Stress plateau

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). 

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 above percent deflections are based on total pad heights of 1.775 and 4.30 in., respectively. Adjusted for strut height, they would correspond to deflections of about 0.5 and 0.35 in., respectively, which are well within the norm2il stress plateau. 

The stress plateau of plastic deformation, being the most pronounced at 296 K, decreases with increasing temperature and ... 

A clearly visible application for the grafted from materials is also in ballistic protection. With a relatively low modulus (e.g., 148 MPa for polystyrene-crosslinked samples -Table 13.2) and bulk density (0.46 gcm ), it is calculated that the speed of sound (equal to [modulus/bulk density] ) is 635 m s This value is very low for a solid material and highly desirable because it will extend the duration of an impact reducing the effective force on the material. The relatively low yield stress (7.2 MPa) will allow early activation of the energy absorption mechanism, while the long stress plateau will allow for large energy absorption. 

Initially the pseudo-elastic material is in its austenitic phase at room temperature. Initially the material in the austenitic phase deforms like a conventional material linear elastic under load. With increasing loads a stress-induced transformation of the austenitic to the martensitic phase is initiated at the pseudo-yield stress Rpe- This transformation is accompanied with large reversible strains at nearly constant stresses, resulting in a stress plateau shown in Fig. 6.53. At the end of the stress plateau the sample is completely transformed into martensite. Additional loading passing the upper stress plateau causes a conventional elastic and subsequently plastic deformation of the martensitic material. If the load is decreased within the plateau and the stress reaches the lower stress level a reverse transformation from martensite to austenite occurs. Since the strains are fully reversible the material and the sample respectively is completely recovered to its underformed shape. These strains are often called pseudo-elastic because the reversible deformation is caused by a reversible phase transformation and is not only due to a translation of atoms out of their former equilibrium position [74]. 

A well-known feature of yield stress fluids is the appearance of a low-shear-rate stress plateau which marks the yield stress. 

The stress plateau always signals yidding and is often asso-dated with shear banding, as, for example, in stars and hard sphere colloids. ° There are exceptions, however, as in the case of microgds which do not shear band in the plateau region. Recent experimental evidence su ests that the parti-de architecture plays a oudal role as even for stars there are... 

Various shear histories have been applied in order to test the robustness of the stress plateau. The latter has been found to be unique and history independent. This reproducibility is a crucial feature of the nonlinear rheology of wormlike micellar systems [33,138,140,144]. 

The mechanical behavior described above concerns most semidilute wormlike micelles. The simation for concentrated samples is analogous with minor changes the low shear rate branch is purely Newtonian and the transition towards the stress plateau is more abrupt [137]. 

Fig. 12 Generalized flow phase diagram obtained for CPCl/NaSal system derived from a superimposition between flow curves at different concentrations and temperatures, using normalized coordinates ct/Gq and /Tg. No stress plateau is observed beyond the critical conditions Op/Go > 0.9 and y-Tg 3 0.5. From Berret et al. [137]...

During the past decade, many authors have paid close attention to the evolution of the shear stress as a function of time in systems exhibiting a stress plateau. The aim was to identify the mechanisms responsible for the shear-banding transition. In most cases, shear stress time series in response to steady shear rate consists of a slow transient (compared to the relaxation time of the system) before reaching steady state. Nonetheless, more complex fluctuating behaviors such as erratic oscillations suggestive of chaos or periodic sustained oscillations of large amplitude have been observed in peculiar systems. 

Bandyopadhyay et al. focused on the time-dependent behavior of semidilute solutions of hexadecyltrimethylammonium p-toluenesulfonate (CTAT) at weight fractions around 2 wt. % in water, with and without addition of sodium chloride (NaCl). This system is well known to exhibit stress plateau or pseudo-plateau in the flow curve for concentrations ranging between 1.3 and 20 wt. % [80,203,206,207,236]. 

Two additional observations may provide clues as to the origin of the compressive stress. First of all, if the growth is interrupted while the stress magnitude is at its plateau value, the stress magnitude falls off rapidly. Then, upon resumption of the deposition flux, the falloff in stress magnitude is fully reversed and the same compressive stress plateau is eventually re-established (Shull and Spaepen (1996), Floro et al. (2001)). The second observation concerns the role of grain boundaries. It has been demonstrated that the stress in Pd films deposited on polycrystalline Pt substrates becomes compressive while the stress in otherwise identical films deposited onto single crystal Pt surfaces remains tensile (Ramaswamy et al. 2001). 

Fig. 2.32 Polyisoprene extrusion effect of repeated capillary passes at 150 sec on lower stress plateau-stress oscillation region of flow curves [51]. Numbers in graph are the number of extrusion passes.

The common explanation for the shear stress plateau is slip at the walls of the measuring system or shear banding. 

The Giesekus model evidently predicts a shear stress plateau that is equal to the shear modulus. Equation 9.51 can easily be verified, and it was found to be in good agreement... 

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