We have already gained some basic idea about slip from the previous chapters. Slip is nothing but the movement of one crystal part over another causing plastic deforma­tion. Slip occurs only when the shear stress on the slip plane along the slip direction attains a critical value (known as critical resolved shear stress (CRSS)). Generally, the slip planes are the crystallographic planes with the highest atomic density (closest-packed planes (CPPs)) in that particular crystal structure, and the slip directions are the closest-packed directions (CPDs) in the respective crystal structures.1* A combination of slip plane and slip direction is called a slip system. Due to the slip, steps are formed on the prepolished surface of a material that has been plastically deformed. Due to the height variations in the different slip steps, they are observable on the sample surface as lines, and hence known as slip lines. Several slip lines banding together are

1) This is because CPPs are farthest apart and the atoms are closest along CPDs so that the force/stress required for slip to occur on CPPs along CPDs will be the lowest.

An Introduction to Nuclear Materials: Fundamentals and Applications, First Edition.

K. Linga Murty and Indrajit Charit.

© 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.

called slip bands. The slip bands can be seen by observing the prepolished surface of a deformed sample with an optical microscope or a scanning electron microscope. Note that slip is not just a surface phenomenon, the manifestation of slip can be tracked by observing the slip steps on the rightly conditioned surface. If the surface is later repol­ished, the slip lines will be removed as the slip steps showing the height variations will no longer be present. This is demonstrated in Figure 4.1a. For example, a micro­graph of copper with slip lines is shown in Figure 4.1b.

Let us first discuss an example from an FCC metal. As seen in Chapter 1, the close-packed planes in the FCC crystal are {111} with the close-packed directions being {110) (face diagonals). They are the slip planes and slip directions in FCC, respectively. Planes {111} are called octahedral planes as they form the faces of an octahedron inside the FCC crystal. There are eight (effective number) such octahe­dral planes per FCC unit cell. However, one plane is parallel to the other plane, thus leaving four independent slip planes. Now each such {111} plane contains three {110) directions (reverse directions are not taken into consideration as they are essentially the same directions), as shown in Figure 4.2. Thus, an FCC crystal would have 12 (4 x 3) slip systems. Generally, FCC metals show straighter slip lines as shown in Figure 4.1b. An easy way whether a crystallographic direction [uvw] is

indeed a slip direction on a slip plane (hkl) is to satisfy the relation h-u + k-v + l-w = 0 (dot product of the direction and the plane normal). For example, [110] resides on the slip plane (111) as (—1)(1) + (1)(1) + (0)(1) = 0.

A BCC crystal does not have a close-packed plane. Its closest-packed plane is {110}, closely followed by {112} and {123} due to their relatively high atomic den­sity. However, the BCC crystal has only one slip direction, the close-packed direc­tion {111). There are 48 possible slip systems in a BCC crystal. As none of the slip planes is close packed in BCC crystals, higher shearing stresses are required to cre­ate slip. So, there are multiple slip planes, but slip always occurs in a close-packed direction. As (screw) dislocations in BCC crystals can move from one slip plane to another, the slip lines produced have irregular wavy appearance. By observing the slip in the {111) direction more or less independent of the slip plane, Taylor coined the term pencil glide for describing slip in BCC crystals. Screw dislocations can cross-slip readily from one plane to another, thus forming such slip bands.

In the HCP metals, the close-packed plane is basal plane {0002}. The а-axes are the close-packed directions having Miller index, (1120), serving as the slip direc­tion. Slip along this direction regardless of the slip plane does not produce any strain parallel to c-axis. Only certain HCP metals like zinc, magnesium, cobalt, and cadmium show basal slip. There is only one type of close-packed plane and three slip directions in HCP crystal leading to the total number of available slip systems to be only three. That is why they exhibit limited ductility and extreme orientation dependence of properties. They all have one thing in common — their c/а ratios are close to the ideal (1.633). Interestingly, beryllium with a c/а ratio quite less than the ideal ratio primarily shows basal slip closely followed by prismatic slip. The stress required for pyramidal slip is much greater and can lead to fracture. Figure 4.3 shows the scenario in terms of stress-strain curves. On the other hand, alpha-Ti

and alpha-Zr (c/a ratio less than the ideal ratio) under normal conditions undergo prismatic slip ({1010}(1120)). But Poirier downplayed the effect of c/a ratio on the slip behavior of HCP metals and attributed the diverse slip behaviors to the anisot­ropy of the HCP crystals. Twinning can produce small strains in the HCP crystals even along the c-axis, but the main role of twinning in HCP crystals is to help orient unfavorable slip systems favorably for slip to take place.

Additional slip systems can be activated depending on test temperature. For example, {110} slip planes in aluminum start taking part in slip deformation at elevated temperatures even though the crystal structure remains FCC. Magnesium is known for its basal slip, but at a higher temperature (~225 °C), secondary slip systems involving {1011} pyramidal planes get activated.

■ Example 4.1

Zr alloys with low c/a ratio exhibit prism slip ({1010}(1120)). Show on a single HCP crystal a slip system and the Miller indices of the plane and direction chosen.

Solution

In the following figure, the slip plane (ABDF) is (1010) and the slip direc­tion AB is [І210] so that the slip system is (1010)[І210].

4.1.1