Dynamic mechanical measurements viscoelastic behavior

Filler-filler interaction (Payne effect) - The introduction of reinforcing fillers into rubbery matrices strongly modifies the viscoelastic behavior of the materials. In dynamic mechanical measurements, with increasing strain amplitude, reinforced samples display a decrease of the storage shear modulus G. This phenomenon is commonly known as the Payne effect and is due to progressive destruction of the filler-filler interaction [46, 47]. The AG values calculated from the difference in the G values measured at 0.56% strain and at 100% strain in the unvulcanized state are used to quantify the Payne effect. 

Dynamic mechanical measurements are performed at very small strains in order to ensure that linear viscoelasticity relations can be applied to the data. Stress-strain data involve large strain behavior and are accumulated in the nonlinear region. In other words, the tensile test itself alters the structure of the test specimen, which usually cannot be cycled back to its initial state. (Similarly, dynamic deformations at large strains test the fatigue resistance of the material.)... 

Viscoelastic behavior is a time-dependent mechanical response and usually is characterized with creep compliance, stress-relaxation, or dynamic mechanical measurements. Since time is an additional variable to deformation and force, to obtain unique characterizing functions in these measurements one of the usual variables is held constant. 

Generally, two different types of measurement are applied to determine the linear viscoelastic behavior, namely static (or equilibrium) and dynamic mechanical measurements. Static tests involve the imposition of a step change in stress and the observation of any subsequent development in time of the strain, whereas dynamic tests involve the application of a harmonically varying strain. In ordinary thermoplastic polymer systems, test conditions such as strain or frequency must be in the linear range otherwise, the results will be dependent on the experimental details rather than on the material under test. 

Dynamic mechanical analysis (DMA) has been used to study the flow behavior of hot-melt adhesives.Drummer and co-workers used DMA to study the viscoelastic behavior of adhesives. They found that dynamic mechanical measurements in adhesives provided insight in the macromolecular mobility of the polymer or rubber system studied. The viscoelastic behavior at various temperatures can be correlated with standard measurements such as adhesive force, shear strength, and tack. The authors concluded that three-dimensional DMA plots from frequency-temperature sweeps provide a complete overview of the frequency and temperature dependence ofthe adhesive. Foster, etal., characterized the hot-tack differences in hot-melt adhesives using DMTA. 

Rheological Properties Measurements. The viscoelastic behavior of the UHMWPE gel-like systems was studied using the Rheometric Mechanical Spectrometer (RMS 705). A cone and plate fixture (radius 1.25 cm cone angle 9.85 x 10" radian) was used for the dynamic frequency sweep, and the steady state shear rate sweep measurements. In order to minimize the error caused by gap thickness change during the temperature sweep, the parallel plates fixture (radius 1.25 cm gap 1.5 mm) was used for the dynamic temperature sweep measurements. 

Isothermal measurements of the dynamic mechanical behavior as a function of frequency were carried out on the five materials listed in Table I. Numerous isotherms were obtained in order to describe the behavior in the rubbery plateau and in the terminal zone of the viscoelastic response curves. An example of such data is shown in Figure 6 where the storage shear modulus for copolymer 2148 (1/2) is plotted against frequency at 10 different temperatures. 

In this section we are going to examine such viscoelastic properties in some detail and we will start by examining in turn three important mechanical methods of measurement creep, stress relaxation, and dynamic mechanical analysis. This will lead us to interesting things like time-temperature equivalence and a discussion of the molecular basis of what we have referred to as relaxation behavior. 

The mechanical behavior of the hydrogels can be described by the theories of rubber elasticity and viscoelasticity, which are based on time-independent and time-dependent recovery of the chain orientation and structure, respectively. Mechanical properties due to rubber elastic behavior of hydrogels can be determined by tensile measurements, while the viscoelastic behavior can be determined through dynamic mechanical analysis. 

These equations are often used in terms of complex variables such as the complex dynamic modulus, E = E + E", where E is called the storage modulus and is related to the amount of energy stored by the viscoelastic sample. E" is termed the loss modulus, which is a measure of the energy dissipated because of the internal friction of the polymer chains, commonly as heat due to the sinusoidal stress or strain applied to the material. The ratio between E lE" is called tan 5 and is a measure of the damping of the material. The Maxwell mechanical model provides a useful representation of the expected behavior of a polymer however, because of the large distribution of molecular weights in the polymer chains, it is necessary to combine several Maxwell elements in parallel to obtain a representation that better approximates the true polymer viscoelastic behavior. Thus, the combination of Maxwell elements in parallel at a fixed strain will produce a time-dependent stress that is the sum of all the elements ... 

S.3.2 Dynamic Mechanical Analysis (DMA) Storage and Loss Modulus Dynamic mechanical analysis (DMA) is typically performed to measure the viscoelastic behavior of polymer networks. A sinusoidal force (stress) is applied to a material and the resulting displacement (strain) is measured, allowing one to determine the complex modulus. 

The study of elastic and viscoelastic materials under conditions of cyclic stress or strain is called dynamic mechanical analysis, DMA. The periodic changes in either stress or strain permits the analysis of the dynamic response of the sample in the other variable. The analysis has certain parallels to the temperature-modulated differential thermal analysis described in Sect 4.4, where the dynamic response of the heat-flow rate is caused by the cyclic temperature change. In fact, much of the description of TMDSC was initially modeled on the more fully developed DMA. The instruments which measure stress versus strain as a function of frequency and temperature are called dynamic mechanical analyzers. The DMA is easily recognized as a further development of TMA. Its importance lies in the direct link of the experiment to the mechanical behavior of the samples. The difficulty of the technique lies in understanding the macroscopic measurement in terms of the microscopic origin. The... 

In order to investigate the viscoelastic behavior of crosslinked EVA, rheological measurements were made to determine at what temperatures the phase transitions occur and their effect on the dynamic mechanical modulus. The complex dynamic modulus E expression is given by Eq. (6). 

Viscoelastic behavior can be viewed as three fundamental modulus characteristics G orE =complex modulus, G or E = storage or dynamic modulus, and G" or E" = loss or viscous modulus. The moduli are related by the angle of phase lag 5 in stress-to-strain phase lag. They are derived from measurements of the complex modulus and phase angle 8 relationships of stress to strain, by dynamic mechanical analysis (DMA) using a Rheometric Solids Analyzer, RSA, supplied by TA Instruments [19]. Further information on loss modulus, storage modulus, and DMA is found in Chap. 2, Products and Designs, and Chap. 3, Properties. ... 

While TMA refers to a measurement of a static mechanical property, there are also techniques that employ dynamic measurement. In the torsional braid analysis (TEA), a sample is subjected to free torsional oscillation. The natural frequency and the decay of oscillations are measured. This provides information about the viscoelastic behavior of materials. However, these measurements are elaborate and time consuming. In dynamic mechanical analysis (DMA), a sample is exposed to forced oscillations. A large number of useful properties can be measured by this technique see also Section 6.2.6.5. 

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