Principles and Instrumentation of DMA

The study of elastic and viscoelastic materials under conditions of cyclic stress or strain is called dynamic mechanical analysis, DMA. The periodic changes in either stress or strain permits the analysis of the dynamic response of the sample in the other variable. The analysis has certain parallels to the temperature-modulated differential thermal analysis described in Sect 4.4, where the dynamic response of the heat-flow rate is caused by the cyclic temperature change. In fact, much of the description of TMDSC was initially modeled on the more fully developed DMA. The instruments which measure stress versus strain as a function of frequency and temperature are called dynamic mechanical analyzers. The DMA is easily recognized as a further development of TMA. Its importance lies in the direct link of the experiment to the mechanical behavior of the samples. The difficulty of the technique lies in understanding the macroscopic measurement in terms of the microscopic origin. The 

Dynamic mechanical analyzers can be divided into resonant and defined frequency instruments. The torsion pendulum just described is, for example, a resonant instrument. The schematic of a defined-frequency instrument is shown in Fig. 4.155. The basic elements are the force generator and the strain meter. Signals of both are collected by the module CPU, the central processing unit, and transmitted to the computer for data evaluation. The diagram is drawn after a commercial DMA which was produced by Seiko. At the bottom of Fig. 4.155, a typical sample behavior for a DMA experiment is sketched. An applied sinusoidal stress, o, is followed with a phase lag, 6, by the strain, e. The analysis of such data in terms of the dynamic moduli (stress-strain ratios, see Fig. 4.143) at different frequencies and temperature is the subject of DMA. 

In the description of the basics of thermomechanical analysis in the first part of this section the mechanical properties were assumed to result from perfect elasticity, i.e., the stress is direcdy proportional to the strain and independent of the rate of strain. Hooke s law expresses this relationship with a constant modulus as sketched at the top of Fig. 4.157 for the example of tensile stress and strain. 

The theory of hydrodynamics similarly describes an ideal liquid behavior making use of the viscosity (see Sect 5.6). The viscosity is the property of a fluid (liquid or gas) by which it resists a change in shape. The word viscous derives from the Latin viscum, the term for the birdlime, the sticky substance made from mistletoe and used to catch birds. One calls the viscosity Newtonian, if the stress is directly proportional to the rate of strain and independent of the strain itself. The proportionality constant is the viscosity, q, as indicated in the center of Fig. 4.157. The definitions and units are listed, and a sketch for the viscous shear-effect between a stationary, lower and an upper, mobile plate is also reproduced in the figure. Schematically, the Newtonian viscosity is represented by the dashpot drawn in the upper left comer, to contrast the Hookean elastic spring in the upper right. 

The idealized laws just reviewed can, however, not describe the behavior of matter if the ratios of stress to strain or of stress to rate of strain is not constant, known as stress anomalies. Plastic deformation is a common example of such non-ideal behavior. It occurs for solids if the elastic limit is exceeded and irreversible deformation takes place. Another deviation from ideal behavior occurs if the stress depends simultaneously on both, strain and rate of strain, a property called a time anomaly. In case of time anomaly the substance shows both solid and liquid behavior at the same time. If only time anomalies are present, the behavior is called linear 

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