Large amplitude oscillatory shear of pseudoplastic and elastoviscoplastic materials

We explore the utility of strain-controlled large amplitude oscillatory shear (LAOS) deformation for identifying and characterizing apparent yield stress responses in elastoviscoplastic materials. Our approach emphasizes the visual representation of the LAOS stress response within the framework of Lissajous curves with strain, strain rate, and stress as the coordinate axes, in conjunction with quantitative analysis of the corresponding limit cycle behavior. This approach enables us to explore how the material properties characterizing the yielding response depend on both strain amplitude and frequency of deformation. Canonical constitutive models (including the purely viscous Carreau model and the elastic Bingham model) are used to illustrate the characteristic features of pseudoplastic and elastoplastic material responses under large amplitude oscillatory shear. A new parameter, the perfect plastic dissipation ratio, is introduced for uniquely identifying plastic behavior. Experimental results are presented for two complex fluids, a pseudoplastic shear-thinning xanthan gum solution and an elastoviscoplastic invert-emulsion drilling fluid. The LAOS test protocols and the associated material measures provide a rheological fingerprint of the yielding behavior of a complex fluid that can be compactly represented within the domain of a Pipkin diagram defined by the amplitude and timescale of deformation.     

Rheological behavior of fiber-filled polymers under large amplitude oscillatory shear flow

Small and large amplitude oscillatory shear measurements (SAOS and LAOS) were used to investigate the rheological behavior of short glass fibers suspended in polybutene and molten polypropylene. Raw torque and normal force signals obtained from a strain-controlled instrument (ARES rheometer) were digitized using an analog to digital converter (ADC) card to allow more precise data analysis. The fiber concentration did not affect the torque signal in the SAOS mode, except for its magnitude, whereas the normal force signal was too low to be measurable. With increasing strain amplitude, the magnitude of the torque became a function of time. Depending on the applied frequency and strain rate, the stress in the filled polybutene increased with time, whereas for reinforced polypropylene (viscoelastic matrix), the behavior was opposite, i.e. the stress decreased with time. These effects were more pronounced at high fiber content. In addition the primary normal stress differences were no longer negligible at large deformation amplitude and exhibited a non-sinusoidal periodic response. Fast Fourier transform (FFT) analysis was performed and the resulting spectra, along with Lissajous figures of the shear stress and the primary normal stress differences, are explained in terms of fiber orientation. The experimental results for the suspensions in polybutene are well predicted by the Folgar-Tucker-Lipscomb (FTL) model.     

On secondary loops in LAOS via self-intersection of Lissajous–Bowditch curves

When the shear stress measured in large amplitude oscillatory shear (LAOS) deformation is represented as a 2-D Lissajous–Bowditch curve, the corresponding trajectory can appear to self-intersect and form secondary loops. This self-intersection is a general consequence of a strongly nonlinear material response to the imposed oscillatory forcing and can be observed for various material systems and constitutive models. We derive the mathematical criteria for the formation of secondary loops, quantify the location of the apparent intersection, and furthermore suggest a qualitative physical understanding for the associated nonlinear material behavior. We show that when secondary loops appear in the viscous projection of the stress response (the 2-D plot of stress vs. strain rate), they are best interpreted by understanding the corresponding elastic response (the 2-D projection of stress vs. strain). The analysis shows clearly that sufficiently strong elastic nonlinearity is required to observe secondary loops on the conjugate viscous projection. Such a strong elastic nonlinearity physically corresponds to a nonlinear viscoelastic shear stress overshoot in which existing stress is unloaded more quickly than new deformation is accumulated. This general understanding of secondary loops in LAOS flows can be applied to various molecular configurations and microstructures such as polymer solutions, polymer melts, soft glassy materials, and other structured fluids.     

Large amplitude oscillatory shear behavior of PEO-PPO-PEO triblock copolymer solutions

Rheological properties of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO) triblock copolymer solution in both linear and nonlinear regions have been investigated. PEO-PPO-PEO triblock copolymer solution shows a dramatic change in mechanical properties as temperature changes. PEO-PPO-PEO triblock copolymer undergoes a transition from sol to gel with increase of temperature. During this transition the copolymer solution passes through three different stages, namely sol, soft gel, and hard gel. In our previous research (Hyun et al. in J Non-Newtonian Fluid Mech 55:51–65, 2002), large amplitude oscillatory shear (LAOS) behavior was found to be very sensitive to the generated microstructures. In this study, we investigated the relationship between the LAOS type and the microdomain structure. Newtonian behavior is observed in sol region, while there appear two kinds of LAOS types in the soft gel region. One is type I (G′, G′′ decreasing) and the other is a combination of type I and type IV (G′, G′′ increasing followed by decreasing). Type III (G′ decreasing, G′′ increasing followed by decreasing) is observed in the hard gel region. We compared the shape of stress curves, Lissajous pattern, and Fourier transform (FT) rheology of hard gel and soft gel under LAOS, and tried to relate the complex LAOS behavior with the microstructural change. From these investigations, it was found that the LAOS behavior and the stress pattern at large strain are closely related to the microdomain structure of PEO-PPO-PEO triblock copolymer, and provide a lot of useful information on the microstructures induced by large deformation.     

Large amplitude oscillatory shear behavior of graphene derivative/polydimethylsiloxane nanocomposites

Rheological properties of three different nanocomposites, consisting of graphene oxide (GO), reduced graphene oxide (rGO), and polyhedral oligomeric silsesquioxane grafted reduced graphene oxide (rGO-POSS) as nanofillers and polydimethylsiloxane (PDMS), were investigated by large amplitude oscillatory shear (LAOS). The viscoelastic nonlinearity of the three nanofluids groups was studied by Lissajous curves, local nonlinear viscoelastic moduli of an oscillatory shear cycle, and Fourier transform rheology as a function of filler concentration and increasing and decreasing strain magnitude. The nonlinear behavior of the nanofluids was compared to understand the variation of internal microstructures. Firstly, GO/PDMS composites behave with higher moduli and smaller linear viscoelastic range comparing to that of other two composites. Secondly, the elastic stress Lissajous curves of these composites changed from elliptic to rectangular with round the corner with increasing the filler level and strain amplitude. Thirdly, all these three nanofluids exhibited intra-cycle strain stiffening with increasing strains and shear thickening at intermediate strain and then shearing thinning with increasing strain further. Fourthly, higher harmonic intensity of rGO/PDMS increased with increasing strain and came to a plateau, while that of other two nanofluids reached a maximum and then decreased. It suggested that different surface functionalization of nanoparticles will present different rheological behavior due to formed different network and LAOS could be used as a potential helpful method to characterize rheological properties of nanocomposites, especially at higher shear strain.     

A rheological criterion to determine the percolation threshold in polymer nano-composites

In this work, the effect of multi-walled carbon nanotube (CNT) and montmorillonite nanoclay on polymer chain dynamics is investigated around the percolation concentration for systems based on ethylene vinyl acetate (EVA) copolymer. Then, the results obtained are compared with literature data to determine if, regardless of particle characteristics, a universal rheological behavior can be detected at percolation. To do so, rheological analyses are performed under small amplitude oscillatory shear (SAOS), large amplitude oscillatory shear (LAOS), and transient shear step. SAOS data showed that, while the dynamics related to the Rouse relaxation time (τ _R) were not significantly influenced, the reptation relaxation time (τ _D) was strongly increased by the presence of nanoparticles. In step shear transient tests, the critical shear rate \( \left({\dot{\upgamma}}_{\mathrm{cr}}\right) \) for overshoot appearance was decreased due to chain confinement, and the formation of particle network strongly increased the level of stress overshoot. Particle networks increased significantly the nonlinear parameters (I ₃/I ₁ and Q ₀) obtained under LAOS and quantified by FT-rheology. In all measurements, due to the higher surface area associated to its size and density as well as hollow structure, CNT showed stronger effects compared to clay. Moreover, while the percolation concentration was different for CNT and clay, both systems showed similar behavior at percolation: a 0.5 scaling for G′ indicating a Rouse-dominated behavior.     

Obtaining Fourier series graphically from large amplitude oscillatory shear loops

Large amplitude oscillatory shear (LAOS) flow has been used to characterize the nonlinear viscoelasticity of polymer melts and solutions. Results are frequently reported with shear stress versus strain loops, or with shear stress versus shear rate loops. A Fourier analysis of the stress response to LAOS is often desired for comparison with theory, or for quantitative comparison between resins. A method is presented which employs the discrete Fourier transform to obtain the Fourier series coefficients from LAOS loops.     

A unified approach to model elasto-viscoplastic thixotropic yield-stress materials and apparent yield-stress fluids

A constitutive model for elasto-viscoplastic thixotropic materials is proposed. It consists of two differential equations, one for the stress and the other for the structure parameter, a scalar quantity that indicates the structuring level of the microstructure. In contrast to previous models of this kind, the structure parameter varies from zero to a positive and typically large number. The lower limit corresponds to a fully unstructured material, whereas the upper limit corresponds to a fully structured material. When the upper limit is finite, the model represents a highly shear-thinning, thixotropic, and viscoelastic liquid that possesses an apparent yield stress. When it tends to infinity, the behavior of a true yield-stress material is achieved. Predictions for rheometric flows such as constant shear rate tests, creep tests, SAOS, and large-amplitude oscillatory shear (LAOS) are presented, and it is shown that, in all cases, the trends observed experimentally are faithfully reproduced by the model. Within the framework of the model, simple explanations are given for the avalanche effect and the shear banding phenomenon. The LAOS results obtained are of particular importance because they provide a piece of information that so far is absent in the literature, namely a quantitative link between the Lissajous–Bowditch curve shapes and rheological effects such as elasticity, thixotropy, and yielding.     

Flow of concentrated solutions of starlike micelles under large-amplitude oscillatory shear

The non-linear viscoelasticity of concentrated solutions and glasses of soft starlike micelles has been studied by large-amplitude oscillatory shear (LAOS). The non-linear response has been analysed using current schemes of Fourier transform (FT) rheology, and its character has been determined by the phase of the third harmonic contribution to the stress. The limitations of FT rheology and related analysis methods are discussed, and an alternative method is presented that takes into account all the higher harmonics. This method reveals a strain-hardening character of intracycle non-linearities at large strain amplitudes for all volume fractions. We also show that, although the relation of LAOS with steady shear measurements works qualitatively, due to inherent limitations of LAOS, steady shear data cannot be reproduced quantitatively.     

Large amplitude oscillatory shear rheology of three different shear-thickening particle dispersions

We present a large amplitude oscillatory shear rheology (LAOS) investigation of three different shear-thickening particle dispersions - fumed silica in polyethylene oxide (FLOC), fumed silica in polypropylene glycol (HydroC), and cornstarch in water (JAM). These systems shear-thicken by three different mechanisms - shear-induced formation of particle clusters flocculated by polymer bridging, hydrocluster formation, and jamming. The viscoelastic non-linearities of the three fluids were studied as a function of strain and strain-rate space through the use of Lissajous-Bowditch curves and local nonlinear viscoelastic moduli of an oscillatory shear cycle. The nonlinear behaviors of the three fluids were compared and contrasted to understand the nonlinear shear-thickening mechanism of each. Both HydroC and JAM dispersions were found to exhibit strong strain stiffening of the elastic moduli and strain thickening of the loss moduli behavior associated with possible hydrocluster formation and particle jamming. However, the FLOC dispersion, in contrast, showed strong strain softening and strain thinning behavior at large strain amplitudes associated with yielding of the microstructure. The expected thickening of the loss modulus of FLOC in LAOS with increasing strain was not observed even though viscosity of FLOC was found to shear-thicken in steady-shear measurements. This disagreement is likely due to very large strain amplitudes required for shear-thickening to occur by shear-induced polymer bridging mechanism. The hypothesis was confirmed through stress growth experiments. Conversely, the HydroC and JAM dispersions required relatively small applied strains for shear-thickening to occur by hydrocluster and jamming mechanism. The comparison of local intra-cycle nonlinearity through Lissajous-Bowditch plots and nonlinear viscoelastic parameters indicated that the elastic nonlinearities of all three systems are primarily driven by a strong dependence on the magnitude of the applied strain-rates within an oscillatory cycle rather than the amplitude of the applied strain. A close inspection of the LAOS data reveals strong differences in the viscoelastic nonlinearities of these three different shear-thickening dispersions which can be used to create a nonlinear rheological fingerprint for each and offers valuable new insights into the nonlinear dynamics associated with each of the shear-thickening mechanisms.     

Strain stiffening of non-colloidal hard sphere suspensions dispersed in Newtonian fluid near liquid-and-crystal coexistence region

Concentrated hard sphere suspensions often show an interesting nonlinear behavior, called strain stiffening, in which the viscosity or modulus starts to increase at critical strain amplitude. Sudden increase of rheological properties is similar to shear thickening; however, the particle dynamics in the strain stiffening under oscillatory shear flow does not necessarily coincide with the mechanism of shear thickening under step shear flow. In this study, we have systematically investigated the nonlinear rheology of non-colloidal (>1???m) hard sphere suspensions dispersed in Newtonian fluid near liquid-and-crystal coexistence region in order to better understand the strain stiffening behavior. The suspensions near liquid-and-crystal coexistence region are known to locally form the closed packing structure. The critical strain amplitude which is the onset of strain stiffening was different for the storage and loss modulus. But they converged to each other as the suspension forms a more crystalline structure. The critical strain amplitude was independent of medium viscosity, imposed angular frequency, and particle size, but was strongly dependent upon particle volume fraction. The onset of strain stiffening was explained in terms of shear-induced collision due to particle motion in the closed packing structure. Nonlinear stress wave-forms, which reflect the micro-structural change, were observed with the onset of strain stiffening. During the strain stiffening, enhanced elastic stress before and after flow reversal was observed which originates from changes in the suspension microstructure. Nonlinearity of the shear stress in terms of Fourier intensity was extremely increased up to 0.55. Beyond the strain stiffening, the suspension responded liquid-like and the nonlinearity decreased but the elastic shear stress was still indicating the microstructure rearrangement within a cycle.     

Nonlinear rheological behavior of diphenylmethylvinyl silicone gum: an example of homogeneous shear

The present work shows, based on an effective particle-tracking velocimetric (PTV) method, that a commercial diphenylmethylvinyl silicone gum displays nonlinear rheological responses to startup shear and large amplitude oscillatory shear (LAOS) in a homogeneous manner, in contrast to monodisperse melts. Using an effective cone-partitioned plate (CPP) setup along with PTV, rheological characterizations of shear thinning in continuous shear and strain softening in LAOS are carried out reliably without the inherent experimental complication associated with edge fracture. Conversely, based on the CPP, the rheological effects of edge fracture are also illustrated for both startup shear and LAOS.     

Polymer motion as detected via dielectric spectra of 1,4-cis-polyisoprene under large amplitude oscillatory shear (LAOS)

In order to investigate the global polymer chain motion under large amplitude oscillatory shear (LAOS), the dielectric properties under LAOS are measured by a new rheo-dielectric combination. The design of the rheo-dielectric setup including a new fixture and modified oven is explained in detail. For 1,4-cis-polyisoprene, having type-A dipoles parallel to the backbone, the dielectric dipoles can detect the global polymer chain motion via the end-to-end vector. Thus rheological and dielectric (rheo-dielectric) properties reflect the dynamics of the polymer chain motion under LAOS. In this study, we investigate the rheo-dielectric properties under LAOS with 1,4-cis-polyisoprene as model component. As the strain amplitude was increased under LAOS, the relaxation strength from dielectric properties decreased for the whole spectra without changing the shape of the dielectric spectra. These results are analyzed on the basis of the molecular model of dynamic tube dilation (DTD) induced by the convective constraint release (CCR). It is found that the global chain motion under LAOS flow is affected by both rheological frequency and strain amplitude. It is also observed that segmental motion is affected via the oscillatory frequency under LAOS. This result differs from experiments under steady shear.     

Probing shear-banding transitions of the VCM model for entangled wormlike micellar solutions using large amplitude oscillatory shear (LAOS) deformations

We explore the use of large amplitude oscillatory shear (LAOS) deformation to probe the dynamics of shear-banding in soft entangled materials, primarily wormlike micellar solutions which are prone to breakage and disentanglement under strong deformations. The state of stress in these complex fluids is described by a class of viscoelastic constitutive models which capture the key linear and nonlinear rheological features of wormlike micellar solutions, including the breakage and reforming of an entangled network. At a frequency-dependent critical strain, the imposed deformation field localizes to form a shear band, with a phase response that depends on the frequency and amplitude of the forcing. The different material responses are compactly represented in the form of Lissajous (phase plane) orbits and a corresponding strain-rate and frequency-dependent Pipkin diagram. Comparisons between the full network model predictions and those of a simpler, limiting case are presented.     

Comparison of stress-controlled and strain-controlled rheometers for large amplitude oscillatory shear

In linear viscoelastic region, it is well known that dynamic modulus and dynamic compliance can be converted to each other. However, it is questionable whether there exists an interconversion between large amplitude oscillatory shear (LAOS) data measured from different types of rheometers—stress-controlled and strain-controlled rheometers. Hence, we tried to prove the existence by use of polyethylene oxide (PEO) aqueous solutions with well-developed entanglements. From this experiment, we can conclude that a stress-controlled rheometer can simulate LAOS behavior measured from a strain-controlled rheometer under the conditions where inertia effect is not significant. Furthermore, it is investigated whether the LAOS data of the stress-controlled rheometer obey stress–frequency superposition as the strain–frequency superposition found by Cho et al. (J Rheol 54:27–63, 2010) from LAOS data measured by the strain-controlled rheometer. This scaling relation shows that the dimensionless stress amplitude is a function of zeta which is the product of the stress amplitude and linear viscoelastic function J′(ω). The plot shows that all of the data are superposed in a single curve without regard to frequency, molecular weight, and concentration of PEO aqueous solutions.     

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.     

From period-doubling to folding in stiff film/soft substrate system: The role of substrate nonlinearity

Uniaxial compressed stiff films on soft substrates can evolve into the period-doubling and folding instabilities, beyond the onset of sinusoidal wrinkling. The substrate is modeled as a neo-Hookean solid with a pre-stretch prior to film attachment, and its nonlinearity is obtained. Both the pre-stretch and the external nominal strain imposed on the film/substrate system can induce different substrate nonlinearity, and thus have different effects on the post-buckling mode evolution of the system. This study shows that the critical strain of period-doubling instability is linear to the pre-stretch. As the compressive nominal strain increases, the folding mode occurs beyond the onset of period-doubling in both the pre-tension and the pre-compression case, due to the softening/hardening effects for the inward/outward displacements generated by the positive substrate nonlinearity.     

液滴在大振幅振荡剪切流动中的非线性行为研究

利用YB模型预测了黏性液滴在黏性基质中的形状和取向的非线性变化,并对比前人 的理论和实验工作,讨论了YB模型大振幅剪切流场中的适用性. 还着重 讨论了非线性行为的评估,提出了``峰高比加和法'和``峰面积 比加和法'两种新的评估方法.     

Large-amplitude oscillatory shear flow from the corotational Maxwell model

Using the single relaxation time corotational Maxwell fluid, we derive explicit analytical expressions for the first, third, and fifth harmonics of the alternating shear stress response in large-amplitude oscillatory shear (LAOS). We also derive corresponding expressions for the zeroth, second, and fourth harmonics of both the first and second normal stress differences. These harmonics are found to depend upon just two dimensionless groups: the Deborah and Weissenberg numbers, each of which causes non-Newtonian behavior. The form of the solution for the corotational Maxwell model in LAOS matches the forms of the analytical solutions for two molecular models for dilute solutions and one for concentrated solutions or melts. We also derive an analytical solution for the corotational Maxwell model after startup of LAOS. For this we find that both small and large amplitude cases approach a periodic limit cycle (alternance) at the same rate for both the shear stress response and for the normal stress differences. For molten high density polyethylene that is lightly filled with carbon black, we find good quantitative agreement with measured LAOS behavior when our analytical solution is superposed for multiple relaxation times.