Stretching velocity

Several generalizations of the inelastic theory to large deformations are developed in Section 5.4. In one the stretching (velocity strain) tensor is substituted for the strain rate. In order to make the resulting constitutive equations objective, i.e., invariant to relative rotation between the material and the coordinate frame, the stress rate must be replaced by one of a class of indifferent (objective) stress rates, and the moduli and elastic limit functions must be isotropic. In the elastic case, the constitutive equations reduce to the equation of hypoelastidty. The corresponding inelastic equations are therefore termed hypoinelastic. 

Fig. 23a. Stress-strain-diagram of a Polyethylene (Vestolen A 6042) film (stretching velocity 0,26 mm/s) b) Experimental (row I), synthesized (row II), and resolved (row III) bands of the CHj-rocking bands. The experimental spectra were scanned at the indicated positions (circled numbers) of the stress-strain-diagram (a).

Fig. 24. Dichroic ratios (A /A X) and stress (a) as function of strain (e) (stretching velocity 0.008 mm/s.x CH2-rocking band (BJp) between 736 and 726 cm"1, V CH2-rocking band (B2)j) between 726 and 710 cm"1, + stress-strain-diagram.

A piston driven stretching device has been developed by Koch et al. Stretching occurred in a fraction of a second. The sample can be heated by a stream of hot air. For stretching velocities up to 0.75 mm s , a stretching device has been developed by Holland Moritz and Stach which can also be used for real time fourier transformed infrared (FTIR) experiments. Both the force and elongation are transferred to a PDF 11/24 computer by a CAMAC based voltage/frequency converter (Fig. 31). 

The stretch induced transformation of initially unoriented orthorhombic polyethylene (Vestolen A) into the monoclinic modification was studied by Heise, Riekel and Stach for stretching velocities down to 0.26 mm s"T The coexistence of both modifications and the formation of two domains of monoclinic material was established by the Vidicon detector. 

To which extent metal is degraded by hydrogen is influenced by strain (tension, frequency, stretch velocity), specimen geometry (notches, bad welds, geometric inhomogeneities), the medium (pressure variation, temperature, impurities), and material (chemical composition, fabrication, heat treatment, welding joints) [67]. 

Fig. 4.41 Force-elongation curves of the radial and spiral threads prepared from an Argiope bruennuichii spider with a weight of 0.949 g. Stretching velocity 3.3 X10 m/s.

Fig. 4.49 Stress-strain curve of a dragline secreted from a N. clavata spider with a weight of 471 mg, at a stretching velocity of 3.3X10" m/s. Elastic limit stress (ELS) and elastic limit strain (ELN) are defined, respectively, as the stress and the strain at which the stress-strain curve shifts from the linear to the nonlinear region.

Fig. 4.50 Relationship between the elastic limit strength (ES) and stretching velocity (V) for draglines secreted from N. clavata spiders of different weights.

Stretching velocity of 3.3x10 m/s was plotted against spider weight W in Fig. 4.51. The ES, defined as the mechanical strength at the elastic limit point, increased linearly with increasing W. Experimentally, we may express ES as... 

Fig. 4.51 ES at a stretching velocity of 3.3 X 10 m/s for a M clavata spider s dragline is plotted against the spider s weight (W). The spider s weight is more than 50 mg.

The relationship between BS and W was examined for N. clavata spider draglines at a stretching velocity of 3.3 x 10 m/s. The breaking strength also increased linearly with increasing weight, with the slope determined to be near 6. The relationship between the BS and W was found to be expressed by the following empirical equation ... 

The most probable desorption force at a given stretching velocity, which is obtained from the histogram of desorption force, is about 41 pN, as shown in Fig. 30.10b. Such a distribution varies with the stretching velocity. The linear dependence of the most probable desorption force on the... 

PAMPS and its random copolymer containing 18-crown-6 (PAMPS -co-crown), are used to further study the nonelectrostatic contribution to desorption force [56]. The primary structures of polymers are shown in Scheme 30.5. As shown in Fig. 30.12, the typical force curves of PAMPS with a plateau are obtained from amino-modified quartz in the buffer of water. The long plateau suggests that the desorption process of the PAMPS chain from the substrate is smooth and that it adopts a train-like conformation at the interface and the desorption force remains about 120 pN. The desorption-adsorption process is in equilibrium in the experimental time scale, which is confirmed by the constant desorption force when changing the stretching velocity. The desorption force of PAMPS from the amino-modified quartz has been... 

FIGURE 30.10. (a) Statistics of the distance between two adjacent peaks in the measured force curves, (b) Distribution of the measured desorption force for linear PNIPAM-seg-PS chains adsorbed on hydrophobic polystyrene substrate, where the stretching velocity is kept at 4,600 nm/s. Reproduced from Macromolecules (2003) with permission from American Chemical Society [50]. 

Fig. 6.3. Dichroic ratios and stress as functions of strain and time (stretching velocity) for polyethylene for the CH2 rocking modes at 730cm (x) and 720 cm ( ). The stress-strain diagram is given by ( ). From K. Holland-Mortiz and K. van Werden, Makromol. Chem., 182 (1981), 651. (Reproduced with permission. Copyright 1981 Hiithig Wepf Verlag.)...

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