Anelasticity internal friction

Measurements of <5 yield direct information about the magnitude of the energy dissipation and the phase angle. 0 measures the fractional energy loss per cycle due to the anelasticity and is often termed the internal friction. According to the discussion above, 8 will be a function of the frequency, to should approach zero at both low and high frequencies and will have a maximum at some intermediate frequency. The maximum occurs at a frequency that is the reciprocal of the relaxation time for the re-population of the point defects. 

In an ideal elastic solid, a one-to-one relationship between stress and strain is expected. In practice, however, there are often small deviations. These are termed anelastic effects and result from internal friction in the material. Part of the strain develops over a period of time. One source of anelasticity is thermoelasticity, in which the volume of a body can be changed by both temperature and applied stress. The interaction will depend on whether a material has time to equilibrate with the surroundings. For example, if a body is rapidly dilated, the sudden... 

In many materials, the mechanical response can show both elastic and viscous types of behavior the combination is known as viscoelasticity. In elastic solids, the strain and stress are considered to occur simultaneously, whereas viscosity leads to time-dependent strain effects. Viscoelastic effects are exhibited in many different forms and for a variety of structural reasons. For example, the thermoelastic effect was shown earlier to give rise to a delayed strain, though recovery of the strain was complete on unloading. This delayed elasticity is termed anelastic-ity and can result from various time-dependent mechanisms (internal friction). Figure 5.9 shows an example of the behavior that occurs for a material that has a combination of elastic and anelastic behavior. The material is subjected to a constant stress for a time, t. The elastic strain occurs instantaneously but, then, an additional time-dependent strain appears. On unloading, the elastic strain is recovered immediately but the anelastic strain takes some time before it disappears. Viscoelasticity is also important in creep but, in this case, the time-dependent strain becomes permanent (Fig. 5.10). In other cases, a strain can be applied to a material and a viscous flow process allows stress relaxation (Fig. 5.11). 

Time-dependent hysteresis effects can also occur in crystalline materials and these lead to mechanical damping. Models, such as the SLS and the generalized Voigt model, have been used extensively to describe anelastic behavior of ceramics. It is, thus, useful to describe the sources of internal friction in these materials that lead to anelasticity. The models discussed in the last section are also capable of describing permanent deformation processes produced by creep or densification in crystalline materials. For polycrystalline ceramics, creep is usually considered from a different perspective and this will be discussed further in Chapter 7. 

Num] Internal friction, anelastic and magnetic relaxation <2.2 mass% Cr, < 0.3 mass% N, heat treatment... 

Anelastic Mechanical behavior in which the stress and strain are not single-valued functions of each other. This occurs particularly when a periodic stress is applied due to internal friction in a viscoelastic material. 

If the internal frictions are not dependent on the amplitude, then the plot of the Napierian logarithm of the amplitudes versus the number of cycles is linear with a slope equal to the logarithmic decrement. Moreover, during damping of a sound wave, the anelastic behavior leads to a lag between the stress and strain, and the phase angle, 8, between the two waves is then related to the Napierian logarithmic decrement by the simple equation ... 

The external manifestation of reorientation relaxation under an applied stress is the anelastic strain that accompanies a net change of orientational order. In contrast to the elastic strain, the anelastic strain develops in a time-dependent manner governed by the rate of the reorientation jump. Under a static stress, the relaxation may therefore be observed as a limited (and recoverable) creep process. Frequently, however, it is more desirable for reasons of sensitivity or convenience to observe the relaxation dynamically as a loss-peak, via internal friction measurements made as a function of temperature and/or vibration frequency. Figure 2 shows the oxygen Snoek peak in polycrystalline thin film niobium, tested in the same vibrating-reed apparatus" - used for our studies of... 

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