Page 272 - Materials Science and Engineering An Introduction

244 • Chapter 7 / Dislocations and Strengthening Mechanisms

• The driving force for recrystallization is the difference in internal energy between
strained and recrystallized material.
• For a cold-worked metal that experiences recrystallization, as temperature increases
(at constant heat-treating time), tensile strength decreases and ductility increases (per
Figure 7.22).
• The recrystallization temperature of a metal alloy is that temperature at which recrys-
tallization reaches completion in 1 h.
• Two factors that influence the recrystallization temperature are percent cold work
and impurity content.
Recrystallization temperature decreases with increasing percent cold work.
It rises with increasing concentrations of impurities.
• Plastic deformation of a metal above its recrystallization temperature is hot working;
deformation below its recrystallization temperature is termed cold working.

Grain Growth • Grain growth is the increase in average grain size of polycrystalline materials, which
proceeds by grain boundary motion.
• The driving force for grain growth is the reduction in total grain boundary energy.
• The time dependence of grain size is represented by Equation 7.9.

Equation Summary

Equation Page
Number Equation Solving For Number
7.2 t R = s cos f cos l Resolved shear stress 223
7.4 t crss = s y (cos f cos l) max Critical resolved shear stress 224
Yield strength (as a function of average grain size)—
7.7 s y = s 0 + k y d -1/2 Hall–Petch equation 230

7.8 %CW = a A 0 - A d b * 100 Percent cold work 232
A 0
7.9 d - d 0 = Kt Average grain size (during grain growth) 240
n
n

List of Symbols

Symbol Meaning
A 0 Specimen cross-sectional area prior to deformation
A d Specimen cross-sectional area after deformation
d Average grain size; average grain size during grain growth
d 0 Average grain size prior to grain growth
Material constants
K, k y
t Time over which grain growth occurred
n Grain size exponent—for some materials has a value of approximately 2
l Angle between the tensile axis and the slip direction for a single crystal
stressed in tension (Figure 7.7)
(continued)