Assignment#9_Chapter-8
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Old Dominion University *
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Dec 6, 2023
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MAE 201: Materials Science
Instructor: Dr. Dipankar Ghosh
Assignment #9 (Chapter-8)
Due date: 11/22/2022, 11.59 pm (Submission link provided in Canvas)
Late submission is NOT accepted
Answer all the questions and show all the steps clearly
1.
A Pb-Sn alloy contains 40 wt % β and 60 wt % α at 50°C. What is the average
composition of Pb and Sn in this alloy?
C
2
−
C
0
C
2
−
C
1
=
w
α
=
0.60
100
−
C
0
100
−
2.8
=
0.60
1.029
−
C
0
97.2
=
0.6
C
0
97.2
=
0.42881
C
0
=
41.68
wt %Sn
100
−
41.68
=
58.32
wt %Pb
2. A Pb-Sn alloy consists of 60 wt % proeutectic β at 183°C - ΔT. Calculate the average
composition of this alloy.
C
2
−
C
0
C
2
−
C
1
=
w
α
=
0.60
61.9
−
C
0
61.9
−
19.2
=
0.60
25.62
=
61.9
−
C
0
C
0
=
36.28
wt %Sn
100
−
36.28
=
63.72
wt %Pb
L
+
α
L
+
β
α
+
β
200
Temperature (°C)
19.2
wt% Sn
à
20
60
80
100
0
300
100
L
(liquid)
α
183°C
61.9
97.5
β
40
100%
Pb
100%
Sn
a
b
c
L
+
α
L
+
β
α
+
β
200
Temperature (°C)
19.2
wt% Sn
à
20
60
80
100
0
300
100
L
(liquid)
α
183°C
61.9
97.5
β
40
100%
Pb
100%
Sn
a
b
c
1
MAE 201: Materials Science
Instructor: Dr. Dipankar Ghosh
3. An alloy of 30 wt % Pb and 70 wt % Sn is slowly cooled from 250°C to 27°C.
(a) Is this alloy hypoeutectic or hypereutectic?
Hypereutectic
(b) What is the composition of the first solid to form?
19.2%Sn/80.8%Pb
(c) What are the amounts and compositions of each phase that is present at
183°C+ΔT?
L
=
¿
97.5
−
70
97.5
−
61.9
=
77.25
%L
w
¿
w
β
=
70
−
97.5
61.9
−
97.5
=
22.75
%β
(d) What is the amount and composition of each phase that is present at 183°C-ΔT?
w
α
=
97.5
−
70
97.5
−
19.2
=
35.12
%α
w
β
=
70
−
19.2
97.5
−
19.2
=
64.88
%β
(e) What are the amounts of each phase present at room temperature?
w
α
=
100
−
70
100
−
1.5
=
30.45
%α
w
β
=
70
−
1.5
100
−
1.5
=
69.55
%β
2
MAE 201: Materials Science
Instructor: Dr. Dipankar Ghosh
4. For the Pb-Sn phase diagram, answer the following questions.
(a) What is the maximum solubility of Sn in α? At what temperature?
19.2wt%Sn at 183
°C
(b) What is the maximum solubility of Pb in β? At what temperature?
2.5wt%Pb at 183
°C
5. A Pb-Sn alloy has a composition of 36 wt.% Sn at 300°C (shown by the solid red
vertical line).
(a) Is it a hypereutectic alloy?
yes
(b) Three locations are indicated along the red vertical line (shown by
a
,
b
and
c
).
For each location, write down the phase(s) present.
a: The only phase present is Liquid.
b: The Liquid and
α
phases are present.
c: It is completely solid containing the
α
and
β
phases.
(c) Also, indicate the type of α and β phases (i.e., proeutectic and/or eutectic).
αpro
αeut
βeut
L
+
α
L
+
β
α
+
β
200
Temperature (°C)
19.2
wt% Sn
à
20
60
80
100
0
300
100
L
(liquid)
α
183°C
61.9
97.5
β
40
100%
Pb
100%
Sn
a
b
c
3
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MAE 201: Materials Science
Instructor: Dr. Dipankar Ghosh
6. A Pb-Sn alloy has a composition of 36 wt.% Sn at 300°C (shown by the solid red
vertical line). Draw the microstructures at
a
,
b
and
c
locations as the alloy is cooled to
room temperature.
L
+
α
L
+
β
α
+
β
200
Temperature (°C)
19.2
wt% Sn
à
20
60
80
100
0
300
100
L
(liquid)
α
183°C
61.9
97.5
β
40
100%
Pb
100%
Sn
a
b
c
4