Multiple slip

6.3.5 Multiple slip

The fact that slip bands, each consisting of many slip lines, are observed on the surface of deformed crystals shows that deformation is inhomogeneous, with extensive slip occurring on certain planes, while the crystal planes lying between them remain practically undeformed. Figure 6.11a and b shows such a crystal in which the set of planes shear over each other in the slip direction. In a tensile test, however, the ends of a crystal are not free to move ‘sideways’ relative to each other, since they are constrained by the grips of the tensile machine. In this case, the central portion of the crystal is altered in orientation, and rotation of both the slip plane and slip direction into the axis of tension occurs, as shown in Figure 6.11c. This behavior is more conveniently demonstrated on a stereographic projection of the crystal by considering the rotation of the tensile axis relative to the crystal rather than vice versa. This is illustrated in Figure 6.12a for the deformation of a crystal with fcc structure.

The tensile axis, P, is shown in the unit triangle and the angles between P and [¯1 0 1], and P and (1 1 1) are equal to λ and φ respectively. The active slip system is the (1 1 1) plane and the [¯1 0 1] direction, and as deformation proceeds the change in orientation is represented by the point, P, moving along the zone, shown broken in Figure 6.12a, towards [¯1 0 1], i.e. λ decreasing and φ increasing.

As slip occurs on the one system, the primary system, the slip plane rotates away from its position of maximum resolved shear stress until the orientation of the crystal reaches the [0 0 1]–[¯1 1 1] symmetry line. Beyond this point, slip should occur equally on both the primary system and a second system (the conjugate system) (¯1 ¯1 1)–[0 1 1], since these two systems receive equal components of shear stress. Subsequently, during the process of multiple or duplex slip the lattice will rotate so as to keep equal stresses on the two active systems, and the tensile axis moves along the symmetry line towards [¯1 1 2]. This behavior agrees with early observations on virgin crystals of aluminum and

302 Physical Metallurgy and Advanced Materials

Slip plane

Slip direction

Lattice bending

(a)

Lattice rotation

Slip direction

(b)

(c)

Figure 6.11 (a) and (b) show the slip process in an unconstrained single crystal; (c) illustrates the plastic bending in a crystal gripped at its ends.

Conjugate plane [1 0 1]

Critical plane [1 0 1]

Cross plane

[1 0 1] Primary plane

(a)

Figure 6.12 Stereographic representation of slip systems in fcc crystals (a) and overshooting of the primary slip system (b).

copper, but not with those made on certain alloys, or pure metal crystals given special treatments (e.g. quenched from a high temperature or irradiated with neutrons). Results from the latter show that the crystal continues to slip on the primary system after the orientation has reached the symmetry line, causing the orientation to overshoot this line, i.e. to continue moving towards [¯1 0 1], in the direction of primary slip. After a certain amount of this additional primary slip the conjugate system suddenly operates, and further slip concentrates itself on this system, followed by overshooting in the opposite direction. This behavior, shown in Figure 6.12b, is understandable when it is remembered that slip on the conjugate system must intersect that on the primary system, and to do this is presumably more difficult than to ‘fit’ a new slip plane in the relatively undeformed region between those planes on which slip has already taken place. This intersection process is more difficult in materials which have

a low stacking-fault energy (e.g. α-brass).

Mechanical properties I 303

Specimen B,

(multiple slip)

200 Specimen A,

Shear stress (g mm 100

(single slip)

Glide

Figure 6.13 Stress–strain curves for aluminum deformed by single and multiple slip (after Lücke and Lange, 1950).