Thermally activated deformation

the activation rate of eq. (3.30) is expected to be valid in the classical range in nearly all cases of interest, well below the usual Debye temperature 0u = hvY)/k of atomic vibrations, where h and k are Planck s constant and Boltzmann s constant, respectively. 

In principle, the accomplished shear relaxation can be reversed by a reverse fluctuation of the cluster to erase the effect of the forward relaxation, albeit with the need to overcome a much larger energy barrier AG AG. Then, the net plastic-shear-strain rate becomes 

The pre-exponential factor which gives the scale of the deformation rate has a composition of 

However, as the temperature approaches Tg and the deformation resistance markedly decreases as ajz c 1.0, AG and AG become of comparable magnitude. Then, an expansion of the energy barriers around r — 0 gives 

Finally, when o-7 Qf/2 kT the expression gives a linear viscous form of response 

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The deformation is essentially a thermally activated process and the strain at the molecular level determines the overall macroscopic plastic deformation. 

The promise of luminescent methodology is based on many types of information that can be derived from mineralogical samples. These include RE from Ce to Yb, identities down to the ppb range, the valence states of the RE, the nature of the sites at which RE reside and the ways of compensating the charge, and features related to the presence of other ions (donors, activators). All this information can be used to determine the chemical, thermal, and deformational history of the material. 

Annealing in metals can first lead to stress relaxation in which stored internal strain energy due to plastic deformation is relieved by thermally activated dislocation motion (see Figure 5.18). Because there is enhanced atomic mobility at elevated temperatures, dislocation density can decrease during the recovery process. At still higher temperatures, a process known as recrystallization is possible, in which a new set of... 

Since an understanding of the importance of any one process contributing to the failure in thermoplastics and the control over these processes is only partly attainable, a knowledge and understanding of the nature of endurance Hmits is of extreme importance for successful use of plastics, in particular engineered thermoplastics [27]. In terms of the failure type, polymer fracture may occur as a rapid extension of an initial defect, plastic flow of the matter and the thermally activated flow of the macromolecules. In all these cases, however, fracture is a localized phenomenon characterized by a large inhomogeneity of deformations. 

A second difference from the continuum model is that large stresses near the reaction center should undergo thermally activated relaxation. According to the molecular mechanism of stress relaxation proposed above, such irreversible, or plastic, deformations occur in UP when the two decyl radicals back away from the reaction center by rotational translation along their long axes. In the process of making more room for the two new C02 molecules, each radical chain is driven into the adjacent interface between two layers of peroxide molecules. Introduction of a defect or a hole at the end of the peroxide chain should facilitate this motion and allow efficient relaxation of the stress. 

Values from tables of friction coefficients always have to be used with caution, since the experimental results not only depend on the materials but also on surface preparation, which is often not well characterized. In the case of plastic deformation, the static coefficient of friction may depend on contact time. Creeping motion due to thermally activated processes leads to an increase in the true contact area and hence the friction coefficient with time. This can often be described by a logarithmic time dependence... 

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