Basal-plane deformation

This process, referred to as complementary climb systems [52] is conceptually identical to the mechanisms of basal-plane deformation in the hexagonal simple metals Zn and Be [47] and in decagonal Al-Ni-Co [53]. 

Beryllium is a light metal (s.g. 1 -85) with a hexagonal close-packed structure (axial ratio 1 568). The most notable of its mechanical properties is its low ductility at room temperature. Deformation at room temperature is restricted to slip on the basal plane, which takes place only to a very limited extent. Consequently, at room temperature beryllium is by normal standards a brittle metal, exhibiting only about 2 to 4% tensile elongation. Mechanical deformation increases this by the development of preferred orientation, but only in the direction of working and at the expense of ductility in other directions. Ductility also increases very markedly at temperatures above about 300°C with alternative slip on the 1010 prismatic planes. In consequence, all mechanical working of beryllium is carried out at elevated temperatures. It has not yet been resolved whether the brittleness of beryllium is fundamental or results from small amounts of impurities. Beryllium is a very poor solvent for other metals and, to date, it has not been possible to overcome the brittleness problem by alloying. 

Normally, dislocation-based plastic deformation is irreversible, that is, it is not possible to return the material to its original microstructural state. Remarkably, fully reversible dislocation-based compressive deformation was recently observed at room temperature in the layered ternary carbide Ti3SiC2 (Barsoum and El-Raghy, 1996). This compound has a hexagonal stmcture with a large cja ratio and it is believed that the dominant deformation mechanism involves dislocation movement in the basal plane. 

The initial dislocation density of the sample was estimated to be less than 10 m ". The orientation of the samples was chosen in order to align the torsion axis as close as possible with the c-axis ( 1°). The maximum resolved shear stress is then applied on the basal planes. The plastic deformation is accommodated by the glide of screw dislocations on the... 

Figure 5 represents a typical evolution of the dislocation pattern during the deformation. The simulation was performed in a 20 mm diameter crystal, with 2 initial basal planes activated (one system in each plane) at the beginning of the deformation. It clearly appears that the double cross-slip mechanism propagates the plasticity in many other basal planes. One can also notice the asymmetry in the plane expansion due to the dislocation interactions. 

Figure 3. Thermally averaged deformation maps. Section (a) at z = 0.75 in the basal plane, (b) at z = 0.625 (containing the tetrahedral position) and (c) at z = 0.5 (containing the octahedral position). The origin is at the top left comer and the a and b axes increase across and down the page respectively. Contours are at intervals of 0.015 a.u. and dotted lines are negative, solid lines are positive.

The elastic part includes deformation of the ice crystal, its mounting and the testing machine as a whole while, in a well-designed experiment, Cp should be wholly confined to the crystal under test. The actual plastic deformation is caused by motion of dislocations in the basal plane, a subject to which we return presently. If, then, n is the concentration, v the velocity and b the magnitude of the Burgers vector of these dislocations, we can write, g j... 

So far we have considered only slip parallel to the basal plane in ice and, though this is a very strongly preferred deformation mode, it is not the only one which can occur. Experiments to... 

The A structure has a hexagonal symmetry (with a S axis only), while the B structure is monoclinic. In A the slabs of complex cations are parallel to the basal plane (00.1), while they are parallel to the (20l) plane in B (figs. 2 and 4). The B structure can be described as a deformation of A both in the basal plane... 

However, in sharp contradistinction, the mechanical properties of the MAX phases cannot be more different than those of their binary cousins. The mechanical properties of the MAX phases are dominated by the fact that basal-plane dislocations multiply and are mobile at temperatures as low as 77 K and higher. The presence of basal slip is thus crucial to understanding their response to stress. This is true despite the fact that the number of independent slip systems is less than the five needed for ductility. In typical ceramics at room temperature, the number of independent slip systems is essentially zero. The MAX phases, thus occupy an interesting middle ground, in which in constraineddeformationmodes,highly oriented microstructures, and/or at higher temperatures they are pseudo-ductile. In unconstrained deformation, and especially in tension at lower temperatures, they behave in a brittle fashion. 

As noted above, basal plane - and only basal plane - dislocations are responsible for how the MAX phases respond to stress. There are no credible reports that twins and/or nonbasal dislocations participate in any meaningftil way in their deformation. It follows that at all times the number of slip systems active is less than the five are needed for polycrystalline ductility. As will become apparent shortly, most of the present understanding on the deformation of the MAX phases is based on early work carried out on Ti3SiC2, which is the most extensively MAX phase studied and best understood to date. However, there is little doubt - as confirmed by more recent studies - that what applies to Ti3SiC2 also applies to other MAX phases. 

As noted above and discussed below, the key micro-mechanism in the deformation of the MAX phases is the kink band (KB). The KBs in crystalline solids were first observed in Cd single crystals loaded parallel to their basal planes by Orowan, who... 

A mechanism which begins with delaminations that are initiated at opposite ends of a single grain, but on different basal planes. With further deformation, the torque separates the lamellae between the two delamination cracks to ultimately form crack bridges not unlike those shown in Figure 7.18b. 

This reaction can occur by glide in the basal plane only for screw dislocations, and is thought to be the mechanism for the formation of a dislocation network in crystals undergoing deformation by prism plane slip [97]. Alternatively, the dislocation can lower its energy by dissociating into three collinear partials according to the reaction (see also Table 9.3) ... 

Figure 9.15 Dislocations in sapphire deformed on the basal plane to 3.6% shear strain at 1400°C. Examples of glide dislocations (C), regular dipoles (D), faulted dipoles (F),...

Among the oxides described in this chapter, deformation twinning is most important in the case of sapphire. Two twinning systems are known, on the rhombohedral and basal planes, and dislocation models for each have been suggested and confirmed using TEM. 

Source Reprinted with permission from Northolt MG, Veldhuizen LH, Jansen H, Tensile deformation of carbon fibres and the relationship with the modulus for shear between the basal planes. Carbon, 29,1267,1991. Copyright 1991, Elsevier. 

Wu and Wang [55] analyzed the dissociation of perfect dislocations into partials in BaTiOa by TEM. Figure 3.68 illustrates the results for this hexagonally-structured ceramic, in which the basal plane is commonly involved in the deformation. 

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