Shear stress growth experiment

Next, let us consider the predictions for a shear stress growth experiment. In a stress growth experiment, a linearly increasing shear is imposed, i.e. 

Using the cone and plate geometry, stress growth experiments have also been performed using different temperatures and different shear rates. Correct tangential (X+(t,Y) Tj+(t,Y)) and normal stress (Ni(t,Y) Vi(t,Y)) data were... 

The aim of a stress growth experiment is to observe how the stresses change with time as they approach their steady shear flow values. This is done by assuming that the fluid sample trapped in a small gap between two parallel plates is at rest for all times previous to t = 0 implying that there are no stresses in the fluid when steady shear flow is initiated at f = 0. For t > 0 when a constant velocity gradient is imposed, the stress is monitored with respect to time tUl it reaches steady state value. 

Fig. 7.16. Results of stress growth experiments in shear, and extension,...

Figure 9.18 refers to two other standard experiments. It depicts the results of stress growth experiments, conducted again on a polyethylene melt. The figure includes both measurements probing shear and tensile properties, thus facilitating a direct comparison. Curves show the building-up of shear stress upon inception of a steady state shear flow at zero time and the development of tensile stress upon inception of a steady state extensional flow. Measurements were carried out for various values of the shear rate 7 or the Hencky rate of extension ch ... 

The stress growth experiment of Figure 2(c) involves the study of the time evolution of the stresses when a fluid is brought instantaneously from a state of rest at t = 0 to a state of steady-state shear flow this is an idealized experiment which presumes that in the experiment one can effectively minimize inertial effects and achieve the linear velocity profile within an acceptably short time interval. One can then define the growth functions associated with the shear stress and the two normal-stress differences for t > 0 as follows... 

FIGURE 3.7 Transient shear behavior of PPS at 330 °C. The shear and primary normal stress difference are recorded at the startup of shear flow and on cessation of flow. After 10 s the stress growth experiment is repeated. 

Stress Growth. For startup of shear flow (the stress growth experiment), Yyxif) is given by... 

The maximum strain rate (e < Is1) for either extensional rheometer is often very slow compared with those of fabrication. Fortunately, time-temperature superposition approaches work well for SAN copolymers, and permit the elevation of the reduced strain rates kaj to those comparable to fabrication. Typical extensional rheology data for a SAN copolymer (h>an = 0.264, Mw = 7 kg/mol,Mw/Mn = 2.8) are illustrated in Figure 13.5 after time-temperature superposition to a reference temperature of 170°C [63]. The tensile stress growth coefficient rj (k, t) was measured at discrete times t during the startup of uniaxial extensional flow. Data points are marked with individual symbols (o) and terminate at the tensile break point at longest time t. Isothermal data points are connected by solid curves. Data were collected at selected k between 0.0167 and 0.0840 s-1 and at temperatures between 130 and 180 °C. Also illustrated in Figure 13.5 (dashed line) is a shear flow curve from a dynamic experiment displayed in a special format (3 versus or1) as suggested by Trouton [64]. The superposition of the low-strain rate data from two types (shear and extensional flow) of rheometers is an important validation of the reliability of both data sets. 

The model experiments of Xu and Rosakis on low-speed impact over sandwich structures were simulated applying cohesive models. The simulation captures qualitatively the main experimental observations. The most relevant correspondence is in the development of the first crack at the interface between the layers, the presence of shear stresses along the interface, which renders the crack shear driven and often inter-sonic, and the transition between interlayer crack growth and intra-layer crack branching. The effects of impact speed and bond shear strength are also investigated and highly satisfactory predictions are obtained. 

ABSTRACT The mean flow features of two types of wall jets used often in hydraulic engineering are analyzed. They include the results of a plane jet and a three-dimensional wall jet. The required flow field was obtained from CFD simulations, the point source method and some limited experiments. These are compared with the available equations in vogue, which predict the growth of the jet, the decay of the maximum mean velocity and concentration of tracers. The variation of the wall shear stress along the flow is also analyzed. The CFD results for the distribution of the mean velocity and the tracer concentration exhibit self-similarity . However, the predicted growth rate of the jets differs from the available data. 

The transient shear flow experiments described in Figure 2 may provide the most insight into development of orientation and structure in LCP. We first look at stress growth at the start up of shear flow. In this experiment the stress build up at the start up of flow is monitored as a function of time. Some representative data for a 60 mole % PHB/PET copolyester are presented in Figure 16. At this particular temperature we observe two stress peaks. 

The shear reversal experiment was repeated but in this case reversal was carried out directly from steady shear flow rather than after allowing the stresses to relax. Results from this experiment are presented in Figure 6. The stress growth curve is significantly... 

Recently, Hanratty presented a comprehensive review of the attempts to account for the interfacial waviness in modelling the interfacial shear stress for the stability analysis of gas-liquid two-phase flows [53]. Basically, the approach taken was to implement the models obtained for the surface stresses in air flow over a solid wavy boundary as a boundary condition for the momentum equation of the liquid layer over its it mobile wavy interface. Craik [98] adopted the interfacial stresses components which evolve from the quasi-laminar model by Benjamin [84]. Jurman and McCready [99], Jurman et al. [100], and Asali and Hanratty [101] used correlated experimental values of shear stress components (phase and amplitude) based on turbulent models which consider relaxation effects in the Van Driest mixing length. Since the characteristics of the predicted surface stresses are dependent on the wave number, Asali and Hanratty picked the phase and amplitude values which correspond to the wave lengths of the capillary ripples observed in their experiments of thin liquid layers sheared by high gas velocities [101]. It was shown that the growth of these ripples is controlled by the interfacial shear stress component in phase with the wave slope. 

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