Viscoelastic isothermal

The theoretical description of a non-isothermal viscoelastic flow presents a conceptual difficulty. To give a brief explanation of this problem we note that in a non-isothennal flow field the evolution of stresses will be affected by the... 

The non-isothermal viscoelastic cell model was used to study foam growth in the continuous extrusion of low density foam sheet. Surface escape of blowing agent was successfully incorporated to describe the foaming efficiency. Reasonable agreement was obtained with experimental data for HCFC-22 blown LDPE foam in the sub-centimetre thickness domain. 11 refs. 

A series of modulus-time curves was also made for temperatures covering the entire viscoelastic spectrum. At higher temperatures, the instrument was first allowed to reach the desired temperature and was held there for half an hour. Samples were then quickly inserted. After 10 minutes moduli were measured as a function of time up to 1000 seconds. Total measuring time for each isotherm thus was kept to less than 30 minutes to minimize chemical decomposition and plasticizer evaporation. 

Although all polymer processes involve complex phenomena that are non-isothermal, non-Newtonian and often viscoelastic, most of them can be simplified sufficiently to allow the construction of analytical models. These analytical models involve one or more of the simple flows derived in the previous chapter. These back of the envelope models allow us to predict pressures, velocity fields, temperature fields, melting and solidification times, cycle times, etc. The models that are derived will aid the student or engineer to better understand the process under consideration, allowing for optimization of processing conditions, and even geometries and part performance. 

S. K. Goyal, E. Chu, and M. R. Kamal, Non-isothermal Radial Filling of Center-gated Disc Cavities with Viscoelastic Polymer Melts, J. Non-Newt. Fluid Meek, 28, 373-406 (1988). 

Isothermal draw resonance is found to be independent of the flow rate. It occurs at a critical value of draw ratio (i.e., the ratio of the strand speed at the take-up rolls to that at the spinneret exit). For fluids that are almost Newtonian, such as polyethylene terephthalate (PET) and polysiloxane, the critical draw ratio is about 20. For polymer melts such as HDPE, polyethylene low density (LDPE), polystyrene (PS), and PP, which are all both shear thinning and viscoelastic, the critical draw ratio value can be as low as 3 (27). The maximum-to-minimum diameter ratio decreases with decreasing draw ratio and decreasing draw-down length. 

Petrie and Ito (84) used numerical methods to analyze the dynamic deformation of axisymmetric cylindrical HDPE parisons and estimate final thickness. One of the early and important contributions to parison inflation simulation came from DeLorenzi et al. (85-89), who studied thermoforming and isothermal and nonisothermal parison inflation with both two- and three-dimensional formulation, using FEM with a hyperelastic, solidlike constitutive model. Hyperelastic constitutive models (i.e., models that account for the strains that go beyond the linear elastic into the nonlinear elastic region) were also used, among others, by Charrier (90) and by Marckmann et al. (91), who developed a three-dimensional dynamic FEM procedure using a nonlinear hyperelastic Mooney-Rivlin membrane, and who also used a viscoelastic model (92). However, as was pointed out by Laroche et al. (93), hyperelastic constitutive equations do not allow for time dependence and strain-rate dependence. Thus, their assumption of quasi-static equilibrium during parison inflation, and overpredicts stresses because they cannot account for stress relaxation furthermore, the solutions are prone to numerical instabilities. Hyperelastic models like viscoplastic models do allow for strain hardening, however, which is a very important element of the actual inflation process. 

Isothermal measurements of the dynamic mechanical behavior as a function of frequency were carried out on the five materials listed in Table I. Numerous isotherms were obtained in order to describe the behavior in the rubbery plateau and in the terminal zone of the viscoelastic response curves. An example of such data is shown in Figure 6 where the storage shear modulus for copolymer 2148 (1/2) is plotted against frequency at 10 different temperatures. 

Detailed analysis of the isothermal dynamic mechanical data obtained as a function of frequency on the Rheometrics apparatus lends strong support to the tentative conclusions outlined above. It is important to note that heterophase (21) polymer systems are now known to be thermo-rheologically complex (22,23,24,25), resulting in the inapplicability of traditional time-temperature superposition (26) to isothermal sets of viscoelastic data limitations on the time or frequency range of the data may lead to the appearance of successful superposition in some ranges of temperature (25), but the approximate shift factors (26) thus obtained show clearly the transfer viscoelastic response... 

The engineering property that is of interest for most of these applications, the modulus of elasticity, is the ratio of unit stress to corresponding unit strain in tension, compression, or shear. For rigid engineering materials, unique values are characteristic over the useful stress and temperature ranges of the material. This is not true of natural and synthetic rubbers. In particular, for sinusoidal deformations at small strains under essentially isothermal conditions, elastomers approximate a linear viscoelastic... 

Fig. 11 shows master curves extrapolated with the model. These have the same general features as master curves plotted by shifting data isotherms. The two differ slightly because different assumptions are involved. The conventional method of shifting data makes all isotherms congruent the same viscoelastic processes are assumed at all temperatures. The phenomenological model is not limited to this assumption. When the thermal spread varies with frequency, the model extrapolates to isotherms like fig. 11. Note... 

Fourier transform mechanical analysis (FTMA) measures isothermal viscoelastic properties of pol)nmers over a wider range of frequencies in a shorter period of time than is possible with other techniques. 

We will discuss in this section the variations of the viscoelastic parameters derived from linear viscoelastic measurements all these parameters may be derived from any t3rpe of measurement (relaxation or creep experiment, mechanical spectroscopy) performed in the relevant time or frequency domain. The discussion will be focused however on the complex shear modulus which is the basic function derived from isothermal frequency sweep measurements performed with modem rotary rheometers. 

A real example of the effect of temperature on the viscoelastic functions at T > Tg is shown in Figure 8.2. Here double logarithmic plots of the compliance function J t) versus time are shown at several temperatures for a solution of polystyrene My — 860,000) in tri-ra-tolyl phosphate (1) in which the weight fraction of polymer is 0.70. Because the glass transition temperature of the solution is 15°C, the isotherms were registered at... 

Isotherms at several temperatures showing the frequency dependence of the real component / (co) of the complex compliance / (coi) of a viscoelastic material are plotted on a double logarithmic scale in Figure 8.9 (7). At high temperatures and low frequencies, J (co) decreases slightly with increas-... 

---