Static Yield Stress

Figure 6.8. Plot of the quasi-static reloaded yield stress of shock-loaded copper versus the natural logarithm of residual strain for a 10 GPa symmetric shock with 1 /is pulse duration.

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

Linear viscoelasticity Linear viscoelastic theory and its application to static stress analysis is now developed. According to this theory, material is linearly viscoelastic if, when it is stressed below some limiting stress (about half the short-time yield stress), small strains are at any time almost linearly proportional to the imposed stresses. Portions of the creep data typify such behavior and furnish the basis for fairly accurate predictions concerning the deformation of plastics when subjected to loads over long periods of time. It should be noted that linear behavior, as defined, does not always persist throughout the time span over which the data are acquired i.e., the theory is not valid in nonlinear regions and other prediction methods must be used in such cases. 

Microindentation hardness normally is measured by static penetration of the specimen with a standard indenter at a known force. After loading with a sharp indenter a residual surface impression is left on the flat test specimen. An adequate measure of the material hardness may be computed by dividing the peak contact load, P, by the projected area of impression1. The hardness, so defined, may be considered as an indicator of the irreversible deformation processes which characterize the material. The strain boundaries for plastic deformation, below the indenter are sensibly dependent, as we shall show below, on microstructural factors (crystal size and perfection, degree of crystallinity, etc). Indentation during a hardness test deforms only a small volumen element of the specimen (V 1011 nm3) (non destructive test). The rest acts as a constraint. Thus the contact stress between the indenter and the specimen is much greater than the compressive yield stress of the specimen (a factor of 3 higher). 

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. 

By equating the vertical component of the yield stress over the surface of the sphere to the weight of the particle, a critical value of = 0.17 is obtained (Chhabra, 1992). Experimentally, however, the results appear to fall into groups one for which F(i fa 0.2 and one for which F(i fa 0.04—0.08. There seems to be no consensus as to the correct value, and the difference may well be due to the fact that the yield stress is not an unambiguous empirical parameter, inasmuch as values determined from static measurements can differ significantly from the values determined from dynamic measurements. 

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. 

By virtue of its yield stress, an unsheared viscoelastic material is capable of supporting the immersed weight of a particle for an indefinite period of time, provided that the immersed weight of the particle does not exceed the maximum upward force which can be exerted by virtue of the yield stress of the fluid. The conditions for the static equilibrium of a sphere are now discussed. 

Many investigators 35 have reported experimental results on the necessary conditions for the static equilibrium of a sphere. The results of all such studies may be represented by a factor Z which is proportional to the ratio of the forces due to the yield stress xY and those due to gravity. 

Having performed the yield stress test, each category is then divided into static or dynamic methods. Dynamic methods indicate an actual flow test of a certain type, whereas the static methods indicate tests such as rotational flow between two cylinders. 

The materials are melt-process able and a critical stress for flow is observed, similar to conventional PP/EPDM-based TPVs. Application of static crosslinking leads to (partial) connectivity of the rubber particles via chemical bridging of grafted PE chains. Dynamic preparation conditions caused the connected structure to break-up, which led to a significant enhancement of the mechanical properties and the melt processability. The addition of 25-80 wt% extender oil resulted in a reduced complex viscosity and yield stress in the melt, without deteriorating the mechanical properties. The relatively good elastic recovery and excellent final properties of these high hardness TPVs can be explained in terms of the submicrometer rubber dispersions. 

Besides impact testing, quasi-static measurements are carried out to assess the Young modulus, E, the yield stress, cry, and the elongation at break, break> as the most current parameters. They follow international standards (e.g. ISO 527 for tensile tests, ISO 178 for bending measurements). 

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).

Table 4-10 Magnitudes of Static (oos) and Dynamic (rrod) Yield Stress and Angular Deformation (6>) of 5% Amioca - 30% Sugar SDs, Pasted in Rotavapor (RV) or Retort (RT)...

Table 4-13 Comparison of static yield stress (YSS), Pa, ofxanthangum, starch-water and starch-xanthan gum mixtures, and of interactions...

Table 4-13 contains the static yield stresses of the xanthan dispersions in water (Column A), of the three starches in water (Column B) and their sum (Column C), and those of the mixed starch-xanthan dispersions (Column D). One can say that there is synergism between xanthan and starch if values in Column D are higher than those in Column C if they are lower, there is antagonism. From the table, it seems that WXM (except with 1% xanthan concentration) and CWS starches exhibited synergistic... 

The stress to break the bonds between the floes may be calculated as the difference between the static, aos, and the dynamic, aod, yield stresses of the samples with undisrupted and disrupted structure, respectively. 

Figure 5-18 Static (S) and Dynamic (D) Yield Stresses of Structured Foods Determined Using the Vane Method at Different Shear Rates. Products studied apple sauce— AS, ketchup— KH, mustard—MF, tomoato concentrate—ID, and mayonnaise MX (Genovese and Rao, 2005).

In addition, other measurement techniques in the linear viscoelastic range, such as stress relaxation, as well as static tests that determine the modulus are also useful to characterize gels. For food applications, tests that deal with failure, such as the dynamic stress/strain sweep to detect the critical properties at structure failure, the torsional gelometer, and the vane yield stress test that encompasses both small and large strains are very useful. 

Stress required to break the aggregate network. Pa Static yield stress. Pa Tangential components of stress. Pa Stress dissipated due to viscous drag. Pa Stress tensor... 

Fits of these expressions to experimental data produce values of cxy that often differ from the true dynamic or static yield stress (see Sections 8.2.2.2 and 8.2.2.3 for a more general... 

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