Elongational strain rate

Fig. 52. Degradation yield as a function of strain-rate e(0) and solvent viscosity (e(0) maximum elongational strain-rate along the centerline) Except for the high MW series, all the data refer to the same PS fraction with Mw = 1.03 x 106, Mw/M = 1.017 ...

Fig. 57. Entrance elongational strain rate (e ) calculated along the centerline of the flow tube for the different nozzle geometries (the origin of the abscissa is taken at the orifice entrance) (-----) abrupt contraction (-----) 14° conical inlet (---) 5° conical inlet...

Consider a stream of liquid that is subject to a purely elongational flow in the x-direction. The elongational rate of strain may be defined as the velocity gradient in the direction of flow, ie dvjdx. Now consider the case in which the elongational strain rate is constant ... 

Quotient of the difference between the longitudinal stress (cth) and the lateral stress (ctzi) and the elongational strain rate ( ) in steady uniaxial flow... 

With the average elongational strain rate of the flow field between the eddies and the relaxation time of the polymer molecules, one can define a dimensionless characteristic number, the Deborah number, which represents the ratio of a characteristic time of flow and a characteristic time of the polymer molecule, and thus one can transfer considerations in porous media flow to the turbulent flow region. 

PS, and in the range 142-155 °C for PC. The following mechanical test has been adopted the specimens are stretched at constant elongational strain rate (0.05 s l for PS and 0.025 s l for PC) up to a final extension ratio L/Lq close to 2.5 for all of the samples. The stress is then allowed to relax at constant deformation. 

In Fig. 18 are presented the results obtained for generalized Oldroyd-B and multimode PTT simulations (see Chapter III-2). It can be seen that, in this transient elongational situation at high strain rate (the elongational strain rate can reach approximately 120 s l), the proportionality between birefringence and stress difference is only valid up to 0.2 MPa. 

Consider now a polymer sample of current volume V responding by craze plasticity to an imposed current elongational strain rate e, developing a tensile (dilatational) flow resistance until a final fracture strain is achieved as shown in Fig. 1. The specific toughness W or the total deformational energy absorbed per unit volume for this polymer is the area under the stress strain curve, or... 

From the above equations it can be seen that orientation increases with aspect ratio and elongational strain rate. 

Figure 9.11 shows that the average angle a of whiskers decreases with the elongational strain rate, Figure 9.12 shows the effect of the aspect ratio of ferrite on the apparent permeability of a composite. Both sets of experimental data are consistent with the model. The orientation of fiber increases with the elongational strain rate and fiber aspect ratio. 

Figure 9.11. The average polar angle, a vs, elongational strain rate, e. [Data from Kobayashi M, Takahashi T, Takimoto J, Koyania K, Polymer, 36, No.20, 1995, 3927-33.]...

Much of the work done in recent years on polymer mechanochemistry has made use of the high elongational strain rates observed around collapsing cavitation bubbles in sonicated solutions, as outlined in the section on mechanoluminescence [27]. In addition to the distinctive features of sonochemically-induced mechanical reactivity described above, further attention needs to be paid to the sonication conditions in the case of mechanochemical catalysis, because catalyst lifetime and turnover number are reduced by sonochemical byproducts. Implosion of cavitation bubbles is essentially an adiabatic process which leads to formation of local hotspots within the bubble in which temperature and pressure increases drastically. The content of cavitation bubbles pyrolyses under these extreme conditions and results in formation of reactive species, such as radicals and persistent secondary byproducts acidic byproducts may also form from the degradation of the substrates [75]. Chemical impurities deactivate the reactive catalyst partially if not completely. Recent studies in our group have shown that heat capacity of gas... 

Ishizuka, O., and K. Koyama. 1980. Elongational viscosity at a constant elongational strain rate of polypropylene melt. Polymer 21 164-170. 

If the practical tensile strain is defined as e = L/Lo 1. where L and Lq are the stretched and unstretched lengths respectively, the practical tensile strain rate is (1 /Lo)dL/dt (cf. equation 60 of Chapter 3), and a constant e can be achieved by pulling the clamps apart at a constant rate. However, if the elongational strain rate is defined as the ratio of the velocity of a material point to its displacement, this quantity, denoted ci, is ( /L)dL/dt and it will remain constant only if the clamps are pulled apart at a rate which increases exponentially with time. Several instruments which accomplish this have been described. oo-io2a Qf... 

When the elongational strain rate e becomes larger than a critical value (e ), the crystallization behavior, structure, and physical properties change discontinu-ously. In the case of s larger than e, we obtain a morphology we call nano-oriented crystals (NOCs). The NOCs show high crystallinity (nearly equal to unity) and ultrahigh performance. 

---