Extensional creep

Rg. 7.10 A schematic diagram of apparatus for studying extensional creep. 

Ward, I.M. (1964) The temperature dependence of extensional creep in polyethylene terephthalate. Polymer, 5, 59. 

Collected results for the nine compliance constants are shown in Table 8.9. The 3 axis is the initial draw direction and the 1 axis lies in the plane of the sheet, following the convention indicated in Figure 8.2. in and 533 were obtained from measurements of extensional creep in a dead loading creep machine and refer to the 10s response at 0.1% strain, was obtained from the deformation of an electron microscope grid printed on the surface of the sample [97], and 12 and S23 by the Michelson interferometer method [12]. S22 was determined by increasing the compressive strain of strips under load in a compressional creep apparatus [7]. S55 was determined by the torsion of rectangular samples cut with their long axes parallel to 3 and 1 respectively [18], 44 and see were also determined in this way... 

Strain-softening polymers are very prone to ductile failure in extension, and this poses a major challenge for the experimentalist. If there is a small variation in diameter along the sample, the resistance to further deformation will be reduced at that point, leading to instability and failure. This instability has been treated theoretically by McKinley and Hassager [158]. Because of this instability, it is difficult to continue an experiment to steady-state in such a material. This analysis [158] implies that if the stress passes through a smooth maximum before undergoing ductile failure, this maximum is the steady-state stress, and the extensional viscosity 7e (f) can be calculated. However, experience has shovm that it is difficult to be certain whether a maximum in the curve of rj t, e) versus time implies that steady state has been reached. If the tensile stress, rather than the Hencky strain rate, is held constant, the extensional creep compliance D t, steady state is achieved, the compliance becomes linear with time, and the intercept of this line with the vertical axis is the steady-state extensional creep compliance... 

Stadlbauer etal. [200] developed an extensional creep rheometer especially for use at high tensile stresses. The tensile force is produced by a pneumatic cylinder, and end effects are minimized by use of a flexible end clamp. 

One technique for measurement of extensional flow that has been used to study various doughs is that of Cogswell (1972, 1978) for entrance flows. The analysis is based on several assumptions (Padmanabhan and Bhattacharya, 1993) (1) The flow is isothermal and creeping (negligible inertial effects), (2) the fluid is incompressible and has a pressure-independent viscosity, (3) the shear viscosity follows the power law model, t]a = Ky" (4) there is no slip at the edge of the converging profile, and (5) that the entrance pressure drop (Ape) in converging flow from a circular barrel in to a circular die can be considered to be made up of that due to shear (Ape,s) and extensional flow (Ape,E) ... 

Generally, the operative frequency range for the torsional pendulum method is 0.01 to 50 Hz, the upper limit of the frequency defined by the dimensions of the oscillatory frequency relative to the dimensions of the sample. At higher investigative temperatures, the polymeric materials may undergo extensional deformation (creep) due to the weight of the inertia bar. Under such circumstances, a modified torsion pendulum apparatus may be used in which an inertia disk is attached directly onto the end of the sample (12). In addition, this method is frequently employed to measure the torsion modulus at low frequencies. 

Problem 7-12. Bubble in an Axisymmetric Flow. A gas bubble is immersed in a viscous Newtonian fluid that is undergoing an axisymmetric extensional flow. The fluid is viscous enough that the relevant Reynolds number is small so that the creeping-motion approximation can be applied. The capillary number based on the extension rate, E, and the surface tension, a, is small, i.e.,... 

Interpretation of mechanical measurements in terms of molecular structure was until fairly recently confined essentially to identification of the temperatures of the major viscoelastic relaxations through extensional or torsional dynamic mechanical studies. Now, however, investigations of the elastic constants and their temperature dependence—allied with dynamic mechanical, creep and both wide and small angle X-ray diffraction— are yielding fairly detailed pictures of the interrelation of the crystalline and less well ordered regions of some oriented solid polymers. 

Instead of imposing a constant stretch rate on a sample and measuring the steady-state stress, one may impose a constant stress and determine the resulting extensional strain. This is a creep experiment, and if the strain, initially zero, begins to increase linearly with time, a constant stretch rate is achieved. The extensional viscosity is again obtained as the ratio of the imposed stress to the resulting constant stretch rate. 

As discussed in Chapters 10 and 11, rheology can be very sensitive to the microstructure of liquids. For example, the viscosity of entangled polymer melts depends on molecular weight to the 3.4 power, T]o Ml . Equilibrium creep compliance is very sensitive to molecular weight distribution. The yield stress and low frequency G are good indicators of the flocculation state of colloids. Extensional viscosity can be an important indicator of bread dough quality (Padmanabhan, 1993). 

As shown in Figure 15.4, the sudden application of stress to a Maxwell element causes an instantaneous stretching of the spring to an equilibrium value of xJG (or aJE if a tensile stress is applied), where Xg is the constant applied shear stress (or Og is the constant applied extensional stress). The dashpot extends linearly with time with a slope of xjx] (or Maxwell element is a fluid, because it will continue to deform as long as it is stressed. The creep response of a Maxwell element is therefore... 

It has been observed that steady state is achieved substantially faster in a constant stress experiment than in a constant strain rate experiment, and this is advantageous because of the very large sample length and very small diameter that are involved in continuing a constant rate experiment to steady state. If the extensional viscosity is the property of interest, the use of tensile creep is therefore advantageous. However, most of the data that have been reported were measured at constant strain rate. 

Melt behavior has been studied using uniaxial (also called simple or tensile), biaxial, and planar extensional flows [9, Ch. 6]. However, only the first two of these are in general use and will be discussed here. A uniaxial extensional rheometer is designed to generate a deformation in which either the net tensile stress Tg or the Hencky strain rate e (defined by Eq. 10.89) is maintained constant. The material functions that can, in principle, be determined are the tensile stress growth coefficient / (f, ), the tensile creep compliance, andthetensile... 

The Mtinstedt tensile rheometer (MTR) is an end-separation device in which the sample is stretched vertically in a cylindrical oil bath [ 199]. This is an improved version of the universal extensional rheometer described by Mtinstedt etal. [177]. The basic idea is illustrated in Fig. 10.23. The specimen is fastened by an adhesive to small metal plates, one of which is attached to a force transducer at the bottom of the bath, and the other is coupled to a pull rod that is vertically displaced by a toothed belt driven by a motor. This instrument has been used for a number of important studies [ 158,191 ]. The MTR can reach strain rates of 5 s and can be used for creep measurements. The temperature is limited to about 220 °C because of the physical properties of the silicone oil used to fill the bath. 

Stadlbauer, M., Janeschitz-Kriegl, H., Lipp, M., Eder, G., Forstner, R. Extensional rheometer for creep at high tensile stress. Part I. Description and validation. /. Rheol. (2004) 48, pp. 611-629... 

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