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.     

A discrete model for an ill-posed nonlinear parabolic PDE

We study a finite-difference discretization of an ill-posed nonlinear parabolic partial differential equation. The PDE is the one-dimensional version of a simplified two-dimensional model for the formation of shear bands via anti-plane shear of a granular medium. For the discretized initial value problem, we derive analytically, and observed numerically, a two-stage evolution leading to a steady-state: (i) an initial growth of grid-scale instabilities, and (ii) coarsening dynamics. Elaborating the second phase, at any fixed time the solution has a piecewise linear profile with a finite number of shear bands. In this coarsening phase, one shear band after another collapses until a steady-state with just one jump discontinuity is achieved. The amplitude of this steady-state shear band is derived analytically, but due to the ill-posedness of the underlying problem, its position exhibits sensitive dependence. Analyzing data from the simulations, we observe that the number of shear bands at time t decays like t^−1/3. From this scaling law, we show that the time-scale of the coarsening phase in the evolution of this model for granular media critically depends on the discreteness of the model. Our analysis also has implications to related ill-posed nonlinear PDEs for the one-dimensional Perona–Malik equation in image processing and to models for clustering instabilities in granular materials.     

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.     

Self-organization, localization of shear bands, and aging in loose granular materials

We introduce a mesoscopic model for the formation and evolution of shear bands in loose granular media. Numerical simulations reveal that the system undergoes a nontrivial self-organization process which is governed by the motion of the shear band and the consequent restructuring of the material along it. High density regions are built up, progressively confining the shear bands in localized regions. This results in an inhomogeneous aging of the material with a very slow increase in the mean density, displaying an unusual glassylike system-size dependence.     

Towards a Landau–Ginzburg-Type Theory for Granular Fluids

In this paper we show how, under certain restrictions, the hydrodynamic equations for the freely evolving granular fluid fit within the framework of the time dependent Landau–Ginzburg (LG) models for critical and unstable fluids. The granular fluid, which is usually modeled as a fluid of inelastic hard spheres (IHS), exhibits two instabilities: the spontaneous formation of vortices and of high density clusters. We suppress the clustering instability by imposing constraints on the system sizes, in order to illustrate how LG-equations can be derived for the order parameter, being the rate of deformation or shear rate tensor, which controls the formation of vortex patterns. From the shape of the energy functional we obtain the stationary patterns in the flow field. Quantitative predictions of this theory for the stationary states agree well with molecular dynamics simulations of a fluid of inelastic hard disks.     

Strain localization and its connection with the deformed state of the material

The detection of the passage of a shear band over an undeformed material poses a new question about the causal connection between the strain and the formation of shear bands. The collapse of a thick-walled tube is considered from the standpoint of the spall mechanism, according to which localized strain bands under pulsed loading are the result of interference of unloading waves; the negative stresses in the extension zone in this case do not exceed the strength of the material. It is found that radial cracks and their continuations in the form of shear bands appear at the unloading stage after the strained state of the material has already formed as a result of collapse. In other words, damageability is superimposed on the deformed material, and both these processes are independent and accompany each other.     

Transients in sheared granular matter

As dense granular materials are sheared, a shear band and an anisotropic force network form. The approach to steady-state behavior depends on the history of the packing and the existing force and contact network. We present experiments on shearing of dense granular matter in a 2D Couette geometry in which we probe the history and evolution of shear bands by measuring particle trajectories and stresses during transients. We find that when shearing is stopped and restarted in the same direction, steady-state behavior is immediately reached, in agreement with the typical assumption that the system is quasistatic. Although some relaxation of the force network is observed when shearing is stopped, quasistatic behavior is maintained because the contact network remains essentially unchanged. When the direction of shear is reversed, a transient occurs in which stresses initially decrease, changes in the force network reach further into the bulk, and particles far from the wheel become more mobile. This occurs because the force network is fragile to changes transverse to the force network established under previous shear; particles must rearrange before becoming jammed again, thereby providing resistance to shear in the reversed direction. The strong force network is re-established after displacing the shearing surface , where d is the mean grain diameter. Steady-state velocity profiles are reached after a shear of . Particles immediately outside of the shear band move on average less than 1 diameter before becoming jammed again. We also examine particle rotation during this transient and find that mean particle spin decreases during the transient, which is related to the fact that grains are not interlocked as strongly.Received: 5 March 2004, Published online: 24 August 2004PACS: 45.70.-n Granular systems - 83.80.Fg Granular solids     

Collective rearrangement at the onset of flow of a polycrystalline hexagonal columnar phase

Creep experiments on polycrystalline surfactant hexagonal columnar phases show a power law regime, followed by a drastic fluidization before reaching a final stationary flow. The scaling of the fluidization time with the shear modulus of the sample and stress applied suggests that the onset of flow involves a bulk reorganization of the material. This is confirmed by x-ray scattering under stress coupled to in situ rheology experiments, which show a collective reorientation of all crystallites at the onset of flow. The analogy with the fracture of heterogeneous materials is discussed.     

Flow of wet granular materials

The transition from frictional to lubricated flows of a dense suspension of non-Brownian particles is studied. The pertinent parameter characterizing this transition is the Leighton number Le=eta(s)gamma / sigma, the ratio of lubrication to frictional forces. Le defines a critical shear rate below which no steady flow without localization exists. In the frictional regime the shear flow is localized. The lubricated regime is not simply viscous: the ratio of shear to normal stresses remains constant and the velocity profile has a universal form in both frictional and lubricated regimes. Finally, a discrepancy between local and global measurements of viscosity is identified, which suggests inhomogeneity of the material under flow.     

The effect of the shear flow on directional solidification of SCN-3wt% Salol alloy

The directional solidification process of SCN-3wt% Salol transparent alloy is investigated in the presence of the shear flow at the liquid-solid interface. It is found that the shear flow induces a stabilizing effect on planar interface. At higher pulling rates, oscillation of the growth pattern together with fluctuation of the growth velocity takes place. With the increase of the pulling rate, the interface growth pattern transits from “planar-cellular” oscillation to “cellular-dendritic” oscillation, and the periodicity increases. The modification of the growth pattern is due to the effect of the shear flow on solute distribution, and the time and history dependent character of interface morphology evolution also plays an important role in the formation of the oscillating growth pattern. Supported by the National Natural Science Foundation of China (Grant Nos. 50331040 and 50702046)     

The mechanisms of plastic strain accommodation during the high strain rate collapse of corrugated Ni–Al laminate cylinders

The Thick-Walled Cylinder method was used on corrugated Ni–Al reactive laminates to examine how their mesostructures accommodate large strain, high strain rate plastic deformation and to examine the potential for intermetallic reaction initiation due to mechanical stimuli. Three main mesoscale mechanisms of large plastic strain accommodation were observed in addition to the bulk distributed uniform plastic flow: (a) the extrusion of wedge-shaped regions into the interior of the cylinder along planes of easy slip provided by angled layers, (b) the development of trans-layer shear bands in the layers with orientation close to radial and (c) the cooperative buckling of neighbouring layers perpendicular to the radius. These mesoscale mechanisms acted to block the development of periodic patterns of multiple, uniformly distributed, shear bands that have been observed in all previously examined solid homogeneous materials and granular materials. The high-strain plastic flow within the shear bands resulted in the dramatic elongation and fragmentation of Ni and Al layers. The quenched reaction between Al and Ni was observed inside these trans-layer shear bands and in a number of the interfacial extruded wedge-shaped regions. The reaction initiated in these spots did not ignite the bulk of the material, demonstrating that these mesostructured Ni-Al laminates are able to withstand high-strain, high-strain rate deformation without reaction. Numerical simulations of the explosively collapsed samples were performed using the digitized geometry of corrugated laminates and predictions of the final, deformed mesostructures agree with the observed deformation patterns.     

多孔脆性介质冲击波压缩破坏的细观机理和图像

本文采用一种具有良好定量性质的离散元模型研究了带孔洞的各向同性脆性介质在细观尺度上的压缩破坏特征. 通过对孤立孔洞、三种简单的孔洞排布方式和大量孔洞随机排布等几种情况的模拟, 认识到了剪切破坏和局域拉伸破坏是冲击波压缩下多孔介质的基本破坏模式; 孔洞之间的损伤贯通会促进孔洞在较低应力下发生塌缩, 但损伤区的应力松弛过程却会对一定范围内的介质起到损伤屏蔽作用; 不同区域中损伤促进和损伤屏蔽的综合效果是在多孔脆性介质中形成一种高损伤区与低损伤区间错排布的奇特损伤分布. 本文的研究结果为深入理解脆性材料冲击波压缩破坏的演化过程和机理提供了细观尺度上的初步物理图像.     

Temporal oscillations of the shear stress and scattered light in a shear-banding-shear-thickening micellar solution

The results of optical and rheological experiments performed on a viscoelastic solution (cetyltrimethylammonium bromide + sodium salicylate in water) are reported. The flow curve has a horizontal plateau extending between two critical shear rates characteristic of heterogeneous flows formed by two layers of fluid with different viscosities. These two bands which also have different optical anisotropy are clearly seen by direct observation in polarized light. At the end of the plateau, apparent shear thickening is observed in a narrow range of shear rates; in phase oscillations of the shear stress and of the first normal stress difference are recorded in a shearing device operating under controlled strain. The direct observation of the annular gap of a Couette cell in a direction perpendicular to a plane containing the vorticity shows that the turbidity of the whole sample also undergoes time dependent variations with the same period as the shear stress. However no banding is observed during the oscillations and the flow remains homogeneous.     

Long-time behavior of sand ripples induced by water shear flow

The formation of sand ripples under water shear flow in a narrow annular channel and the approach of the ripple pattern towards a steady state were studied experimentally. Four results are obtained: i) The mean amplitude, the average drift velocity and the mean sediment transport rate of the evolving bed shape are strongly related. A quantitative characterization of this relation is given. ii) The ripple pattern reaches a stationary state with a finite ripple amplitude and wavelength. The time needed to reach the state depends on the shear stress and may be several days. iii) The onset of ripple formation is determined by the bed shear stress, but it seems neither to depend on the grain diameter nor on the depth of the water layer. iv) The ripple amplitude, drift velocity and sediment transport in this stationary state depend on the grain size. This dependency is neither captured by the particle Reynolds number nor by the Shields parameter: an empirical scaling law is presented instead.     

Deformation band evolution in [110] Al single crystals strained in tension

Several types of deformation bands form during uniaxial extension of Al single crystals for which the tensile axis is initially parallel to [110]. The objectives of the present work are to analyse crystal orientation evolution in the deformation bands and adjoining regions, and to integrate the experimental observations with a crystal mechanics model. The most prominent deformation bands contain secondary slip traces and exhibit crystal rotations consistent with unpredicted slip on a secondary slip system. These special bands of secondary slip (SBSS) become more closely aligned with the tensile axis as extension increases. The evolution of SBSS inclination with extension indicates that SBSS form initially as kink bands and that SBSS boundaries are immobile. SBSS grow during straining by expansion of the volume of material in which secondary slip operates. Deformed matrix (DM) bands are zones between SBSS; primary slip predominates in DM bands. Small intra-DM bands result from spatial variation of the shear amplitudes for the two primary slip systems. The evolution of intra-DM band inclination with extension indicates that intra-DM bands form initially as kink bands and that the band boundaries are mobile, at least to some extent.     

Transient and oscillatory granular shear flow

The forces and particle motion during transient and oscillatory shear of granular material are investigated experimentally. In a shear cell of Taylor-Couette-type we find that how a granular shear flow starts depends strongly on the prior shear direction. If the shear direction is reversed, the material goes through a transient period during which the material compacts, the shear force is small, and the shear band is wide. Three-dimensional confocal imaging of particle rearrangements during shear reversal shows that bulk and surface flows are comparable. Repeated reversals, or oscillations of the shear direction, lead to additional compaction, which can be described by a stretched exponential, similar to compaction induced by tapping.     

Microstructuration stages during gelation of gelatin under shear

We study gelation under shear of aqueous gelatin by measuring the evolution of the apparent viscosity, thus extending the previous study by de Carvalho and Djabourov (W. de Carvalho, M. Djabourov, Rheol. Acta 36, 591 (1997)). From a set of experiments under constant stress, we deduce that the microstructure evolves through the following succession of regimes: i) nucleation and growth until crowding of a microgel suspension; ii) coalescence into strata parallel to the flow; iii) gradual thickening of these strata via transverse cross-linking until the flow finally localizes into two interfacial sliding bands which close sequentially. The transition between these regimes occurs at characteristic viscosity values. This scenario is fully confirmed by experiments performed at constant shear rates. We expect it to be relevant for all materials forming thermoreversible gels.     

Plastic Strain Localization and Its Stages in Al-Mg Alloys

The paper describes an experimental technique based on the use of a Vic-3D contactless digital optical system and digital image correlation for research in the mechanical behavior of a solid and its plastic deformation with space-time inhomogeneities. Using this technique, we analyze the evolution of inhomogeneous strain and local strain rate fields in AMg2m alloy at constant uniaxial tension rates. The analysis reveals quasi-periodic strain field homogenization in jerky flow: alternating phases of active local plastic flow (shear banding) and macroscale strain levelling. Also analyzed are the parameters of localized microscale plastic flow such as the height and width of shear bands, their velocity, and coefficient of plastic strain inhomogeneity. From a series of mechanical tests, the influence of the specimen geometry and loading rate on these parameters is estimated.     

Simultaneous birefringence,small‐ and wide‐angle X‐ray scattering to detect precursors and characterize morphology development during flow‐induced crystallization of polymers

An experimental configuration that combines the powerful capabilities of a short‐term shearing apparatus with simultaneous optical and X‐ray scattering techniques is demonstrated, connecting the earliest events that occur during shear‐induced crystallization of a polymer melt with the subsequent kinetics and morphology development. Oriented precursors are at the heart of the great effects that flow can produce on polymer crystallization (strongly enhanced kinetics and formation of highly oriented crystallites), and their creation is highly dependent on material properties and the level of stress applied. The sensitivity of rheo‐optics enables the detection of these dilute shear‐induced precursors as they form during flow, before X‐ray techniques are able to reveal them. Then, as crystallization occurs from these precursors, X‐ray scattering allows detailed quantification of the characteristics and kinetics of growth of the crystallites nucleated by the flow‐induced precursors. This simultaneous combination of techniques allows unambiguous correlation between the early events that occur during shear and the evolution of crystallization after flow has stopped, eliminating uncertainties that result from the extreme sensitivity of flow‐induced crystallization to small changes in the imposed stress and the material. Experimental data on a bimodal blend of isotactic polypropylenes are presented.