Page 270 - Materials Science and Engineering An Introduction

242 • Chapter 7 / Dislocations and Strengthening Mechanisms

This leads to
-3
2
-2
(2.7 * 10 mm) - (8.2 * 10 mm) 2
K =
12.5 min
2
-5
= 5.29 * 10 mm >min
To determine the grain diameter after a heat treatment at 500 C for 100 min, we must
manipulate Equation 7.10 such that d becomes the dependent variable—that is,
2
d = 2d 0 + Kt
And upon substitution into this expression of t 100 min as well as values for d 0 and K, yields
2
2
-3
-5
d = 2(8.2 * 10 mm) + (5.29 * 10 mm >min)(100 min)
= 0.0732 mm

SUMMARY

Basic Concepts • On a microscopic level, plastic deformation corresponds to the motion of dislocations
in response to an externally applied shear stress. An edge dislocation moves by the
successive and repeated breaking of atomic bonds and shifting by interatomic dis-
tances of half planes of atoms.
• For edge dislocations, dislocation line motion and direction of the applied shear stress
are parallel; for screw dislocations, these directions are perpendicular.
• Dislocation density is the total dislocation length per unit volume of material. Its units
are per square millimeter.
• For an edge dislocation, tensile, compressive, and shear strains exist in the vicinity of
the dislocation line. Shear lattice strains only are found for pure screw dislocations.

Slip Systems • The motion of dislocations in response to an externally applied shear stress is
termed slip.
• Slip occurs on specific crystallographic planes, and within these planes only in certain
directions. A slip system represents a slip plane–slip direction combination.
• Operable slip systems depend on the crystal structure of the material. The slip plane
is that plane that has the densest atomic packing, and the slip direction is the direction
within this plane that is most closely packed with atoms.
• The slip system for the FCC crystal structure is 5111681109; for BCC, several are pos-
sible: 5110681119, 5211681119, and 5321681119.

Slip in Single Crystals • Resolved shear stress is the shear stress resulting from an applied tensile stress that is
resolved onto a plane that is neither parallel nor perpendicular to the stress direction.
Its value is dependent on the applied stress and orientations of plane and direction
according to Equation 7.2.
• Critical resolved shear stress is the minimum resolved shear stress required to initi-
ate dislocation motion (or slip) and depends on yield strength and orientation of slip
components per Equation 7.4.
• For a single crystal that is pulled in tension, small steps form on the surface that are
parallel and loop around the circumference of the specimen.