Page 263 - Materials Science and Engineering An Introduction

7.11 Recovery • 235

EXAMPLE PROBLEM 7.2

Tensile Strength and Ductility Determinations for Cold-Worked Copper
Compute the tensile strength and ductility (%EL) of a cylindrical copper rod if it is cold
worked such that the diameter is reduced from 15.2 mm to 12.2 mm (0.60 in. to 0.48 in.).
Solution
It is first necessary to determine the percent cold work resulting from the deformation. This is
possible using Equation 7.8:
15.2 mm 2 12.2 mm 2
a b p - a b p
2 2
%CW = * 100 = 35.6%
15.2 mm 2
a b p
2
The tensile strength is read directly from the curve for copper (Figure 7.19b) as 340 MPa
(50,000 psi). From Figure 7.19c, the ductility at 35.6%CW is about 7%EL.

In summary, we have discussed the three mechanisms that may be used to strengthen
and harden single-phase metal alloys: strengthening by grain size reduction, solid-solution
strengthening, and strain hardening. Of course, they may be used in conjunction with one
another; for example, a solid-solution strengthened alloy may also be strain hardened.
It should also be noted that the strengthening effects due to grain size reduction
and strain hardening can be eliminated or at least reduced by an elevated-temperature
heat treatment (Sections 7.12 and 7.13). In contrast, solid-solution strengthening is unaf-
fected by heat treatment.

As we shall see in Chapters 10 and 11, techniques other than those just discussed
may be used to improve the mechanical properties of some metal alloys. These alloys
are multiphase and property alterations result from phase transformations, which are
induced by specifically designed heat treatments.

Recovery, Recrystallization, and Grain Growth

As outlined earlier in this chapter, plastically deforming a polycrystalline metal specimen at
temperatures that are low relative to its absolute melting temperature produces microstruc-
tural and property changes that include (1) a change in grain shape (Section 7.6), (2) strain
hardening (Section 7.10), and (3) an increase in dislocation density (Section 7.3). Some frac-
tion of the energy expended in deformation is stored in the metal as strain energy, which is
associated with tensile, compressive, and shear zones around the newly created dislocations
(Section 7.3). Furthermore, other properties, such as electrical conductivity (Section 18.8)
and corrosion resistance, may be modified as a consequence of plastic deformation.
Tutorial Video: These properties and structures may revert back to the precold-worked states by
Annealing appropriate heat treatment (sometimes termed an annealing treatment). Such restora-
What is Annealing and tion results from two different processes that occur at elevated temperatures: recovery
What Does It Do? and recrystallization, which may be followed by grain growth.
7.11 RECOVERY
recovery During recovery, some of the stored internal strain energy is relieved by virtue of dis-
location motion (in the absence of an externally applied stress), as a result of enhanced
atomic diffusion at the elevated temperature. There is some reduction in the number