Modulus static measurement

Young s modulus can be deterrnined by measuring the stress—strain response (static modulus), by measuring the resonant frequency of the body... 

An instrument for measuring the mechanical properties of rubbers in relation to their use as materials for the absorption and isolation of vibration. These properties are resilience, modulus (static and dynamic), kinetic energy, creep and set. The introduction of an improved version has recently been announced. 

Besides impact testing, quasi-static measurements are carried out to assess the Young modulus, E, the yield stress, cry, and the elongation at break, break> as the most current parameters. They follow international standards (e.g. ISO 527 for tensile tests, ISO 178 for bending measurements). 

Tg from static measurements or the maximum in the loss modulus-temperature curve. 

This isothermal bulk modulus (Kj) measured by static compression differs slightly from the aforementioned adiabatic bulk modulus (X5) defining seismic velocities in that the former (Kj) describes resistance to compression at constant temperature, such as is the case in a laboratory device in which a sample is slowly compressed in contact with a large thermal reservoir such as the atmosphere. The latter (X5), alternatively describes resistance to compression under adiabatic conditions, such as those pertaining when passage of a seismic wave causes compression (and relaxation) on a time-scale that is short compared to that of thermal conduction. Thus, the adiabatic bulk modulus generally exceeds the isothermal value (usually by a few percent), because it is more difihcult to compress a material whose temperature rises upon compression than one which is allowed to conduct away any such excess heat, as described by a simple multiplicative factor Kg = Kp(l + Tay), where a is the volumetric coefficient of thermal expansion and y is the thermodynamic Griineisen parameter. 

Figure 3.24 shows some typical experimental data. It is seen that Tg is easily identifiable as a peak in the tan (5 or the loss modulus trace. These maxima do not coincide exactly. The maximum in tan d is at a higher temperature than that in G" (o), because tan 6 is the ratio of G (w) and G (oj) (see Equation 3.96) and both these moduli are changing in the transition region. At low frequencies (about 1 Hz) the peak in tan (5 is about 5°C higher than Tg from static measurements or the maximum in the loss modulus-temperature curve. 

The static measurements of Hadley et al. using a grade of Rigidex polymer showed considerable differences compared with low density material. Apart from shallow minima in 0 and G at low draw ratios the behaviour at room temperature appeared rather straightforward (Fig. 11). With increase of draw ratio Eq increased steeply, the torsion modulus increased slightly and 90 varied only a little V12 and vjs were generally not inconsistent with a value of 0-50, and seemed insensitive to the... 

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. 

The quantities E and G refer to quasi-static measurements. When cyclic motions of stress and strain are involved, it is more convenient to use dynamical mechanical moduli. The complex Young s modulus is then defined as = " + iE", where E is the storage modulus and " the loss modulus. The storage modulus is a measure of the energy stored elastically during deformation the loss modulus is a measure of the energy converted to heat. Similar definitions hold for G, J, and other mechanical properties. 

In addition to the adiabatic or isothermal difference, acoustically determined elastic constants of polymers differ from static values because polymer moduli are frequency-dependent. The deformation produced by a given stress depends on how long the stress is applied. During the short period of a sound wave, not as much strain occurs as in a typical static measurement, and the acoustic modulus is higher than the static modulus. This effect is small for the bulk modulus (on the order of 20%), but can be significant for the shear and Young s modulus (a factor of 10 or more) (5,6). 

Strain dependence should also be considered when comparing acoustically measured elastic constants with statically measured values. As an example, for polyethylene at room temperature, the modulus is independent of strain up to a strain of about 10 (7). Beyond this point, the modulus decreases as the strain increases. Typically, acoustic measurements are made in the strain range 10 where the moduli are strain-independent, but static measin-ements... 

The Yerseley Mechanical Oscillograph supplied by ATS FAAR measures, according to ASTM D945 [142], the mechanical properties of rubber vulcanisations in the small range of deformation that characterises many technical applications. These properties include resilience, dynamic modulus, static modulus, kinetic energy, creep, and set under a given force. 

Before entering into a detailed discussion of the glass transition, the five regions of viscoelastic behavior are briefly discussed to provide a broader picture of the temperature dependence of polymer properties. In the following, quasi-static measurements of the modulus at constant time, perhaps 10 or 100 s, and the temperature being raised l°C/min will be assumed. 

For quasi-static measurements such as illustrated in Figure 8.2, the glass transition temperature, Tg, is often taken at the maximum rate of turndown of the modulus at the elbow, where E = lO Pa. Often the glass transition temperature is defined as the temperature where the thermal expansion coefficient (Section 8.3) undergoes a discontinuity. (Enthalpic and dynamic definitions are given in Section 8.2.9. Other, more precise definitions are given in Section 8.5.)... 

EXTAR 6000 Dynamic Mechanical Spectrometer This instrument applies various deformations, such as bending, tension, compression, and shear, to a solid sample and operates in the oscillatory mode as well as the static mode for stress relaxation and creep. For dynamic measurements, a new synthetic oscillation mode has been added to the existing high-precision sine wave oscillation mode. The synthetic oscillation mode can measure multiple frequencies at an extremely fast rate, which allows the instrument to measure samples with extremely rapid elastic modulus transformations. Measurements from -150 °C are fully automatic using the automatic gas cooling unit. 

However, it was found that the obtained values are lower than the modulus obtained from quasi-static measurements, indicating that a direct comparison between the results from both techniques is not straightforward. A weak tendency of increasing E with increasing HA content is seen up to 20% ceramic content. As observed before, this formulation also optimised the ultimate strength, being in principle the material with better mechanical performance. 

Elastic modulus values are classified into two groups one is the static modulus, and the other is the dynamic modulus. The former is called the isothermal modulus and is obtained from the linear relationship between load and displacement of a specimen. The latter is called the adiabatic modulus and is determined from the resonance frequency or the velocity of an ultrasonic wave (USW) in a specimen. The difference between them is caused by thermal expansion, which results from the adiabatic behavior of the specimen during the propagation of an ultrasonic wave pulse in the latter. Some difficulties cannot be avoided in the determination of the isothermal modulus. For example, a relatively large specimen is needed for the static measurement of a small strain. Thus, the elastic modulus is usually determined from the velocity of an ultrasonic wave in a single crystal of a material, for which it is difficult to prepare a large specimen. 

The radiation and temperature dependent mechanical properties of viscoelastic materials (modulus and loss) are of great interest throughout the plastics, polymer, and rubber from initial design to routine production. There are a number of laboratory research instruments are available to determine these properties. All these hardness tests conducted on polymeric materials involve the penetration of the sample under consideration by loaded spheres or other geometric shapes [1]. Most of these tests are to some extent arbitrary because the penetration of an indenter into viscoelastic material increases with time. For example, standard durometer test (the "Shore A") is widely used to measure the static "hardness" or resistance to indentation. However, it does not measure basic material properties, and its results depend on the specimen geometry (it is difficult to make available the identity of the initial position of the devices on cylinder or spherical surfaces while measuring) and test conditions, and some arbitrary time must be selected to compare different materials. 

Some tests, while undergoing deformation, are usually referred to as static in that they are performed at slow speeds or low cycles. Examples of these tests are stretch modulus, ultimate tensile, and elongation to break, ie, a measure of total energy capabiUties or mpture phenomena. 

The important elastic properties of a material undergoing deformation under static tension are stiffness, elastic strength and resilience. For a material obeying Hooke s law, the modulus of elasticity, E (= o/e), can be taken to be a measure of its stiffness. The elastic... 

Being a very sensitive quantity, however, the relative energy part of the modulus is different for some of the samples, if calculated from static or dynamic data, respectively. (For the calculation method, compare ref. 2J3, K ) Table III gives the values for the relative energy part. ore(j u/ored the ener9Y part calculated from stress-strain measurements Gy/G is the corresponding number obtained from dynamic data at 0.5 Hz. 

Dynamic properties are more relevant than the more usual quasi-static stress-strain tests for any application where the dynamic response is important. For example, the dynamic modulus at low strain may not undergo the same proportionate change as the quasi-static tensile modulus. Dynamic properties are not measured as frequently as they should be simply because of high apparatus costs. However, the introduction of dynamic thermomechanical analysis (DMTA) has greatly widened the availability of dynamic property measurement. 

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