Slip bands intersecting

The stress-strain behavior of ceramic polycrystals is substantially different from single crystals. The same dislocation processes proceed within the individual grains but these must be constrained by the deformation of the adjacent grains. This constraint increases the difficulty of plastic deformation in polycrystals compared to the respective single crystals. As seen in Chapter 2, a general strain must involve six components, but only five will be independent at constant volume (e,=constant). This implies that a material must have at least five independent slip systems before it can undergo an arbitrary strain. A slip system is independent if the same strain cannot be obtained from a combination of slip on other systems. The lack of a sufficient number of independent slip systems is the reason why ceramics that are ductile when stressed in certain orientations as single crystals are often brittle as polycrystals. This scarcity of slip systems also leads to the formation of stress concentrations and subsequent crack formation. Various mechanisms have been postulated for crack nucleation by the pile-up of dislocations, as shown in Fig. 6.24. In these examples, the dislocation pile-up at a boundary or slip-band intersection leads to a stress concentration that is sufficient to nucleate a crack. 

Fig. 8.11 Crack nucleation at slip band intersection in MgO crystal [39]. With kind permission of Elsevier...

As the projected surface area of the emitter in a field-ion microseope is typically 10 io A, it is obvious that this technique can reveal emergent dislocations only when the dislocation density is quite high. Nevertheless, much beautiful work on the dislocation content of metals has been carried out (92, 95). It has, for example, been possible to observe a (3T7)[110] type emergent edge dislocation on a platinum surface (92) and slip bands, and complex patterns of intersecting dislocations have been photographed. While it is not possible to locate... 

Fig. 3.85 Slip bands in the intermediate region of the indented volume, a Slip band planarity and evidence of profuse pile-ups. The dislocations exhibiting paired lines in the boxed area are not dipoles but dissociated dislocations since the distance between partials is constant whether the dipole is imaged with the g or -g reflecting plane, b Intersecting slip bands, c The slight misalignment and differences in pile-up projected widths indicate that the slip bands are parallel to at least two crystallographically distinct planes [31]. With kind permission of Elsevier...

Nevertheless, after long and systematic studies, it is common opinion that persistent shp bands form prevalently on the surface of metals and are favored by the tendency to cross slip and intersecting shp band that form only on the surface and... 

Fig. 2.4 Evidence of intersecting slip bands and cross slip in an Armco iron [10]...

An example for a pileup at the intersection of two slip bands is shown in Figure 6.8. This pileup is the result of the application of a tensile load. Dislocations move at an angle of 45° to the tensile stress produced. 

Dislocation pileup at the intersection of two slip bands resulting in the nucleation of a crack. 

The criteria (Eqs. 11 and 12) are similar and are derived from studies on materials that are elastic at initiation of crazing, while more ductile materials like polycarbonate show a more pronounced sensitivity to the hydrostatic tension. This has been found experimentally by Ishikawa and coworkers [1, 27] for notched specimens of polycarbonate. Crazing appears ahead of the notch root, at the intersection of well-developed shear bands. From a slip fine field analysis, the tip of the plastic zone corresponds to the location of the maximum hydrostatic stress. This has been confirmed by Lai and Van der Giessen [8] with a more realistic material constitutive law. Therefore, Ishikawa and coworkers [1,27] suggested the use of a criterion for initiation based on a critical hydrostatic stress. Such a stress state condition can be expressed by Eq. 11 with erg = 0 and I r = B°/A°. Thus, the criterion (Eq. 11) can be considered general enough to describe craze initiation in many glassy polymers. For the case of polycarbonate, a similar criterion is proposed in [28] as... 

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