Extensional strain rate

Extensional flows occur when fluid deformation is the result of a stretching motion. Extensional viscosity is related to the stress required for the stretching. This stress is necessary to increase the normalized distance between two material entities in the same plane when the separation is s and the relative velocity is ds/dt. The deformation rate is the extensional strain rate, which is given by equation 13 (108) ... 

A method for measuring the uniaxial extensional viscosity of polymer soHds and melts uses a tensile tester in a Hquid oil bath to remove effects of gravity and provide temperature control cylindrical rods are used as specimens (218,219). The rod extmder may be part of the apparatus and may be combined with a device for clamping the extmded material (220). However, most of the mote recent versions use prepared rods, which are placed in the apparatus and heated to soften or melt the polymer (103,111,221—223). A constant stress or a constant strain rate is appHed, and the resultant extensional strain rate or stress, respectively, is measured. Similar techniques are used to study biaxial extension (101). 

From Fig. 5.3 it may be seen that this exceeds the shear rate for non-laminar flow (approximately 30 s ) so that the entry to this region would need to be streamlined. Fig. 5.3 also shows that the extensional strain rate, k, in the tapered entry region should not exceed about 15 s if turbulence is to be avoided. 

Fig. 2.8.8 (a) Implementation of four-roll mill device, (b) Speed image obtained across a horizontal slice by combining separate x- and y-velocity images, (c) Velocity profile taken across the x-axis of the cell showing the uniform extensional strain rate 8, such that x= ex (adapted from Ref. 15]). 

Extensional flow describes the situation where the large molecules in the fluid are being stretched without rotation or shearing [5]. Figure 4.3.3(b) illustrates a hypothetical situation where a polymer material is being stretched uniaxially with a velocity of v at both ends. Given the extensional strain rate e (= 2v/L0) for this configuration, the instantaneous extensional viscosity r e is related to the extensional stress difference (oxx-OyY), as... 

Analyze lubricated squeezing flow to determine biaxial extensional viscosity (T)R), which is calculated from biaxial stress (cB) and biaxial extensional strain rate (eB). 

Biaxial extensional flow is extensional flow in two directions with the same constant extensional strain rate qe. If the volume is constant then... 

Often, it is not possible to reach a steady state in extension and it is convenient to define a transient extensional viscosity, tje, that is a function of time, t, and the extensional strain rate, e, (Barnes et al., 1989). 

Figure 2 shows the calculated distribution of average volumetric strain rate for the assumed stress field. The location of six points (0= 30° to 0 = 69°) where fluid pressure changes were evaluated and interval P4 of borehole FEX 95.002 are also shown. Simulation results, as well as analytical solutions, reveal that a pore-pressure increase will only occur at the four points located in the contracted zone of compressive strain rate (0 > 45° in Figure 2). However, the P4 interval (0 = 14° in Figure 2) is located in the zone of extensional strain rate, and therefore no pore pressure increase can occur in at that location for the assumed stress field.

Figure 2. Simulated strain rates distribution indicating zones of contraction (compressive strain rate) and extension (extensional strain rate) and locations for evaluation of pore-pressure variations.

Poly(bulylene succinate) (PBS) is another biodegradable polymer which is not commonly blended with polyolefins. However, Yang et al. [94] investigated the eflect of PBS content, extrusion rate, and extensional strain rate on the melt strength and extensional viscosity of LDPE/PBS blends using a melt-spinning technique, and developed extensional master curves. Based on both the extensional master curve and a neural network method, they compared the predicted extensional viscosities with the experimental data of the LDPE/PBS blends. 

Fig. 8.1 Compression stress-strain curves of annealed and quenched PS at T = 296 K and at an extensional strain rate of e = 10 s , with a number of stress removals showing Bauschinger reverse strains (from Hasan and Boyce (1993) courtesy of Elsevier).

Here dv/dr is the extensional strain rate, and 77 is the extensional viscosity. The correlation between the ideal extensional viscosity and the shear viscosity for a Newtonian fluid can be described by the Trouton s ratio (Trouton 1906), as given by... 

In polymer processes such as film blowing, fiber spinning, and blow molding, the extensional properties and melt strength of a material are crucial pieces of information. Melt tensile testers are devices which pull on a melt strand as it is extruded from the capillary die and measure the force necessary to generate a desired draw ratio or melt extension. These instruments are capable of measuring very small forces and can generate the extensional strain rates found in many processes. 

Based on the early work of Ide and Ophir [33], the total amount of applied extensional strain, or draw ratio, was shown to be the propertydetermining factor. This conclusion was developed from studying the effects of extensional stress and strain rate by varying the temperature profile in the spinline and measuring take-up stress. By observing that no changes in the resulting filament stiffness occurred for equivalent draw ratio, they were able to show that extensional stress and extensional strain rate do not influence stiffness and by implication orientation. 

Typical output Extensional stress as a fimction of extensional strain rate/ time. 

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