Dynamic Mechanical Analysis, strain

Glass-transition temperatures are commonly determined by differential scanning calorimetry or dynamic mechanical analysis. Many reported values have been measured by dilatometric methods however, methods based on the torsional pendulum, strain gauge, and refractivity also give results which are ia good agreement. Vicat temperature and britde poiat yield only approximate transition temperature values but are useful because of the simplicity of measurement. The reported T values for a large number of polymers may be found ia References 5, 6, 12, and 13. 

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. 

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. 

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). 

Small deformation dynamic mechanical analysis on compressed or blown fdms was done using a Rheometrics Scientific RSA II Solids Analyzer. Samples were tested using an initial applied force of 150 grams, an applied strain of 0.1%, and were heated from -100°C to 200°C at 10°C/min. A triplicate set of tests were performed for each samples... 

The dynamic mechanical analysis method deter-minesl l elastic modulus (or storage modulus, G ), viscous modulus (or loss modulus, G"), and damping coefficient (tan A) as a function of temperature, frequency or time. Results are usually in the form of a graphical plot of G, G", and tan A as a function of temperature or strain. DMA may also be used for quality control and product development purposes. 

Dual Cure. Films were prepared for Dynamic Mechanical Analysis (DMA). All films were cast on release paper with a 4.5 mil draw down bar, and partially cured with two 200 watt/inch lamps at half power and a belt speed of 200 ft/min. The films were intentionally under cured to facilitate cutting with minimal flaws. After the films were cut into ii-inch test pieces, they were cured with two 200 watt/inch lamps at 100 ft/min, equal to 260 millijoules/cm dose. The instrument used for the DMA work was a Rheometrics RSA II Solids Analyzer. All tests were made at a frequency of 11 hz with a nominal strain of 0.05%, under nitrogen. Both temperature scans, at 2°C/minute, and isothermal runs were made. 

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) ... 

Dynamic Mechanical Analysis and Stress Relaxation Behavior. Samples were compression molded into bars of the dimensions 38.xl2.5x0.78 0.007 mm and 65.x9.7xl.7 0.007 mm in a Carver laboratory hot press model C. A TA Instruments 983 DMA, which was operated in the fixed frequency mode, was used to characterize the storage and loss moduli as a function of temperature. Samples were scanned at fi-equencies from 0.05 to 10.0 Hz over a temperature range from -150 C to above the glass transition temperature. The displacement was 0.4 - 0.6 mm. Stress relaxation curves were determined for the same size samples at a constant strain. The sample was displaced for 10.0 minutes and then allowed to recover for 10.0 minutes. The stress data were taken in five degree increments. A microprocessor controlled Liquid Nitrogen Cooling Accessory (LNCA) was used for sub-ambient operations. 

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 dynamic mechanical analysis (DMA) was carried out using a Model Q-800 (Thermal Analysis). The strain rate mode can be used to collect stress versus strain data equivalent to that obtained from a universal testing machine. In this mode, a 10 mm gauge length ofeliber sample was stretched at a strain rate of 500 p /min until the sample broke or yielded at 2 °C. 

A Shitnadzu 1601 and a Caiy 5000 were employed for UV- fis and NIR spectroscopy, respectively. Mechanical tests were carried out using a dynamic mechanical analysis (DMA) instmment Q-800 (TA series) in strain rate mode to record the force -displacement data generated at constant temperature (10 mm gauge length, 0.5 mm/ min). 

Dynamic mechanical analysis (DMA) is a technique used to study and characterize materials, proved to be extremely useful for studying viscoelasticity. With the complex modulus of the sample determined by the measurement of the strain response to a sinusoidal... 

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