Slip directions

Numerous observations of the effect in ionic crystals were carried out by Mineev and Ivanov in the Soviet Union [76M01]. This is a class of crystals in which a number of materials factors can be confidently varied. By choice of crystallographic orientation, various slip directions can be invoked. By choice of various crystals other physical factors such as dielectric constant, ionic radius, and an electronic factor thought to be representative of dielec-... 

Dislocation movement in copper is described by a slip plane 111 and a slip direction, the direction of dislocation movement, [110]. Each 111 plane can be depicted as a hexagonal array of copper atoms (Fig. 3.11a). The stacking of these planes is represented by the sequence. .. ABC. .. where the first layer is labeled A, the second layer, which fits into the dimples in layer A is labeled B... 

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... 

Figure 5.12 Schematic illustration of the relationship between tensile axis, slip plane, and slip direction used in calculating the resolved shear stress for a single crystal. Reprinted, by permission, from W. Callister, Materials Science and Engineering An Introduction, 5th ed., p. 160. Copyright 2000 by John Wiley Sons, Inc.

Consider a single crystal of BCC Mo oriented such that a tensile stress of 52 MPa is apphed along a [010] direction. From Table 5.1, we see that the slip plane for BCC Mo is (110) and the slip direction is [111]. 

Person 2 Determine the angle, X, between the slip direction and the applied stress direction. You will find it helpful to draw a cubic cell with the [010] and [111] directions as two sides of a triangle, the third side being a face diagonal. At this point. Table 1.8 may be helpful in establishing a relationship between the length of these sides in terms of the lattice parameter, a. You can then use some simple geometry to find X. 

In semicrystalline polymers such as polyethylene, yielding involves significant disruption of the crystal structure. Slip occurs between the crystal lamellae, which slide by each other, and within the individual lamellae by a process comparable to glide in metallic crystals. The slip within the individual lamellae is the dominant process, and leads to molecular orientation, since the slip direction within the crystal is along the axis of the polymer molecule. As plastic flow continues, the slip direction rotates toward the tensile axis. Ultimately, the slip direction (molecular axis) coincides with the tensile axis, and the polymer is then oriented and resists further flow. The two slip processes continue to occur during plastic flow, but the lamellae and spherullites increasingly lose their identity and a new fibrillar structure is formed (see Figure 5.69). 

A single crystal of alnminum is oriented for a tensile test snch that its slip plane normal makes an angle of 28.1° with the tensile axis. Three possible slip directions make angles of 51.2°, 36.0°, and 40.6° with the same tensile axis. Which of these three slip directions is most favored ... 

This is slip that occurs simultaneously on several slip planes having Ihe same slip direction. See Fig. 14. This type of plastic deformation is normally associated with the movement of screw dislocations. Screw dislocations can move on any slip plane that passes through the dislocation. This is a result of the fact that the slip plane of a dislocation is that plane which contains both the dislocation and its Burgers veclor, and the fact that the Burgers vector of a screw dislocation lies parallel io the dislocation itself,... 

A Burgers vector has both a direction and a magnitude. Its direction is the direction of the displacement that would be caused by movement of the dislocation, and the magnitude is the length of that displacement. The direction and magnitude normally correspond to a slip direction and slip displacement. The common notation indicates the direction by Miller indices. A scalar in front indicates the magnitude. For example, b = (a/2)[l 10] indicates a vector a/2, a/2, 0, where... 

Polanyi and Mark discovered the slip properties of single-crystal tin, while Schmid worked out a law for the shear stress component along the slip direction in a slip plane. [44]... 

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. 

Crystal Structure Slip Plane Slip Direction Number of Nonparallel Planes Slip Directions per Plane Number of Slip Systems... 

Movement of dislocations is a primary mechanism for plastic deformation. A dislocation s motion is impeded when they encounter obstacles, causing the stress required to continue the deformation process to increase. Grain boundaries are one of the obstacles that can impede dislocation glide, so the number of grain boundaries along a slip direction can be expected to influence the strength of a material. In the early 1950s, two researchers, Hall (1951) and Petch (1953),... 

Figure 10.6. Application of a tensile force to a cylindrical single crystal causes a shear stress on some crystal planes. When the shear stress is equal to the critical-resolved shear stress (the yield stress), glide proceeds along the slip direction of the planes.

According to Schmid s law (Schmid and Boas, 1935), plastic flow in a pure and perfect single crystal occurs when the shear stress, acting along (parallel to) the shp direction on the slip plane, reaches some critical value known as the critical resolved shear stress, Tc. From Figure 10.6, it can be seen that the component of the force acting in the slip-direction is Fcos A and it acts over the plane of area A/cos (where A is the cross-sectional area). Thus the resolved shear stress is as = (F/A)cos cos A. Schmid s law states that slip occurs at some critical value of cTj, denoted as... 

The applied tensile stress direction, as well as the slip plane and the slip direction, are normally specified by direction indices (called direction numbers in linear algebra). That information, and Eq. 10.57 below can be used to calculate the angles between the different directions, 4> and A, in Eq. 10.56. In general, the angle between any two directions, specified by their direction indices [ui Vi wi] and [1/2 2 > 2], in a direct-space lattice is given by the dot product ... 

In a manner similar to Figure 10.5, show two different close-packed 1 1 1) slip directions in the 1 1 0 planes of the BCC lattice. 

The same sequence of events also explains more subtle features. For example, the consistently observed gradual increase in shearing intensity (i.e., density of fault-parallel D-shears) within the sandy portion of a fault zone as one moves against the relative slip direction on either side of a clay smear, i.e., in the direction of increasing total slip displacement of sand against sand (cf. Fig. 2). 

In the Berg-Barrett topographs of Fig. 8-33 explain why only screw dislocations are revealed in (b), only edges in (c), and screws and edges in (d). Give the indices of the operating slip systems, i.e., the indices of each slip plane and of the slip direction in that plane. (Slip in a LiF crystal occurs on 110 planes in <110> directions, but the experimental observations in Fig. 8-33 are inconsistent with the assumption that slip occurred on all possible slip systems. Note also that only those dislocations which intersect a crystal face will be distinctly observed by x-ray examination of that face.)... 

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... 

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