Plasticity in single crystals and polycrystalline materials

Consider a single crystal being subjected to uniaxial tension or compression, as shown in Fig. 6.20. Clearly, the ease with which plastic deformation is activated will depend not only on the ease of dislocation glide for a particular slip system but also the shear stress acting on each system. This is similar to the problem discussed in Section 2.10 (Eq. (2.44)) though one should note the plane normal, the stress direction and the slip direction are not necessarily coplanar, ( +A)5 90°. In other words, slip may not occur in the direction of the maximum shear stress. The resolved shear stress acting on the slip plane in the slip direction is 

The uniaxial yield stress o-y will determine when a critical resolved shear stress is obtained for slip on a particular plane and direction (slip system), i.e.. 

The onset of yielding is not always as smooth as that depicted in Fig. 6.21 and it can be accompanied by a stress drop (strain softening). In some cases, the drop occurs over a range of strain whereas, in the other cases, it is instantaneous. The former behavior occurs when yielding is associated with a rapid increase in the dislocation density. This allows the dislocation velocity to drop (Eq. (6.16)) and, hence, yielding can continue at a lower stress. A sharper yield drop is usually associated with dislocations being pinned by impurity atmospheres and, once the dislocations escape, yielding continues at a lower stress. 

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. 

For NaCl, the activation of the secondary slip systems at temperatures 200 C is required before ductility in polycrystals is obtained. A similar brittle to ductile transition occurs in KCl at 250 °C. For MgO, this transition occurs 1700 C. Some cubic materials, such as TiC, p-SiC and MgO.AljOj have sufficient independent primary systems but, unfortunately, the dislocations tend to be immobile in these materials. Thus, overall it is found that most ceramic polycrystals lack sufficient slip systems or have such a high Peierls stress that they are brittle except under extreme conditions of stress and temperature. 

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