Slip systems independent

Table 3.8. Vickers Hardness on (001) Plane of Some Cubic Crystals and Slip Systems Independently Identified...

Burgers vector type Slip direction Slip plane type Total slip systems Independent... 

At room temperature, NiAl deforms almost exclusively by (100) dislocations [4, 9, 10] and the availability of only 3 independent slip systems is thought to be responsible for the limited ductility of polycrystalline NiAl. Only when single crystals are compressed along the (100) direction ( hard orientation), secondary (111) dislocations can be activated [3, 5]. Their mobility appears to be limited by the screw orientation [5] and yield stresses as high as 2 GPa are reported below 50K [5]. However, (110) dislocations are responsible for the increased plasticity in hard oriented crystals above 600K [3, 7]. The competition between (111) and (110) dislocations as secondary slip systems therefore appears to be one of the key issues to explain the observed deformation behaviour of NiAl. 

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... 

Crystal Slip System Number of Independent Systems Comments... 

Mono- and polycrystalline natural and synthetic materials are not subject to plastic strain and have no independent slip system. Stress concentration occurs in them at.crack tips and at flaws in the material, affecting the maximum strength which originates from the chemical or physical cohesion forces present. Non-plastic materials (crystals, rocks, ceramics, glass) show brittle cracks—forming at very low plastic strain—usually originating from surface flaws. 

Slip occurs along specific crystal planes (slip planes) and in specific directions (slip directions) within a crystal structure. Slip planes are usually the closest-packed planes, and slip directions are the closest-packed directions. Both face-centered-cubic (FCC) and hexagonal-close packed (HCP) structure are close packed structures, and slip always occurs in a close packed direction on a closepacked plane. The body-centered-cubic (BCC) structure is not, however, close packed. In a BCC system, slip may occur on several nearly close packed planes or directions. Slip planes and directions, as well as the number of independent slip systems (the product of the numbers of independent planes and directions), for these three structures are listed in Table 7.2. 

Of the 12 slip systems possessed by the CCP stmcture, five are independent, which satisfies the von Mises criterion. For this reason, and because of the multitude of active slip systems in polycrystalline CCP metals, they are the most ductile. Hexagonal close-packed metals contain just one close-packed layer, the (0 0 0 1) basal plane, and three distinct close-packed directions in this plane [I I 2 0], [2 I I 0], [I 2 I 0] as shown in Figure lO.Vh. Thus, there are only three easy glide primary slip systems in HCP metals, and only two of these are independent. Hence, HCP metals tend to have low... 

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 observed dislocation slip systems do not differ from those of the other DO22 phases, and again twinning, which does not affect the order, is a major deformation mode at low and high temperatures. The number of independent deformation modes is smaller than prescribed by the Von Mises criterion, which contributes to the observed brittleness (see Sec. 2.3). The ductility at high temperatures results from... 

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. 

A polycrystal needs five independent slip systems before it can undergo an arbitrary strain. This requirement is known as the von Mises criterion. A slip system is independent if the same strain caimot be produced from a combination of slip on other systems. From Table 17.4 you can see why MgO might be ductile when stressed as a single crystal but in polycrystalline form it is brittle except at high temperature where secondary slip systems operate. For polycrystalline MgO the brittle-to-ductile transition occurs at 1700°C as shown in Figure 17.8. 

TABLE 17.4 Independent Slip Systems for Some Ceramics ... 

Lattice type Crystal Slip system Number of independent systems... 

Some cubic materials, e.g., TiC and MgAl204, do have enough independent slip systems, but the Peierls-Nabarro stress is high making dislocations immobile except at high temperature. 

Parks, D. M. and Ahzi, S. (1990) Polycrystalline plastic deformation and texture evolution for crystals lacking five independent slip systems, J. Mech. Phys. Solids, 38, 701-724. 

The crystalline phase follows a few independent slip systems in which classical crystal plasticity theories cannot be utilized to model them [93-95]. Similar to the metallic crystalline phases, inelastic deformation in crystalline polymeric systems follows three different mechanisms (a) crystallographic slip, (b) twining, and (c) Martensite transformations [96]. All these mechanisms leave the crystallographic axis inextensible and provide less than five independent... 

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. 

In order to understand the response of the M +iAX phases to stress, it is imperative to understand the nature of their dislocations and, equally important, how they assemble. The dislocations and their arrangement are described in Section 7.6.2, while the implications of having fewer than the necessary five independent slip systems is discussed in Section 7.6.3. The most important deformation mode of kinking - both incipient and regular - is described in Section 7.6.4, while Section 7.6.5 deals with the room-temperature mechanical properties. The final section is devoted to the mechanical response at elevated temperatures. 

The MAX phases, ice and graphite, and other layered minerals such as mica, are plastically anisotropic. This plastic anisotropy, combined with the fact that they lack the five independent slip systems needed for ductility, quickly lead to a very uneven states of stress when a polycrystalline sample is loaded [129]. The glide of basal plane dislocations takes place only in favorably oriented or soft grains, which rapidly transfer the load to hard grains - that is, those not favorably oriented to the applied stress. Needless to say, this leads to high internal stresses. 

As the name implies, the hexagonal close-packed crystal has the highest possible packing density. Its stacking sequence (cf. figure 1.9) differs from that of the face-centred cubic lattice. Only the 0001 -basal planes are close-packed. They contain the three (1120) close-packed directions, resulting in only three independent slip systems (figure 6.16). 

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. 

That the number of slip systems to be activated is five can be explained as follows An arbitrary deformation has six independent components of the strain tensor (see section 2.4.2). Because plastic deformation does not change the volume, each one of these components is dependent on the others, and five independent components remain, corresponding to the required five slip systems. 

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. 

Lee B J, Ahzi S and Asaro R J (1995) On the plasticity of low symmetry crystals lacking five independent slip systems, Mech Mater, 20 1-8. 

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