Nonuniform straining

FIGURE 9 Schematic representation of the effect of microstrain defined as the modification of an ideally equidistant lattice (top) by uniform (unidirectional) strain (center) or nonuniform strain (2-D) (bottom). Note the different effects on the diffraction line. 

Because the nonuniform strain due to residual microstress is the major cause of line broadening, we usually find that the broad diffraction lines characteristic of cold-worked metal partially sharpen during recovery. When recrystallization occurs, the lines attain their maximum sharpness. During grain growth, the lines become increasingly spotty as the grain size increases. 

Microabsorption and extinction, if present, can seriously decrease the accuracy of the direct comparison method, because this is an absolute method. Fortunately, both effects are negligible in the case of hardened steel. Inasmuch as both the austenite and martensite have the same composition and only a 4 percent difference in density, their linear absorption coefficients are practically identical. Their average particle sizes are also roughly the same. Therefore, microabsorption does not occur. Extinction is absent because of the very nature of hardened steel. The change in specific volume accompanying the transformation of austenite to martensite sets up nonuniform strains in both phases so severe that both kinds of crystals can be considered highly imperfect. If these fortunate circumstances do not exist, and they do not in most other alloy systems, the direct comparison method should be used with caution and checked by some independent method. 

Suppose the profile of is as shown in Figure 16.5 that is, suppose it continues to be of the same basic type as in Chapter 13. By itself, such a profile would drive self-diffusion of the ensemble (A, B)X across the interface without change of composition, just as in Chapter 13, with length scales B fixed by (2N K y. The material that travels is specifically wafers normal to z the interface moves with respect to remote points because of nonuniform strain rates e, as shown in Figure 13.2d. 

The driving mechanisms for the island vertical correlation have been the subject of extensive studies over the past years. Because the buried islands produce a nonuniform strain field at the surface of the spacer layer, i.e. the regions above the islands are tensely strained while the regions in between islands remain compressed, exciting models have treated the island distribution at the spacer layer surface by considering the effect of such a strain field on surface diffusion [4] or on island nucleation [3]. Recent calculations have taken into account the effect of the elastic anisotropy of the materials [16], the surface energy [18] or the elastic interaction between the buried islands with newly deposited ones [19]. However, in all of the above models it was assumed that the surface of the spacer layer becomes perfectly flat before the deposition of a new layer. From the experimental point of view, this... 

Besides the center frequency shift, the FBG spectrum develops other more intricate changes representative of proximal structural damage. For example, the processing and detailed analysis of the FBG spectrum has been used to extract the effect of nonuniform strain field in the proximity of matrix cracks and delaminations [11,12]. 

Guasto, J. S. Gollub, J. P. (2007). Hydrodynamic irreversibility in particle suspensions with nonuniform strain, Phys. Rev. E 81 061401. 

Fig. 8.32. Free energy change per unit volume of island of material due to reorganization of uniformly strained film material to a nonuniformly strained conical island. The parameter Z, defined in (8.153), represents the size of the island relative to the natural system length Q.

Nonuniform Strains and Higher-Order Effects Bending Piezoelectricity,... 

A liquid crystal (LC) in which the electric dipoles point in the same direction as the respective LC directors should exhibit not only a nonuniform strain but also a piezoelectric response when it undergoes one or more of the three nonuniform deformation modes that are identified as splay, bend, and twist. Accordingly, three different modes of piezoelectricity from nonuniform strain distributions were postulated for liquid crystals (Meyer 1969), but it was not clear whether the resulting piezoelectric effects were large enough to be observed in real experiments (Helfrich 1971). In the meantime, since the early concepts, a whole new field - flexoelectricity in liquid crystals (Buka and Eber 2013) - has developed from the pioneering work of Meyer and Helfrich on splay and bend deformation in liquid crystals. 

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