Stress viscoelastic

When a viscoelastic material is subjected to a constant strain, the stress initially induced within it decays in a time-dependent manner. This behavior is called stress relaxation. The viscoelastic stress relaxation behavior is typical of many TPs. The material specimen is a system to which a strain-versus-time profile is applied as input and from which a stress-versus-time profile is obtained as an output. Initially the material is subjected to a constant strain that is maintained for a long period of time. An immediate initial stress gradually approaches zero as time passes. The material responds with an immediate initial stress that decreases with time. When the applied strain is removed, the material responds with an immediate decrease in stress that may result in a change from tensile to compressive stress. The residual stress then gradually approaches zero. 

Viscoelastic stress-relaxation data are usually presented in one of two ways. In the first, the stress manifested as a function of time. Families of such curves may be presented at each temperature of interest. Each curve representing the stress-relaxation behavior of the material at a different level of... 

In all three equations Ex and E > are now the complex moduli the storage and loss moduli for the blend are obtained by direct substitution into these equations and separation of the real and imaginary parts to obtain separate mixture rules for each. Analytical expressions have been obtained for these, but they are lengthy and cumbersome. All the calculations described, therefore, were carried out by computer. The substitution of complex moduli into the solution of the equivalent purely elastic problem is justified by the correspondence principle of viscoelastic stress analysis (6). 

Polymer Viscoelasticity Stress and Strain in Practice, Evaristo Riande, Ricardo Diaz-Calleja, Margarita G. Proiongo, Rosa M. Masegosa, and Catalina Salom... 

For the viscoelastic stress, we can use differential or integral constitutive models (see Chapter 2). For differential models we have the general form... 

In order to solve viscoelastic problems, we must select the most convenient model for the stress and then proceed to develop the finite element formulation. Doue to the excess in non-linearity and coupling of the viscoelastic momentum equations, three distinct Galerkin formulations are used for the governing equations, i.e., we use different shape functions for the viscoelastic stress, the velocity and the pressure... 

Very important phenomena in polymer behaviour, such as viscoelasticity, stress, strain, volume and enthalpy relaxation, ageing, etc., are characterised by time-dependence of the polymer properties. 

Rippie, E. G., and Danielsson, D. W. (1981), Viscoelastic stress/strain behaviour of pharmaceutical tablets Analysis during unloading and postcompression periods, J. Pharm. Sci., 70,476-482. 

The viscoelastic stress-strain equation, Equation (4) can be expressed in finite element formulation which relates the stress tensor a.. at time index n and cell centre (ij) to the corresponding strain tensor arising from the movement of the adjoining cell corners. Using backward differences for the time step, at time index n. 

Thus, viscoelastic stresses are produced by distortions of the distribution of polymer configurations. For Gaussian distributions, the stress tensor is proportional to the second... 

The temporary network model predicts many qualitative features of viscoelastic stresses, including a positive first normal stress difference in shear, gradual stress relaxation after cessation of flow, and elastic recovery of strain after removal of stress. It predicts that the time-dependent extensional viscosity rj rises steeply whenever the elongation rate, s, exceeds 1/2ti, where x is the longest relaxation time. This prediction is accurate for some melts, namely ones with multiple long side branches (see Fig. 3-10). (For melts composed of unbranched molecules, the rise in rj is much less dramatic, as shown in Fig. 3-39.) However, even for branched melts, the temporary network model is unrealistic in that it predicts that rj rises to infinity, whereas the data must level eventually off. A hint of this leveling off can be seen in the data of Fig. 3-10. A more realistic version of the temporary network model... 

Figure 9.2 Schematic phase diagram of a polymer/solvent mixture, where y is the Flory chi parameter, and xe = 1/2 is x at the theta temperature. The quantity Xe X along the ordinate is a reduced temperature, and is the polymer volume fraction. CP is the critical point, and BL is the binodal line. SSL and KSL are the static symmetry line and the kinetic symmetry line, respectively. These lines define the phase-inversion boundaries during quenches. In quenches that end at the right of such a line, the polymer-rich phase is the continuous phase, while to the left of the line the solvent-rich phase is the continuous one. SSL applies at long times, after viscoelastic stresses have relaxed, while KSL applies at shorter times before relaxation of viscoelas-...

For a viscosity ratio M of order unity or less, r is the relaxation time of the droplet shape and of the resulting viscoelastic stress in the dispersion. Thus, for rjs I cP, F 10 dyn/cm, a (xm, we obtain t 10 sec, and the stress in the emulsion relaxes almost instantly after cessation of flow. However, when the fluid medium is more viscous and the droplets are bigger, say, rjg 100 P, a 10 jxm, with the same F, we obtain T 0.01 sec. Although this latter value of r corresponds to rather fast relaxation, it can produce appreciable normal stress differences at high shear rates thus (Choi and Schowalter 1975)... 

Indentation methods as a special type of analysis of viscoelastic stress or displacement are studied in Chapter 16. It should be noted that indentation... 

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