Dynamic modulus, measurement methods

The above expressions confirm the known (Ferry 1980) method of reducing the dynamic modulus measured at different temperatures to an arbitrarily chosen standard temperature Tref, while offering a relatively insignificant improvement on the usual shift coefficient... 

The measurements of Young s modulus in dependence of the temperature (dynamic-mechanical measurements, see Sect. 2.3.5.2) and the differential thermal analysis (DTA or DSC) are the most frequently used methods for determination of the glass transition temperature. In Table 2.10 are listed and values for several amorphous and crystalline polymers. 

Studies of rheokinetics over the whole range of polyester curing is based (as for other materials) on a dynamic method, i.e., on measurements of the time dependence of the dynamic modulus at a fixed frequency, from which the time dependence of the degree of conversion (3(t). The observed dependence P(t) for polyester resins can be analyzed by an equation of the type used for other materials. Thus the following general equation was proposed for the kinetics of curing polyester and epoxy resins 69 72... 

Experimentally, the glass transition has also manifested itself by a sharp increase in relative rigidity (measured by dynamic-mechanical methods) and a simultaneous drastic decrease in the rate constant of the autocatalytic epoxy-amine reaction The mobility or rigidity of the system is a function of reaction conversion a in the pre-gel region it can be characterized by dynamic viscosity which is proportional to M of the reacting system. Beyond the gel point, still in the rubbery region but not close to the gel point, the dynamic modulus, G, is at low frequencies proportional to " (m a 1)... 

Glass transition temperature, Tg, and storage modulus, E , were measured to explore how the pigment dispersion affects the material (i.e. cross-link density) and mechanical properties. Both Tg and E were determined from dynamic mechanical analysis method using a dynamic mechanical thermal analyzer (DMTA, TA Instruments RSA III) equipped with transient testing capability. A minimum of 3 to 4 specimens were analyzed from each sample. The estimated uncertainties of data are one-standard deviation. 

Many relatively slow or static methods have been used to measure Tg. These include techniques for determining the density or specific volume of the polymer as a function of temperature (cf. Fig. 11-1) as well as measurements of refractive index, elastic modulus, and other properties. Differential thermal analysis and differential scanning calorimetry are widely used for this purpose at present, with simple extrapolative eorrections for the effects of heating or cording rates on the observed values of Tg. These two methods reflect the changes in specific heat of the polymer at the glass-to-rubber transition. Dynamic mechanical measurements, which are described in Section 11.5, are also widely employed for locating Tg. 

An alternative method for examining the dynamic mechanical properties of liquids is to coat them onto an inert support (typically a glass fibre braid). This measurement is termed Torsional Braid Analysis and does not provide quantitative modulus measurements since it is difficult to decouple the response of the substrate from that of the sample. 

Processing production of coal sample and physical mechanic parameters test are in strict accordance with the provisions of Measurement method of coal and rode physical and mechanical properties (GB/T 23561-2009), and Measurement method of coal seam impact tendency classification index (MT/T 866-2000). The experiment determined natural apparent density, compressive strength, consistent coefficient, elastic modulus, deformation modulus, wave velocity, rock burst energy index, elastic energy index, dynamic failure time, and other parameters. The determination results as shown in Table 1. 

The dynamic modulus E and the loss modulus E" of specimens have been measured by a Rheovibron DDV-II and a vibrating reed method. The dielectric constant g and the dielectric loss factor g " of specimens were measured by the transformer bridge-type at each measuring frequency from 110 Hz to 1 MHz. 

Modulus The ratio of stress to strain in a material over the range for which this value is constant. The type of modulus, which is measured, depends on the method of measurement, e.g., dynamic modulus, compressive modulus, elastic or tensile (Young s) modulus, shear modulus, torsion modulus, sonic modulus. 

Another characteristics feature of the glass transition is the associated change in the modulus. The stress, elongation, is related to the strain, the force applied to a material by the modulus. Conventionally there are two approaches to the measurement of the modulus static and dynamic. The static method involves measurement of the stress strain profile and from the slope of the curve the elastic modulus can be determined. The dynamic method subjects the sample to a periodic oscillation and explores the variation of the amplitude and phase of the response of the sample as a function of temperature. A small sample of the test material is subjected to displacement as shown in Figure 7.3. 

Interrelationships among the Viscoelastic Material Functions. There is a continuing disagreement within the molecular viscoelasticity commimity about which of the above methods should be used to characterize a material (20). In fact, if one can obtain the zero shear rate viscosity and any of the other functions, these methods are all equivalent. The issue, however, revolves aroimd the fact that some features that appear in the dynamic modulus disappear if the compliance is used as the function to represent the data and vice versa. Also, some measurements are more or less dominated by the viscosity contribution. As a result, some problems of misinterpretation of data could be averted if workers who prefer modulus representations would calculate the compliances. In addition, those who measure the compliance should calculate the moduli in order to provide the data in the format that is more common in the field because of the large number of commercial instruments that obtain dynamic moduli. The advent of modern software packages that make the interrelationships easily calculated makes this dispute seem to go away. The pathways to determine the different material functions, one from the other, are shown in Figure 6. 

The temperature-modulated mode of operation has been well known for many decades in calorimetry [33], but became well established only during the 1990s, when commercial DSC was modified this way [34], The idea is to examine the behavior of the sample for periodic rather than for isothermal or constant-heating-rate temperature changes. In this way it is possible to obtain information on time-dependent processes within the sample that result in a time-dependent generalized (excess) heat capacity function or, equivalently, in a complex frequency-dependent quantity. Similar complex quantities (electric susceptibility, Young s modulus) are known from other dynamic (dielectric or mechanical) measurement methods. They are widely u.sed to investigate, say, relaxation processes of the material. 

Dynamic viscoelastic measurements are useful in studying the structure of polymers, because these mechanical properties are sensitive to glass transition, crystallinity, cross-linking, filling systems (filler or plasticizer), molecular aggregation, and phase separation. To determine dynamic viscoelastic properties, such as storage modulus, loss modulus, and tan, various methods have been proposed, and recently many types of instruments are commercially available. Typical methods to measure the dynamic viscoelasticity are classified into three categories damped free vibration, resonance free vibration, and nonresonance forced vibration. These methods are standardized by the international standard ISO 6721 [3]. 

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