Plastic behavior of some yield stress fluids: from creep to long-time yield

The yielding of several reversible yield stress fluids is studied during scissometric-like creep experiments. The temporal evolution of the apparent deformation is recorded for applied stresses close and below the usual yield stress. Similarly to solids, three main creep regimes are observed. First, a primary creep regime displaying a temporal power law evolution of the deformation rate occurs, followed by a temporal minimum, which leads to an apparent flow of the material. This local minimum, defined as the “transition time,” and the subsequent fluidization can be observed at long times. The evolution of this time as a function of the applied stress appears to follow a universal law reminiscent of fracture behavior in hard solids.     

An investigation of squeeze flow as a viable technique for determining the yield stress

A systematic study of squeeze flow (SF) was performed on different concentrations of Carbopol with varying yield stresses. A sample of constant volume was placed between two parallel plates and a series of constant force steps applied, following the plate separation as a function of time. Precise rheological measurements of the model yield stress fluids were performed in addition to the well-controlled SF tests. These rheological measurements were used in conjunction with the SF equations to determine the time-dependent plate separation, allowing a direct comparison of theory and experiment throughout the entire test. The limiting height achieved during constant force SF reveals information about the yield stress of the fluid as predicted by the theory. It appears that by carefully controlling the experimental conditions of the squeeze test one can obtain yield stress values that agree with the rheological measurements within 10%. Additionally, the validity of the lubricational theory was tested; not only for the determination of the yield stress but throughout the flow as well.     

An analytical and experimental stress analysis of a practical mode II fracture test specimen

A boundary-collocation method has been employed to determine the Mode II stress-intensity factors for a pair of through-the-thickness edge cracks in a finite isotropic plate. An elastostatic analysis has been carried out in terms of the complete Williams stress function employing both even and old components. The results of the numerical analysis were verified by a two-step procedure whereby the symmetric (Mode I) and antisymmetric (Mode II) portions of the solution were independently compared with existing solutions. Since no previous analytical solutions existed for the asymmetric loading of an edge-cracked plate, the complete solution was verified by comparison with a photoelastic analysis. A compact shear (CS) specimen of Hysol epoxy resin was loaded in a photoelastic experiment designed to study the isochromatic-fringe patterns resulting from the Mode II crack-tip stress distribution. The experiment verified that a pure mode II stress distribution existed in the neighborhood of the crack tips, and confirmed the accuracy of the boundary-collocation solution for the Mode II stress-intensity factors. Specimen center-line stress-distribution data were obtained photoelastically and employed to refine the boundary-collocation analysis. Agreement between the analytically and experimentally determined Mode II stress-intensity factors was excellent.     

THE PRECISE AND NEW ANALYSIS FOR A MODE Ⅲ GROWING CRACK IN AN ELASTIC-PERFECTLY PLASTIC SOLID

The near crack line field analysis method has been used to investigate into ModeⅢ quasistatically propagating crack in an elastic-perfectly plastic material.Thesignificance of this paper is that the usual small scale yielding theory has been brokenthrough.By obtaining the general solutions of the stresses and the displacement rate ofthe near crack line plastic region,and by matching the general solutions with theprecise elastic fields(not the usual elastic K-dominant fields)at the elastic-plasticboundary,the precise and new solutions of the stress and deformation fields,the sizeof the plastic region and the unit normal vector of the elastic-plastic boundary havebeen obtained near the crack line.The solutions of this paper are sufficiently precisenear the crack line region because the roughly qualitative assumptions of the smallscale yielding theory have not been used and no other roughly qualitative assumptionshave been taken,either.The analysis of this paper shows that the assumingly“steady-state cas     

Quasi-static bubble in a yield stress fluid: elasto-plastic model

The influence of the yield stress of Carbopol® gel dispersions on the behaviour of quasi-static bubbles was investigated. Many fluids, from many different industrial fields, have yield stress behaviour. Most of them contain gas bubbles. To study bubble behaviour in such suspensions, a transparent model fluid (dispersion of Carbopol® in water) was used. The experimental device allowed to quasi-statically increase bubble internal pressure with small pressure step to reach a maximum target internal pressure and the pressure setpoint was inverted to return to the initial pressure. Hysterical behaviour of the bubbles was highlighted as they did not regain their initial shape because of yield stress. We show that the rheological behaviour is related to the internal pressure, bubble geometry and yield stress in quasi-static conditions. A modification of the Laplace law depending on the yield stress of the fluid and bubble sphericity was proposed and validated.     

Some stress intensity factors for self-similar cracks,derived from path-independent integrals

Summary A new method of computing stress intensity factors for self-similar cracks in the plane is discussed. It is based on some known path-independent integrals whose forms make them suited for use in elastic fields showing expansional invariance. General integral formulas for the various segments of a chosen integration contour are presented and also applied. The integrals generally express the total energy release rate at self-similar growth, but for the expansion loaded star crack and the symmetrically cracked wedge opened by concentrated forces the stress intensity factors are obtained in closed form.

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Zusammenfassung Ein neues Verfahren der Berechnung von Spannungsintensitätsfaktoren zugehörig selbstähnlichen Riss-systemen in der Ebene wird diskutiert. Es beruht auf einigen bekannten wegunabhängigen Integralen, deren Formen sie in expansionsinvariablen elastischen Feldern anwendbar machen. Die allgemeinen Integralformeln der verschiedenen Abschnitte eines speziell gewählten Integrationsweges werden sowohl vorgezeigt als angewandt. Gewöhnlicherweise drücken die Integrale die totale Energiefreisetzung eines Rissystems bei selbstähnlichem Zuwachs aus. Für den expansionsbelasteten Sternriss und für den symmetrisch gespaltenen Keil, der von Punktkräften geöffnet wird, werden aber die Spannungsintensitätsfaktoren in abgeschlossener Form erhalten.

     

Mesoscopic natural element analysis of elastic moduli, yield stress and fracture of solids containing a number of voids

A two-dimensional mesoscale simulation method based on the natural element method, which is a kind of meshless method, is developed and applied to the analysis of overall elastic moduli, macro yield stress and void-linking fracture. The calculated results are compared with the theoretical solutions for overall elastic moduli, the experimental macro yield stress for aluminum and brass as well as the improved Gurson’s yield function, and the experimental void linking fracture to show the validity of the proposed method.     

A new interpretation of viscosity and yield stress in dense slurries: Coal and other irregular particles

Illinois coal was ground and wet-sieved to prepare three powder stocks whose particle-size distributions were characterized. Three suspending fluids were used (glycerin, bromonaphthalene, Aroclor), with viscosities _s that differed by a factor of 100 and with very different chemistries, but whose densities matched that of the coal. Suspensions were prepared under vacuum, with coal volume fractions that ranged up to 0.46. Viscosities were measured in a cone-and-plate over a shear rate range 10^–3–10² s^–1. Reduced viscosity _r = /_s is correlated in the high-shear limit ( ) with/ _M, where _M is the maximum packing fraction for the high-shear microstructure, to reveal the roles of size distribution and suspending fluid character. A new model that invokes the stress-dependence of _M is found to correlate _r well under non-Newtonian conditions with simultaneous prediction of yield stress at sufficiently high; a critical result is that stress and not governs the microstructure and rheology. Numerous experimental anomalies provide insight into suspension behavior.     

Half-fringe photoelasticity: A new approach to whole-field stress analysis

This paper presents a new method for whole-field stress analysis based on a symbiosis of two techniques—classical photoelasticity and modern digital image analysis. The resulting method is called ‘half-fringe photoelasticity (HFP)’. Classical photoelasticity demands materials with high birefringence, which leads to extensive use of plastics as model materials. Since the behavior of these materials is often different from that of the prototype materials, their use distorts the similitude relationships. In many contemporary problems this distortion is untenable. HFP offers a way out of this dilemma. It permits materials and loads to be chosen so that no more than one half of a fringe order appears in the area of interest. Thus, for example, glass, which behaves linearly up to high stress levels and over a wide range of temperatures, could be used as model material. Alternatively, models from polymeric materials could be used under very low load in order to stay within the linear part of the stress-strain diagram and to prevent large deformations. The half-fringe-photoelasticity system, which is described here, utilizes the resulting low levels of birefringence for effective stress analysis. This paper describes the system. It outlines a calibration routine and illustrates its application to two simple problems using glass models.     

A new method for stress analysis of a cyclically symmetric structure

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Physical characterisation and yield stress of a concentrated Miscanthus suspension

We present yield stress measurements of a concentrated suspension of Miscanthus x giganteus, a biomass substrate for the production of biofuels and chemicals. The particle porosity and the apparent solid packing fraction are quantified, and a simple relationship between volume and mass fractions proposed. The relationship between yield stress and solid concentration was measured with the maximum torque method of Dzuy and Boger (J Rheol 27: 321–349, 1983) for concentrations between 11 and 15 %, just below maximum packing. In the range of concentrations considered, the measured dependence of the yield stress on concentration appears to be significantly stronger than that reported for corn stover, a plant for which reliable data is available: the apparent power law exponent is found to be larger than 10, while the corresponding exponent reported for corn is in the range 4–6. We argue that differences in particle rigidity between corn and Miscanthus may play a role in explaining this result.     

Field-induced gelation, yield stress, and fragility of an electro-rheological suspension

 Electro-rheological suspensions (ERS) are known to undergo liquid-to-solid transition under the application of an electric field. Long-range interaction between neighboring particles results in sample-spanning particulate structures which behave as soft solids. Here, we studied the rheological expression of this field-induced transition which has many similarities with chemical gelation. This similarity shows in mechanical spectroscopy on a suspension of monodisperse silica in PDMS as model ERS. Upon application of the electric field, dynamic moduli G′, G′′ grow by orders of magnitude and evolve in a pattern which is otherwise typical for gelation of network polymers (random chemical or physical gelation). At the gel point, the slow dynamics is governed by power-law relaxation behavior (frequency-independent tan δ). A low field strength is sufficient to reach the gel point and, correspondingly, the percolating particle structure at the gel point is still very fragile. It can be broken by the imposition of low stress. For inducing a finite yield stress, the field strength needs to be increased further until the long-range electrostatic interaction generates string-like particle alignments which become clearly visible under the optical microscope. The onset of fragile connectivity was defined experimentally by the tan δ method. The ERS was probed dynamically at low frequencies where the transition is most pronounced, and also in steady shear where the rate of structure formation equals the rate of internal breaking. Received: 1 May 2001 Accepted: 11 August 2001     

Heat transfer and flow of a thermodependent and yield stress fluid

In this paper, we study the flow of a fluid possessing a yield stress, in a cylindrical pipe being the wall heated with a constant flux; experimental and numerical results being presented here. We are interested in the influence of the different parameters on the Nusselt number, and in the pressure variation. We propose a model which enables us to estimate the Nusselt number and pressure variation, which takes into account the variation of the physical properties due to temperature variations. The proposed correlations agree well with experimental measurement.

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Wärmeübertragungs- und Strömungsverhalten eines Fluids mit temperatur- und scherspannungsabhängigem Fließvermögen

Zusammenfassung In dieser Arbeit wird das Strömungsverhalten eines Fluids mit temperatur- und scherspannungsabhängigem Fließvermögen in einem mit konstanter Wärmestromdichte beaufschlagten Kreisrohr untersucht. Hierbei fallen experimentell und numerisch gefundene Ergebnisse an. Besonders interessiert der Einfluß verschiedener Parameter auf die Nusselt-Zahl und den Druckverlust. Es wird ein Modell zur Berücksichtigung der Auswirkung temperaturabhängiger Stoffwerte auf beide Intensitätsparameter vorgeschlagen. Die hieraus resultierenden Korrelationen stimmen gut mit den experimentellen Befunden überein.

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Nomenclature a, b K =a e ^–bT - C f friction factor - C f* reduced friction factor - C _p specific heat capacity (J/Kg/°C) - D internal diameter (m) - h heat transfer coefficient (W/m² °C) - H free energy - Hb Herschel-Bulkley number - K fluid consistency (Pa · sⁿ) - L axial length (m) - mass flow (Kg · m^–3) - n flow behaviour index - Nu Nusselt number - p pressure (Pa) - Pe Peclet numberRe ·Pr=Re _g ·Pr _g - Pr Prandtl numberPr _g =kC _p / - Pr _g generalised Prandtl numberPr _g =kC _p /(U ₀/D ^n–1 - r radial coordinate (m) - R pipe radius (m) - R _c plug radius - Re Reynolds number - Re Metzner Reynolds number (Ostwald fluid) - Re _g generalised Reynolds number - Re _s Metzner Reynolds number (Herschel-Bulkley fluid) - t time (s) - T temperature (°C) - T _e entrance temperature (°C) - T _m mean temperature (°C) - T _p wall temperature (°C) - U ₀ mean velocity (m/s) - u axial velocity (m/s) - v radial velocity (m/s) - X ⁺ Cameron number - y, r radial coordinate (m) - z axial coordinate (m) Greek symbols R _c /R - exponent used forNu - shear rate (s^–1) - (3n + 1)/4n - * /((1 –a)) - thermal conductivity (W/m °C) - _a apparent viscosity (Pa · s) - density (kg/m³) - shear stress (Pa) - ₀ wall shear stress (Pa) - =b _p D/2 - _p heat flux (W/m²) - =1+2n/2n+1+2n ²/(2n+1)(n+1) ² - p*/z p*/z=p/z/p/z (isothermal) Indices p wall - i axial index - j radial index     

Shear properties and a stress analysis obtained from vinyl-ester losipescu specimens

The use of losipescu specimens for the determination of the shear properties of a vinyl-ester resin was investigated. The antisymmetric four-point bend and the Adams and Walrath fixtures were studied for their suitability in loading these specimens. Photoelastic and strain-gage data in addition to published finite-element results show that the latter fixture distorts the stress field in the gage section. The antisymmetric four-point bend fixture is found to give the purest shear-stress field in the gage section and to yield the most reliable shear-modulus values. A refined photoelastic analysis shows that the shear-stress distribution between the notch roots is essentially uniform with a relative maximum or minimum at the centroid depending on the depths of the notches. Also, stress risers of up to 30 percent are observed near the notch roots. Except at the roots, finite-element predictions are presented which are in excellent agreement with photoelastic data. The failure mode of this vinyl-ester resin is tensile and the corresponding tensile stress calculated from the average shear stress in the gage section of the losipescu specimen is in excellent agreement with failure data acquired in tension.     

Inertial,viscous and yield stress effects in Bingham fluid filling of a 2-D cavity

The present study concentrates on Bingham fluid filling of a 2-D cavity and examines the relative importance of inertial, viscous and yield stress effects on the filling profile. The results presented are obtained using PAM-CAST/SIMULOR, which was modified by introducing a regularized Bingham fluid constitutive relation. The results identify five different flow patterns: “mound,” “disk,” “shell,” “bubble,” and a “transition flow” between that of mound and bubble patterns. A complete map of the flow patterns as a function of the Reynolds and Bingham numbers is also presented and discussed using dimensional and physical arguments within a simplified theoretical framework.     

Obtaining the shear stress shear rate relationship and yield stress of liquid foods from Couette viscometry data

A method based on Tikhonov regularisation is used to convert the Couette viscometry data of a number of liquid foods into shear stress vs shear rate relationships. For liquid foods that have a yield stress and if the viscometry data cover the appropriate range of shear stress, Tikhonov regularisation is used to compute simultaneously the yield stress. The versatility of Tikhonov regularisation is demonstrated by applying it to process data from wide as well as narrow gap Couette viscometers. The results generated by Tikhonov regularisation are compared against that obtained by methods currently employed by rheologists.     

Non-linear viscoelasticity and temporal behavior of typical yield stress fluids: Carbopol, Xanthan and Ketchup

The viscoelastic properties of yield stress fluids are difficult to measure outside the linear viscoelastic regime, in particular above their yield stress. These properties are investigated for several common yield stress fluids using inertio-elastic oscillations. From this coupling between the instrument’s inertia and the viscoelasticity of the materials, the complete simple shear rheology can be determined, including viscoelasticity under flow. Findings show that the tested materials have an almost constant elasticity below and above the yield stress, even for applied stresses several times larger than the yield stress. Moreover, the temporal behavior of the materials is unambiguously determined. Concentrated Xanthan is shown to be thixotropic, while Ketchup mainly shows retarded viscoelasticity. Carbopol does not show long-term temporal dependance but apparently exhibits fracturation.     

Relations between cubic equation,stress tensor decomposition,and von Mises yield criterion

Inspired by Cardano's method for solving cubic scalar equations, the additive decomposition of spherical/deviatoric tensor (DSDT) is revisited from a new viewpoint. This decomposition simplifies the cubic tensor equation, decouples the spherical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.     

Derivation of a second-order model for Reynolds stress using renormalization group analysis and the two-scale expansion technique

With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples:turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder (GL) model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.