Particular slip systems

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 critical resolved shear stress, Terss, is the minimum shear stress required to initiate slip for a particular slip system defined when a = 0/. 

Virtually all observations of dislocation glide in bulk covalent crystals at stress levels above some modest threshold level on the order of 10 N/m reveal that the normal glide velocity on a particular slip system of a given material varies with resolved shear stress on the glide plane r es = o ijTi bi/b and absolute temperature T according to an Arrhenius relationship of the form... 

Beside dislocation density, dislocation orientation is the primary factor in determining the critical shear stress required for plastic deformation. Dislocations do not move with the same degree of ease in all crystallographic directions or in all crystallographic planes. There is usually a preferred direction for slip dislocation movement. The combination of slip direction and slip plane is called the slip system, and it depends on the crystal structure of the metal. The slip plane is usually that plane having the most dense atomic packing (cf. Section 1.1.1.2). In face-centered cubic structures, this plane is the (111) plane, and the slip direction is the [110] direction. Each slip plane may contain more than one possible slip direction, so several slip systems may exist for a particular crystal structure. Eor FCC, there are a total of 12 possible slip systems four different (111) planes and three independent [110] directions for each plane. The... 

Our geometric model of the crystal is most appropriate for polycrystals since we have hypothesized that any and all planes and slip directions are available for slip (i.e. the discrete crystalline slip systems are smeared out) and hence that slip will commence once the maximum shear stresses have reached a critical value on any such plane. This provides a scheme for explicitly describing the yield surface that is known as the Tresca yield condition. In particular, we conclude that yield occurs when... 

Because of the high symmetry of cubic crystals, there are a wide variety of equivalent slip systems. In particular, in the fee case, each of the four 111 planes... 

The micromechanisms of deformation and in particular the dislocation reactions have been analyzed in detail and have been discussed with respect to strength and ductility (Koss etal., 1990 Kim and Froes, 1990 Yamaguchi and Umakoshi, 1990 Froes et al., 1991 Umakoshi et al., 1993 a, b). In the DOjg structure five independent slip systems are possible (Kim and Froes,... 

The cubic LI 2 structure is more symmetric than the tetragonal DO22 structure (see Fig. 1) and has a sufficient number of slip systems according to the Von Mises criterion, and thus it should also be more deformable (George et al., 1991 b). In particular, after the successful ductilization of NijAl and NijV (see Secs. 4.1 and 4.2) the LI 2 structure is regarded as most advanta-... 

To this point, the motion of dislocations on slip planes in particular slip directions has been discussed. The factors that control the choice of these slip systems have not, however, been clearly identified, particularly with respect to crystal structure. It was established earlier (Eq. (6.3)) that the easiest slip process should be one that involves the smallest (unit) displacement on planes that are most... 

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.. 

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. 

In single crystals, there are preferred planes where dislocations may propagate, referred to as slip planes. For a particular crystal system, the planes with the greatest atomic density will exhibit the most pronounced slip. For example, slip planes for bcc and fee crystals are 110 and 111, respectively other planes, along with those present in hep crystals, are listed in Table 2.9. Metals with bcc or fee lattices have significantly larger numbers of slip systems (planes/directions) relative to hep. For example, fee metals have 12 slip systems four unique 111 planes, each... 

For polyamide 6 crystals the slip systems are (001) [010] chain slip at 16.24 MPa, (100)[010] chain slip at 23.23 MPa and (001)[100] transverse slip [71]. Relatively little attention was paid to the plastic deformation of other semicrystalline polymers [98,110]. In particular, there are only a few papers [111,112] describing the investigations of the yield behavior and plastic resistance of oriented iPP. 

The Peierls-Nabarro model has been used to determine properties of dislocation cores, the misfit energy and particularly changes with pressure. This is based on the assumption of a planar core which is the most able to ghde. It has direct implications for slip systems. In order to move, a dislocation must overcome an energy barrier under an applied stress. The Peierls-Nabarro model has been used to constrain dislocation core sizes and Peierls stresses in several oxides and sihcates relevant to the Earth s mantle, particularly periclase [439], ohvine [440,441], ringwoodite [80],... 

Dislocations do not move with the same degree of ease on all erystallographie planes of atoms and in all crystallographic directions. Typically, there is a preferred plane, and in that plane there are specific directions along which dislocation motion occurs. This plane is called the slip plane it follows that the direction of movement is called the slip direction. This combination of the slip plane and the slip direction is termed the slip system. The slip system depends on the crystal structure of the metal and is such that the atomic distortion that accompanies the motion of a dislocation is a minimum. For a particular crystal structure, the slip plane is the plane that has the densest atomic packing—that is, has the greatest planar density. The slip direction corresponds to the direction in this plane that is most closely packed with atoms—that is, has the highest linear density. Planar and linear atomic densities were discussed in Section 3.11. 

Slip occurs along (110)-type directions within the ill planes, as indicated by arrows in Figure 7.6. Hence, lll (ll0) represents the slip plane and direction combination, or the slip system for FCC. Figure 7.6b demonstrates that a given slip plane may contain more than a single slip direction. Thus, several slip systems may exist for a particular crystal structure the number of independent slip systems represents the different possible combinations of slip planes and directions. For example, for face-centered cubic, there are 12 slip systems four unique (ill) planes and, within each plane, three independent (110) directions. 

The plastic deformation of crystalline solids proceeds by a process of slip and/or twinning on certain crystal planes and in certain crystal directions. In metals the slip planes (denoted by ) are usually those having the highest atomic density and they are the most widely spaced. The slip directions (denoted by < >) in the plane are those having the highest linear atomic density. A particular combination of slip plane and slip direction is referred to as a slip system. 

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