Page 275 - Materials Science and Engineering An Introduction

Questions and Problems • 247

Briefly describe the defect that results when these Figure 3.3. Also, simple cubic is the crystal struc-
two dislocations become aligned with each other. ture for the edge dislocation of Figure 4.4, and
for its motion as presented in Figure 7.1. You
may also want to consult the answer to Concept
Check 7.1.
(b) On the basis of Equation 7.11, formulate an
7.3 Is it possible for two screw dislocations of oppo- expression for the magnitude of the Burgers vec-
site sign to annihilate each other? Explain your tor, b , for the simple cubic crystal structure.
answer.
7.4 For each of edge, screw, and mixed dislocations, Slip in Single Crystals
cite the relationship between the direction of the 7.11 Sometimes cos f cos l in Equation 7.2 is termed
applied shear stress and the direction of disloca- the Schmid factor. Determine the magnitude
tion line motion. of the Schmid factor for an FCC single crystal
oriented with its [120] direction parallel to the
Slip Systems loading axis.
7.5 (a) Define a slip system.
7.12 Consider a metal single crystal oriented such
(b) Do all metals have the same slip system? that the normal to the slip plane and the slip di-
Why or why not? rection are at angles of 60 and 35 , respectively,
7.6 (a) Compare planar densities (Section 3.11 and with the tensile axis. If the critical resolved shear
Problem 3.60) for the (100), (110), and (111) stress is 6.2 MPa (900 psi), will an applied stress
planes for FCC. of 12 MPa (1750 psi) cause the single crystal to
yield? If not, what stress will be necessary?
(b) Compare planar densities (Problem 3.61) for
the (100), (110), and (111) planes for BCC. 7.13 A single crystal of zinc is oriented for a tensile
test such that its slip plane normal makes an an-
7.7 One slip system for the BCC crystal structure is gle of 65 with the tensile axis. Three possible slip
5110681119. In a manner similar to Figure 7.6b, directions make angles of 30 , 48 , and 78 with
sketch a 51106-type plane for the BCC structure, the same tensile axis.
representing atom positions with circles. Now,
using arrows, indicate two different 81119 slip (a) Which of these three slip directions is most
directions within this plane. favored?
7.8 One slip system for the HCP crystal structure is (b) If plastic deformation begins at a tensile
500016811209. In a manner similar to Figure 7.6b, stress of 2.5 MPa (355 psi), determine the critical
sketch a 501116-type plane for the HCP structure resolved shear stress for zinc.
and, using arrows, indicate three different 811209 7.14 Consider a single crystal of nickel oriented such
slip directions within this plane. You may find that a tensile stress is applied along a [001] direc-
Figure 3.9 helpful. tion. If slip occurs on a (111) plane and in a [101]
7.9 Equations 7.1a and 7.1b, expressions for Burgers direction and is initiated at an applied tensile
vectors for FCC and BCC crystal structures, are stress of 13.9 MPa (2020 psi), compute the critical
of the form resolved shear stress.
a 7.15 A single crystal of a metal that has the FCC
b = 8uyw9 crystal structure is oriented such that a tensile
2
stress is applied parallel to the [100] direction. If
where a is the unit cell edge length. The mag- the critical resolved shear stress for this material
nitudes of these Burgers vectors may be deter- is 0.5 MPa, calculate the magnitude(s) of applied
mined from the following equation: stress(es) necessary to cause slip to occur on the
(111) plane in each of the [101], [101], and [011]
a
b = (u + y + w ) (7.11) directions.
2
2
2 1>2
2
7.16 (a) A single crystal of a metal that has the BCC
determine the values of b for copper and iron. crystal structure is oriented such that a tensile
You may want to consult Table 3.1. stress is applied in the [100] direction. If the mag-
7.10 (a) In the manner of Equations 7.1a to 7.1c, nitude of this stress is 4.0 MPa, compute the re-
specify the Burgers vector for the simple cubic solved shear stress in the [111] direction on each
crystal structure whose unit cell is shown in of the (110), (011), and (101) planes.