Interpretation:
The strain hardening coefficient of metal needs to be determined. Whether the metal is FCC, BCC or HCP needs to be determined.
Concept introduction:
Strain hardening coefficient is denoted by 'n' it is a material constant it is used for stress-strain behavior calculated in strain hardening.
Answer to Problem 8.11P
The strain hardening coefficient 'n' for the metal is 0.51. It is in the range of FCC.
Explanation of Solution
Given Information:
The measurements in the plastic region are as follows:
Force (N) | Change in gage length (cm) | Diameter(cm) |
16,240 | 0.6642 | 1.2028 |
19,066 | 1.4754 | 1.0884 |
19,273 | 2.4663 | 0.9848 |
Calculation:
The diameter of the metal bar =1.33 cm
Gage length of bar = 3 cm
When force = 16240 N, true stress-strain of the bar is given by
The stress is given by a general case:
Where,
Equation (1) becomes,
Engineering strain is given by when change length
Strain hardening is given by,
Where,
Similarly, at f = 19066 N and d =1.0884 cm.
Equation (1) becomes,
Now at,
Equation (2) becomes,
Also, true strain is given by at
Similarly, at F=19273, d=0.9848.
From equation (1),
Also, at
Equation (2) become,
The true strain is given by,
Putting all value in the table,
Sr.no. | Force | Engineering strain | Diameter | True stress | True strain |
1 | 16240 | 0.2214 | 12.028 | 143 | 0.200 |
2 | 19066 | 0.4918 | 10.884 | 205 | 0.400 |
3 | 19273 | 0.8221 | 9.848 | 213 | 0.600 |
Strength coefficient formula is given by
Here,
Substitute,
Equation (2) becomes,
Applying natural logarithm on both sides,
Similarly substituting,
Equation (4) becomes,
Applying logarithm on both sides,
Equating equation (a) and (b),
Thus, strain hardening coefficient for the metal in FCC is 0.51.
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Chapter 8 Solutions
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