Nonlinear viscoelasticity, polymeric materials

There are many ways to fabricate and model viscoelastic polymeric materials [22-32]. Fabrication often involves nonlinear flows that are spatially inhomogeneous, nonisothermal, and temporally complex. The flows also may involve material phase changes, and/or a wide range (1-5 decades) of strains and strain rates. Rheology is often the bridge between resin design and fabrication performance, and remains an active area of research [22]. 

In a number of cases, polymer films that are most certainly not acoustically thin have been studied the viscoelastic nature of some polymeric materials makes them acoustically thick even at thicknesses well below 1% of a wavelength. Because other relationships that contribute to the overall response are often nonlinear (e.g., the solubility of organic vapor in the polymer, particularly at high concentrations), the additional nonlinearity introduced by an acoustically thick polymer film does not invariably cause difficulty, provided calibration is carried out over the entire concentration range of interest. There are some situations, however, where an acoustically thick film can cause confusion, such as when (counterintuitive) positive frequency shifts occur as a result of an increase in the concentration of species sorbed by the film due to viscoelastic effects [13] in such cases, the fiequency change vs concentration plot can be multivalued, i.e., two or more very different concentrations of an analyte give an identical frequency shift [14]. 

Fourier transform rheology is a new technique, which has as yet not been widely employed. In the future, it will provide quantitative information on non-linear viscoelasticity, in particular on the onset of nonlinearity. Combined with structural probes such as small angle scattering, this will enhance enormously our understanding of nonlinear viscoelasticity in soft polymeric materials. 

Below the glass temperatin-e, the nonlinear viscoelastic response of polymeric materials has been much less widely studied than has the behavior of melts and solutions. One reason for this is the lack of an adequate theory of behavior. Therefore the discussion about amorphous materials below the glass tem-peratiu e focuses on recent measin-ements of the nonlinear response as well as... 

Experimental data seem to indicate that the origin of nonlinearity is the same for crosslinked rubbers and polymeric melts. Existing molecular models are inconsistent with this finding because they are designed to explain the nonlinear viscoelastic behaviour of one of the two types of material only. This situation calls for the development of a unified model which deals with the nonlinearity of both crosslinked and non-crossiinked materials. 

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. 

K. Qsaki, K. Nishizawa, and M. Kurata. Material time constant characterizing the nonlinear viscoelasticity of entangled polymeric systems. Macromolecules, 15 (1982), 1068-1071. 

Osaki, K., Nishizawa, K., Kurata, M. Material time constant characterization of nonlinear viscoelasticity of entangled polymeric solutions. Macromol. (1982) 15, pp. 1068-1071... 

Transient Response Creep. The creep behavior of the polymeric fluid in the nonlinear viscoelastic regime has some different features from what were foimd with the linear response regime. First, there are no ready means of relating the creep compliance to the relaxation modulus as was done in the linear viscoelastic case. In fact, the relationship between the relaxation properties and the creep properties depends entirely on the exact constitutive relationship chosen for the response of the material, and numerical inversion of the specific constitutive law is ordinarily necessary to predict creep response from the relaxation behavior (or vice versa). For most cases, the material properties that appear in the constitutive equations are written in terms of the relaxation response. We discuss this subsequently in the context of the K-BKZ model. 

The Knauss-Emri Model. There have been several works in the literature in which volume- or ee-ooZume-dependent clocks were used to describe the nonlinear viscoelastic response of polymeric glasses. The chief success among these is the ICnauss-Emri model (163) in which the reduced time was defined in terms of a shift factor that depended on temperature, stress, and concentration of small molecules in such a way that the responses depended on the free volume induced by each of these parameters. For an isothermal single phase and homogeneous material, the equations are... 

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