HW7 solution
Restricting or hindering dislocation motion renders a material harder and stronger.
According to the equation related to yield strength and grain size, we can get two equations as
y
o
k
MPa
0
.
10
230
+
=
σ
and
y
o
k
MPa
91
.
12
275
+
=
σ
which yield the values
MPa
4
.
75
0
=
σ
and
2
/
1
)
(
49
.
15
mm
MPa
k
y
=
.
At a yield strength of 310 MPa, we have
2
/
1
)
46
.
15
(
4
.
75
310
−
+
=
d
Therefore,
)
(
10
34
.
4
3
mm
d
−
×
=
In order for these two cylindrical specimens to have the same deformed hardness, they must be deformed to the
same percent cold work. For the first specimen
CW
r
r
r
A
A
A
CW
d
d
%
36
100
)
15
(
)
12
(
)
15
(
100
100
%
2
2
2
2
0
2
2
0
0
0
=
×
−
=
×
−
=
×
−
=
For the second specimen, the deformed radius is computed using the above equation and solving for
d
r
as
)
(
80
.
8
100
36
1
11
100
%
1
0
mm
CW
r
r
d
=
−
=
−
=
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Computing the value of the constant
A
(in the equation provided in the problem statement) from the one set of
data as
mm
MPa
mm
MPa
MPa
A
D
crss
−
×
=
−
=
−
=
−
−
3
2
0
10
21
.
6
)
(
10000
)
(
069
.
0
)
(
69
.
0
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 Spring '08
 Zhang
 Tensile strength, MPa, QC

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