Dynamic mechanical damping

Figure 6. Dynamic mechanical damping of CE 339/1300 at low temperatures. (Reproduced from reference 8.)...

Dynamic Mechanical Damping of 50% Styrene S/I/S Bonded Joint and Free Film at 110 Hz. Bond Thicknesses Shown on Curves in CM for Joints. Free Film = B. 

Dynamic Mechanical Damping of a Block Copolymer Film with Molecular Orientation Parallel (X) and Perpendicular ( ) to the Testing Direction at 110 Hz. 

Fig. 8. Dynamic mechanical damping spectrum for poly(dicyclooctyl itaconate). ("Reproduced from J.M.G. Cowie, R. Ferguson, and I.J. McEwen, Polymer, 23, 605 (1982), by permission of the publishers, Butterworth and Co. (Publishers) Ltd. "). 

Another resonant frequency instmment is the TA Instmments dynamic mechanical analy2er (DMA). A bar-like specimen is clamped between two pivoted arms and sinusoidally oscillated at its resonant frequency with an ampHtude selected by the operator. An amount of energy equal to that dissipated by the specimen is added on each cycle to maintain a constant ampHtude. The flexural modulus, E is calculated from the resonant frequency, and the makeup energy represents a damping function, which can be related to the loss modulus, E". A newer version of this instmment, the TA Instmments 983 DMA, can also make measurements at fixed frequencies as weU as creep and stress—relaxation measurements. 

Similar information can be obtained from analysis by dynamic mechanical thermal analysis (dmta). Dmta measures the deformation of a material in response to vibrational forces. The dynamic modulus, the loss modulus, and a mechanical damping are deterrnined from such measurements. Detailed information on the theory of dmta is given (128). 

Dynamic mechanical tests measure the response or deformation of a material to periodic or varying forces. Generally an applied force and its resulting deformation both vary sinusoidally with time. From such tests it is possible to obtain simultaneously an elastic modulus and mechanical damping, the latter of which gives the amount of energy dissipated as heat during the deformation of the material. 

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. 

An associated technique which links thermal properties with mechanical ones is dynamic mechanical analysis (DMA). In this, a bar of the sample is typically fixed into a frame by clamping at both ends. It is then oscillated by means of a ceramic shaft applied at the centre. The resonant frequency and the mechanical damping exhibited by the sample are sensitive measurements of the mechanical properties of a polymer which can be made over a wide range of temperatures. The effects of compositional changes and methods of preparation can be directly assessed. DMA is assuming a position of major importance in the study of the physico-chemical properties of polymers and composites. 

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. 

Dynamic mechanical testers apply a small sinusoidal stress or strain to a small sample of the polymer to be examined and measure resonant frequency and damping versus temperature and forced frequency. Instrument software computes dynamic storage modulus (G ), dynamic loss modulus (G") and tan delta or damping factor. Measurements over a wide range of frequency and temperature provide a fingerprint of the polymer with sensitivity highly superior to DSC. 

Dynamic mechanical experiments yield both the elastic modulus of the material and its mechanical damping, or energy dissipation, characteristics. These properties can be determined as a function of frequency (time) and temperature. Application of the time-temperature equivalence principle [1-3] yields master curves like those in Fig. 23.2. The five regions described in the curve are typical of polymer viscoelastic behavior. 

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. 

Dynamic mechanical tests measure the response of a material to a periodic force or its deformation by such a force. One obtains simultaneously an elastic modulus (shear, Young s, or bulk) and a mechanical damping. Polymeric materials are viscoelastic-i.e., they have some of the characteristics of both perfectly elastic solids and viscous liquids. When a polymer is deformed, some of the energy is stored as potential energy, and some is dissipated as heat. It is the latter which corresponds to mechanical damping. 

The variation of the damping factor (tan 5) with temperature was measured using a Polymer Laboratories Dynamic Mechanical Thermal Analyzer (DMTA). The measurements were performed on the siloxanfe-modified epoxies over a temperature range of — 150° to 200 °C at a heating rate of 5 °C per minute and a frequency of 1 Hz. The sample dimensions were the same as those used for flexural modulus test specimens. 

Dynamic-Mechanical Measurement. This is a very sensitive tool and has been used intensively by Nielsen (17) and by Takayanagi (18). When the damping curves from a torsion pendulum test are obtained for the parent components and for the polyblend and die results are compared, a compatible polyblend will show a damping maximum between those of the parent polymers whereas the incompatible polyblend gives two damping maxima at temperatures corresponding to those of the parent components. Dynamic mechanical measurement can also give information on the moduli of the parent polymer and the polyblend. It can be shear modulus or tensile modulus. If the modulus-temperature curve of a polyblend locates between those of the two parent polymers, the polyblend is compatible. If the modulus-temperature curve shows multiple transitions, the polyblend is incompatible. 

As shown in Chapter 10, molecular dynamics in polymers is characterized by localised and cooperative motions that are responsible for the existence of different relaxations (a, (3, y). These, in turn, are responsible for energy dissipation, mechanical damping, mechanical transitions and, more generally, of what is called a viscoelastic behavior - intermediary between an elastic solid and a viscous liquid (Ferry, 1961 McCrum et al., 1967). 

The stiffness modulus is, in most cases, measured in dynamical - mechanical experiments, for instance with a torsion pendulum, on a time scale of a few seconds. This experiment results in the shear modulus, G (which is related to Young s modulus, E), while the damping shows a strong maximum at Tg. 

Various types of vibration experiments can be carried out to measure E and E2 at a certain frequency. An example is the torsion pendulum, in which the sample, connected to an auxiliary mass, is brought into a free torsional oscillation. From the frequency of the pendulum (around 1 to 10 sec) E is calculated, from the rate of damping tan 8 and E2. Other types of dynamic mechanical measurements can be carried out at higher frequencies, such as bending vibrations with or without extra mass, wave propagation, etc. By combining a number of these different techniques, a time scale ranging from 10 to 10"8 sec can be covered. 

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