Yield stress asymptotic

The tensile yield stress variation as a function of W for a material which has a von Mises-type yield locus is illustrated schematically in Figure 5. This variation is caused by the fact that as the width of the specimen increases, the biaxiality also increases toward the asymptotic value at plane strain. If the material obeys the von Mises yield criterion exactly, the plane strain yield stress should be 15% higher than it would be for simple tension. On the other hand, if the material obeys the Tresca yield criterion, the plane strain yield stress should be identical... 

At W/t 20 (W/b — 7), the PC specimen was essentially at plane strain because the yield stress approached an asymptotic value, as de-... 

A major advantage of the simplified Fj -model is that it allows for asymptotic expansions that qualitatively capture the flow curves. They can thus be investigated in detail addressing such questions as, e.g., for the existence of power-law shear thinning [1], or the dependence of the yield stress on separation parameter. Figure 17 shows an overview of the numerically obtained flow curves and the corresponding... 

An example of an indirect method is the use of a steady-shear-rate sweep test, which examines the steady-shear viscosity rf) and shear stress a as functions of shear rate (/). The results, once obtained, may be plotted in terms of steady-shear viscosity (tj) versus shear stress (shear stress is indicative of a yield stress, and the asymptotic stress is defined as the yield stress (measurable yield stress. This is shown diagrammatically in Figure 4.3. 

Viscoplastic fluids. In the case of a spherical bubble in a translational Stokes flow of a viscoplastic Shvedov-Bingham fluid with a small yield stress, the following two-term asymptotic expansion is valid for the drag coefficient [37] ... 

In the beginning, the time has been established which is needed for reaching the quasi-equilibrium values of the rheological parameters. It is interesting to note that the time dependencies of the interfacial viscosity, the yield stress and the elastic modules are non-monotonous. Initially, during the first hours of layer formation, rheological parameters increase and reach their maxima for approximately 4 hours (Fig. 4 built for elastic modules). Then the rheological parameters decrease and they reach their asymptotic values in 6-8 hours. 

Even this simple hydrostatic formula clarifies the nature of the surface tension. The concentration variation within the interfacial region leads to a nonuniform stress tensor. The neglect of this nonuniformity gives rise to the conventional description of bulk phases. The iterative subtractive procedure demanded by the convergent expression given by Equation 5 corrects for this oversimplification at the boundary of the phases and yields an asymptotic correction (2) to the free energy of the total system in terms of its geometrical properties. 

A correct asymptotics of Eq. (56) at /i -> 0 is obtained by observing that the surface tension is negligible in a thin and almost flat precursor film , so that the viscous stress is balanced by disjoining pressure, contrary to a spurious balance between surface tension and disjoining pressure in the static solution (58). This yields... 

Fig. 12. Cnmpiirisiin nl calculated iiucrfacial normal stress when the adhesive layer yields with imcrl ace-eomer singultirity and perl eeily plastic asymptotic solutions.

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