Elongational strain

Magnesium alloys have a Young s modulus of elasticity of approximately 45 GPa (6.5 x 10 psi). The modulus of rigidity or modulus of shear is 17 GPa (2.4 X 10 psi) and Poisson s ratio is 0.35. Poisson s ratio is the ratio of transverse contracting strain to the elongation strain when a rod is stretched by forces at its ends parallel to the rod s axis. 

One of the most informative properties of any material is their mechanical behavior specifically the determination of its stress-strain curve in tension (ASTM D 638). This is usually accomplished in a testing machine by measuring continuously the elongation (strain) in a test sample as it is stretched by an... 

Fig. 33. Axial velocity distribution (right scale ordinate) (------) and elongational strain...

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... 

When an electric field E is applied, Eq changes by an amount proportional to E, as usually expressed by (a — 1) E/4n, where e is the dielectric constant. When a strain is applied to the film, changes in and hence changes in polarization are divided into two components 1. displacement equal to the macroscopic displacement and 2. residual displacement. The latter is the internal strain and causes the intrinsic piezoelectricity. The effect of internal strain on P is expressed by eu, where e is the intrinsic piezoelectric constant and u is the elongational strain along the x-axis. The electric displacement D can therefore be written... 

Fig. 16. Complex electrostriction constant, k — in", for elongational strain in as-cast polyfvinylidene fluoride) film plotted against frequency (Hayakawa and...

Fig. 24. Piezoelectric stress constant of roll-drawn polyfvinylidene fluoride) films plotted against angle 0 between draw-axis and elongational strain (O) draw-ratio =2.1, ( ) draw-ratio = 1.6. Drawn after Nakamura and Wada [J. Polymer Sci. A-2,9,161 (1971)] by permission of John Wiley Sons, Inc.

As would be expected from Eq. (29) (eint=0 in this ease), the anisotropy should be ascribed to the electrostriction constant k. It should be noted that e and k in Eq. (29) refer to the elongational strain along the x-axis, Su whereas e in Fig. 24 is related to the elongational strain S in the yz-plane. If the film is assumed to be elastically isotropic,... 

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. 

Figure E7.2 compares a stepwise increase in interfacial area in simple shear flow with optimal initial orientation, and simple shear flow where, at the beginning of each step, the interfacial area element is placed 45° to the direction of shear. The figure shows that, whereas in the former case the area ratio after four shear units is 4.1, in the latter case the ratio is 6.1, with a theoretical value of 7.3 when the 45° between the plane and direction of shear is maintained at all times. We note, however, that it is quite difficult to generate steady extensional flows for times sufficiently long to attain the required total elongational strain. This is why a mixing protocol of stepwise stretching and folding (bakers transformation) is so efficient. Not only does it impose elongational stretching, but it also distributes the surface area elements over the volume.

A very important diagram for fibres and yams is the stress—strain diagram, where the specific stress is plotted as a function of the elongation (extensional strain) in %. The curve starts at an elongation of zero and ends in the breaking point at the ultimate specific stress (=tensile strength or tenacity) and the ultimate elongation (=strain at break). 

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. 

Correlation function Elongational strain Strain rate Craze strain Elastic strain Shear strain Interfacial length Extension ratio... 

The question arises as to whether intrinsic craze formation is sufficient to account for the observed plastic strain, Following the approach made by Bucknall and Clayton and Heikens et al. in their studies on multiphase systems, the totcil elongational strain, e, must be assumed to have contributions from elasticity, crazing, and shear deformation, e, . Assuming the additivity of these components gives ... 

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... 

Dynamic rheological studies can be used also to study the characteristics of solid foods. Often it is convenient to impose a sinusoidal compressive or elongational strain, so that storage and loss moduli obtained are denoted as E and E", respectively (Rao et al., 1995). 

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