Parabolic markings

However, when stable-unstable fracture occurs (between Transitions 0 and I), evidence of secondary crack nucleation has been obtained by SEM on postmortem fracture surfaces. These cracks lead to parabolic markings ahead of the main blunt crack propagating in the plastic zone. Figure 8a shows an example of such secondary cracks developed at the boundary between the stable growth region and the unstable fracture surface in a 2 L45 specimen tested at 0.1 m/s. 

Figure 8. 2 L45 tested at 0.1 m/s (a) SEM fractographic observation of the intermediate region between stable and unstable crack propagation and (b) direction of the main and secondary cracks, indicated by arrows, according to the three regions (see text) containing parabolic marks.

Note the parabolic markings. Arrow indicates the direction of fracture propagation. 

Parabolic markings on a PMMA fracture surface caused by the nucleation of disc like cracks ahead of the main crack, which has moved to the left. 

The specimen failed after K c was reached. These different stages exist in most cases of tensile brittle fracture, but their duration, their relative importance, and additional structural features (Wallner lines in impact, parabolic markings due to the initiation of secondary cracks, striations in fatigue) depend on the stress-time history (19). 

Fig. 9.28. Higher magnification of the middle section of Fig. 9.27 showing parabolic markings. (Courtesy W. Doll, IFKM Freiburg).

Also, the deviations from a parabolic shape are greater with some solutions than with others. Electrocapillaiy curves show, for instance, a marked sensitivity to the nature of the anions present in the electrolyte (Fig. 6.63). In contrast, the curves do not seem to be affected significantly by the cations present unless they are large organic cations, e.g., tetraalkylammonium ions. 

Near the minimum of the ground electronic surface, the anharmonicities generally play the role of perturbations so that the spectra are regular and the first mechanism is weak. It should become more important when the potential surface deviates significantly from the parabolic shape. The second mechanism, by contrast, may have a very marked effect, as illustrated by the example of N02 [5, 6],... 

Figure 1.70 (a) Schematic of a 3-inlet/9-outlet microfluidic network, (b) Linear and (c, d) parabolic gradients of fluorescein in solution. The inlet concentrations are indicated by I,. The plots show the fluorescence intensity profile across the broad outlet channel. The theoretically calculated concentration profiles and the contributions of the individual inlets are marked [117] (by courtesy of ACS). 

Fig. 4 Battery sales in Japan from 1992 to 1997 (from Ref. 12). The sales showed a parabolic trend. In all the years, the sales showed a positive marked growth with respect to the previous year.

Interfacial tension against electrode potential curves have a parabolic shape with a maximum value which depends on the nature and concentration of the electrolyte (see fig. 10.1). Detailed results for the mercury aqueous solution interface were initially reported by Gouy [7, G5]. Examination of these data for the alkali metal halides shows that the interfacial tension depends markedly on the nature of the electrolyte at positive potentials. On the other hand, the variation with electrolyte at negative potentials is rather small. It follows that the anions in the electrolyte strongly affect the interfacial tension when they predominate in the double layer. 

Stage 2 also follows logarithmic kinetics, reflecting competition between parabolic oxide growth and short circuit diffusion down preferred channels. Initially, the short circuit paths account for the early observed rapid scale growth. A transition is later observed to parabolic kinetics, which marks the onset of the third stage of scale growth in hot salt accelerated oxidation of -y-TiAl. 

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