Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

GTBL042-08 GTBL042-Callister-v3 October 4, 2007 11:51

2nd Revised Pages

8.6 Slip in Single Crystals • 251

Slip plane

Direction

of force

Figure 8.8 Macroscopic slip in a single crystal.

that determines when yielding occurs. The single crystal plastically deforms or yields

whenτR(max)=τcrss, and the magnitude of the applied stress required to initiate

yielding (i.e., the yield strengthσy)is

σy=

τcrss

(cosφcosλ)max

(8.4)

Yield strength of a

single crystal—

dependence on the

critical resolved

shear stress and the

orientation of most

favorably oriented

slip system

The minimum stress necessary to introduce yielding occurs when a single crystal is

oriented such thatφ=λ= 45 ◦; under these conditions,

σy= 2 τcrss (8.5)

For a single-crystal specimen that is stressed in tension, deformation will be as in

Figure 8.8, where slip occurs along a number of equivalent and most favorably ori-

ented planes and directions at various positions along the specimen length. This slip

deformation forms as small steps on the surface of the single crystal that are parallel

to one another and loop around the circumference of the specimen as indicated in

Figure 8.8. Each step results from the movement of a large number of dislocations

along the same slip plane. On the surface of a polished single crystal specimen, these

steps appear as lines, which are calledslip lines. A zinc single crystal that has been

plastically deformed to the degree that these slip markings are discernible is shown

in Figure 8.9.

With continued extension of a single crystal, both the number of slip lines and

the slip step width will increase. For FCC and BCC metals, slip may eventually begin

along a second slip system, the system that is next most favorably oriented with

the tensile axis. Furthermore, for HCP crystals having few slip systems, if the stress

axis for the most favorable slip system is either perpendicular to the slip direction

(λ= 90 ◦) or parallel to the slip plane (φ= 90 ◦), the critical resolved shear stress will

be zero. For these extreme orientations the crystal ordinarily fractures rather than

deforming plastically.

Concept Check 8.2

Explain the difference between resolved shear stress and critical resolved shear stress.

[The answer may be found at http://www.wiley.com/college/callister (Student Companion Site).]