Internal friction measurement

A perfectly elastic material, i.e. one that obeys Hooke's law and is subjected to cyclic stress, will vibrate, in the elastic domain, with no loss of energy except through possible friction with the atmosphere. In reality, materials do not behave so ideally, and their vibrations are damped faster than can be explained by the loss of energy due to external friction.

Internal friction is the property of solid materials subjected to cyclic stresses to absorb energy, transforming mechanical energy into heat. This effect manifests itself in the case of small deformations characteristic of the elastic domain.

The first techniques used to measure internal friction generally allowed measurements at fixed frequencies or in a restricted frequency range. Thus, a pendulum, usually inverted to avoid stress on the sample, allows measurements at frequencies in the hertz range; in this case, the internal friction is δ/π where δ is the logarithmic decrement of the free oscillations. Measurements in the kilohertz range are carried out on resonant blades or bars, this time with internal friction related to the width at 1/ e of the resonance peak. Finally, the attenuation of ultrasonic waves enables measurement in the megahertz range. With these techniques, it is therefore necessary to vary the measurement temperature to fully describe the anelastic behavior, assuming a frequency-temperature equivalence which, in fact, is rarely verified.

This is why it is preferable to be able to measure internal friction directly over a wide frequency range (5 or 6 decades), either with dynamic analyzers used mainly for polymer studies, or with very high natural frequency pendulums (200 Hz) used in sub-resonant forced vibration. In both cases, internal friction is directly related to the tangent of the phase shift angle between the applied stress and the resulting strain.

Internal friction can be associated with various mechanisms, among which we generally distinguish :

• the relaxation process in the case of a viscoelastic material ;

• mechanical hysteresis ;

• resonance in a solid that can be considered as a viscous medium.

Internal friction due to hysteresis depends on vibration amplitude, unlike in the other two cases.

We shall limit ourselves here to internal friction by relaxation, the formalism of which we shall establish after defining the viscoelastic behavior; examples corresponding to various types of material will then be presented.