Modulus and damping

A technique for performing dynamic mechanical measurements in which the sample is oscillated mechanically at a fixed frequency. Storage modulus and damping are calculated from the applied strain and the resultant stress and shift in phase angle. 

Dynamic Mechanical and Thermomechanical Analysis. A DuPont Model 981 DMA was used to determine the dynamic modulus and damping characteristics of baseline and irradiated specimens. Transverse composite samples 1.27 cm x 2.5 cm were used so that the modulus and damping data were primarily sensitive to matrix effects. Data were generally determined from -120°C through the glass transition temperature (Tg) of each material using a heating rate of 5°C/min. 

Bank and co-workers [19] have proposed using thermal analysis to measure other parameters for detecting local moisture content, changes in modulus and damping, and crystallinity in composite materials. 

Derive an analytical relationship between openloop oiajumum log modulus and damping coeflident for a second-order underdamped openloop system with a gain of unity. Show that a damping coeflident of 0.4 corresponds to a maximum log modulus of +2J dedbels. 

DMTA graph of storage Young s modulus and damping (tan 5) versus temperature, for EVA foam of density... 

It is difficult to specify accuracy in this experiment. One reason is that there may be sampling effects, i.e., wide variability in the samples used. Consequently, the sample should be homogeneous and representative. There is a strong dependence of the modulus and damping behavior on molecular and structural parameters. Entrapped air/gas may affect the results obtained using powder or pellet samples. 

Dynamic Mechanical Tests. Plasticizer efficiency, can be measured, not only be the lowering of T , but also by temperature dependence of typical dynamic mechanical properties, such as modulus and damping. 

While there are many methods for measuring modulus and damping, one of the simplest involves using a torsion pendulum (23, 24, 25) as illustrated in Figure 11. 

Figure 11. Schematic diagram of a torsion pendulum for measuring dynamic shear modulus and damping. A typical damped oscillation curve is illustrated at the bottom of the figure (25)...

Figure 12 shows typical modulus and damping curves for an uncross-linked, amorphous polymer (a copolymer of styrene and butadiene) 25),... 

For T measurements, calorimetry (DSC-990 Du-Pont), linear and volume cubic thermal expansion (TMS-2 Perkin-Elmer), thermo-stimulated discharge (TSD) technique, dynamic mechanical Young modulus and damping (DMA-981 DuPont) and dielectric (102-105 Hz) measurements have been used as experimental techniques. All methods gave very well correlated values of T 19). 

While the design of such coatings is straightforward, selection of appropriate materials is not. Usually materials with the properties required for a particular application are not readily available, and some custom laboratory fabrication is necessary. This usually involves selecting a polymer composite which somewhat approximates the required physical properties. Then minor alterations to the chemical constituents or fillers are used on a trial basis and the acoustic properties (some combination of Young s Modulus and damping factor, sound speed, attenuation, density, and front-face reflectivity) of these sample formulations are measured. This continues until a suitable formulation is achieved. 

The changes which occur in thermosetting resins undergoing cure have been studied by a variety of techniques. Supported sample methods have been used to monitor the relative changes modulus and damping behavior from the initial low viscosity liquid to the fully cured rubbery or glassy state. Torsional braid analysis (TBA) employs a resin sample impregnated on a... 

DMA provides materials scientists, pol5mer chemists, and design engineers with detailed information on the elastic and inelastic (plastic) deformation of materials, modulus, and damping (energy dissipation) properties of materials. The damping behavior of S5mthetic and natural mbbers is important in vibration and acoustic application, for example. 

Physical Property Evaluation. A Rheovibron (direct reading dynamic viscoelastometer, model RHEO-200, manufactured by Toyo Measuring Instruments Co.) was used to measure the temperature dependence of the complex modulus and damping, tan 6, at 11 Hz. 

Polymers are also used in adhesives and Avalon [11] noted that TG can be used in combination with a database of information about the components of the product and the product itself to compare the maximum mass loss temperature and profile of the TG curve to provide a quantitative analysis of the product. The database of information can be either a strength or weakness of this approach, depending on the completeness of the data available for the comparative work. The use of DSC, DMA/TMA and TG were also discussed [12] relative to adhesive applications. Among the properties examined were % crystallinity, Tg, cure state, environmental stability, blend ratios, modulus and damping, thermal expansion and shrinkage, composition, volatiles and plasticizer levels. 

A viscoelastic response to deformation, with modulus and damping properties strongly influenced by temperature and frequency... 

Half way between conventional thermomechanical analysis and dynamic mechanical analysis is the technique of dynamic force (or load) TMA. This method uses a standard TMA instrument but the force is changed between two values in a stepwise (or sometimes sinusoidal) fashion. The dimensional changes of the specimen are monitored as a function of time (and temperature) but no attempt is made to determine the modulus and damping properties of the material. 

The dynamic modulus and damping of a Maxwell unit as a function of frequency are schematically shown in Figure 3.23. The nature of the curves in Figure 3.23 can be explained qualitatively as follows. 

Figure 25 Typical transition behavior in mechanical storage modulus and damping for a semicrystalline polymer. Relaxations in the amorphous phase are labeled with Greek letters (a, p, 7) with... 

Rg. 7.12 A torsion pendulum for the determination of shear modulus and damping at frequencies near 1 Hz. The support wire has negligible torsional rigidity. (Reproduced by permission of L. C. E. Struik.)... 

ASTM D4015.2007. Standard Test Method for Modulus and Damping of Soils by Resonant Column Method. American Society for Testing and Materials, Philadelphia, PA, p. 10. 

Hardin, B.O., and Dmevich, V.R 1972. Shear modulus and damping in soils Design equations and curves. Journal of the Soil Mechanics and Foundations Division, ASCE, 98, No. 7, pp. 667-692. 

Figure 2. Modulus and damping (tan 5) during isothermal cure of DGEBF/DDM at three different tenqieratures.

Nonlinear soil behavior Is modeled by the equivalent linear method, In which an approximate nonlinear solution Is obtained by Iterating a linear solution until the soil shear modulus and damping values used In the analysis are compatible with the effective shear strain amplitudes computed at all points in the soil mass system. 

However, the mechanical consequences of physical ageing are fortunately reduced considerably by fibre reinforcement. Moreover it is found that the alterations in at least some of the mechanical properties, such as modulus and damping, caused by physical ageing are confined to a limited temperature range around the ageing temperature and do not affect ambient temperature performance unless ageing has been carried out at ambient temperature [20] in which case the deterioration would probably take decades. 

---