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QUESTION/ANSWER BOOKLET CHEMMAT 121
SUMMER SCHOOL 2020
CHEMICAL AND MATERIALS ENGINEERING
Materials Science
1. The above graph shows the result of a 120mm long aluminium rod 8mm in diameter being
pulled in tension until failure.
[5 marks]
a) What is the yield stress of the aluminium rod?
Yield Stress = ________________
b) At the ultimate tensile strength, if the load was removed, what would be the new length of
the rod?
Length = _________________
c) What is the Young’s Modulus of the aluminium?
Young’s Modulus = _______________
d) After failure, the diameter of the rod at the fracture site is 6.34mm. What is the ductility of
the aluminium?
Ductility = ________________
2. A piece of 10mm thick aluminium sheet is to be rolled to a final thickness of 1.2mm so that
it can be used to manufacture drink cans. This is done via a series of cold rolling followed
by annealing.
[11 marks]
a) If the thickness before the final cold rolling step was 2.8mm, calculate the cold work
done to the aluminium.
% Cold Work = _______________
b) By cold rolling the aluminium, the yield stress will increase. Identify and describe the
process by which this occurs.
c) The following graph describes the relationship between the final grain size present in the
final annealed aluminium sheet, d (in mm), and its yield strength. If the drink can is
required to have a yield strength greater than 80 MPa, what must the grain size be?
Grain size = _____________
(mm
-1/2
)
d) Complete the following table to name and describe the 3 stages of annealing:
Driving Force: Description:
Stage 1:
N/A
Stage 2:
Stage 3:
e) The final annealing step is conducted at 180 ˚C and takes 220 minutes. The
manufacturer wishes to speed up this final step to improve efficiency. Using the
information provided, what temperature should the aluminium be annealed at to finish in
only 60 minutes?
Q = 148 kJ/mol R = 8.314 J/mol.K
Temperature = _______________
3. On the set of axes provided, construct a phase diagram from the following information:
a) Pure metals A and B for a binary eutectic phase diagram.
b) Pure metal A melts at 750 ˚C, pure metal B melts at 500 ˚C.
c) For an overall composition of 65 wt% B, 100% liquid exists down to 400 ˚C at which
point it transforms into two solid phases.
d) The maximum solubility of metal B in metal A is 10 wt%
e) The maximum solubility of metal A in metal B is 25 wt%
f) Both metals have complete insolubility in each other at room temperature.
[5 marks]
4. The following phase diagram shows the interstitial solid solution of carbon in iron to create
steel. Use this diagram to answer questions 4. a) – e).
[6 marks]
a) Consider a steel consisting of 1.5 wt% carbon. How much austenite is present at the
following temperatures:
i. 1000 ˚C: __________________
ii. 800 ˚C: ___________________
iii. 600 ˚C: ___________________
b) For the steel described in part a), draw the microstructure of the steel as it is slow cooled at
the following temperatures:
1000 ˚C 800 ˚C 600 ˚C
c) Consider a steel consisting of 0.5 wt% carbon. What is the composition of the austenite
phase at 728 ˚C?
Wt% Fe = _______________
Wt% C = _______________
d) For a steel of eutectoid composition at room temperature, what is the ratio of ferrite to
cementite in the pearlite present?
5. Alloy systems can utilise a number of different strengthening mechanisms to increase yield
strength.
[13 marks]
a) Explain the general rule of thumb behind how strengthening mechanisms work.
b) Explain, using a diagram, how solid solution strengthening can increase yield strength.
c) Explain, using a diagram, how multiphase strengthening can increase yield strength.
d) Explain, by filling in the following table, how age-hardening heat treatment is performed.
Description: Microstructure:
Stage 1:
Solution
Heat-Treat
Stage 2:
Quench into
2-phase region
Stage 3:
Ageing
e) Describe two of the potential problems that can occur during the quenching process, and
explain how these can be overcome.
f) When an age-hardening alloy is quenched into the two phase region, a metastable solid
phase is formed. Explain what is meant by the term “metastable”, and use a diagram to
demonstrate how this metastable phase is formed in the iron-carbon alloy system (also
known as martensite).
6. Ceramics are a class of engineering materials that consist of a combination of metallic and
non-metallic elements.
[7 marks]
a) Using an appropriate diagram, explain why ceramics are typically very brittle.
b) Would you expect ceramic fibres to be stronger or weaker than bulk ceramic? Briefly
explain your answer using an appropriate diagram.
c) Clay is an example of a traditional ceramic with a silicate structure that can be formed into a
vase using a technique called “hydroplastic forming”. Using an appropriate diagram, briefly
explain why the addition of a small amount of water makes clay very plastic AND why the
drying and firing process is necessary to harden the clay.
7. When molten silica is cooled slowly, it forms a crystalline ceramic. However, if it is cooled
rapidly, it would form an amorphous glass instead.
[4 marks]
a) In the following diagram, sketch what would be observed if molten silica is cooled rapidly.
Label the glass transition temperature Tg in the horizontal axis.
Note: the existing curve shows what happened when molten silica was cooled slowly to form
a crystalline ceramic solid.
b) Briefly explain why glass is usually optically transparent.
Tmelt
Crystalline
solid
V
o
lu
m
e
V
o
lu
m
e
Temperature
Liquid SiO2
Slow-cooling
8. Polymers are a collection of many long chains of molecules (usually hydrocarbons) packed
together to form a solid.
[9 marks]
a) The mechanical properties of polymers are greatly influenced by the degree of
polymerisation (DP), as shown in the following diagram. Using this diagram, briefly explain
why:
i. Polymers with very small DP show virtually zero yield strength.
ii. Polymers with relatively small DP show lower yield strength than polymers with
high DP.
iii. There is a maximum amount of yield strength that can be achieved by increasing the
DP of the polymer.
Y
ie
ld
S
tr
en
g
th
Degree of Polymerisation (DP)
b) Elastomers are a class of polymers that can exhibit large elastic strain. Briefly state THREE
requirements for a polymer to show large-strain elastomeric behaviour.
c) Viscoelastic models that involve springs and dashpots can model the mechanical behaviour
of polymers. Complete the missing information in the table below regarding these
viscoelastic models.
Model Response over time under
CONSTANT STRESS
Description
Fully _________________
instantaneous deformation.
Most likely caused by
polymer chains stretching
and contracting.
Also known as the Kelvin-
Voigt model.
Consists of a spring and a
dashpot in ____________
configuration.
Also known as the
Maxwell model.
Describes the stress-
relaxation behaviour of
polymers when
CONSTANT STRAIN is
applied.
S
tr
ai
n
Time
Unloading
9. BCC metals (such as the ferrite phase in steel) are typically ductile, but can exhibit brittle
failure at low temperatures.
[12 marks]
a) In the set of axes provided below, sketch the response that you would expect to see for a
BCC metal sample undergoing the Charpy impact test at different temperatures. Clearly
label the ductile-brittle transition temperature TT, and label the regions where you think the
metal is brittle and where it is ductile.
b) Briefly state and explain FOUR different ways you can decrease the ductile-brittle transition
temperature of steel.
Way to decrease Explanation
Im
p
ac
t
E
n
er
g
y
(
J)
Temperature (°C)
10. During a routine inspection, an engineer located a
6.1 cm deep edge crack on one of the steel cables
sustaining a particular harbour bridge as shown in the
diagram to the right.
There are 256 identical cables sustaining the bridge.
Assume that any force on the bridge is evenly
distributed to every single steel cable.
Unfortunately, that particular steel cable fractured uncontrollably during a traffic jam where
4,000 identical cars, each with two passengers, were on the bridge at the same time.
Assume:
 Each car (with two passengers) has the same mass of 1,500 kg.
 The harbour bridge has a mass of 52,800,000 kg.
 Each steel cable has the same perfectly circular diameter of 100 mm.
 Gravitational acceleration, = 9.81 /2.
 The geometric factor = 1.0 for the steel cable.
 The failure only occurred because at that point 1 > 1 for that particular steel
cable and no other factor is involved.
[8 marks]
a) Determine the stress that each steel cable was subjected to, assuming that the only forces
acting on the cable were due to the mass of the bridge and the 4,000 cars.
b) Determine the fracture toughness of the particular steel cable.
Bridge
Steel
cable
with
crack
11. Briefly state and explain TWO different ways you can improve the creep resistance of
metallic alloys.
[4 marks]
I. __________________________________________________________________________
Explanation:
II. __________________________________________________________________________
Explanation:
12. Corrosion is a big problem in the engineering world wherever metals are used, as it leads to
major economic loss and hazards. The following table shows the galvanic series that can be
used to predict the corrosion behaviour of engineering materials.
[5 marks]
a) Based on the galvanic series, state what would happen if a cobalt metal coated with silver
was scratched and the base metal was exposed to moist aerated conditions.
b) Based on the galvanic series, state what would happen if plates in the hull of a boat made
out of aluminium were joined together with copper bolts. Will this situation lead to a slow or
a rapid corrosion?
13. A stainless steel tank containing orange juice is undergoing corrosion where it uniformly
loses 0.0025 mm of thickness over a surface area of 12.5 m
2
in one year. Determine the
corrosion current that is responsible for this process.
Assume:
 Density of stainless steel is 8,000 kg/m3.
 Faraday’s constant is 96,500 A.s / mol.
 The anodic reaction is
→ 2+ + 2−.
 There are 365 days in a year.
 Molecular weight of iron is 56 g/mol.
[5 marks]
14. The following diagrams shows the stress-strain curves of a certain ceramic fibre, a certain
polymer matrix, and a composite made out of those fibres and polymer.
[6 marks]
a) Label the curve that you think shows the ceramic fibre response as F, the curve that you
think shows the polymer matrix response as M, and the curve that you think shows the
composite response as CM.
b) Using the diagram above, briefly explain what you think happens to the composite material
when it is subjected to a tensile stress bigger than 50 MPa. Do you think it will lead to a
catastrophic failure?
S
tr
es
s
Strain
50
MPa