Yield stress measurements

Fig. 10. Concentration dependence of a modulus in the region of low-frequency plateau (i.e. yield stress , measured by a dynamic modulus). Dispersion medium poly (butadiene) with M = 1.35 x 105 (7), silicone oil (2) polybutadiene with M = 1 x I04 (3). The points are taken from Ref. [6], The straight line through these points is drawn by the author of the present paper. In the original work the points are connected by a curve in another manner...

Interpretation of data obtained under the conditions of uniaxial extension of filled polymers presents a severe methodical problem. Calculation of viscosity of viscoelastic media during extension in general is related to certain problems caused by the necessity to separate the total deformation into elastic and plastic components [1]. The difficulties increase upon a transition to filled polymers which have a yield stress. The problem on the role and value of a yield stress, measured at uniaxial extension, was discussed above. Here we briefly regard the data concerning longitudinal viscosity. 

Lower values of the yield stress measured in tension compared to those measured in compression suggest that the effect of pressure, which is important for polymers, is not accounted for in this criterion. Hence, appropriate correction has to be made in order to account for the effect from external pressure. The most frequent version of pressure-dependent yield criterion is the modified von Mises criterion [20] ... 

Thermosets, like other amorphous polymers, can exhibit physical aging when kept at temperatures below Tg (Chapter 10). The upper yield stress measured at room temperature (below Tg) increases with prolonged aging time (Cook et al., 1999), like the modulus or the specific density. 

Dzuy, N. Q. and Boger, D. V. 1983. Yield stress measurement for concentrated suspensions. J. Rheol. 27 321-349. 

Figure 14.8 shows stress-strain curves for polycarbonate at 77 K obtained in tension and in uniaxial compression (12), where it can be seen that the yield stress differs in these two tests. In general, for polymers the compressive yield stress is higher than the tensile yield stress, as Figure 14.8 shows for polycarbonate. Also, yield stress increases significantly with hydrostatic pressure on polymers, though the Tresca and von Mises criteria predict that the yield stress measured in uniaxial tension is the same as that measured in compression. The differences observed between the behavior of polymers in uniaxial compression and in uniaxial tension are due to the fact that these materials are mostly van der Waals solids. Therefore it is not surprising that their mechanical properties are subject to hydrostatic pressure effects. It is possible to modify the yield criteria described in the previous section to take into account the pressure dependence. Thus, Xy in Eq. (14.10) can be expressed as a function of hydrostatic pressure P as... 

For the evaluation of the rheology of the silica dispersions, different test methods were applied (a) a shear rate-controlled relaxation experiment at = 0.5 s (conditioning), 500 s (shear thinning), and 0.5 s (relaxation) to evaluate the apparent viscosity, the relaxation behavior, and thixotropy (b) shear yield-stress measurements using a vane technique introduced by Nguyen and Boger [5] (c) low deformation dynamic tests at a constant frequency of 1.6 s in a stress range of ca. 0.5 - 100 Pa. All samples contained 3 wt% of fumed silica. 

Yanez, J.A. etal.. Shear modulus and yield stress measurements of attractive alumina particle networks in aqueous slurries, 7. Am. Ceram. Soc., 19, 2917, 1996. 

Figure 4.4. The vane-rheometer configuration used for direct yield-stress measurements. Reprinted from Figure 9.9 (Collyer and Clegg, 1988).

The measurement of yield stress at low shear rates may be necessary for highly filled resins. Doraiswamy et al. (1991) developed the modified Cox-Merz rule and a viscosity model for concentrated suspensions and other materials that exhibit yield stresses. Barnes and Camali (1990) measured yield stress in a Carboxymethylcellulose (CMC) solution and a clay suspension via the use of a vane rheometer, which is treated as a cylindrical bob to monitor steady-shear stress as a function of shear rate. The effects of yield stresses on the rheology of filled polymer systems have been discussed in detail by Metzner (1985) and Malkin and Kulichikin (1991). The appearance of yield stresses in filled thermosets has not been studied extensively. A summary of yield-stress measurements is included in Table 4.6. 

Yield Stress Measurement. The foundations of the rheological treatment to fluids exhibiting a yield stress are due to Bingham (5). Under steady flow conditions, it is common to neglect the contribution from elastic deformation and to use the term Bingham fluid response. Normally, the Herschel-Bulkley equation 9 is used to characterize the flow. 

Run Speed is the motor speed for the YR-1 at which the material is tested. Choices range from 0.01-5.0 rpm. It is common for materials to appear stiffer when tested at higher speeds. That is, the slope of the torque-versus-time or stress-versus-strain curve increases with increasing speed. This is because the material structure has less time in which to react to dissipate the applied stress. Increasing the speed will, in most cases, increase the yield stress measured by the instrument. Most yield tests are conducted at relatively low speeds (<1 rpm) to minimize any inertial effects when using vane spindles. 

Nguyen, Q.D. Boger. D.V. Direct yield stress measurement with the Vane method. J, Rheol.. 29(3) 335-347. 1984. 

The latter procedure is an adaptation of that usually employed to generate creep compliance data a creep yield stress is determined by extrapolating creep-rate data to zero rate, with the corresponding value of applied stress being taken as the yield stress [Lohnes etal., 1972], In addition to its use in yield stress measurement, the vane has foimd application as the basis of... 

Yield stress measurements were made at 20 C on three pofypro-pylene materials, each containing different volume fractions of rubber particles. Table 5.1 gives values of yield stress as a function of e and <. Calculate V for each pofymer, and suggest why V varies with 4>. 

The above equations are deduced assuming the existence of dislocation activity. Although dislocation activity has been shovm in YTZP [17, 63, 64], this is likely to be an artifact (for details, see Section 15.3.1). Recently, superplastically deformed nano-MgO with grain size of 37 nm has been reported to deform at temperatures between 700 and 800 °C, and the stress exponent results in a value of 2. Dislocation activation in this system with this grain size requires an applied compressive stress in excess of 3 GPa. Such calculated stresses are far higher than the yield stresses measured experimentally (i.e., 190 to 640 MPa) [79]. 

Conservation modulus measured at 25 °C and 1 Hz Compressive yield stress measured at a strain rate of 2 x 10 s ... 

Barnes is a leading proponent of the idea that the yield stress is not a material property. Yield stress measurement is addressed in... 

The values of apparent yield stresses measured for different sorts of liquidlike foods range over the following values. 

The above analysis was repeated for the samples made with 3350 and 8000 MW PEG binders. The effect of the molecular weight of the PEG binder on the measured yield stress is shown in Fig. 6. This represents an example of the kind of trend that can be elucidated using the compaction curve method. In this case, the yield stress of the agglomerate samples shows an apparent power-law trend with the molecular weight of the PEG binder. The Kawakita method show a similar power-law trend, with the value of the Kawakita stress consistently 2-3x the apparent yield stress measured by compaction curve onset analysis. 

The efficacy of the PE-PEP diblock additives at preventing the formation of waxy gels in oil upon cooling below the wax solubility limit was studied by yield stress measurements in parallel with optical microscopy observations [15]. The effect of a lowMw diblock (1.5-5 K) on the yielding properties of waxy gels at a 4% wax level at 0 °C is shown in Fig. 31 for the different wax molecules considered. All gels display similar behavior with increasing additive concentration. At low polymer addition, the yield stresses of the gel drop... 

Usually, experiments and numerical simulations are rather complementary and it may be difficult to make meaningful comparisons. Nevertheless, there are two cases where this can be done. The first one is related to the mobility of non-dissociated dislocations. The computed Peierls stress for the non-dissociated shuffle screw dislocation is 4 GPa, in good agreement with the order of magnitude of the extrapolation at OK of flow stress measurements below 300°C (Section 2.3.2). In addition, the extrapolation at OK of yield stress measurements performed in the medium temperature range fits quite well the computed values of the Peierls stress for glide dislocations. Numerical simulations revealed that the thermally activated motion of non-dissociated screw dislocations was possible at 300 °C under an applied stress of 1.5 GPa, as reported from yield stress measurements (Section 2.3.2). The second case concerns the nucleation of dislocations. Molecular dynamics simulations of the dislocation nucleation from surface steps... 

The yield stress measures the maximum stress that can be stored in the system before yielding (diamond symbol in Fig. 3). 

Hence the shear yield stress is predicted to be 1/V3 times the tensile yield stress. This should be compared with the Tresca criterion which predicts that the shear yield stress is cr /2. On the other hand, it can be readily seen that both criteria predict that the yield stresses measured in uniaxial tension and compression will be equal. 

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