You are asked to hot roll a plate of cartridge brass (Cu-30Zn) 3 m long × 700 mm wide × 200 mm thick to a thickness of 12 mm at 800°C. The brass must then be cold rolled to 2 mm with a final yield stress of 500 MPa. The rolls are turning at 100 rpm.
Using the information provided, answer the two following questions. The numerical values given in each question may not correspond with those calculated in the previous question. Make sure you read the caption on the accompanying figure.
Figure 1. True Stress-Strain Curves in Tension at Room Temperature for Various
Metals.
The point of intersection of each curve at the ordinate is the
yield stress s; thus, the elastic portions of the
curves are not indicated. When the K and n values are determined
from these curves, they may not agree with those given in Table 2 because of
the different sources from which they were collected.
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TABLE 1. Metric Conversions
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|||||
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To convert from
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To
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Multiply by
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To convert from
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To
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Multiply by
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ft
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m (meter)
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3.0480 × 10-1
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lbf
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n | 4.4482 |
| ft-lbf |
J
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1.3558
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mpa
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Pa | 106 |
| ft-lbf |
N·m
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1.3558
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N/m2
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Pa | 1.0000 |
| ft-lbf/s |
W
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1.3558
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N·m
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J | 1.0000 |
| Kgf |
N
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9.80665
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N·m/s
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W | 1.0000 |
| Ksi |
Mpa
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6.8948
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27,934 ft3
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| N = Newton = force to move 1 kb with an acceleration of 1 meter per second | |||||
Useful Information:
a = effective moment arm relating to torque in a rolling mill
L = projected area of contact between the roll and the material being rolled.
P = Rolling mill force
Rps = revolutions per second
Work of one revolution of a rolling mill,J, = 2×2Pa
P
Power of rolling mill, KW, = 2×2pa P(rps)/1000
rps = revolutions per second
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L = [R(ho - hf)]1/2
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a/L
0.5 |
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s = Cem
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s = ken
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DH = m2R
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TABLE 2. Approximate range of values for C and
m for various annealed metals at true strains ranging from 0.2
to 1.0
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C
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Material
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Temperature, °C
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psi × 103
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MPa
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m
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Aluminum
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200-50
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12-2
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82-14
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0.07-0.23
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| Aluminum alloys |
200-500
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45-5
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310-35
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0.00-0.20
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| Copper |
300-900
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35-3
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240-20
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0.06-0.17
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| Copper alloys (brasses) |
200-800
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60-2
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415-14
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0.02-0.30
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| Lead |
100-300
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1.6-0.3
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11-2
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0.10-0.20
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| Magnesium |
200-400
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20-2
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140-14
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0.07-0.43
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| Steel | ||||
| Low-carbon |
900-1,200
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24-7
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165-48
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0.08-0.22
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| Medium-carbon |
900-1,200
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23-7
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160-48
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0.07-0.24
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| Stainless |
600-1,200
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60-5
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415-35
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0.02-0.40
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| Titanium |
200-1,200
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135-2
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930-14
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0.04-0.30
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| Titanium alloys |
200-1,200
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130-5
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900-35
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0.02-0.30
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| Ti-64l-4V* |
815-930
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9.5-1.6
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65-11
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0.50-0.80
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| Zirconium |
200-1,000
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20-4
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830-27
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0.04-0.40
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| * At a strain rate of 2 × 10-4/s | ||||
| NOTE: As temperature increases, C decreases and m increases. As strain increases, C increases and m may increase or decrease, or it may become negative within certain ranges of temperature and strain. | ||||
If the average flow stress at an intermediate stage of hot rolling to 12 mm
is s’ = 50 MPa and the length of contact is
77 mm, then the approximate roll force (MN) would be most nearly:
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(A)
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0.004
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(B)
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2.7
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(C)
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4,000
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(D)
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2.7 × 106
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