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100
80
60
40
20
0
0
0.002
0.004
0.006
0.008
0.01
0.012
Strain, in./in.
FIGURE P1.11
1.12 Use Problem 1.11 to graphically determine the following:
a. Modulus of resilience
b. Toughness
Hint:
The toughness can be determined by calculating the
area under the stress-strain curve
1
u
t
2
e
f
u
t
=
3
s de
0
where is the strain at fracture. The preceding integral can be
approximated numerically by using a trapezoidal integration
technique:
e
f
n
n
1
2
u
t
=
a
u
i
=
a
1
s
i
+ s
i - 1
2
1
e
i
- e
i - 1
2
i = 1
i = 1
c. If the specimen is loaded to 40 ksi only and the lateral strain was
found to be
- 0.00057 in./in.,
what is Poisson's ratio of this
metal?
d. If the specimen is loaded to 70 ksi only and then unloaded, what
is the permanent strain?
1.13 Figure P1.13 shows the stress-strain relations of metals A and B
during tension tests until fracture. Determine the following for the
two metals (show all calculations and units):
a. Proportional limit
b. Yield stress at an offset strain of 0.002 in./in.
c. Ultimate strength
d. Modulus of resilience
e. Toughness
f. Which metal is more ductile? Why?
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