Three-dimensional imaging of colloidal glasses under steady shear

Using fast confocal microscopy we image the three-dimensional dynamics of particles in a yielded hard-sphere colloidal glass under steady shear. The structural relaxation, observed in regions with uniform shear, is nearly isotropic but is distinctly different from that of quiescent metastable colloidal fluids. The inverse relaxation time tau(alpha)(-1) and diffusion constant D, as functions of the local shear rate gamma*, show marked shear thinning with tau(alpha)(-1) proportional to D proportional to gamma*(0.8) over more than two decades in gamma*. In contrast, the global rheology of the system displays Herschel-Bulkley behavior. We discuss the possible role of large scale shear localization and other mechanisms in generating this difference.     

Generation of magnetic field by combined action of turbulence and shear

The feasibility of a mean-field dynamo in nonhelical turbulence with a superimposed linear shear is studied numerically in elongated shearing boxes. Exponential growth of the magnetic field at scales much larger than the outer scale of the turbulence is found. The characteristic scale of the field is lB proportional S(-1/2) and the growth rate is gamma proportional S, where S is the shearing rate. This newly discovered shear dynamo effect potentially represents a very generic mechanism for generating large-scale magnetic fields in a broad class of astrophysical systems with spatially coherent mean flows.     

A universal criterion for plastic yielding of metallic glasses with a (T/Tg) 2/3 temperature dependence

Room temperature (TR) elastic constants and compressive yield strengths of approximately 30 metallic glasses reveal an average shear limit gammaC=0.0267+/-0.0020, where tauY=gamma CG is the maximum resolved shear stress at yielding, and G the shear modulus. The gammaC values for individual glasses are correlated with t=TR/Tg , and gamma C for a single glass follows the same correlation (vs t=T/Tg). A cooperative shear model, inspired by Frenkel's analysis of the shear strength of solids, is proposed. Using a scaling analysis leads to a universal law tauCT/G=gammaC0-gammaC1(t)2/3 for the flow stress at finite T where gammaC0=(0.036+/-0.002) and gammaC1=(0.016+/-0.002).     

Fluctuations in granular media

Dense slowly evolving or static granular materials exhibit strong force fluctuations even though the spatial disorder of the grains is relatively weak. Typically, forces are carried preferentially along a network of "force chains." These consist of linearly aligned grains with larger-than-average force. A growing body of work has explored the nature of these fluctuations. We first briefly review recent work concerning stress fluctuations. We then focus on a series of experiments in both two- and three-dimension [(2D) and (3D)] to characterize force fluctuations in slowly sheared systems. Both sets of experiments show strong temporal fluctuations in the local stress/force; the length scales of these fluctuations extend up to 10(2) grains. In 2D, we use photoelastic disks that permit visualization of the internal force structure. From this we can make comparisons to recent models and calculations that predict the distributions of forces. Typically, these models indicate that the distributions should fall off exponentially at large force. We find in the experiments that the force distributions change systematically as we change the mean packing fraction, gamma. For gamma's typical of dense packings of nondeformable grains, we see distributions that are consistent with an exponential decrease at large forces. For both lower and higher gamma, the observed force distributions appear to differ from this prediction, with a more Gaussian distribution at larger gamma and perhaps a power law at lower gamma. For high gamma, the distributions differ from this prediction because the grains begin to deform, allowing more grains to carry the applied force, and causing the distributions to have a local maximum at nonzero force. It is less clear why the distributions differ from the models at lower gamma. An exploration in gamma has led to the discovery of an interesting continuous or "critical" transition (the strengthening/softening transition) in which the mean stress is the order parameter, and the mean packing fraction, gamma, must be adjusted to a value gamma(c) to reach the "critical point." We also follow the motion of individual disks and obtain detailed statistical information on the kinematics, including velocities and particle rotations or spin. Distributions for the azimuthal velocity, V(theta), and spin, S, of the particles are nearly rate invariant, which is consistent with conventional wisdom. Near gamma(c), the grain motion becomes intermittent causing the mean velocity of grains to slow down. Also, the length of stress chains grows as gamma-->gamma(c). The 3D experiments show statistical rate invariance for the stress in the sense that when the power spectra and spectral frequencies of the stress time series are appropriately scaled by the shear rate, Omega, all spectra collapse onto a single curve for given particle and sample sizes. The frequency dependence of the spectra can be characterized by two different power laws, P proportional, variant omega(-alpha), in the high and low frequency regimes: alpha approximately 2 at high omega; alpha<2 at low omega. The force distributions computed from the 3D stress time series are at least qualitatively consistent with exponential fall-off at large stresses. (c) 1999 American Institute of Physics.     

Calculation of the Viscosity of Polymer Melts Based on Measurements of the Recovered Rubber-Like Deformation

On the basis of a model of polymer flow, considering the forces of entropic elasticity of extended macromolecules within the Eyring's concept, the relationships between the shear rate, shear stress, viscosity, and recovered rubber-like deformation were derived. The reduction of activation energy of the flow, by an amount proportional to the recovered rubber-like deformation, leads to an exponential decrease of viscosity with increasing shear rates; this nonlinear dependence of viscosity on shear rate (and shear stress) is defined as the viscosity anomaly of polymers. The measurement of deformation recovery after the cessation of polymer flow in the mode of constant shear rate or shear stress on a rotational viscometer confirmed the validity of the theoretical dependences.     

Non-linear rheology of lamellar liquid crystals

We measure the non-linear relation between the shear stress and shear rate in the lyotropic lamellar phase of C₁₂E₅ /water system. The measured shear thinning exponent changes with the surfactant concentration. A simple rheology theory of a lamellar or smectic phase is proposed with a prediction ∼ σ^3/2 , where is the shear rate and σ is the shear stress. We consider that the shear flow passed through the defect structure causes the main dissipation. As the defect line density varies with the shear rate, the shear thinning arises. The defect density is estimated by the dynamic balance between the production and annihilation processes. The defect production is caused by the shear-induced layer undulation instability. The annihilation occurs through the shear-induced defect collision process. Further flow visualization experiment shows that the defect texture correlates strongly with the shear thinning exponent.     

Linear and nonlinear rheology of wormlike micelles

Several surfactant molecules self-assemble in solution to form long, cylindrical, flexible wormlike micelles. These micelles can be entangled with each other leading to viscoelastic phases. The rheological properties of such phases are very interesting and have been the subject of a large number of experimental and theoretical studies in recent years. We shall report our recent work on the macrorheology, microrheology and nonlinear flow behaviour of dilute aqueous solutions of a surfactant CTAT (Cetyltrimethylammonium Tosilate). This system forms elongated micelles and exhibits strong viscoelasticity at low concentrations (∼0.9 wt%) without the addition of electrolytes. Microrheology measurements of G(θ) have been done using diffusing wave spectroscopy which will be compared with the conventional frequency sweep measurements done using a cone and plate rheometer. The second part of the paper deals with the nonlinear rheology where the measured shear stress σ is a nonmonotonic function of the shear rate . In stress-controlled experiments, the shear stress shows a plateau for larger than some critical strain rate, similar to the earlier reports on CPyCl/NaSal system. Cates et al have proposed that the plateau is a signature of mechanical instability in the form of shear bands. We have carried out extensive experiments under controlled strain rate conditions, to study the time-dependence of shear stress. The measured time series of shear stress has been analysed in terms of correlation integral and Lyapunov exponent to show unambiguously that the behaviour is typical of low dimensional dynamical systems.     

Plasticity and dynamical heterogeneity in driven glassy materials

Many amorphous glassy materials exhibit complex spatio-temporal mechanical response and rheology, characterized by an intermittent stress strain response and a fluctuating velocity profile. Under quasistatic and athermal deformation protocols this heterogeneous plastic flow was shown to be composed of plastic events of various sizes, ranging from local quadrupolar plastic rearrangements to system spanning shear bands. In this paper, through numerical study of a 2D Lennard-Jones amorphous solid, we generalize the study of the heterogeneous dynamics of glassy materials to the finite shear rate ( [(g)\dot] \dot{{\gamma}} 1 \neq 0 and temperature case (T 1 \neq 0 . In practice, we choose an effectively athermal limit (T ∼ 0 and focus on the influence of shear rate on the rheology of the glass. In line with previous works we find that the model Lennard-Jones glass follows the rheological behavior of a yield stress fluid with a Herschel-Bulkley response of the form, s \sigma = s_Y \sigma_{{Y}}^{} + c ₁ [(g)\dot]^b \dot{{\gamma}}^{{\beta}}_{} . The global mechanical response obtained through the use of Molecular Dynamics is shown to converge in the limit [(g)\dot] \dot{{\gamma}} ? \rightarrow 0 to the quasistatic limit obtained with an energy minimization protocol. The detailed analysis of the plastic deformation at different shear rates shows that the glass follows different flow regimes. At sufficiently low shear rates the mechanical response reaches a shear-rate-independent regime that exhibits all the characteristics of the quasistatic response (finite-size effects, cascades of plastic rearrangements, yield stress, ...). At intermediate shear rates the rheological properties are determined by the externally applied shear rate and the response deviates from the quasistatic limit. Finally at higher shear the system reaches a shear-rate-independent homogeneous regime. The existence of these three regimes is also confirmed by the detailed analysis of the atomic motion. The computation of the four-point correlation function shows that the transition from the shear-rate-dominated to the quasistatic regime is accompanied by the growth of a dynamical cooperativity length scale x \xi that is shown to diverge with shear rate as x \xi μ \propto [(g)\dot]^-n \dot{{\gamma}}^{{-\nu}}_{} , with n \nu ∼ 0.2 -0.3. This scaling is compared with the prediction of a simple model that assumes the diffusive propagation of plastic events.     

Shear flow in the two-body Boltzmann gas. II. Small and large γ expansion of the shear viscosity

In two and three dimensions, the relaxation time Boltzmann equation can be solved analytically for the distribution function for a system of two hard particles subject to isothermal shear. The previous solutions of Morriss, and Ladd and Hoover are shown to be formally equivalent. The integral representation for the average of each of the elements of the pressure tensor in the steady state is obtained for both sllod and dolls tensor equations of motion. Rigorous equations are derived which relate the viscosity and the normal stress differences in these two methods. We obtain asymptotic expansions for each element of the pressure tensor for both small and large. For high shear rates, the viscosity is found to vanish as ^–2 log in both two and three dimensions.     

Cooperative nucleation of shear dislocation loops

The mean elastic interaction between randomly distributed transient subcritical shear loops of the same sign, formed in the presence of an applied shear stress, is the "image stress." This stress is proportional to the volume density of loops and has the same sign as the applied stress. The image stress promotes the cooperative nucleation of shear loops, and leads to an instability in which the number of loops and the image stress increase rapidly, leading to the generation of stable expanding loops. The critical stress at which the instability is predicted is relatively high.     

Activated dynamics and effective temperature in a steady state sheared glass

We conduct nonequilibrium molecular dynamics simulations to measure the shear stress sigma, the average inherent structure energy E{IS}, and the effective temperature T{eff} of a sheared model glass as a function of bath temperature T and shear strain rate gamma. For T above the glass transition temperature T0, the rheology approaches a Newtonian limit and T{eff}-->T as gamma-->0, while for T相似文献   

Subcritical crack growth: the microscopic origin of Paris' law

We investigate the origin of Paris' law, which states that the velocity of a crack at subcritical load grows like a power law, da/dt ~ (DeltaK)(m), where DeltaK is the stress-intensity-factor amplitude. Starting from a damage-accumulation function proportional to (Deltasigma)(gamma), Deltasigma being the stress amplitude, we show analytically that the asymptotic exponent m can be expressed as a piecewise-linear function of the exponent gamma, namely, m=6-2gamma for gamma or =gamma(c), reflecting the existence of a critical value gamma(c)=2. We perform numerical simulations to confirm this result for finite sizes. Finally, we introduce bounded disorder in the breaking thresholds and find that below gamma(c) disorder is relevant, i.e., the exponent m is changed, while above gamma(c) disorder is irrelevant.     

Rheology of steady-state draining foams

We developed the foam drainage rheology technique in order to perform rheological measurements of aqueous foams at a set liquid fraction epsilon and fixed bubble radius R without the usual difficulties associated with fluid drainage and bubble coarsening. The shear stress exhibits a power-law dependence on strain-rate, tau approximately gamma[over]n where n approximately 0.2. The stress exhibits an inverse dependence on liquid content, tau approximately (1+h'epsilon)(-1), where h'=theta(10) exhibits a diminishing logarithmic trend with gamma[over]. We propose a model based upon film shearing as the dominant source of viscous dissipation.     

The synergetic theory of the glass transition in liquids

The glass transition is treated as a spontaneous emergence of the shear components of strain and stress elastic fields upon cooling a liquid at a rate exceeding the critical value. The stationary elastic strains and stresses and the effective relaxation time are determined within the adiabatic approximation. It is shown that the glass transition process occurs through the mechanism of a first-order kinetic transition with allowance made for the strain dependence of the shear modulus. The critical cooling rate turns out to be proportional to the thermal diffusivity and unrelaxed shear modulus and inversely proportional to the temperature derivative of the relaxed shear modulus and the square of the heat conductivity length of the sample.     

Tank treading and unbinding of deformable vesicles in shear flow: determination of the lift force

Deformation and tank-treading motion of flaccid vesicles in a linear shear flow close to a wall are quantitatively studied by light microscopy. Velocities of bounded vesicles obey Goldman's law established for rigid spheres. A progressive tilt and a transition of unbinding of vesicles are evidenced upon increasing the shear rate, gamma;. These observations disclose the existence of a viscous lift force, F(l), depending on the viscosity eta of the fluid, the radius R of the vesicle, its distance h from the substrate, and a monotonous decreasing function f(1-v) of the reduced volume v, in the following manner: F(l) = eta(gamma)(R(3)/h)f(1-v). This relation is valid for vesicles both close to and farther from the substrate.     

Molecular dynamics investigations of the strengthening of Al-Cu alloys during thermal ageing

Classical molecular dynamics simulations of the interaction of edge dislocations with solid soluted copper atoms and Guinier-Preston zones (I and II) in aluminium are performed using embedded atom method potentials. Hereby, the strengthening mechanism and its modulus are identified for different stages of thermally aged Al-Cu alloys. Critical resolved shear stresses are calculated for different concentrations of solid soluted copper. In case of precipitate strengthening, the Guinier-Preston zone size, its orientation and offset from the dislocation plane are taken as simulation parameters. It is found that in case of solid soluted copper, the critical resolved shear stress is proportional to the copper concentration. In case of the two subsequent aging stages both the dislocation depinning mechanism as well as the depinning stress are highly dependent on the Guinier-Preston zone orientation and to a lesser degree to its size.     

Shear-flow-induced unfolding of polymeric globules

The behavior of a single collapsed polymer under shear flow is examined using hydrodynamic simulations and scaling arguments. Below a threshold shear rate gamma[.]{*}, the chain remains collapsed and only deforms slightly, while above gamma[.]{*} the globule exhibits unfolding/refolding cycles. Hydrodynamics are crucial: In the free draining case, gamma[.]{*} scales with the globule radius R as gamma[.]{*} approximately R{-1}, while in the presence of hydrodynamic interactions gamma[.]{*} approximately R. Experiments on the globular von Willebrand protein confirm the presence of an unfolding transition at a well-defined critical shear rate.     

Trapped electron mode turbulence driven intrinsic rotation in Tokamak plasmas

Progress from global gyrokinetic simulations in understanding the origin of intrinsic rotation in toroidal plasmas is reported. The turbulence-driven intrinsic torque associated with nonlinear residual stress generation due to zonal flow shear induced asymmetry in the parallel wave number spectrum is shown to scale close to linearly with plasma gradients and the inverse of the plasma current, qualitatively reproducing experimental empirical scalings of intrinsic rotation. The origin of current scaling is found to be enhanced k(∥) symmetry breaking induced by the increased radial variation of the safety factor as the current decreases. The intrinsic torque is proportional to the pressure gradient because both turbulence intensity and zonal flow shear, which are two key ingredients for driving residual stress, increase with turbulence drive, which is R/L(T(e)) and R/L(n(e)) for the trapped electron mode.     

Bolt axial stress measurement based on a mode-converted ultrasound method using an electromagnetic acoustic transducer

A method is proposed to measure the stress on a tightened bolt using an electromagnetic acoustic transducer (EMAT). A shear wave is generated by the EMAT, and a longitudinal wave is obtained from the reflection of the shear wave due to the mode conversion. The ray paths of the longitudinal and the shear wave are analyzed, and the relationship between the bolt axial stress and the ratio of time of flight between two mode waves is then formulated. Based on the above outcomes, an EMAT is developed to measure the bolt axial stress without loosening the bolt, which is required in the conventional EMAT test method. The experimental results from the measurement of the bolt tension show that the shear and the mode-converted longitudinal waves can be received successfully, and the ratio of the times of flight of the shear and the mode-converted longitudinal waves is linearly proportional to the bolt axial tension. The non-contact characteristic of EMAT eliminates the effect of the couplant and also makes the measurement more convenient than the measurement performed using the piezoelectric transducer. This method provides a promising way to measure the stress on tightened bolts.     

Frictional shear cracks

We discuss crack propagation along the interface between two dissimilar materials. The crack edge separates two states of the interface, “stick” and “slip.” In the slip region, we assume that the shear stress is proportional to the sliding velocity; i.e., the linear viscous friction law is valid. In this picture, the static friction appears as the tile Griffith threshold for crack propagation. We calculate the crack velocity as a function of the applied shear stress and find that the main dissipation comes from the macroscopic region and is mainly due to the friction at the interface. The relevance of our results to recent experiments, Baumberger et al., Phys. Rev. Lett. 88, 075509 (2002), is discussed.