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We present results from a comprehensive investigation of the rheological responses of the gelled waxy crude oils during the yielding transition process by both stress-controlled and strain-controlled tests. If the deformation is within the linear viscoelastic region, G ′ increases slowly with increasing frequency following a power-law relationship. 80% of the total deformation accumulated during creeping is recoverable, and this recoverability remains largely independent of both imposed stress and testing time. The waxy gel relaxes the restored stress slowly with a time scale of ∼100 s. If the induced deformation exceeds the linear viscoelastic region, the elasticity of waxy structure starts to gradually decay with increasing creep stress and creep time, and the plastic contribution has come into play in the nonlinear region. A rapid reduction in the obtained time scale is observed with increasing applied strain. After the structure fractures, both G ′ and G ″ decrease with increasing strain following a power-law relationship. The ratio of the large amplitude shear-thinning exponents of G ′ and G ″ is around 2, indicating a more rapid decay of the elastic property than the viscous property. A brittleness index I is defined to quantitatively describe the brittleness of the waxy gel. The value of I for the waxy gel formed at lower temperatures is smaller, indicating that the waxy gel tends to have a more brittle fracture when yielding. The values of linear storage modulus G ′ ( γ 0 → 0 ) , critical linear strain γ 1 , critical linear stress σ 1 , and yield strain γ y obtained by different rheological testing methods are found to be well consistent. The yielding transition process is found to be strain determined rather than stress determined, and thereby γ 1 and γ y rather than yield stress are suggested to indicate the yielding transition. [ABSTRACT FROM AUTHOR]

We present unique nonlinear rheological data of well-defined symmetric Cayley-tree poly(methyl methacrylates) in shear and uniaxial extension. Earlier work has shown that their linear viscoelasticity is governed by the hierarchical relaxation of different generations, whereas the segments between branch points are responsible for their substantial strain hardening as compared to linear homopolymers of the same total molar mass at the same value of imposed stretch rate. Here, we extend that work in order to obtain further experimental evidence that will help understanding the molecular origin of the remarkable properties of these highly branched macromolecules. In particular, we address three questions pertinent to the specific molecular structure: (i) Is steady state attainable during uniaxial extension? (ii) What is the respective transient response in simple shear? and (iii) How does stress relax upon cessation of extension or shear? To accomplish our goal, we utilize state-of-the-art instrumentation, i.e., filament stretching rheometry and cone-partitioned plate shear rheometry for polymers with 3 and 4 generations, and complement it with state-of-the-art modeling predictions using the branch-on-branch (BoB) algorithm. The data indicate that the extensional viscosity reaches a steady state value, whose dependence on extensional rate is identical to that of entangled linear and other branched polymer melts. Nonlinear shear is characterized by transient stress overshoots and the validity of the Cox-Merz rule. Remarkably, nonlinear stress relaxation is much broader and slower in extension compared to shear. It is also slower at higher generation, and rateindependent for rates below the Rouse rate of the outer segment. For extension, the relaxation time is longer than that of the linear stress relaxation, suggesting a strong "elastic memory" of the material. These results are described by BoB semiquantitatively, both in linear and nonlinear shear and extensional regimes. Given the fact that the segments between branch points are less than three entanglements long, this is a very promising outcome that gives confidence in using BoB for understanding the key features. Moreover, the response of the segments between generations controls the rheology of the Cayley trees. Their substantial stretching in uniaxial extension appears responsible for strain hardening, whereas coupling of stretches of different parts of the polymer appears to be the origin of the slower subsequent relaxation of extensional stress. Concerning the latter effect, for which predictions are not available, it is hoped that the present experimental findings and proposed framework of analysis will motivate further developments in the direction of molecular constitutive models for branched and hyperbranched polymers. [ABSTRACT FROM AUTHOR]

Rheologists have expectations for signatures of linear viscoelastic properties, such as shapes of G'(ω) and G?(ω). Medium amplitude (or asymptotically-nonlinear) oscillatory shear (MAOS) provides additional nonlinear rheological information with low dimensional, well-defined material functions [Ewoldt and Bharadwaj, Rheol. Acta 52, 201-209 (2013)]. Here, we develop expectations of signatures (or fingerprints) for the four asymptotically-nonlinear material functions associated with MAOS, [e1](ω), [e3](ω), [v1](ω), [v3](ω). Although the linear fingerprints may be identical for different models, the asymptotically-nonlinear fingerprints may be different in magnitude, frequency-scaling, curve shapes, and sign changes. To perform the analysis, we collect/translate a library of available analytical strain-controlled MAOS fingerprints for seven different constitutive models. Using this library, we identify general trends and highlight key differences of asymptotic-nonlinear viscoelasticity. Asymptotic nonlinearities for all models considered here obey the terminal regime inter-relations and frequency scaling predicted by Bharadwaj and Ewoldt [J. Rheol. 58, 891-910 (2014)]. Unlike the positive linear viscoelastic measures, at least one of the four asymptotic nonlinearities changes signs with Deborah number (De). Following sign interpretations of Ewoldt and Bharadwaj [Rheol. Acta 52, 201-209 (2013)], we show that nonlinearities tend to be driven by strain-rates at small De, and by strains at large De, a trend observed for nearly all the constitutive models studied here, the exception being the model for dilute rigid dumbbell suspensions of Bird et al. [J. Chem. Phys. 140, 074904 (2014)]. Some constitutive models exhibit multiple sign changes at intermediate De and there may be no universal behavior of asymptotically-nonlinear fingerprints in this regime. Therefore, frequency-dependent signatures can be material-specific. This will allow inverse problems to infer structure, select models, and fit model parameters using asymptotically-nonlinear signatures. To illustrate this aspect, we demonstrate a fingerprint matching exercise with experimental measurements on a transiently cross-linked hydrogel system. We find that currently available model fingerprints can match the qualitative magnitudes and frequency dependence, but not the signs of the experimental transient network response. [ABSTRACT FROM AUTHOR]

We propose, in this paper, a model for predicting the rheological response of both vibrated and sheared 3D granular suspensions in stationary and nonstationary conditions. The major assumption of this model is the inherent bimodal behavior of chain forces in granular packings. The model is set up from a kinetic equation describing the dynamic exchange between a population of strongly correlated caged particles and a population of slightly correlated free particles. To compare the predictions of the model to experimental results, the kinetic equation is transformed into a differential constitutive equation, relating stress to strain, by including the effect of the interstitial fluid on the suspension. With only four adjustable parameters intrinsic to the system (i.e., independent of the type of rheological test used), the model is in very close agreement with experiments. Despite the fact that our approach remains at a mean-field level, it is able to predict and describe several rheological behaviors, in stationary, nonstationary conditions, linear and nonlinear regimes, including Newtonian and frictional Coulombian regimes, as well as elastic Hookean and viscoelastic Maxwellian behaviors. It then appears that this two-state approach allows capturing both the viscoelastic behavior of dry granular materials and granular suspensions. Vibrated dense suspensions and granular media are thus unified under a common framework. [ABSTRACT FROM AUTHOR]

It has recently been shown that the dynamics of complex interfaces can be treated by hyperelastic finite deformation, and the Cauchy stress tensor can be written as a tensor derivative of the interfacial energy. In the present study, the analytical nature of this tensor derivative was further explored, resulting in a more useful constitutive relation between the stress tensor and the Finger strain tensor. To accommodate the interfacial relaxation effects, an energy balance principle was adopted in developing a nonlinear relaxation model which was then used in a visco-hyperelastic formulation for stress determination. Case studies on this visco-hyperelastic model were performed, and validations against known results were attempted. While at small deformation rates, the new model agrees with the linear viscoelastic calculations, as well as Doi and Ohta's scaling predictions, high nonlinearity was observed at large deformation rates. [ABSTRACT FROM AUTHOR]

The main aim of this work is to study the flow, failure, and rupture dynamics of a benchmark low-density polyethylene (BASF Lupolen 1840H) in true tensile creep conditions in both the viscoelastic and elastic deformation regimes. For this, we used a novel extensional rheometer that for the first time allows real controlled-stress conditions to be applied to the materials (as opposed to nominally controlled-stress) until physical rupture occurs (as opposed to being limited by maximum Hencky strain). We observed that constant strain rate was achieved for all flow conditions, and depending on the level of applied tensile stress, one or two states were obtained. In the former case, the observed mode of rupture was ductile, or liquid-like, and in the latter was cohesive, or elastic-like. The coupling at the molecular level between these flow and rupture mechanisms is not yet fully understood, although some recent studies in the literature may be able to offer at least partial explanations. [ABSTRACT FROM AUTHOR]

Non-linear correlations are found between the melt strength and fundamental shear flow properties such as low frequency loss tangent, crossover frequency, and zero-shear-rate viscosity for a series of polypropylene (PP) melts. The very good non-linear correlations suggest rheotens as a reliable rheological test to characterize extensional rheology relevant to fabrication, despite its non-homogeneous and non-isothermal flow kinematics. The rheotens model of Doufas [J. Rheol. 50, 749-769 (2006)] with a modified Giesekus (MG) viscoelastic constitutive equation is expanded to the case of PP melts. A single set of molecular parameters per material predicts the rheotens force curves very well over a wide range of processing conditions. The rheotens model is proposed as a tool for determination of rheological parameters of constitutive equations applicable to the simulation of complex polymer processes. Molecular considerations and predictions of the rheotens model are extensively discussed. A multi-mode MG model predicts the non-linear steady shear data (shear and first normal stresses) very favorably satisfying linear viscoelasticity. The oscillatory shear data and model predictions satisfy both the Cox-Merz [J. Polym. Sci. 28, 619-621 (1958)] and Laun [J. Rheol. 30, 459-501 (1986)] rules. The model exhibits stable numerical behavior without singularities or turning points in the prediction of steady shear viscosity even at quite high shear rates (e.g., on the order of 20 000 s-1), problems that have been reported for other constitutive equations. [ABSTRACT FROM AUTHOR]

Two-step reversing flows are severe tests of constitutive equations for polymer melts and have attracted interest for testing the response of branched polymers. Here we report on single-step and three types (types B, C, and D) of reversing torsional flows on branched and linear polyethylenes (PEs). The responses were analyzed using Kaye–Bernstein–Kearsley–Zapas (K-BKZ) theory. Comparisons between data and theory in type B and C flows for the two branched PEs (LD 103 and LD 146) and a linear HDPE are presented. For the LD 146 material and to strains higher than previously examined, the results agree with prior studies, i.e., the K-BKZ theory provides a good description of the response of branched polymers in reversing flows while the opposite is the case for the linear polymers. Surprisingly, it is found that the other branched polymer (LD 103) behaves more like a linear polymer and not a branched polymer in that it does not follow the K-BKZ theory. In the type D flow, one which was not previously investigated, the K-BKZ theory describes the normal force (NF) responses for branched LD 146 but not for the linear PE. Also, isochronal derivatives of the strain potential function (W1 and W2) were calculated from torque (T) and NF responses in single-step tests. The damping function fits to a modified sigmoidal formula and is close to the BKZ limit as reported by Wagner (2004a) for branched polystyrenes. The normal stress difference ratio and damping function were extracted from W1 and W2. Finally, the Cox–Merz rule was examined for one of the branched PEs. [ABSTRACT FROM AUTHOR]

A recent, nonlinear viscoelastic theory for predicting the thermomechanical response of glassy polymers has been shown to predict behaviors from enthalpy relaxation to temperature-dependent mechanical yield in various modes of deformation quite well. The foundation of this theory rests on a “material clock” that depends on the potential energy of the system. The molecular basis for the clock and the Rational Mechanics framework for the constitutive equation are briefly reviewed. The theory is then used to predict and explain much more complicated behavior of glassy polymers: the change in compressive yield stress during physical aging at different temperatures, the peculiar enthalpic response of glassy polymers previously compressed to different strains, “volumetric implosion” on samples subjected to tensile strains, and the dependence of the shift factor on aging time and applied stress. [ABSTRACT FROM AUTHOR]