Yield shear experiment

Rheology has also been used to locate sol-gel transitions in concentrated block copolymer solutions, as described in Chapter 4. Gels exhibit a finite yield stress (i.e. they are Bingham fluids), which can be measured in steady shear experiments. 

Table 12 Worked example E5 Shearing stresses in internal yield loci experiments...

Commonly, the thickening of liquids by hydrophilic silica is explained by the formation of H-bonds between the silanol groups of silica particles [6]. According to this model, the stability of silica gels in styrene and toluene, two fluids with comparable dielectrical properties, should be more or less identical. Figure 2 depicts the shear yield-stress experiments using the vane geometry of HDK N20 in styrene and toluene. 

Alternatively, from steady shearing experiments, which yield rio directly in the limit of low shear rate, the steady-state recoverable compliance can be obtained from the first normal stress coefficient, which is the ratio of the first normal stress difference to the square of the shear rate, measured at low shear rate... 

The two yield criteria can also be normalised to agree for a shear experiment with (T2 = In this case, the von Mises ellipse is completely enclosed by the Tresca hexagon and touches it at the six linear sections. 

The situation is more complex for rigid media (solids and glasses) and more complex fluids that is, for most materials. These materials have finite yield strengths, support shears and may be anisotropic. As samples, they usually do not relax to hydrostatic equilibrium during an experiment, even when surrounded by a hydrostatic pressure medium. For these materials, P should be replaced by a stress tensor, <3-j, and the appropriate thermodynamic equations are more complex. 

Returning to the Maxwell element, suppose we rapidly deform the system to some state of strain and secure it in such a way that it retains the initial deformation. Because the material possesses the capability to flow, some internal relaxation will occur such that less force will be required with the passage of time to sustain the deformation. Our goal with the Maxwell model is to calculate how the stress varies with time, or, expressing the stress relative to the constant strain, to describe the time-dependent modulus. Such an experiment can readily be performed on a polymer sample, the results yielding a time-dependent stress relaxation modulus. In principle, the experiment could be conducted in either a tensile or shear mode measuring E(t) or G(t), respectively. We shall discuss the Maxwell model in terms of shear. 

The square root of viscosity is plotted against the reciprocal of the square root of shear rate (Fig. 3). The square of the slope is Tq, the yield stress the square of the intercept is, the viscosity at infinite shear rate. No material actually experiences an infinite shear rate, but is a good representation of the condition where all rheological stmcture has been broken down. The Casson yield stress Tq is somewhat different from the yield stress discussed earlier in that there may or may not be an intercept on the shear stress—shear rate curve for the material. If there is an intercept, then the Casson yield stress is quite close to that value. If there is no intercept, but the material is shear thinning, a Casson plot gives a value for Tq that is indicative of the degree of shear thinning. 

This line represents the critical shear stress that a powder can withstand which has not been over or underconsolidated, i.e., the stress typically experienced by a powder which is in a constant state of shear, when sheared powders also experience fiiciion along a wall, this relationship is described by the wall yield locus, or... 

Accordingly, the activation volume v can be determined from yield experiments performed at various shear rates. 

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. 

Application of both approaches to describe simple elongation experiments yields that either theory predicts the so-called reduced stress a to be equal to the shear modulus G and to be independent of strain. 

The Bingham yield value, xft, was obtained by extrapolating the linear portion of the curve to zero shear rate. In these experiments, a 25% w/w latex B was used, where the particles were fully coated with PVA, and results were obtained as a function of Na2S04 concentration at constant temperature (20+l°C) or as a function of temperature at a constant Na2S0 ... 

The transition from ideal elastic to plastic behaviour is described by the change in relaxation time as shown by the stress relaxation in Fig. 66. The immediate or plastic decrease of the stress after an initial stress cr0 is described by a relaxation time equal to zero, whereas a pure elastic response corresponds with an infinite relaxation time. The relaxation time becomes suddenly very short as the shear stress increases to a value equal to ry. Thus, in an experiment at a constant stress rate, all transitions occur almost immediately at the shear yield stress. This critical behaviour closely resembles the ideal plastic behaviour. This can be expected for a polymer well below the glass transition temperature where the mobility of the chains is low. At a high temperature the transition is a... 

The experiment here is a small rapid shear-strain at time zero - after this the shear stress in a viscoelastic liquid will not vanish instantaneously, but decay as a characteristic function with time. When normalised by the strain to yield the dimensions of modulus, this is G(f). 

While the surface modification is not effective to suppress cavitation, Yee and coworkers performed an experiment to suppress the cavitation mechanically in a rubber-modified epoxy network. They applied hydrostatic pressure during mechanical testing of rubber toughened epoxies [160]. At pressures above BOSS MPa the rubber particles are unable to cavitate and consequently no massive shear yielding is observed, resulting in poor mechanical properties just like with the unmodified matrix. These experiments proved that cavitation is a necessary condition for effective toughening. 

The non-aqueous HIPEs showed similar properties to their water-containing counterparts. Examination by optical microscopy revealed a polyhedral, poly-disperse microstructure. Rheological experiments indicated typical shear rate vs. shear stress behaviour for a pseudo-plastic material, with a yield stress in evidence. The yield value was seen to increase sharply with increasing dispersed phase volume fraction, above about 96%. Finally, addition of water to the continuous phase was studied. This caused a decrease in the rate of decay of the emulsion yield stress over a period of time, and an increase in stability. The added water increased the strength of the interfacial film, providing a more efficient barrier to coalescence. 

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