Slip pyramidal

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... 

Dislocation-dissociation in quartz was first observed by McLaren ef al. [32] in a natural dry quartz deformed at 500 °C, and has been studied most recently by Cordier and Doukhan [33] in a synthetic crystal containing 100 at. ppm [H]/[Si]. By using a crystal oriented to have high Schmid factors for (0001)1/3 (1120)basal slip, 1120 [0001] prismplaneslip, and 1010 1/3 (1213) pyramidal slip, and deformed under a hydrostatic pressure of 1.0-1.1 GPa, Cordier and Doukhan found a flow stress at 500 °C of almost 3 GPa, which decreased to 2 GPa at 900 °C. These high flow stresses correspond to a significant fraction of the shear modulus and reflect the fact that the quartz is relatively dry. Slip at 500 °C was heterogeneous (in slip bands). 

The availability of sizable single crystals has led to a significant literature on the deformation of sapphire of various orientations, and at various temperatures. As already noted, the first such study was by Wachtman and Maxwell in 1954 [6], who activated (0001) 1/3 (1120) basal slip at 900 °C via creep deformation. Since that time, it has become clear that basal slip is the preferred slip system at high temperatures, but that prism plane slip, 1120 (1100), can also be activated and becomes the preferred slip system at temperatures below 600°C. Additional slip systems, say on the pyramidal plane 1012 1/3 (1011), have very high CRSSs and are thus difficult to activate. Both, basal and rhombohedral deformation twinning systems, are also important in AI2O3 (these are discussed later in the chapter). 

Further below, time-dependent deformation (creep) iiutiated by climb will be extensively discussed. In this section, an example of dislocation climb is illustrated. Figure 3.70 shows dislocation climb in an AI2O3-YAG specimen. Here, climb was assisted by thermal activation. Such a dislocation network, resulting from the reaction of dislocations from the basal and pyramidal slip systems, involves dislocation climb. It is a diffusion-controlled deformation mode characterizing creep deformation and, in this particular case, the activation energy determined is Q = 670 kJ/mol. 

Fig. 3. Orientation of the sample. A. The sample map (arrow). B. The position of the block before (thin arrow) and after (thick arrows) the detachment from the cover slip. C. The sample before its trimming the external view of the block. D. Scheme of the grid and the position of the cell (green, thick arrow) and cavities (circles, thin arrows). The cavities should form a horizontal line (red broken line). E. Position of the pyramid. F. The position of the sample after the orientation and trimming of the upper and lower edges (thick arrows) of the sample. The cell of interest is shown by the double arrow. The small arrow indicates the position of the glass knife related to the pyramid.

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. 

The residual tensile force P, has to be modeled, and a precompressed linear spring acting through the center of the slipped material and indentation pyramid is chosen... 

For the reasons developed in Chapters 2 and 5, we would not usually recommend the use of spherical or conical indenters for hardness measurements in materials with a marked tendency to brittle behavior because of the circumferential tensile stress, or where a significant amount of pile-up, controlled by discrete slip planes, may cause distorted indentations. Consequently, in this part of Chapter 3, we shall be concerned only with pyramidal indenters such as the Knoop, Vickers, and Berkovich indenters as well as the pentagonal indenter, which was designed with the advantages of the pyramidal indenters in mind but so as to offset the intrinsic anisotropy of crystals. Here we shall identify the orientation of a given indenter with respect to its facets, as sketched in Figures 2.3 and 2.5, rather than its diagonals. 

Verner, 2002, p. 165. Accretion layers were a common form of construction suited to making a tomb as large as possible yet ready for an uncertain death. This is not the soundest structure. The Meidum pyramid (2600 bc) had catastrophic design flaws. Although the weakness of in-built slip-planes could... 

T13AI has an ordered DOig structirre that contains three independent slip systems that account for dislocation motion on the hasal 0001, prism 1010, and pyramidal 0221 planes ( f 1, 2). Prism shp requires only a single dislocation without creating a near-neighbor antiphase boundaiy, and additional shp requires movement of two dislocations (superdislocations) (Ref 3). In addition, two independent shp systems involving (c + a) shp occur to satisfy the Von Mises criterion for viniform deformation. 

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. 

The basal plane in the hep metals Zn and Cd is the most densely packed plane and slip generally occurs in this plane and in the <1120> direction. Prismatic and pyramidal systems, in addition to the basal system, have been shown to operate at room and elevated temperatures, depending on the mode of deformation. The c/a ratio plays an important role in determining the ease with which other slip systems... 

A closest packed pyramid of cannonballs. Oranges at a fruit stand are often packed in cubic closest packed pyramids so that they will not slip. 

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