Strain sweep

Fixed frequency (0.1 or 1 Hz) and follow G. G and G with strain amplitude yq 

is the critical strain above which system shows non-linear response (break down of structure) 

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Over the last few years at the Flexsys laboratories in Akron, OH, data has been collected on both RPA and PICO abrasion as discussed above. In total more than 500 compounds have been tested. RPA loss modulus strain sweeps and PICO abrasion results have been collected and compiled into a database. The diversity of this database is rather broad. Many formulations based on NR,... 

Strain Sweep Test Protocols for Nonlinear Viscoelasticity Investigations.826... 

It is clear that this data treatment is strictly valid providing the tested material exhibits linear viscoelastic behavior, i.e., that the measured torque remains always proportional to the applied strain. In other words, when the applied strain is sinusoidal, so must remain the measured torque. The RPA built-in data treatment does not check this y(o )/S (o)) proportionality but a strain sweep test is the usual manner to verify the strain amplitude range for constant complex torque reading at fixed frequency (and constant temperature). 

At sufficiently low strain, most polymer materials exhibit a linear viscoelastic response and, once the appropriate strain amplitude has been determined through a preliminary strain sweep test, valid frequency sweep tests can be performed. Filled mbber compounds however hardly exhibit a linear viscoelastic response when submitted to harmonic strains and the current practice consists in testing such materials at the lowest permitted strain for satisfactory reproducibility an approach that obviously provides apparent material properties, at best. From a fundamental point of view, for instance in terms of material sciences, such measurements have a limited meaning because theoretical relationships that relate material structure to properties have so far been established only in the linear viscoelastic domain. Nevertheless, experience proves that apparent test results can be well reproducible and related to a number of other viscoelastic effects, including certain processing phenomena. 

Strain Sweep Test Protocols eor Nonlinear Viscoelasticity Investigations... 

According to strain sweep test protocols described above, RPA-FT experiments and data treatment yield essentially two types of information, which reflects how the main torque component, i.e., r(l[Pg.829]

Figure 6.17 Plot of the pseudo-melting curve calculated from a strain sweep. This data is for a polyvinylidene fluoride latex. Similar curves can be obtained for silica and polystyrene latex dispersions...

The interaction between two fillers particles can be investigated by measuring the Payne effect of a filled rubber compounds. In this measurement, dynamic properties are measured with strain sweep from a very small deformation to a high deformation. With the increased strain, the filler-filler network breaks and results in a lower storage modulus. This behavior is commonly known as the Payne effect... 

Experiments on recovery of dynamic functions after the application of large strain amplitude perturbation were performed to understand the modulus recovery kinetics. To determine the recovery kinetics, samples underwent the following test sequences (a) frequency sweep, (b) strain sweep, (c) relaxation time of 2 min, (d) frequency sweep, (e) strain sweep, (f) relaxation time of 2 min, (g) frequency sweep, and (h) strain sweep [50]. Figure 7 shows the comparative subsequent strain sweep results performed immediately after a relaxation time of... 

Because the duration for one measurement is very short (e.g., with a 1-Hz input, a cycle is completed in 1 sec), a dynamic test is suitable for gaining information in a short time frame or for monitoring time-dependent changes in gel network properties. When monitoring the gelation process at a fixed frequency, it usually takes a few hours for G to become approximately constant. The constancy can be judged by a constant value of G at a fixed frequency during a subsequent frequency or strain sweep test, which usually takes several minutes. 

Dynamic-mechanical testing of cross-linked samples are often carried out with high precision on specimen strips in torsion mode, e.g., with a Rheo-metrics Dynamic Analyzer II (RDA) with a sample size of 28x10x2 mm. Here, temperature-and strain sweeps are performed in a displacement range from 0.01% to about 5% strain and a frequency range between 0.1 and 100 Hz. Dynamic mechanical testing of uncross-linked samples can be made, e.g., with a Rubber Process Analyzer RPA 2000 (Alpha Technologies) from 0.28% to 350% strain at various frequencies and elevated temperatures. 

Fig. 1 a,b. Strain amplitude dependence of the complex dynamic modulus E E l i E" in the uniaxial compression mode for natural rubber samples filled with 50 phr carbon black of different grades a storage modulus E b loss modulus E". The N numbers denote various commercial blacks, EB denotes non-commercial experimental blacks. The different blacks vary in specific surface and structure. The strain sweeps were performed with a dynamical testing device EPLEXOR at temperature T = 25 °C, frequency f = 1 Hz, and static pre-deformation of -10 %. The x-axis is the double strain amplitude 2eo... 

Fig. 2. Comparison of strain sweeps in shearing mode and uniaxial compression mode for different static offsets. Obviously, the influence of offsets is weaker in shearing. The strain sweeps were performed with a dynamical testing device EPLEXOR at temperature T = 25 °C, frequency f = 10 Hz...

Fig.4.a Cole-Cole like plots of the strain sweep data from Fig. 1 (polymer matrix natural rubber).b Similar shaped Cole-Cole plots under equal testing conditions in synthetic rubber samples containing the same carbon blacks as indicated in Fig. 4a. The synthetic polymer networks consist of statistical styrene-butadiene copolymers with 23 wt % styrene content (SBR 1500)...

Fig. 6. Strain sweeps for the dynamic loss (shear) modulus G" of styrene-butadiene rubber samples filled with various carbon blacks (from [81])...

The actual operational parameters must be determined for each individual material. This involves running the frequency and strain sweeps mentioned earlier at the various temperatures of interest. It is then a matter of deciding the best linear operating conditions to be employed. There are several operator techniques, however, which will greatly increase precision if followed. 

Figure 3-40 Illustration of Estimation of Critical Stress from a Stress Sweep at a Fixed Frequency Dynamic Rheological Experiment. Alternatively, as described in the text, one may conduct a strain sweep experiment.

In addition, other measurement techniques in the linear viscoelastic range, such as stress relaxation, as well as static tests that determine the modulus are also useful to characterize gels. For food applications, tests that deal with failure, such as the dynamic stress/strain sweep to detect the critical properties at structure failure, the torsional gelometer, and the vane yield stress test that encompasses both small and large strains are very useful. 

No influence of strain on the viscoelastic properties was found. A strain sweep to 14% oscillatory strain was performed with frequencies ranging from 1 rad/sec to 10 rad/sec. and gave an essentially linear viscoelastic respons. 

Fig. 7 The Payne Effect measured on a rheometrics dynamic analyzer (RDA II), using a 10 Hz strain sweep from 0.05% to 10% strain, 65° C, on a typical tire tread containing 50phr HAF black. (View this art in color at www.dekker.com.)...

Rheology Rheological measurements were performed at 25°C with an ARES 2 KFRT controlled strain rheometer (Rheometric Scientific). For the measurements parallel plates of 50 mm diameter were used. The gels were loaded between the plates (2-mm gap) and allowed to rest for 3 min. A strain sweep (0.1 to 100%) was performed at 1 Hz frequency to determine the range of viscoelasticity for each sample and a 2% strain was selected for all samples. A frequency sweep test (0.1 to 16 Hz) was then performed. Samples of 30 and 50% s/w concentration could not be analyzed because of the difficulty in obtaining samples of proper and constant geometry. 

An advanced rheometric expansion system (ARES) is used to determine Tg of samples. Strain sweep experiments from 0.01 to 1% strain are conducted to ensure that experiments are carried out in the linear viscoelastic region. All experiments are done at a frequency of IHz and a strain level of 0.05%, which is in the linear region. Temperature sweeps are conducted at a heating rate of 5°C/min over a temperature range which covers the glassy and rubbery regions of the soy flour samples at different water activities. The temperature at which the loss modulus (G") was at a maximum is used to estimate the T . 

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