Yield stress function

Figure 31 Yield stress function Y(0) = XQR320 0 vs. O for typical polydisperse emulsions. Solid points are experi-mental data curve is drawn according to Eq. (89). (From Ref. 126, with permission from Academic Press.)...

Colloidal dispersions often display non-Newtonian behaviour, where the proportionality in equation (02.6.2) does not hold. This is particularly important for concentrated dispersions, which tend to be used in practice. Equation (02.6.2) can be used to define an apparent viscosity, happ, at a given shear rate. If q pp decreases witli increasing shear rate, tire dispersion is called shear tliinning (pseudoplastic) if it increases, tliis is known as shear tliickening (dilatant). The latter behaviour is typical of concentrated suspensions. If a finite shear stress has to be applied before tire suspension begins to flow, tliis is known as tire yield stress. The apparent viscosity may also change as a function of time, upon application of a fixed shear rate, related to tire fonnation or breakup of particle networks. Thixotropic dispersions show a decrease in q, pp with time, whereas an increase witli time is called rheopexy. 

Fig. 2. Yield stress as a function of temperature for NiAl, Ni Al, and several commercial superaUoys where <001> is the paraHel-to-tensile axis for single crystals and (° ) are data points for NiAl + (2). See text. To convert MPa to psi, multiply by 145.

Whereas a linear relation between flow stress and lattice-parameter change is obeyed for any single solute element in nickel, the change in yield stress for various solutes in nickel is not a single-valued function of the lattice parameter, but depends directly on the position of the solute in the Periodic Table... 

For a Hquid under shear the rate of deformation or shear rate is a function of the shearing stress. The original exposition of this relationship is Newton s law, which states that the ratio of the stress to the shear rate is a constant, ie, the viscosity. Under Newton s law, viscosity is independent of shear rate. This is tme for ideal or Newtonian Hquids, but the viscosities of many Hquids, particularly a number of those of interest to industry, are not independent of shear rate. These non-Newtonian Hquids may be classified according to their viscosity behavior as a function of shear rate. Many exhibit shear thinning, whereas others give shear thickening. Some Hquids at rest appear to behave like soHds until the shear stress exceeds a certain value, called the yield stress, after which they flow readily. 

A powder s strength increases significantly with increasing previous compaction. The relationship between the unconfined yield stress/, or a powder s strength, and compaction pressure is described by the powder s flow function FE The flow function is the paramount characterization of powder strength and flow properties, and it is calculated from the yield loci determined from shear cell measurements. [Jenike, Storage and Flow of Solids, Univ. of Utah, Eng. Exp. Station Bulletin, no. 123, November (1964). See also Sec. 21 on storage bins, silos, and hoppers.]... 

In an ideal fluid, the stresses are isotropic. There is no strength, so there are no shear stresses the normal stress and lateral stresses are equal and are identical to the pressure. On the other hand, a solid with strength can support shear stresses. However, when the applied stress greatly exceeds the yield stress of a solid, its behavior can be approximated by that of a fluid because the fractional deviations from stress isotropy are small. Under these conditions, the solid is considered to be hydrodynamic. In the absence of rate-dependent behavior such as viscous relaxation or heat conduction, the equation of state of an isotropic fluid or hydrodynamic solid can be expressed in terms of specific internal energy as a function of pressure and specific volume E(P, V). A familiar equation of state is that for an ideal gas... 

Figure 7.3. Dislocation densities required to fit the precursor curves as a function of the initial quasi-static yield stress.

How does yield stress depend on a filler concentration It is shown in Fig. 9 that appreciable values of Y appear beginning from a certain critical concentration cp and then increase rather sharply. Though the existence of cp seems to be quite obvious from the view point of the possibility of contacts of the filler, i.e. the beginning of a netformation in the system, practically the problem turns on the accuracy of measuring small stresses in high-viscosity media. It is quite possible to represent the Y(cp) dependence by exponential law, as follows from Fig. 10, for example, leaving aside the problem of the behavior of this function at very low concentrations of the filler, all the more the small values of are measured with a significant part of uncertainty. 

Though due to the fact that it is difficult to interprete amplitude dependence of the elastic modulus and to unreliable extrapolation to zero amplitude, the treatment of the data of dynamic measurements requires a special caution, nevertheless simplicity of dynamic measurements calls attention. Therefore it is important to find an adequate interpretation of the obtained results. Even if we think that we have managed to measure correctly the dependences G ( ) and G"( ), as we have spoken above, the treatment of a peculiar behavior of the G (to) dependence in the region of low frequencies (Fig. 5) as a yield stress is debatable. But since such an unusual behavior of dynamic functions is observed, a molecular mechanism corresponding to it must be established. 

There is evidence to suggest that the yield stress of thin hlms grows with the time of experiments, over a remarkably long duration—minutes to hours, depending on the liquid involved. Figure 9 gives the critical shear stress of OMCTS, measured by Alsten and Granick [26], as a function of experiment time. The yield stress on the hrst measurement was 3.5 MPa, comparable to the result presented in Ref. [8], but this value nearly tripled over a 10-min interval and then became stabilized as the time went on. This observation provides a possible explanation for the phenomenon that static friction increases with contact time. 

During the creep of PET and PpPTA fibres it has been observed that the sonic compliance decreases linearly with the creep strain, implying that the orientation distribution contracts [ 56,57]. Thus, the rotation of the chain axes during creep is caused by viscoelastic shear deformation. Hence, for a creep stress larger than the yield stress, Oy,the orientation angle is a decreasing function of the time. Consequently, we can write for the viscoelastic extension of the fibre... 

Structural dements resist blast loads by developing an internal resistance based on material stress and section properties. To design or analyze the response of an element it is necessary to determine the relationship between resistance and deflection. In flexural response, stress rises in direct proportion to strain in the member. Because resistance is also a function of material stress, it also rises in proportion to strain. After the stress in the outer fibers reaches the yield limit, (lie relationship between stress and strain, and thus resistance, becomes nonlinear. As the outer fibers of the member continue to yield, stress in the interior of the section also begins to yield and a plastic hinge is formed at the locations of maximum moment in the member. If premature buckling is prevented, deformation continues as llic member absorbs load until rupture strains arc achieved. 

Figure 6.11 The Bingham yield stress as a function of volume fraction for the system with the potential shown in Figure 5.9...

From dimensional considerations, the drag coefficient is a function of the Reynolds number for the flow relative to the particle, the exponent, nm, and the so-called Bingham number Bi which is proportional to the ratio of the yield stress to the viscous stress attributable to the settling of the sphere. Thus ... 

A unified approach to the glass transition, viscoelastic response and yield behavior of crosslinking systems is presented by extending our statistical mechanical theory of physical aging. We have (1) explained the transition of a WLF dependence to an Arrhenius temperature dependence of the relaxation time in the vicinity of Tg, (2) derived the empirical Nielson equation for Tg, and (3) determined the Chasset and Thirion exponent (m) as a function of cross-link density instead of as a constant reported by others. In addition, the effect of crosslinks on yield stress is analyzed and compared with other kinetic effects — physical aging and strain rate. 

The isochronous stress-strain curves for the creep of PP bead foams (254) were analysed to determine the effective cell gas pressure po and initial yield stress do as a function of time under load (Figure 11). po falls below atmospheric pressure after 100 second, and majority of the cell air is lost between 100 and 10,000 s. Air loss is more rapid than in extruded PP foams, because of the small bead size and the open channels at the bead boundaries, do reduces rapidly at short yield times <1 second, due to proximity of the glass transition, and continues to fall at long times. 

The cohesion of the concrete will be a function of the yield stress of the cement paste. 

Stress/strain behaviour in the elastic region, i.e. below the yield stress, as a function of volume fraction, 4>, contact angle, 0, and film thickness, h, was examined [51]. The yield stress, t , and shear modulus, G, were both found to be directly proportional to the interfacial tension and inversely proportional to the droplet radius. The yield stress was found to increase sharply with increasing <(>, and usually with increasing 6. A finite film thickness also had the tendency to increase the yield stress. These effects are due to the resulting increase in droplet deformation which induces a higher resistance to flow, as the droplets cannot easily slip past one another. 

Shear stress (F/A), lb.p/sq. ft. t refers to the shear stress at the wall of a round pipe (DAP/ 4L) and r< to the shear stress at the wall of a viscometer bob Yield value or yield stress of a Bingham-plastic fluid, lb.F/sq. ft. Indicator of an unspecified functional relationship... 

Z3. PMDA-ODA on MgO. PMDA-ODA peel force data shown in Fig. 7 exhibit a very interesting phenomenon as a function of T H exposure. The peel force is significantly increased as the time in T H is increased. This is somewhat unusual, but apparently repeatable. The exposure to APS has not made much difference in the results, which is understandable from the initial surface analyses after IPA cleaning and APS exposure. The XPS data show no detectable amount of APS on the thus exposed MgO surface. The reasons for the peel force increase as a function of T H exposure are not clear at this time. This is, however, due to increased interfacial strength, and not due to the polyimide mechanical properties (Young s modulus and yield stress) changes. If the latter were the case, then we should see similar effects also in the first two cases, which is not seen. However, more detailed analysis is essential to clarify the exact mechanism and this observation merits further study. 

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