SEM212
School of Engineering and technology
Callister, chapter 10
Tutorial Notes
10.8
This problem gives us the value of
y
(0.30) at some time
t
(100 min), and also the
value of
n
(5.0) for the recrystallization of an alloy at some temperature, and then asks
that we determine the rate of recrystallization at this same temperature. It is first
necessary to calculate the value of
k
. We first rearrange Equation 10.17
)
exp(
1
n
kt
y
−
−
=
as
)
exp(
1
n
kt
y
−
=
−
(1)
and then take natural logarithms of both sides:
n
kt
y
−
=
−
)
1
ln(
(2)
Now solving for
k
gives
11
10
57
.
3
)
1
ln(
−
=
=
−
−
x
k
t
y
n
(3)
using the values cited above for
y
,
n
, and
t.
Remember the definition for the transformation rate:
5
.
0
1
t
rate
=
We therefore now want to compute
t
0.5
, this is the value of
t
for
y
= 0.5, which means
that it is necessary to establish a form of Equation 10.17 in which
t
is the dependent
variable. Rearranging equation (2) gives
n
t
k
y
=
−
−
)
1
ln(
(4)
And solving this expression for
t
leads to
t
k
y
n
=
⎟
⎠
⎞
⎜
⎝
⎛
−
−
/
1
)
1
ln(
(5)
For
t
0.5
, equation (5) takes the form
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 Spring '09
 dunno
 Tensile strength, Austenite, Ferrite, fine pearlite

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