Extension rate

Fig. 2. Cellulose acetate stress—strain properties at standard and wet conditions, tested at 60% min extension rate, 3.9 cm gauge length. Sample conditions standard, 21°C, 65% rh wet, 21°C, water wet. To convert N/tex to gf/den, multiply by 11.33.

Quench. Attempts have been made to model this nonisotherma1 process (32—35), but the complexity of the actual system makes quench design an art. Arrangements include straight-through, and outside-in and inside-out radial patterns (36). The optimum configuration depends on spinneret size, hole pattern, filament size, quench-chamber dimensions, take-up rate, and desired physical properties. Process continuity and final fiber properties are governed by the temperature profile and extension rate. 

Controlled Strain-rate Tests Controlled strain-rate tests were first developed by Parkins (see Ugiansky and Payer ) for the study of stress-corrosion cracking. These took the form of constant strain-rate tests (also known, perhaps more accurately, as constant extension-rate tests). Since then alternative forms of test have been developed to modify the conditions under which the specimen is exposed. 

Fig. 5. Comparison of leaf extension rates in two grasses of contrasted cell size and nuclear DNA amount, (a) Brachypodium pinnatum, 2c DNA = 2.3 pg (b) Bromus erectus, 2c DNA = 22.6 pg., Watered prior to measurement O, droughted for 3 weeks prior to measurement. The 95% confidence limits are indicated by the vertical lines.

FIGURE 26.51 Brasion loss per unit energy (abradability) (—) as function of temperature for four different compounds on a silicon carbide track at a speed of 1 cm/s together with energy density measurements (—) at an extension rate of 10 /s. (From Grosch, K.A. and Schallamach, A., Trans IRI, 40, T80, 1961 Rubber Chem. Technol, 39, 267, 1966. 

Fig. 2.8.17 Director orientation 0 obtained from 2H NMR spectra from the polysiloxane backbone polymer with liquid-crystal side-chain 4-methoxyphenyl-4 -butenyloxybenzoate, as a function of the apparent extension rate, i. The...

The equilibrium shear modulus of two similar polyurethane elastomers is shown to depend on both the concentration of elastically active chains, vc, and topological interactions between such chains (trapped entanglements). The elastomers were carefully prepared in different ways from the same amounts of toluene-2,4-diisocyanate, a polypropylene oxide) (PPO) triol, a dihydroxy-terminated PPO, and a monohydroxy PPO in small amount. Provided the network junctions do not fluctuate significantly, the modulus of both elastomers can be expressed as c( 1 + ve/vc)RT, the average value of vth>c being 0.61. The quantity vc equals TeG ax/RT, where TeG ax is the contribution of the topological interactions to the modulus. Both vc and Te were calculated from the sol fraction and the initial formulation. Discussed briefly is the dependence of the ultimate tensile properties on extension rate. 

Data are also presented that show the dependence of the tensile strength and ultimate elongation on extension rate and temperature. In the discussion, emphasis is placed on the behavior when the stress is sensibly in equilibrium with the strain prior to fracture. 

Figure 1. Stress-time data from stress-strain curves measured in simple tension at 30°C on the LHT-240 polyurethane elastomer at seven extension rates, A from 9.4 X t° 9.4 min 1. Key 0,9, stress as a function of time ( — 1)/X, at the indicated values of strain, ( — 1).

Figure 4 shows stress-strain curves measured at an extension rate of 94% per minute on the TIPA elastomer at 30°, —30°, and —40°C. With a decrease in temperature from 30° to -40°C, the ultimate elongation increases from 170% to 600%. The modulus Ecr(l), evaluated from a one-minute stress-strain isochrone, obtained from plots like shown in Figure 1, increases from 1.29 MPa at 30°C to only 1.95 MPa at —40°C. This small increase in the modulus and the large increase in the engineering stress and elongation at fracture results from viscoelastic processes. 

Figure 4. Stress-strain curves for the TIP A polyurethane elastomer measured at the indicated temperatures at an extension rate of 0.94 min 1. Arrows indicate...

Figure 5. True stress-at-break plotted on doubly logarithmic coordinates against the strain-at-break. Conditions 30°C extension rates from 9.4 X 103 to 9.4 min 1. Quantity A introduced for clarity.

Data are presented which illustrate that the tensile strength and elongation-at-break depend significantly on the extension rate even when the stress remains in equilibrium with the strain prior to fracture. A crude estimate was made of the threshold (lowest possible) values of the true stress-at-break and the elongation-at-break for the TIPA elastomer. The estimated quantities are about 26% less than those found at an extension rate of about 0.01 min-1 at 30°C. 

However, this expression assumes that the total resistance to flow is due to the shear deformation of the fluid, as in a uniform pipe. In reality the resistance is a result of both shear and stretching (extensional) deformation as the fluid moves through the nonuniform converging-diverging flow cross section within the pores. The stretching resistance is the product of the extension (stretch) rate and the extensional viscosity. The extension rate in porous media is of the same order as the shear rate, and the extensional viscosity for a Newtonian fluid is three times the shear viscosity. Thus, in practice a value of 150-180 instead of 72 is in closer agreement with observations at low Reynolds numbers, i.e.,... 

We define the rate of reaction verbally for a species involved in a reacting system either as a reactant or as a product. The system may be single-phase or multiphase, may have fixed density or variable density as reaction proceeds, and may have uniform or varying properties (e.g., p, CA, T, P) with respect to position at any given time. The extensive rate of reaction with respect to a species A, RA, is the observed rate of formation of A ... 

Now the extension rate e in the geometry is given by the rate of change of velocity with distance ... 

Evaluating the integral and using the extension rate we obtain the following expression ... 

Figure 6.25 Plot of the normalised extensional viscosity of an 8% PVP solution with 320 mM sodium dodecyl sulphate. The data is plotted versus the reduced extension rate...

Dirac delta function in three dimensions extension rate extensional strain strain tensor (linear)... 

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