Stress overshoot experiments

Stress overshoot experiments on carbon black filled compounds. 

They also recommend the selection of parameters a and b so as to give the best fit for the stress overshoot data obtained for a constant shear-rate experiment. By following this procedure, good agreement between experiments and theory was obtained, as demonstrated in Fig. E6.14b. 

As mentioned above, it is far more difficult to measure extensional viscosity than shear viscosity, in particular of mobile liquids. The problem is not only to achieve a constant stretch rate, but also to maintain it for a sufficient time. As shown before, in many cases Hencky strains, e = qet, of at least 7 are needed to reach the equilibrium values of the extensional viscosity and even that is questionable, because it seems that a stress overshoot is reached at those high Hencky strains. Moreover, if one realises that that for a Hencky strain of 7 the length of the original sample has increased 1100 times, whereas the diameter of the sample of 1 mm has decreased at the same time to 33 pm, then it will be clear that the forces involved with those high Hencky strains become extremely small during the experiment. 

In transient shear flows starting from an isotropic distribution of fiber orientations, considerably higher viscosities will be initially observed, until the fibers become oriented. In Bibbo s experiments, t]r for isotropically oriented fibers is around 3.5 for v = 75. These viscosities can also be predicted reasonably well by semidilute theory and by simulations (Mackaplow and Shaqfeh 1996). Figure 6-25 shows the shear stress as a function of strain for a polyamide 6 melt with 30% by weight glass fibers of various aspect ratios, where the fibers were initially oriented in the flow-gradient direction. Notice the occurrence of a stress overshoot (presumably due to polymer viscoelasticity), followed by a decrease in viscosity, as the fibers are reoriented into the flow direction. 

The rheological behavior of these materials is still far from being fully understood but relationships between their rheology and the degree of exfoliation of the nanoparticles have been reported [73]. An increase in the steady shear flow viscosity with the clay content has been reported for most systems [62, 74], while in some cases, viscosity decreases with low clay loading [46, 75]. Another important characteristic of exfoliated nanocomposites is the loss of the complex viscosity Newtonian plateau in oscillatory shear flow [76-80]. Transient experiments have also been used to study the rheological response of polymer nanocomposites. The degree of exfoliation is associated with the amplitude of stress overshoots in start-up experiment [81]. Two main modes of relaxation have been observed in the stress relaxation (step shear) test, namely, a fast mode associated with the polymer matrix and a slow mode associated with the polymer-clay network [60]. The presence of a clay-polymer network has also been evidenced by Cole-Cole plots [82]. 

This chapter is devoted to the molecular rheology of transient networks made up of associating polymers in which the network junctions break and recombine. After an introduction to theoretical description of the model networks, the linear response of the network to oscillatory deformations is studied in detail. The analysis is then developed to the nonlinear regime. Stationary nonhnear viscosity, and first and second normal stresses, are calculated and compared with the experiments. The criterion for thickening and thinning of the flows is presented in terms of the molecular parameters. Transient flows such as nonhnear relaxation, start-up flow, etc., are studied within the same theoretical framework. Macroscopic properties such as strain hardening and stress overshoot are related to the tension-elongation curve of the constituent network polymers. 

Fig. 14 Stress overshoot Obs. initial shear stress before the onset of the long-time sigmoidal relaxation and steady-state shear stress tJj, gathered from start-up of flow experiments on the semidilute sample of CPCl/NaSal (12wt.%)in O.SMNaCl brine. The purely Newtonian behavior (Tjof) has been added for comparison. Reprinted from Berret [138]...

To reproduce the complex response at a start up of shear flow for a series of the LDPE/LDH nanocomposites (Fig. 20), it is necessary to take into account the shift of the second stress overshoot to smaller deformations with increasing LDH loading. To our knowledge, this shift can be explained by the effect of strain amplification in the polymer matrix foxmd previously in the case of filled elastomers [103]. Upon shearing, the hard filler particles cannot be stretched however, they can reorganize their positions in the polymer matrix, which hence experiences a noticeably higher effective deformation, yeff> than the strain externally applied to the sheared sample, yo [103] ... 

Memory effects are revealed by experiments in which a complex fluid is subject to a time-dependent shear rate. Included under this rubric are measurements of the startup stress when a constant shear rate is suddenly imposed on an initially stationary system, and the stress when a system subject to some nonzero constant rate of strain suddenly has the rate of strain increased, decreased, or reversed. A prominent feature in measurements of stress on sudden imposition of a large rate of strain is stress overshoot, in which the stress first increases to a value much larger than its steady-state value, and then relaxes back to its steady-state value. Contrariwise, if the shear rate applied to a polymer fluid is held constant for a long time and then suddenly reduced, the stress may show undershoot the stress declines to a value well below its steady-state value and then increases back to its steady-state value. Related features have been seen for N. Bird, et al. also note measurements on responses to superposed flows, in particular the combination of a constant rate of shear flow with an oscillatory shear parallel or perpendicular to the constant shear(7). Bird, et al. further assert that multiple oscillations around the steady-state stress are sometimes observed before the steady state is attained. Recent studies involving step strains or oscillatory shear superposed on steady shear are reported by Li and Wang(8). 

Studies of stress overshoot on sudden imposition of constant rate of strain include Osaki, etal. 0) and Inoue, etal. ). Osaki, etal. also report the time dependence of N. Inoue, et al. note a potential artifact perturbing stress measurements, namely shear-induced phase separation. Representative experiments on double strain rates are presented by Oberhauser, et al. 2) and by Wang and Wang(13). The observed stress has a complex time dependence including overshoot and undershoot ... 

The stress overshoot is amplified by the presence of CB, and the more reinforcing the filler, the stronger the effect. Such experiments, whilst obtained in laboratory conditions, provide results that correspond very well (at least qualitatively) with observations on factory floor. Rubber engineers are indeed well aware of the difficulties associated with the starting-up of extrusion lines when processing highly reinforced compounds. Machine temperature profile and extruder screw speed must be carefully monitored right from the... 

We have carried out standard rheometric tests as done many times in the literature for entangled polymer solutions. These experiments include startup shear, large amplitude oscillatory shear (LAOS) and large step strain. In terms of the rheological features, we observed the same as others. For example, there is a stress overshoot in startup shear in the stress plateau region the apparent G can drop below G" at frequencies of the elastic plateau and amplitudes around and above 100% and relaxation modulus decreases in time after large step strains. 

Figure 6. Schematic representation of the shear rate program, structural history and accompanying stress response of a shear-rate-increase flow. Shear stress (solid curve) is seen to exhibit a lower second overshoot than the corresponding one-step experiment (dashed curve). Model parameters are identical to those used in previous figures,...

The primary normal stress difference also experiences an overshoot during the establishment of steady flow following onset of a constant shear rate. An example is included in Fig. 17-33 the normal stress maximum appears considerably later than the shear stress maximum, as found also in earlier measurements on a solution of polyisobutylene by Huppler and collaborators. In relaxation following cessation of steady-state flow, the primary normal stress difference falls more slowly than the shear stress, as seen in Fig. 2-13 and also the measurements on poly(a-methyl styrene) by Nagasawa and collaborators when normalized by the steady-flow value, the primary normal stress difference appears to fall somewhat more rapidly with increasing 7. 

In fast shearing flows, with shear rates greater than I/Tj, the DEMG theory shows overshoots in both shear stress <7 and first normal stress dilference Nj as functions of time after start-up of steady shearing [21 ], in agreement with experiments (as will be presented in Section 11.5.1.1). These overshoots in both <7 and are an improvement over DE theory, which shows only the... 

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