Slip prismatic

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. 

Figure 6.2 (a) The hexagonal dose-packed structure of a-alumina. (b) Two important slip systems, basal (0001) [0001] and prismatic (0110)[2110], in a hexagonal structure. 

In the present analyses, prismatic dislocation loops distributed on different slip planes are used as agents for dislocation generation. For copper, sources length of about 0.60 p,m are used. It is worthy to mention that the boundary conditions of the computational cell sides are different in FE and DD parts of the code. In DD, periodic boundary condition for the representative volume element RVE is used to ensure both the continuity of the dislocation curves and the conservation of dislocation flux across the boundaries, by that we take into account the periodicity of single crystals in an infinite media. In FE analysis however, the sides are constrained to move only in the z direction so that a imiaxial strain consistent with the shock experiment is achieved. In order for the boundary conditions in FE and DD to be consistent, periodic FE bormdary condition is implemented as well. The result of this implementation is discussed in the next section. 

Microactuators can be implemented in one or more degrees of freedom, leading to another way to classify them as linear (or prismatic), rotary (or revolute), in-plane (1D-3D), and out of plane (1D-6D). A micromotor contains several movable parts, including the microactuator and a transmission system. The transmission system consists of bending (or flexture) joints and links, rigid links, stick-and-slip contact elements, or micromechanical hinges. Like macroscale actuators, microactuators are chosen for different applications based on tradeoffs between ... 

Early studies on BeO single crystals by Bentle and Miller [51] identified four slip systems basal slip, (0001)(1120) prismatic slip, 1100 (1120) and 1100 [0001] and pyramidal slip, Il22 (1123). Not surprisingly, significant plastic anisotropy was found. At 1000 °C, the yield stresses for these systems were as follows 35 MPa for basal slip 49 and llOMPa for prismatic slip along (1120) and [0001], respectively and >250 MPa for pyramidal slip. More recent studies on creep deformation in BeO... 

Fig. 2.4 Critical resolved shear stress for yield (above the transition temperature) in bending for all specimens tested at e = 1.3 x 10" s compared with data obtained by compression tests of Castaing et al. C specimens show prismatic slip and those of A and B show basal slip [26]. With kind permission of Wiley and Sons...

The plastic deformation of the sapphire occurred due to basal and prismatic slip during loading above T. Basal slip was found in A- and B-oriented specimens and prismatic slip in C-oriented specimens. The resolved stresses at yield (according to the author) are comparable to those measured by other researchers under compression in the appropriate slip system. 

In Chap. 2 Sect. 2.2a, the CRSS was shown for AI2O3 at 4.2 x 10 s above Tc, indicating basal and prismatic slip. The Schmidt factors are 0.3916 for (0001) slip for specimens with A and B orientation and 0.4330 for (1100) slip for specimens with C orientation. A and B show basal slip and C has prismatic slip. 

Three independent slip systems are not sufficient for arbitrary deformations. For the hexagonal crystal, this is easily understood because shear deformation out of the common slip plane of the three systems is impossible. Therefore, other, more difficult, slip systems must be activated. Because real metals never show the ideal hexagonal structure, but possess either a stretched or a compressed unit cell (varying ratio <=/ ), it depends on the chemical element which other systems are activated. Table 6.3 gives a synopsis of the most important slip systems. The slip systems with the horizontal slip plane are called basal slip systems. If the slip planes are on the prism faces of the unit cell, they are called prismatic slip systems. The other slip systems are called pyramidal slip systems. 

Figure 3.27. Reciprocal mean effective resolved shear stress curves for Knoop indentation calculated for (a) (0001)(1120) and (b) 12l0 O0T0) slip systems on the prismatic (iTOO) plane of hexagonal crystals.

Slip Modes in the a-Phase. Various modes of slip can occur in a-Ti or in the a-phase of titanium alloys (see Table 4). In general, slip can occur on prismatic, pyramidal and basal planes by the movement of , [c] and -type dislocations. Since the <1120> slip directions are common to aU three planes, the -type dislocations can ghde on prism, pyramid, and basal planes. The -type slip can take place on prismatic and pyramidal planes. The [c]-type glide is restricted to only prismatic planes and generally does not occur. 

At least five independent slip sjrstems are required for extensive ductility in polyciystalline materials. The operation of -type sHp on prismatic, pyramidal, and basal planes provides only four independent sKp sj tems. They do not allow shear straining along the c-direction. The displacement in the c-direction can be achieved by the movement of [c]- or -type dislocations, or even by twins. 

Experimental data suggest that the displacive a-p transition may not strongly influence the dominant slip systems. This is not unexpected because the main basal and prismatic slip systems have hexagonal symmetry. However, textures are... 

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