Dynamic Mechanical Analysis, stress

In a similar fashion. Thermally Stimulated Current spectrometry (TSC) makes use of an appHed d-c potential that acts as the stress to orient dipoles. The temperature is then lowered to trap these dipoles, and small electrical currents are measured during heating as the dipoles relax. The resulting relaxation maps have been related to G and G" curves obtained by dynamic mechanical analysis (244—246). This technique, long carried out only in laboratory-built instmments, is available as a commercial TSC spectrometer from Thermold Partners L.P., formerly Solomat Instmments (247). 

In dynamic mechanical analysis of plastics, the material is subjected to a sinusoidal variation of stress and the strain is recorded so that 1, 2 and S can be determined. The classical variation of these parameters is illustrated in Fig. 2.55. 

Glass transition temperature (Tg), measured by means of dynamic mechanical analysis (DMA) of E-plastomers has been measured in binary blends of iPP and E-plastomer. These studies indicate some depression in the Tg in the binary, but incompatible, blends compared to the Tg of the corresponding neat E-plastomer. This is attributed to thermally induced internal stress resulting from differential volume contraction of the two phases during cooling from the melt. The temperature dependence of the specific volume of the blend components was determined by PVT measurement of temperatures between 30°C and 270°C and extrapolated to the elastomer Tg at —50°C. 

In a way similar to that described for polyethylene fere-phthalate (Sect. 4.2), some antiplasticiser small molecules with a specific chemical structure are able to affect the ft transition and the yield stress of epoxy resins, but they do not have any effect on the y transition. In the case of HMDA networks, an efficient antiplasticiser, EPPHAA, whose chemical structure is shown in Table 8, has been reported [69]. The investigation of such antiplasticised epoxy networks by dynamic mechanical analysis as well as solid-state NMR experiments [70] can lead to a deeper understanding of the molecular processes involved in the ft transition and of their cooperativity. 

When the perturbation is a stress, the response is a strain and S" is the complex compliance, J = J —iJ" (dynamic mechanical analysis DMA)... 

Viscoelasticity is studied using dynamic mechanical analysis. When we apply a small oscillatory strain and measure the resulting stress. Purely elastic materials have stress and strain in phase, so that the response of one caused by the other is immediate. In purely viscous material the phase delay between stress and strain reach 90 degree phase lag. 

The main experimental methodology used is to directly characterize the tensile properties of CNTs/polymer composites by conventional pull tests (e.g. with Instron tensile testers). Similarly, dynamic mechanical analysis (DMA) and thermal mechanical analysis (TMA) were also applied to investigate the tensile strength and tensile modulus. With these tensile tests, the ultimate tensile strength, tensile modulus and elongation to break of composites can be determined from the tensile strain-stress curve. 

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. 

Finally, one of the most useful ways of measuring viscoelastic properties is dynamic mechanical analysis, or DMA. In this type of experiment, an oscillating stress is applied to the sample and the response is measured as a function of the frequency of the oscillation. By using different instruments this frequency can be varied over an enormous range. Actually, the sample is usually stretched a little bit and oscillated about this strain also, the stress necessary to produce an oscillatory strain of a given magnitude is the quantity usually measured. If the sample being oscillated happens to be perfectly elastic, so that its response is instantaneous, then the stress and strain would be completely in-phase. If a sinusoidal shear strain is imposed on the sample we have (Equation 13-72) ... 

Dynamic mechanical analysis (DMA). This technique is mainly used for determining the viscoelastic properties of a sample. The sample is subjected to an oscillating deformation and the amount of energy stored or lost is measured. In a purely elastic material, Hooke s law will be obeyed and the stress and strain will be in-phase. In a viscoelastic material, the ratio of the viscous (or dissipating) energy to elastic (or storage) energy is obtained as tan 8. 

Dynamic mechanical analysis involves the determination of the dynamic properties of polymers and their mixtures, usually by applying a mechanical sinusoidal stress For linear viscoelastic behaviour the strain will alternate sinusoidally but will be out of phase with the stress. The phase lag results from the time necessary for molecular rearrangements and this is associated with the relaxation phenomena. The energy loss per cycle, or damping in the system, can be measured from the loss tangent defined as ... 

It is well known that the elementary theory of beams described above becomes inadequate for beams with transverse dimensions of the same order of magnitude as their length. This section deals with the theory to be applied to thick non-slender beams. This theory appears to be relevant in the context of dynamic mechanical analysis. The first fact to be considered is that when the beam is flexed it experiences a shear stress that provokes a relative sliding of the adjacent transverse sections. As a consequence, the larger the transverse section, the higher is this shear strain. The final effect is an increase in the total deflection of the beam (Fig. 17.5). 

In dynamic mechanical analysis (DMA), the sample is subjected to a periodically varying stress (of usually sinusoidal or angular frequency). The response of the sample to this treatment provides information on the... 

Experimentally, these principles emphasize dynamic measurements that make possible the separation of the dissipative and the conservative components of energy Incident upon the system. Dynamic mechanical analysis has been an Important area of research for over 40 years. Computer-controlled experimentation now makes It possible to apply analogous techniques to the measurement of many other thermodynamic stresses. One example currently under Investigation, dynamic photothermal spectroscopy. Is expected to provide a new approach to predicting the long-term effects of ultraviolet radiation on materials [39]. 

The similarity of TMDSC and dynamic-mechanical analysis (DMA) raised the question vdiether a complex heat ccqxicity would be of use in analogy to the stress/strain ratio (7 4). One writes for the reversing heat C2q>acity of Equation (4) the complex expression for Cp... 

TABLE 20.1 Parameters Measured in a Dynamic Mechanical Analysis (w Is the Frequency of Oscillatory Stress, t Is the Time, and S Is the Phase Angle Between Stress and Strain) ... 

This study compared methacrylate and acrylate polymers to structural analogs with fluorinated ester groups. Two types of relaxations were characterized, the primary relaxation associated with the glass transition and secondary relaxations associated with side group motion and localized segmental motion. Dielectric analysis was used to characterize the response of dipoles to an electric field as a fimction of temperature. Mechanical properties were analyzed via dynamic mechanical analysis and stress relaxation measurements. Relaxation behavior was interpreted in terms of intermolecular and intramolecular mechanisms. 

In this paper, we analyze the effect of fluorine substitution in the polymers listed above by dielectric analysis (DEA), dynamic mechanical analysis (DMA) and stress relaxation measurements. The effect of fluorination on the a relaxation was characterized by fitting dielectric data and stress data to the Williams, Landel and Ferry (WLF) equation. Secondary relaxations were characterized by Arrhenius analysis of DEA and DMA data. The "quasi-equilibrium" approach to dielectric strength analysis was used to interpret the effect of fluorination on "complete" dipole... 

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