Direct Strain Oscillation: a new oscillatory method enabling measurements at very small shear stresses and strains

As shown previously, a rotational rheometer equipped with an electronically commutated motor (EC-motor) allows one to conduct stress and strain experiments with the same rheometer in rotational mode. A new method has now been developed to improve further strain controlled oscillatory measurements by adjusting the strain directly within a single oscillation cycle. Generally, a strain controlled oscillatory test in a stress controlled rheometer consists of the following steps: applying one full oscillation cycle with an arbitrary stress amplitude, measuring the strain amplitude, adjusting the stress in the next oscillation cycle, and repeating this routine until the desired strain amplitude is reached. The newly developed direct strain oscillation mode employs a different approach. It does not require a full oscillation cycle but uses a real-time position control and adjusts to the desired strain directly on the sine wave. Therefore, the actual movement of the measuring system follows directly the required change in strain during each individual oscillation cycle. This new oscillatory mode has several major advantages: (1) the possibility of conducting real strain controlled tests in oscillation, (2) the exact strain setting right from the first oscillation cycle, i.e., no or only very slight overshoot in strain, (3) faster data acquisition even within an oscillation cycle, (4) it allows the measurement at extremely low angular resolution and low torques. Due to the absence of strain overshoots and the ability of testing at small deflection angles and low torques this new method is especially helpful for measurements on samples with low viscosities and weak structures such as gels, emulsions, suspensions, colloids, and foams.     

Differences between stress and strain control in the non-linear behavior of complex fluids

Various techniques have been proposed to characterize the behavior in the non-linear regime. A new theoretical framework, as proposed recently by Ewoldt et al. (J Rheol 52(6):1427–1458, 2008), provides a quantitative analysis of Lissajous figures during large-amplitude oscillatory shear (LAOS). Intra- and intercycle non-linearities, strain stiffening and softening, and shear thinning and thickening are described and can be distinguished. The new LAOS framework from Ewoldt et al. has been extended to a sinusoidal stress input. Measurements on two different samples reveal significant different results for sinusoidal strain or sinusoidal stress input. For both sinusoidal inputs, the results have been verified by cyclic stress and strain loading tests. The sinusoidal input tests are analyzed as an oscillatory test by the rheometer software and firmware, whereas the cyclic loading tests are purely rotational tests. Since both types of testing give the same results, any instrumental artifacts can be excluded. This implies that complex fluids can behave differently whether periodic stress or strain input functions outside the linear visco-elastic range are applied. All tests in controlled strain and stress in rotational and oscillatory modes have been performed with the same rheometer based on an air bearing-supported electrically commutated synchronous motor.     

Coupling between flow and diffusion at polymer/polymer interfaces: large amplitude oscillatory shear experiments

 Coupling between flow and diffusion at symmetric polymer/polymer interfaces has been investigated. Polystyrene/polystyrene sandwich assemblies were subjected to large-amplitude oscillatory shear (LAOS) using a sliding-plate rheometer (SPR) and the stress was monitored as a function of time. The results were treated using a new model combining Wagner's model with the theory of Doi and Edwards. The model explicitly expresses the influence of the strain and stress amplitudes frequency and time on the self-diffusion process. The apparent self-diffusion coefficient was found to increase with welding time, in agreement with our previous results obtained using small-amplitude oscillatory shear measurements. However, it was found in the present case that the self-diffusion coefficient depends strongly on the strain and stress amplitudes and frequency, and its steady state value was found to be larger than that determined from small-amplitude oscillatory shear measurements. It appears that the large strain oscillatory shear field continuously increases the density of chain ends at the interface and thus increases the flux of mass transport. Received: 30 January 2001 Accepted: 12 June 2001     

Transient director patterns upon flow start-up of nematic liquid crystals (an explanation for stress oscillation damping)

In this work we attempt to determine the origin of damped stress oscillations upon flow start-up of a nematic liquid crystalline monodomain. These damped stress oscillations were first observed by Gu et al. (1993) in the cone-plate flow cell and have since also been observed by Mather et al. (1997) in the parallel disk cell. Although Mather's work explained the cause of the stress oscillation damping in the torsional flow cell, the origin of the damping in the cone-plate device remains a mystery. Here we report finding similar damped stress oscillations in the cylindrical Couette cell and combined with the optical experiments reported earlier by Cladis and Torza (1975, 1976) we are able to propose an explanation for the damping in this geometry. We also report new optical experiments using the cone-plate cell in hopes of determining a cause to the damping in the cone-plate cell. Received: 11 August 2000 Accepted: 31 October 2000     

Investigation of the rheological properties of short glass fiber-filled polypropylene in extensional flow

The behavior of short glass fiber–polypropylene suspensions in extensional flow was investigated using three different commercial instruments: the SER wind-up drums geometry (Extensional Rheology System) with a strain-controlled rotational rheometer, a Meissner-type rheometer (RME), and the Rheotens. Results from uniaxial tensile testing have been compared with data previously obtained using a planar slit die with a hyperbolic entrance. The effect of three initial fiber orientations was investigated: planar random, fully aligned in the stretching flow direction and perpendicular to it. The elongational viscosity increased with fiber content and was larger for fibers initially oriented in the stretching direction. The behavior at low elongational rates showed differences among the various experimental setups, which are partly explained by preshearing history and nonhomogenous strain rates. However, at moderate and high rates, the results are comparable, and the behavior is strain thinning. Finally, a new constitutive equation for fibers suspended into a fluid obeying the Carreau model is used to predict the elongational viscosity, and the predictions are in good agreement with the experimental data.     

Measurement of pressure coefficient of melt viscosity: drag flow versus capillary flow

The pressure coefficient of viscosity of poly(α-methylstyrene-co-acrylonitrile) was measured using a high-pressure sliding plate rheometer (HPSPR) and two types of capillary rheometer: a piston-driven device with a throttle at the exit [piston capillary rheometer with throttle (PCRWT)] operated at a fixed flow rate, and a counter-pressure nitrogen capillary rheometer (CPNCR) operated at a fixed pressure drop. In the HPSPR, the pressure, shear rate, density, and viscosity are all uniform throughout the sample, while the analysis of capillary data is complicated by the axial pressure gradient and the radial shear rate gradient. The polymer was found to be piezorheologically simple, and the HPSPR data indicated that the pressure coefficient of viscosity β ≡ dln(a _P)/dP decreased slightly with increasing pressure at high pressure. While β from PCRWT data from different laboratories and instruments agreed fairly well, the β values were on average about 2/3 of that from the HPSPR. The CPNCR yields β about 18% lower than that of the HPSPR.     

Large amplitude oscillatory elongation flow

A filament stretching rheometer (FSR) was used for measuring the elongation flow with a large amplitude oscillative elongation imposed upon the flow. The large amplitude oscillation imposed upon the elongational flow as a function of the time t was defined as where ε is the Hencky strain, is a constant elongational rate for the base elongational flow, Λ the strain amplitude (Λ ≥ 0), and Ω the strain frequency. A narrow molecular mass distribution linear polystyrene with a molecular weight of 145 kg/mol was subjected to the oscillative flow. The onset of the steady periodic regime is reached at the same Hencky strain as the onset of the steady elongational viscosity ( Λ = 0). The integral molecular stress function formulation within the ‘interchain pressure’ concept agrees qualitatively with the experiments.     

Damping Characterization and Viscoelastic Behavior of Laminated Polymer Matrix Composites Using a Modified Classical Lamination Theory

The damping property of materials can be defined as the ratio of dissipated energy over the total strain energy during the loading–unloading process, called the specific damping capacity (SDC). In this study, in order to characterize the damping properties of materials, a test plan in designed to extract the SDC of a single layer composite from hysteresis data. The theory of linear viscoelasticity incorporates a varying Young’s Modulus by using a complex stiffness modulus. Considering different lay-ups, the modified classical lamination plate theory is modified to represent both stiffness and SDC of laminates. The results are compared with experimental results for symmetric laminated specimen. This evaluation shows a very good agreement between theoretical and experimental results in the range of low frequency loading from 0.2 to 4 Hz. The complex compliance matrix changes the governing equation in to a complex form which contains both stiffness and damping properties.     

Viscoelastic properties of MR elastomers under harmonic loading

This paper presents both experimental and modeling studies of viscoelastic properties of MR elastomers under harmonic loadings. Magnetorheological elastomer (MRE) samples were fabricated by mixing carbonyl iron power, silicone oil, and silicone rubber and cured under a magnetic field. Its steady-state and dynamic properties were measured by using a parallel-plate rheometer. Various sinusoidal loadings, with different strain amplitude and frequencies, were applied to study the stress responses. The stress–strain results demonstrated that MR elastomers behave as linear visocoelastic properties. Microstructures of MRE samples were observed with a scanning electron microscope. A four-parameter linear viscoelatic model was proposed to predict MRE performances. The four parameters under various working conditions (magnetic field, strain amplitude, and frequency) were identified with the MATLAB optimization algorithm. The comparisons between the experimental results and the model predictions demonstrate that the four-parameter viscoelastic model can predict MRE performances very well. In addition, dynamic properties of MRE performances were alternatively represented with equivalent stiffness and damping coefficients.     

Dynamic Forces Produced by Swinging Bells

The swinging of bells on belfries is a classical problem in structural dynamics and has been addressed in the Central European specialized bibliography. To carry out our study, the different modalities of swinging bells have been classified in “systems” according to their most relevant characteristics in three groups: Central European, English and Spanish systems. Each group presents some singular characteristics of frequency and oscillation, unbalance and/or turning rate, which give rise to different forces variable in time on their supporting structures. We have analyzed the three systems and, compared the maximum values of the horizontal and vertical forces that appear on the structure as well as its main harmonics. Besides the parameters analyzed, the complete dynamic study of the structure, and therefore the evaluation of its dynamic amplification factor (D.A.F.), requires the knowledge of its dynamic characteristics: main frequencies and damping ratio.     

Determination of the elongational viscosity of polymer melts by melt spinning experiments. A comparison with different experimental techniques

In this work, melt spinning experiments were tentatively used for the determination of the elongational viscosity of polymer melts at different levels of tensile strain and strain rate. The materials examined were two high-density polyethylene grades for blow moulding with similar number-average molecular mass but different polydispersity index. The data from melt spinning tests were compared with transient extensional viscosity data obtained by uniform isothermal tensile tests, performed by means of an extensional rheometer, as well as with those produced by converging flow tests (Cogswell model). The results showed that for high strain and strain rate levels, the melt spinning experiments provide elongational viscosity data quite close to the transient extensional viscosity values obtained from the tensile tests.     

A network model with free-strand dynamics for polymer melts

 A network model for polymer melts is presented in which disentangled strands relax under flow conditions and may rejoin the network before complete relaxation. For simplicity, we study Gaussian strands that move affinely when incorporated in the network. Network strands are created and lost according to a time constant λ. Free strands have their dynamics given by the Bird-DeAguiar model as a crude representation of reptation and the hindered rotation experienced by polymer strands in melts. The model yields a shear-thinning viscosity with overshoot in the start-up viscosity η⁺ (t). The double-step strain results compare well with available experimental data. Received: 10 July 2000 Accepted: 10 July 2001     

Clear and pigmented water epoxy systems: a study on the hardening kinetics on the basis of the variations of the viscoelastic moduli

The hardening reaction of a two-can water epoxy polyamide system was investigated on the basis of the variation of the viscoelastic moduli G′ and G′′. Unpigmented (clear varnish) and TiO₂ pigmented formulations, at two different TiO₂ concentrations, were taken into account. Time and frequency sweep procedures were carried out using the stress-controlled rheometer Haake RS 150. The behavior of G′ and G′′ vs time was fitted to a four-parameter asymptotic model through the whole course of the hardening process. Frequency sweep data, obtained at increasing times during the whole hardening process, were plotted to the generalized Cole and Cole behavior model and the corresponding mechanical spectra were drawn. An interpretation for some aspects of the cross-linking progress is discussed and possible future developments are briefly outlined. Received: 15 January 2000 Accepted: 13 November 2000     

Rheo-PIV of a shear-banding wormlike micellar solution under large amplitude oscillatory shear

We explore the behavior of a wormlike micellar solution under both steady and large amplitude oscillatory shear (LAOS) in a cone–plate geometry through simultaneous bulk rheometry and localized velocimetric measurements. First, particle image velocimetry is used to show that the shear-banded profiles observed in steady shear are in qualitative agreement with previous results for flow in the cone–plate geometry. Then under LAOS, we observe the onset of shear-banded flow in the fluid as it is progressively deformed into the non-linear regime—this onset closely coincides with the appearance of higher harmonics in the periodic stress signal measured by the rheometer. These harmonics are quantified using the higher-order elastic and viscous Chebyshev coefficients e _n and v _n , which are shown to grow as the banding behavior becomes more pronounced. The high resolution of the velocimetric imaging system enables spatiotemporal variations in the structure of the banded flow to be observed in great detail. Specifically, we observe that at large strain amplitudes (γ ₀ ≥ 1), the fluid exhibits a three-banded velocity profile with a high shear rate band located in-between two lower shear rate bands adjacent to each wall. This band persists over the full cycle of the oscillation, resulting in no phase lag being observed between the appearance of the band and the driving strain amplitude. In addition to the kinematic measurements of shear banding, the methods used to prevent wall slip and edge irregularities are discussed in detail, and these methods are shown to have a measurable effect on the stability boundaries of the shear-banded flow.     

Shear-induced crystallization of PB-1 up to processing-relevant shear rates

Two experimental methods to study shear-induced crystallization of poly(butene-1) (PB-1) in the high shear rate region are presented: one using a concentric cylinder rheometer and the other a capillary rheometer equipped with a cylindrical die. The crystallization onset time (t _on) is used as the parameter to monitor crystallization progress through the output signal from each device. By combining the new data with the results from a previous paper (2005) in which a plate–plate rheometer was used, onset time data covering a shear rate range from 10^-4 to 500 s^-1 at temperatures 99–107°C are obtained. In this range, a decrease in onset time spanning five decades is observed. The onset times obtained from the capillary rheometer are larger compared to those from the other two methods, which can be explained from the different type of flow. The data also confirm the procedure to construct a temperature-invariant curve, which can be extended to high shear rates for three PB-1 samples having different molecular weight distributions. The slope of the fitted curve for all three cases is −1, which suggests that a critical value is required for shear-induced crystallization. The morphology of the formed crystals (spherulitic or rod-like) depends on the molecular weight, but this does not affect the validity of the T-invariant curve. Above the melting point, it is shown that the amount of long chains influences the temperature limit where shear-induced crystallization can still take place.The paper was presented at AERC 2005, Grenoble, with the title “Shear-Induced Crystallization of Polybutene-1 Covering a Wide Shear Rate Range.”An erratum to this article can be found at     

On the elastic properties of model suspensions as investigated by creep recovery measurements in shear

 The elastic properties of model suspensions with spherical monodisperse hydrophilic glass spheres that were dispersed in a Newtonian liquid were determined in creep and creep recovery measurements in shear with a magnetic bearing torsional creep rheometer. The creep and creep recovery measurements were performed depending on the applied level of shear stresses ranging from 0.19 Pa to 200 Pa. Since the recoverable creep compliances of the chosen suspending medium (i.e. a low molecular weight polyisobutylene) were far below the lower limit of the resolution of the creep rheometer it can be considered to behave as purely viscous. By applying a large shear stress in the creep tests the investigated suspensions with a volume fraction of Φ _t =0.35 behave as Newtonian liquids, too. For these suspensions no significant recoverable creep compliances could be detected, as well. In contrast to the Newtonian state of suspensions at high shear stresses, where a shear induced ordering of the particles can be expected, a non-Newtonian behaviour arises by applying a very low shear stress in the creep test. In this state large recoverable creep compliances were detected for the suspensions. The magnitude of the recoverable creep compliances of the suspensions exceeded the largest creep compliances of polymer melts that are reported in the literature by more than two decades. From the results obtained by creep recovery measurements with a magnetic bearing torsional creep rheometer it can clearly be concluded that the particle structure present in the chosen model suspension gives rise to a pronounced elasticity. Received: 21 November 2000 Accepted: 12 July 2001     

Electromechanical Characterization of Au Thin Films using Micro-tensile Testing

This paper presents the test technique about measurement of electrical resistance changes of thin films during tensile testing. In this work, we used a real-time digital image correlation strain measurement system coupled with micro-tensile testing unit and voltage/current sourcemeter. This system has the advantage of real time displacement monitoring with a resolution of 50 nm during the micro-tensile testing, with the ability to measure the variation in electrical resistance of the specimen at the same time. We obtained the complete testing data for the stress–strain curve and associated electrical resistance-strain curve for 1 and 2 μm-thick freestanding gold films. Young’s modulus was about 61~69 GPa and 0.2% offset yield strength was about 361~402 MPa. In case of the electrical resistance, rapid change was observed under the elastic regime, while less obvious under the plastic regime. We also conducted finite element analysis, and this result implied that the electrical resistivity would not be constant during micro-tensile testing.     

An updated version of the multimechanism model for cyclic plasticity

In this paper we consider the elastoplastic behavior of the 304L stainless steel under cyclic loading at room temperature. After the experimental investigations presented in Taleb and Hauet (2009), the present work deals with modeling in the light of the new observations. An improved version of the multimechanism model is proposed in which the isotropic variable is revisited in order to take into account the non-proportional effect of the loading as well as the strain memory phenomenon. A particular attention has been paid to the identification process in order to capture the main important phenomena: relative parts of isotropic and kinematic hardening, time dependent effects, non-proportionality effect, strain amplitude dependence. Only strain controlled tests have been used for the identification process. The capabilities of the model with “only” 17 parameters are evaluated considering a number of proportional and non-proportional stress and strain controlled tests.     

Kelvin-Voigt versus Bürgers internal damping in modeling of axially moving viscoelastic web

Stability and oscillation characteristics of two-dimensional axially moving web have been investigated. The application of one-dimensional beam-like models of the web allows the identification of instability regions and the estimation of the critical speed. For the beam material two different models, i.e., Kelvin-Voigt and Bürgers have been considered. The numerical solutions of full non-linear and linearized equations have been compared. The effects of axially travelling speed and the internal damping on dynamical stability of axially moving web have been studied in details. Our numerical studies of Kelvin-Voigt and Burger's models show that both models give similar results for small values of internal damping and can be used to describe the dynamics of axially moving webs made from materials with internal damping coefficient smaller than 3×10⁻⁵. For the materials with larger damping coefficient the Bürgers model gives more reliable results.