Nonlinear Viscoelastic Properties

P. E. Rouse. The theory of nonlinear viscoelastic properties of dilute solutions of scaling polymers. J Chem Phys 27 1273-1280, 1953. 

FT rheometry is a powerful technique to document the nonlinear viscoelastic behavior of pure polymers as observed when performing large amplitude oscillatory strain (LAOS) experiments. When implemented on appropriate instmments, this test technique can readUy be applied on complex polymer systems, for instance, filled mbber compounds, in order to yield significant and reliable information. Any simple polymer can exhibit nonlinear viscoelastic properties when submitted to sufficiently large strain in such a case the observed behavior is so-called extrinsic... 

Although attempts to measure and interpret nonlinear behavior are potentially useful, there are few reports in the literature on the measurement of the nonlinear viscoelastic properties of foods. This has been due to a lack of both suitable instrumentation and suitably developed theory nonlinear behavior, the predominant form of which is the exhibition of normal stresses, and a dependence of viscosity on shear rate, is much more complex than linear behavior (Gunasekaran and Ak, 2002). 

Measurement of Nonlinear Viscoelastic Properties of Polymers in Cyclic Deformation under a Relatively Large Strain Amplitude... 

In mathematical models of healthy human joints, cartilage is often represented as a single-phase, elastic material with homogeneous and isotropic properties. This approximation is valid, provided that only the short-term response of the tissue is of interest when cartilage is loaded for 1 to 5 seconds, its response is more or less elastic (Hayes and Bodine, 1978 Hori and Mockros, 1976 Mak, 1986). In the long term, however, say more than 1 minute, the response of the tissue is dominated by the nonlinear, viscoelastic properties of creep and stress relaxation (Hayes and Mockros, 1971 Mow et al., 1984). 

Equation (10) cannot be applied until A, the equivalent relaxation time for the fluid, is known. However, A is defined by the linear Maxwell model, and actual polymer solutions exhibit marked nonlinear viscoelastic properties [5,6,7]. For both fresh and shear degraded solutions of Separan AP 30 polyacrylamide, which exhibit pronounced drag reduction in turbulent flow, Chang and Darby [8] have measured the nonlinear viscosity and first normal stress functions, and Tsai and Darby [6] have reported transient elastic properties of similar solutions, A nonlinear hereditary integral function containing six parameters has been proposed to represent the measured properties [8], The apparent viscosity function predicted by this model is ... 

E. The Method of Analysis for Nonlinear Viscoelastic Properties of Polymer Liquids... 

The polymeric materials which show the nonlinear viscoelastic properties exhibit dynamic shear stress containing higher-order odd harmonics even under small-amplitude oscillation. These viscoelastic functions can accurately be determined only by many experiments of various strain amplitude, Vq. 

For other method to analyze the nonlinear viscoelastic properties, we assume a constitutive equation of Fourier series type as [8]... 

It is well known that some kinds of polymer solutions such as particle-dispersed polymer solutions and solutions of block copolymers show significant nonlinear viscoelastic properties [6-8]. 

Measurements of normal stress differences during steady shear flow, and of normal stress growth approaching steady-state flow and stress relaxation after cessation of flow, provide additional information about nonlinear viscoelastic properties. The conventional identifications of the normal stresses for simple shear have been shown in Fig. 1-16 their orientations in several examples of experimental geometry are sketched in Fig. 5-5. 

H. APPLICATION OF REDUCED VARIABLES TO BULK AND NONLINEAR VISCOELASTIC PROPERTIES... 

Abstract This chapter describes the influence of three-dimensional nanofillers used in elastomers on the nonlinear viscoelastic properties. In particular, this part focuses and investigates the most important three-dimensional nanoparticles, which are used to produce rubber nanocomposites. The rheological and the dynamic mechanical properties of elastomeric polymers, reinforced with spherical nanoparticles, like POSS, titanium dioxide and nanosdica, were described. These (3D) nanofillers in are used polymeric matrices, to create new, improved rubber nanocomposites, and these affect many of the system s parameters (mechanical, chemical, physical) in comparison with conventional composites. The distribution of the nanosized fillers and interaction between nanofUler-nanofiUer and nanofiller-matrix, in nanocomposite systems, is crucial for understanding their behavior under dynamic-mechanical conditions. 

In this chapter, the rheology and the dynamic-mechanical behavior of iso-dimensional rubber nanocomposites in the non-linear zone have been reviewed. Briefly described were the effect of nanofiller on the nonlinear viscoelastic properties of rubbers and the mechanism of nonlinearity in these polymeric systems. 

The addition of iso-dimensional nanofillers into elastomers causes many changes in mechanical and physical properties, but especially, the effect of nanoparticles on the nonlinear viscoelasticity properties of rubbers has been investigated. In rubber matrices containing nanofillers, exhibition of the Payne effect is strongly connected with the dispersion of the nanofiller and the tendency to create aggregates among the nanoparticles. Filler dispersion plays an important role in determining the nonlinear viscoelastic behavior of these systems— in particular, both the properties of the filler particles and filler-polymer compatibility. 

Leblanc JL (2008) Large amplitude oscillatory shear expeiimenls to investigate the nonlinear viscoelastic properties of highly loaded carbon black rubber eompounds without curatives. J Appl Polym Sci 109 1271-1293... 

Chapter 4 investigates the rheological and the dynamic mechanical properties of rubber nanocomposites filled with spherical nanoparticles, like POSS, titanium dioxide, and nanosilica. Here also the crucial parameter of interfacial interaction in nanocomposite systems under dynamic-mechanical conditions is discussed. After discussing about filled mono-matrix medium in the first three chapters, the next chapter gives information about the nonlinear viscoelastic behavior of rubber-rubber blend composites and nanocomposites with fillers of different particle size. Here in Chap. 5 we can observe a wide discussion about the influence of filler geometry, distribution, size, and filler loading on the dynamic viscoelastic behavior. These specific surface area and the surface structural features of the fillers influence the Payne effect as well. The authors explain the addition of spherical or near-spherical filler particles always increase the level of both the linear and the nonlinear viscoelastic properties whereas the addition of high-aspect-ratio, fiberlike fillers increase the elasticity as well as the viscosity. 

The linear and nonlinear viscoelastic properties of 12-2-12, 2Br" solutions in the presence of salt depend on the electrostatic interactions between micelles [116]. These long-range interactions result in the occurrence of a pronounced correlation peak in the SANS spectra of the solutions [117]. 

V. NONLINEAR VISCOELASTIC PROPERTIES OF ENTANGLED SOLUTIONS OF RODSHAPED MICELLES... 

Woo, S.H. Mechanical properties of tendons and ligaments quasi-static and nonlinear viscoelastic properties. Biorheology 19, 385 (1982)... 

In order to predict the nonlinear viscoelastic properties of concentrated solutions of rigid rodlike macromolecules, one must first solve Eq. (9.1) for the orientational distribution function /(u, t) and then Eq. (9.12) for stresses, for a given velocity field. Owing to the highly nonlinear nature of the system of equations, one must resort to numerical techniques to obtain solutions. Indeed, Kuzuu and Doi (1983, 1984) carried out numerical computations to predict nonlinear viscoelastic behavior. 

In practice, polymers and adhesive joints are often being used under service conditions exceeding the limitations of hnear viscoelasticity. Indications for nonlinear viscoelastic properties include the observation that creep comphance changes for different stress levels and that the mechanical behavior not only depends on the summarized history of previous mechanical incidents but also from the sequence in which they have been apphed. In this case, the simplified constitutive equations of hnear viscoelasticity will fail in describing time-dependent mechanical properties. Further reference to nonlinear viscoelasticity is given in (Haddad 1995 Brinson and Brinson 2008). 

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