Stress decay

A rotational viscometer connected to a recorder is used. After the sample is loaded and allowed to come to mechanical and thermal equiUbtium, the viscometer is turned on and the rotational speed is increased in steps, starting from the lowest speed. The resultant shear stress is recorded with time. On each speed change the shear stress reaches a maximum value and then decreases exponentially toward an equiUbrium level. The peak shear stress, which is obtained by extrapolating the curve to zero time, and the equiUbrium shear stress are indicative of the viscosity—shear behavior of unsheared and sheared material, respectively. The stress-decay curves are indicative of the time-dependent behavior. A rate constant for the relaxation process can be deterrnined at each shear rate. In addition, zero-time and equiUbrium shear stress values can be used to constmct a hysteresis loop that is similar to that shown in Figure 5, but unlike that plot, is independent of acceleration and time of shear. 

Stress-relaxation measurements, where stress decay is measured as a function of time at a constant strain, have also been used extensively to predict the long-term behavior of styrene-based plastics (9,12). These tests have also been adapted to measurements in aggressive environments (13). Stress-relaxation measurements are further used to obtain modulus data over a wide temperature range (14). 

If we accept the assumption that the elastic wave can be treated to good aproximation as a mathematical discontinuity, then the stress decay at the elastic wave front is given by (A. 15) and (A. 16) in terms of the material-dependent and amplitude-dependent wave speeds c, (the isentropic longitudinal elastic sound speed), U (the finite-amplitude elastic shock velocity), and Cfi [(A.9)]. In general, all three wave velocities are different. We know, for example, that... 

This indicates that the stress decays exponentially with a time constant of T)l (see Fig. 2.35). 

Finally, we remark on the plateau moduli. The simulation computed Gq from the normal stress decay. Depending on the evaluation method, moduli evolve that are much smaller than would be expected from Eq. 3.31. While in the experiment the local freedom of a chain to move was found to be about 50% larger than predicted from the modulus (PE d =32 A [77] d =48 A, PEP rfrheo-43 A [7]. nse q simulation appears to tell the opposite the tube... 

We can get a first approximation of the physical nature of a material from its response time. For a Maxwell element, the relaxation time is the time required for the stress in a stress-strain experiment to decay to 1/e or 0.37 of its initial value. A material with a low relaxation time flows easily so it shows relatively rapid stress decay. Thus, whether a viscoelastic material behaves as a solid or fluid is indicated by its response time and the experimental timescale or observation time. This observation was first made by Marcus Reiner who defined the ratio of the material response time to the experimental timescale as the Deborah Number, Dn-Presumably the name was derived by Reiner from the Biblical quote in Judges 5, Song of Deborah, where it says The mountains flowed before the Lord. ... 

However, if this stress is maintained for long periods of time, the compact coils may unravel, permitting the chains to slip past each other forming new coils in a process called stress decay. Stress decay is prevented if a few crosslinks are present, as in vulcanized rubber. 

Stress decay (relaxation) measurements of propellant binders are a way to obtain insight into the network structure of binder systems (29). In addition, high hysteretical losses appear to be associated with good tensile properties. Figure 5 shows a normalized stress-decay vs. time plot of a polyurethane elastomer. If the reference stress, [Pg.105]

Figure 6. Relative stress decay vs. molecular weight between crosslinks of polybutadiene-polyurethane rubber at three temperatures...

Stress Decay at the Termination of Steady Shearing Flow (356-360)... 

Accordingly, plots of a t)/a(0) vs t from different shear rates should superimpose. Experimentally the curves do not superimpose when the shear rate is in the non-Newtonian region, the initial rate of relaxation being increasingly more rapid for higher shear rates. The normal stress decays more slowly than shear stress, but behaves similarly with respect to the effect of previous shearing flow in the non-Newtonian region. 

For shear strains greater than approximately 2 the ratio cr(r)/> 0 for a concentrated polystyrene solution was reduced at all observable times. For the large strains, relaxation proceeded more rapidly at short times, but at longer times the residua] stress decayed with about the same time dependence as that in the linear viscoelastic region. 

Natural rubber exhibits unique physical and chemical properties. Rubbers stress-strain behavior exhibits the Mullins effect and the Payne effect. It strain crystallizes. Under repeated tensile strain, many filler reinforced rubbers exhibit a reduction in stress after the initial extension, and this is the so-called Mullins Effect which is technically understood as stress decay or relaxation. The phenomenon is named after the British rubber scientist Leonard Mullins, working at MBL Group in Leyland, and can be applied for many purposes as an instantaneous and irreversible softening of the stress-strain curve that occurs whenever the load increases beyond... 

At higher shear rates, Watanabe and Kotaka (1983) observed thixotropy, i.e. stress decay increasing as a function of shear rate, in PS-PB diblocks in dibutyl phthalate (DBP), which is a selective solvent for PS.The fact that the flow crossed over from plastic to viscous non-Newtonian on increasing the shear rate indicated the breakdown of the micellar lattice structure, rather than of the individual micelles. This was confirmed by parallel measurements on a cross-linked PB-PS system, where stress decay and recovery were also observed. Thus the... 

The model represents a liquid (able to have irreversible deformations) with some additional reversible (elastic) deformations. If put under a constant strain, the stresses gradually relax. When a material is put under a constant stress, the strain has two components as per the Maxwell Model. First, an elastic component occurs instantaneously, corresponding to the spring, and relaxes immediately upon release of the stress. The second is a viscous component that grows with time as long as the stress is applied. The Maxwell model predicts that stress decays exponentially with time, which is accurate for most polymers. It is important to note limitations of such a model, as it is unable to predict creep in materials based on a simple dashpot and spring connected in series. The Maxwell model for creep or constant-stress conditions postulates that strain will increase linearly with time. However, polymers for the most part show the strain rate to be decreasing with time [23-26],... 

Inn YW, Wang SQ (1994) Rheol Acta 33 108 The observed stress decay at high stresses and slow recovery at lower stresses in PDMS suspensions of glass spheres was thought to arise from interfacial slip and to be controlled by glassy chain dynamics. This interpretation turned out to be completely wrong. See ref. [47]. 

Stress relaxation is an alternative procedure. Here an instantaneous, fixed deformation is imposed on a sample, and the stress decay is followed with time. A very useful modification of these two basic techniques involves the use of a periodically varying stress or deformation instead of a constant load or strain. The dynamic responses of the body are measured under such conditions. 

Fig. 11-17. Left panel Stress decay at various temperatures T < Ti < Master curve for stress decay al temperalure 7 s.

The Bird-Leider model predicted well the maximum and the steady state stresses as well as the times at which they occurred, but its prediction of the shear stress decay was not satisfactory (Dickie and Kokini, 1982). 

Kokini and Dickie (1981) found that the Bird-Leider equation provided moderately good predictions for peak shear stresses (trmax) and the corresponding times (tmax), but the prediction of shear stress decay was poor. They suggested that a series of relaxation times, as opposed to a single exponential term, would be needed for mayonnaise and other materials. 

Complex flnids are viscoelastic when the fluid stiU maintains internal stress after the external shear stress has ceased. The internal stress decays with time the time reqnired for the fluid to recover to the initial state is called the relaxation time. For this case the shear modulus (G ) is a complex number ... 

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