Yield stress dynamic

Here the fitting parameters are the slope of the line (the plastic viscosity, rip) and the Bingham or dynamic yield stress (the intercept, constitutive equations will be introduced later in this volume as appropriate. 

It is important when using the term yield stress to distinguish between an extrapolated value, sometimes called the dynamic yield stress and a true or static yield stress . The latter can only be observed for plastic solids whilst the former is readily obtained with pseudoplastic liquids. In practical terms this can be critical in evaluating the performance of a material. 

The dynamic yield stress (extrapolated to zero shear rates, Figure 8.15) becomes greater with stronger field, indicating the increase of attractive forces between the polarized particles with applied electric field. This phenomenon is attributed to columnar or fibrillar structure formed by the particles as a response to electrostatic interactions induced by electric field. The stronger the field, the larger shear rate is needed to destroy the structure. 

Beside the strength of electric field, the dynamic yield stress significantly depends on the amount of MWCNT in the composite particles. As can be seen in Figure 8.15, for different field strength the yield stress goes up with rising concentration in different ways. While for 1 and 2 kV/mm, it continuously increases with nanotubes content, at 3 kV/mm a saturation effect can be observed. The presence of MWCNT enhances the conductivity of the composite particles and thus influences their ability to be polarized. If the conductivity of the particles is above a certain limit, the current density in the... 

Figure 3-12 Illustration of Static and Dynamic Yield Stress (Keentok, 1982).

The structure of the food sample would be disturbed considerably during the determination of Apminj so that the measured yield stress would be closer to the dynamic yield stress than the static yield stress (Figure 3-10). In contrast, in the vane method for determination of yield stress both the static and dynamic yield stresses can be determined. 

Figure 4-26 Static (-S) and Dynamic (-D) Yield Stress Values of Cross-Linked Waxy Maize (CWM), Tapioca, and Amioca 5% (w/w) Starch Dispersions at Different Shear Rates. Filled symbols are values of static yield stress (aps) open symbols are values of dynamic yield stress (oqj).

Klingenberg et al. (1991a) find in their simulations a dependence of the dynamic yield stress on particle volume fraction 0 that is in qualitative agreement with experiment (see Fig. 8-7). Note that in both experiments and simulation, Oy is roughly linear in 0 for 0 0.30. 

Foams usually possess a finite low-frequency elastic modulus, along with static and dynamic yield stresses. These and other aspects of foam flow and rheology can be captured qualitatively and even semiquantitatively by cellular foam models. 

An example of such a flow curve is presented in Fig. 6, and viscosity as a function of shear strain rate is depicted in Fig. 7. Many pharmaceutical ointments and creams show a similar shape of the flow curve with an extended upper Newtonian region. In these cases, an extrapolation of the linear portion of the flow curve to zero shear strain rate in order to obtain a dynamic yield stress is often utilized.l ... 

Dynamic yield stress of a shear molten glass... 

Because the recent experiments and simulations reviewed here concentrated on the universal aspects of the novel non-equilibrium transition, focus will be laid on the MCT-ITT approach. Reassuringly, however, many similarities between the MCT-ITT equations and the results by Miyazaki and Relchman exist, even though these authors used a different, field theoretic approach to derive their results. This supports the robustness of the mechanism of shear-advection in (7) entering the MCT vertices in (lid, 14), which were derived independently in [40, 41] and [43 5] from quite different theoretical routes. This mechanism had been known from earlier work on the dynamics of critical fluctuations in sheared systems close to phase transition points [61], on current fluctuations in simple liquids [62], and on incoherent density fluctuations in dilute solutions [63], Different possibilities also exist to include shear into MCT-inspired approaches, especially the one worked out by Schweizer and coworkers including strain into an effective free energy [42]. This approach does not recover the (idealized) MCT results reviewed below but starts from the extended MCT where no true glass transition exists and describes a crossover scenario without, e.g., a true dynamic yield stress as discussed below. 

Enforcing steady shear flow melts the glass. The stationary stress of the shear-molten glass always exceeds a (dynamic) yield stress. For decreasing shear rate, the viscosity increases like 1 /y, and the stress levels off onto the yield-stress plateau, cr(y 0,e > 0) c7+(e). 

The existence of a dynamic yield stress in the glass phase is thus seen to arise from... 

Fig. 24 Flow curves O ( ) ) reaching from the supercooled to the glassy state of a simulated binary LJ mixture. The data points correspond to the temperatures T = 0.525,0.5, 0.45,0.44,0.43,0.42,0.4,0.38,0.3,0.2, and 0.01 in LJ-units (from bottom to top). Fj -model curves fitted by eye are included as lines. The inset shows the relation between the fitted separation parameters and temperature. Units are converted by cr =1.5c7(heo and y = 1.3ytheoT from [92]. The arrows mark the values of the extrapolated dynamic yield stresses C7 (fi)...

Fig. 25 Dynamic yield stress estimated from the simulations of a supercooled binary LJ mixture under steady shear shown in Fig. 24, and its temperature dependence (in LJ units) from [81]. The estimate uses the stress values for the two lowest simulated shear rates, namely / = 10 (triangle) and y = 3 x 10 (circle)-, the extrapolation with the F -model is shown by diamonds. At temperatures below T = 0.38. (almost) the same shear stress is obtained for both values of y and the extrapolation, indicating the presence of a yield stress plateau...

The system shows a (dynamic) yield stress cr that can be obtained by extrapolation to zero shear rate [8]. Clearly, at and below cr the viscosity ri-roo. The slope of the hnear curve gives the plastic viscosity ri i- Some systems, such as clay suspensions, may show a yield stress above a certain clay concentration. 

Leonov [1994] introduced kinetics of interactions into his rheological equation of state. The new relation can describe systems with a dynamic yield stress, without resorting to a priori introducing the yield stress as a model parameter (as it has been done in earlier models). 

Figure 7 Schematic flow curve of a c( np]ex vbicoplastic fluid dbplaying a static and a dynamic yield stress.

Simulations of this type can pinpoint an elastic limit where the first (or subsequent) T1 transition(s) take(s) place. It depends extremely strongly on orientation, as does the dynamic yield stress , i.e., the stress integrated over a complete strain cycle. The relevance to die yield stress of real disordered systems is, therefore, quite limited (98). As in 2-D simulations, simulations on more highly disordered systems will undoubtedly bring increased insight. 

With the geometrical details of the specimens, including the initial crack length a, the physical crack length augmented to account for crack tip plastic deformation (the fracture mirror length) aBs> the dynamic yield stress o-y and the dynamic flexural modulus E, the fracture mechanics parameters Ki, Ju and can be calculated [OlGre]. 

Figure 14.4 The dependence of the dynamic yield stress on the relative particle conductivity r(=0p/o ) at various electric field strengths. Ortho-phosphoric acid (solid symbols), tetrafluoroboric acid (open symbols), and original PANl base (divided symbols). Electric field strength E (kV mm ) 0, o 0.5, A A l.O.TV 1.5, 0 2.0, 2.5,...

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