing a stress gradient, such as Taylor-Couette flow, could be misidentified as shear banding. To address this, we present a model-free experimental procedure to distinguish shear banding from strong shear thinning using high-resolution velocimetry. The approach is developed and validated using simulations using the d-Giesekus model and is based upon the behavior of the width of the apparent interface between the high and low shear rate regions. It is then tested using experimental data for model wormlike micellar solutions. The method allows shear banding to be distinguished from shear thinning in cases where this difference is otherwise indistinguishable. As a by-product, it also provides an estimate of the stress diffusivities for shear banding fluids.     

Perspectives on shear banding in complex fluids

In this review, I present an idiosyncratic view of the current state of shear banding in complex fluids. Particular attention is paid to some of the outstanding issues and questions facing the field, including the applicability of models that have “traditionally” been used to model experiments; future directions and challenges for experimentalists; and some of the issues surrounding vorticity banding, which has been discussed theoretically and whose experiments are fewer in number yet, in many ways, more varied in character.     

Micromechanical modelling of shear banding in single crystals

Plastic deformation of a single crystal in double-conjugate single slip was considered. A micromechanical model based on dislocation density evolution was used. The mobile dislocation densities were assumed to relax rapidly to quasi-steady state values dictated by the current values of the slowly varying immobile dislocation densities (“adiabatic” approximation). In this approximation, a uniform time (or strain) dependent solution of the set of the governing equations was obtained. Linear analysis of stability of the uniform plastic flow with respect to band-shaped perturbations was carried out. The correspondence of the instability condition obtained with the results of previous, more macroscopic analyses was examined. Numerical examples illustrating the onset of instability were considered.     

高速切削过程中诱发绝热剪切带形成的热塑性剪切波

提出了高速切削过程中诱发绝热剪切带形成的热塑性剪切波的传播机理,针对锯齿形切屑中热望性区域内的塑性梯度变形特征、动量和能量耗散情况,建立了与切削条件相关的热塑性剪切波的传播模型及剪切带宽度模型.在此基础上,通过淬硬45钢的切削实验并结合改进的Johnson-Cook本构模型分析了热塑性剪切波的传播规律,并将剪切带宽度模型与已提出的DB模型、WR模型和DM模型做了对比,结果表明,由热塑性剪切波传播理论推导的剪切带宽度模型与实验结果较其他模型吻合较好.     

Phenomenology and physical origin of shear localization and shear banding in complex fluids

We review and compare the phenomenological aspects and physical origin of shear localization and shear banding in various material types, namely emulsions, suspensions, colloids, granular materials, and micellar systems. It appears that shear banding, which must be distinguished from the simple effect of coexisting static-flowing regions in yield stress fluids, occurs in the form of a progressive evolution of the local viscosity toward two significantly different values in two adjoining regions of the fluids in which the stress takes slightly different values. This suggests that from a global point of view, shear banding in these systems has a common physical origin: Two physical phenomena (for example, in colloids, destructuration due to flow and restructuration due to aging) are in competition, and depending on the flow conditions, one of them becomes dominant and makes the system evolve in a specific direction.     

Anti-plane shear cracks in ideally plastic crystals

Cracks in ductile single crystals are analyzed here for geometries and orientations such that two-dimensional states of anti-plane shear constitute possible deformation fields. The crystals are modelled as ideally plastic and yield according to critical resolved shear stresses on their slip systems. Restrictions on the asymptotic forms of stress and deformation fields at crack tips are established for anti-plane loading of stationary and quasistatically growing cracks, and solutions are presented for several specific orientations in f.c.c. and b.c.c. crystals. The asymptotic solutions are complemented by complete elastic-plastic solutions for stationary and growing cracks under small scale yielding, based on previous work by Rice (1967, 1984) and Freund (1979). Remarkably, the plastic zone at a stationary crack tip collapses into discrete planes of displacement and stress discontinuity emanating from the tip; plastic flow consists of concentrated shear on the displacement discontinuities. For the growing crack these same planes, if not coincident with the crack plane, constitute collapsed plastic zones in which velocity and plastic strain discontinuities occur, but across which the stresses and anti-plane displacement are fully continuous. The planes of discontinuity are in several cases coincident with crystal slip planes but it is shown that this need not be the case, e.g., for orientations in which anti-plane yielding occurs by multi-slip, or for special orientations in which the crack tip and the discontinuity planes are perpendicular to the activated slip plane.     

On the relation for plastic spin

Summary Within the framework of the theory of finite elastoplasticity based on the known concept of the local, relaxed, isoclinic configuration the large plastic deformations with strain induced anisotropy and emerging plastic spin are studied. The derivation of the relation for plastic spin, based on the analysis on the simple shear problem for rigid-plastic material with kinematic hardening is provided and the experimental verification of the calculated axial elongation in the unconstrained large-strain shear problem is presented. The applicability of the proposed model is discussed.

---

Zur Ermittlung der Stoffgesetze für den plastischen Spin

Übersicht Im Rahmen der Theorie endlicher elastoplastischer Formänderungen unter Verwendung des bekannten Konzepts lokaler, relaxierender, isokliner Konfigurationen werden große plastische Deformationen mit durch Dehnung hervorgerufener Anisotropie und daraus resultierendem plastischen Spin untersucht. Die Gleichung für den plastischen Spin wird mit dem Modell der einfachen Scherung hergeleitet. Dabei wird starr-plastisches, kinematisch verfestigendes Material angenommen. Das Modell des reinen Schubes wird numerisch behandelt und mit experimentellen Ergebnissen tordierter dünnwandiger Zylinder mit unbehinderter axialer Dehnung verglichen. Die Anwendbarkeit des vorgeschlagenen Modells wird diskutiert.

     

Gradient dependent dilatancy and its implications in shear banding and liquefaction

Summary A gradient dependent dilatancy condition is assumed in order to capture the heterogeneous character of deformation in granular soils. This assumption is incorporated into the structure of classical deformation and flow theories of plasticity and its implications in two interesting examples of patterning instability, that is shear banding and liquefaction, are examined. Shear banding is considered within a modified gradient dependent deformation theory, while liquefaction is studied within a modified gradient dependent flow theory of plasticity. In both cases a deformation induced length scale is obtained near the instability, and this is identified with the thickness of the shear band or the spacing of the liquefying strips.

---

Gradientenabhängige Dilatanzbeziehung und ihre Implikationen auf Scherfugenbildung und Verfestigung in Böden

Übersicht Lokale Inhomogenitäten bei der Verformung granularer Materialien sind hier mit Hilfe einer gradientenabhängigen Dilatanzbeziehung beschrieben. Diese Annahme ist in die Struktur einer klassischen Deformations- und Fließtheorie der Plastizität eingebaut, und die hiermit einhergehenden Konsequenzen werden anhand zweier interessanten Fälle der Musterbildung in Böden, nämlich Scherfugenbildung und Verflüssigung, studiert. Scherfugenbildung ist innerhalb einer modifizierten gradientenabhängigen Deformationstheorie untersucht, wogegen Bodenverflüssigung innerhalb einer modifizierten Fließtheorie analysiert wird. In beiden Fällen bekommt man in der Umgebung des Instabilitätszustandes einen deformationsinduzierten Längenmaßstab, der sich als Scherfugendicke oder als Abstand der verflüssigten Bodenstreifen manifestiert.

---

---

Presented at the workshop on Limit Analysis and Bifurcation Theory, held and the University of Karlsruhe (FRG), Febr. 22–25, 1988     

A new constitutive model for shear banding instability in metallic glass

Inelastic deformation of metallic glass is through shear banding, characterized by significantly localized deformation and emerged expeditiously under certain stress state. This study establishes a new constitutive model addressing the physical origin of the shear banding. In the modeling, the atomic structural change and the free volume generation are embodied by the plastic shear strain and the associated dilatation. The rugged free energy landscape is adopted to naturally reflect the rate-independent flow stress and flow serrations. Based on this, the conditions for the onset of shear banding instability are established, which enables the explicit calculation of the shear band inclination angle and its extension speed. The study concludes that shear band angle is significantly influenced by the diltancy factor and pressure sensitivity, that a shear band does not increase its thickness once emanated from a deformation unit, that the spreading speed of a shear band is intersonic, and that more shear bands, which lead to higher ductility, can be induced by high strain rates or by the introduction of a second material phase. The analysis also demonstrates that the ductility of metallic glass depends on the sample geometry and/or the stress state.     

Laminar shear flow of plastic viscoelastic fluids

Summary The theory of plastic viscoelastic fluids was developed by the author to represent the rheological behavior of polymer melts and solutions with high loading of small particles. The present paper develops an asymptotic formulation of the general theory which applies to laminar shear flows. The formulation is analogous to Criminale, Ericksen and Filbey's theory for viscoelastic fluids. We apply this to study plane Poiseuille and Couette flow.With 2 tables     

Anomalous shear banding: multidimensional dynamics under fluctuating slip conditions

The strain-controlled flow of a wormlike micellar solution in cylindrical Couette geometries with smooth and rough glass inner walls is investigated using 2D ¹H NMR velocimetry. We find anomalous shear banding in which fluctuating slip dynamics in combination with surfactant properties lead to a non-lever rule behaviour where the interface position remains constant while the high and low shear rates change. Velocities in the flow direction are imaged in the flow-gradient/vorticity plane. The spatiotemporal resolution achieved reveals fluctuations in flow structure along the vorticity axis and instability of the high shear band.     

Fully plastic center-cracked strip under anti-plane shear

The problem of a center-cracked strip subjected to uniform remote anti-plane shear stress is transformed to a problem in a hodograph plane which is solved exactly by Mellin transform and Wiener-Hopf technique. The material of the strip satisfies a pure power hardening stress strain relation and the results are valid for both deformation and flow theories of placticity. Numerical values are given for the crack opening displacement δ and Rice's path independent J integral for several values of the power hardening exponent n and crack width to strip width ratios. Approximate asymptotic formulas are presented for J and δ for large n.