Page 254 - Materials Science and Engineering An Introduction

226 • Chapter 7 / Dislocations and Strengthening Mechanisms

However, for l, we take [u 1 y 1 w 1 ] = [111] and [u 2 y 2 w 2 ] = [010], and

(-1)(0) + (1)(1) + (1)(0)
-1
l = cos £ §
2
2
2
2
2
2
2[(-1) + (1) + (1) ][(0) + (1) + (0) ]
1
-1
= cos a b = 54.7
13
Thus, according to Equation 7.2,
t R = s cos f cos l = (52 MPa)(cos 45 )(cos 54.7 )
1 1
= (52 MPa)a b a b
12 13
= 21.3 MPa (3060 psi)
(b) The yield strength s y may be computed from Equation 7.4; f and l are the same as for
part (a), and
30 MPa
s y = = 73.4 MPa (10,600 psi)
(cos 45 )(cos 54.7 )

7.6 PLASTIC DEFORMATION OF POLYCRYSTALLINE MATERIALS
Deformation and slip in polycrystalline materials is somewhat more complex.
Because of the random crystallographic orientations of the numerous grains, the
direction of slip varies from one grain to another. For each, dislocation motion oc-
curs along the slip system that has the most favorable orientation, as defined earlier.
This is exemplified by a photomicrograph of a polycrystalline copper specimen that
has been plastically deformed (Figure 7.10); before deformation, the surface was
polished. Slip lines 1 are visible, and it appears that two slip systems operated for
most of the grains, as evidenced by two sets of parallel yet intersecting sets of lines.
Furthermore, variation in grain orientation is indicated by the difference in align-
ment of the slip lines for the several grains.
Gross plastic deformation of a polycrystalline specimen corresponds to the
comparable distortion of the individual grains by means of slip. During deformation,
mechanical integrity and coherency are maintained along the grain boundaries—that
is, the grain boundaries usually do not come apart or open up. As a consequence,
each individual grain is constrained, to some degree, in the shape it may assume by
its neighboring grains. The manner in which grains distort as a result of gross plastic
deformation is indicated in Figure 7.11. Before deformation the grains are equiaxed,
or have approximately the same dimension in all directions. For this particular defor-
mation, the grains become elongated along the direction in which the specimen was
extended.

1 These slip lines are microscopic ledges produced by dislocations (Figure 7.1c) that have exited from a grain and
appear as lines when viewed with a microscope. They are analogous to the macroscopic steps found on the surfaces
of deformed single crystals (Figures 7 .8 and 7 .9).