Dynamic Stress and Strain Properties

In dynamic tests the rubber is subjected to cyclic deformation, and the stress and strain are monitored. Dynamic properties are important in a large number of engineering applications of rubber, including springs and dampers, and are generally much more useful from a design point of view than the results given by the static tests. 

The force vibration machines may operate at resonance or away from resonance. 

There is an international standard ISO 2856 [13] dealing with general requirements for dynamic testing which can be referred to for the classification of test machines, preferred conditions, and recommended test shapes [1]. 

The static tests considered in this chapter treat the rubber as being essentially an elastic, or rather, high elastic material, whereas it is in fact visco-elastic and hence its response to dynamic stressing is a combination of an elastic response and of a viscous response, so that energy is lost in each cycle. The Maxwell model represents this behavior as spring and dashpot in parallel. 

If the rubber were a perfect spring, the stress t would be similarly sinusoidal and in phase with the strain. However, because the rubber is visco-elastic the stress will not be in phase with the strain but can be considered to precede it by the phase angle S, so that Equation 6.1 is rewritten as follows  

---

The four variables in dynamic oscillatory tests are strain amplitude (or stress amplitude in the case of controlled stress dynamic rheometers), frequency, temperature and time (Gunasekaran and Ak, 2002). Dynamic oscillatory tests can thus take the form of a strain (or stress) amplitude sweep (frequency and temperature held constant), a frequency sweep (strain or stress amplitude and temperature held constant), a temperature sweep (strain or stress amplitude and frequency held constant), or a time sweep (strain or stress amplitude, temperature and frequency held constant). A strain or stress amplitude sweep is normally carried out first to determine the limit of linear viscoelastic behavior. In processing data from both static and dynamic tests it is always necessary to check that measurements were made in the linear region. This is done by calculating viscoelastic properties from the experimental data and determining whether or not they are independent of the magnitude of applied stresses and strains. 

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. 

Viscoelasticity deals with the dynamic or time-dependent mechanical properties of materials such as polymer solutions. The viscoelasticity of a material in general is described by stresses corresponding to all possible time-dependent strains. Stress and strain are tensorial quantities the problem is of a three dimensional nature (8), but we shall be concerned only with deformations in simple shear. Then the relation between the shear strain y and the stress a is simple for isotropic materials if y is very small so that a may be expressed as a linear function of y,... 

In the last chapter we discussed the relation between stress and strain (or instead rate-of-strain) in one dimension by treating the viscoelastic quantities as scalars. When the applied strain or rate-of-strain is large, the nonlinear response of the polymeric liquid involves more than one dimension. In addition, a rheological process always involves a three-dimensional deformation. In this chapter, we discuss how to express stress and strain in three-dimensional space. This is not only important in the study of polymer rheological properties in terms of continuum mechanics " but is also essential in the polymer viscoelastic theories and simulations studied in the later chapters, into which the chain dynamic models are incorporated. 

The fundamental property of asphalts related to stress and strain is called stiffness modulus, which is distinguished into dynamic and static stiffness modulus. 

This is because the knot is a weak place at which stresses concentrate, causing tensile properties to decrease. The breaking stress and the work of rupture values were not consistently affected by dynamic stress. Peak strain value was significantly lowered by the application of dynamic stress for 1 h... 

The quantities E and G refer to quasi-static measurements. When cyclic motions of stress and strain are involved, it is more convenient to use dynamical mechanical moduli. The complex Young s modulus is then defined as = " + iE", where E is the storage modulus and " the loss modulus. The storage modulus is a measure of the energy stored elastically during deformation the loss modulus is a measure of the energy converted to heat. Similar definitions hold for G, J, and other mechanical properties. 

The viscoelastic properties of concentrated o/w and w/o emulsions were investigated using dynamic (oscillatory) measurements. For that purpose a Bohlin VOR (Bohlin Reologie, Lund, Sweden) instrument was used. Concentric cylinder platens were used and the measurements were carried out at 25 0.1 °C. In oscillatory measurements, the response in stress of a viscoelastic material subjected to a sinusoidally varying strain is monitored as a function of strain amplitude and frequency. The stress amplitude is also a sinusoidally varying function in time, but for a viscoelastic material it is shifted out of phase with the strain. The phase angle shift between stress and strain, 5, is given by... 

Dynamic Mechanical Properties n (1) The stress-strain properties of a material when subjected to an applied sinusoidally varying stress or strain. For a perfectly elastic material the strain response is immediate and the stress and strain are in phase. For a viscous fluid, stress and strain are 90° out of phase. (2) The mechanical properties of composites as deformed under periodic forces such as dynamic modulus, loss modulus and mechanical damping or internal friction. (Sepe MP (1998) Dynamic mechanical analysis. Plastics Design Library, Norwich, New York)... 

---