Page 277 - Materials Science and Engineering An Introduction

Questions and Problems • 249

7.31 A cylindrical specimen of cold-worked copper required for a specimen of this same material
has a ductility (%EL) of 15%. If its cold-worked (i.e., d 0 1.7 10 2 mm) to achieve a grain
radius is 6.4 mm (0.25 in.), what was its radius diameter of 8.7 10 2 mm while being heated
before deformation? at 450 C. Assume the n grain diameter exponent

7.32 (a) What is the approximate ductility (%EL) has a value of 2.1.
of a brass that has a yield strength of 345 MPa 7.41 The average grain diameter for a brass mate-
(50,000 psi)? rial was measured as a function of time at 650 C,
(b) What is the approximate Brinell hardness of which is shown in the following table at two dif-
a 1040 steel having a yield strength of 620 MPa ferent times:
(90,000 psi)?
Time (min) Grain Diameter (mm)
7.33 Experimentally, it has been observed for single
crystals of a number of metals that the critical 40 5.6 10 2
resolved shear stress t crss is a function of the dis- 100 8.0 10 2
location density r D as
t crss = t 0 + A1r D (7.12) (a) What was the original grain diameter?
where t 0 and A are constants. For copper, the criti- (b) What grain diameter would you predict after
cal resolved shear stress is 0.69 MPa (100 psi) at a 200 min at 650 C?
2
4
dislocation density of 10 mm . If it is known that 7.42 An undeformed specimen of some alloy has an
for copper is 0.069 MPa (10 psi),
the value of t 0 average grain diameter of 0.050 mm. You are
6
2
compute t crss at a dislocation density of 10 mm . asked to reduce its average grain diameter to
0.020 mm. Is this possible? If so, explain the pro-
Recovery cedures you would use and name the processes
Recrystallization involved. If it is not possible, explain why.
Grain Growth
7.43 Grain growth is strongly dependent on tem-
7.34 Briefly cite the differences between the recov- perature (i.e., rate of grain growth increases with
ery and recrystallization processes. increasing temperature), yet temperature is not
7.35 Estimate the fraction of recrystallization from explicitly included in Equation 7.9.
the photomicrograph in Figure 7.21c. (a) Into which of the parameters in this expression
7.36 Explain the differences in grain structure for a would you expect temperature to be included?
metal that has been cold worked and one that has (b) On the basis of your intuition, cite an explicit
been cold worked and then recrystallized. expression for this temperature dependence.
7.37 (a) What is the driving force for recrystallization? 7.44 A non-cold-worked brass specimen of aver-
(b) What is the driving force for grain growth? age grain size 0.01 mm has a yield strength of
150 MPa (21,750 psi). Estimate the yield strength
7.38 (a) From Figure 7.25, compute the length of of this alloy after it has been heated to 500 C
time required for the average grain diameter to is
increase from 0.03 to 0.3 mm at 600 C for this for 1000 s, if it is known that the value of s 0
25 MPa (3625 psi).
brass material.
7.45 The following yield strength, grain diameter,
(b) Repeat the calculation, this time using 700 C. and heat treatment time (for grain growth) data
7.39 Consider a hypothetical material that has a were gathered for an iron specimen that was heat
grain diameter of 2.1 10 2 mm. After a heat treated at 800 C. Using these data, compute the
treatment at 600 C for 3 h, the grain diameter has yield strength of a specimen that was heated at
2
increased to 7.2 10 mm. Compute the grain 800 C for 3 h. Assume a value of 2 for n, the grain
diameter when a specimen of this same original diameter exponent.
2
material (i.e., d 0 2.1 10 mm) is heated for
1.7 h at 600 C. Assume the n grain diameter ex- Grain Yield Heat
ponent has a value of 2. diameter Strength Treating
7.40 A hypothetical metal alloy has a grain diam- (mm) (MPa) Time (h)
eter of 1.7 10 2 mm. After a heat treatment 0.028 300 10
at 450 C for 250 min, the grain diameter has 0.010 385 1
2
increased to 4.5 10 mm. Compute the time