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UNIVERSITY OF SOUTHAMPTON FEEG2005W1
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SEMESTER 2 ASSESSMENT 2021-22
Materials and Structures
DURATION: 8 hours
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Please carefully follow the guidance, instructions, and formatting specified in the
“Generic Assessment Rubric and Instructions: School of Engineering Semester 2
2022” (available on Blackboard under “Final Assessment”).
Your explanations for the Materials questions can be given in clear bullet point form or
full sentences and you should use well annotated diagrams to explain any concepts
you wish to discuss. You can prepare handwritten or typed answers for this final
assessment. You may include figures or diagrams that are digitally scanned or copied
from the lecture notes without referencing. Do not however directly paste text from the
lecture notes into your answers. You are expected to develop your own written
answers and simply copying and pasting lecture slide content will be marked down.
No external references should be used, this paper should be answered from
information available on the FEEG2005 Blackboard course, i.e. from the lecture
notes/tutorial discussions/lab classes, no referencing of the course content in
FEEG2005 is required in your answers. You are reminded of the University’s policies
on academic integrity
This paper contains 3 Questions, 2 Materials questions, each worth 25 marks and 1
Structures question worth 50 marks
Answer ALL 3 questions
An outline marking scheme is shown in brackets to the right of each question.
In a continuous period of focussed working (i.e. without re-reading notes, re-watching
videos etc) we would expect this paper to take the average student who has revised
and understood the course material around 3 or 4 hours effort
Copyright 2021 University of Southampton Page 2 of 10
MQ.1
(a) In designing a turbine blade in an aeroengine (the hottest part of the engine) you are asked to
justify the choice between using a nickel based superalloy alloy and a ceramic matrix composite.
Based on your knowledge from the course:
(i) Define the expected service requirements for the turbine blade and therefore which
properties will be important in making your selection (suggested length of answer ~150-200
words, referencing not required, outline the requirements for at least 4 different materials
properties)
[4 marks]
(ii) Based on this, compare the manufacturing challenges and property benefits you expect
for each material and justify your recommendation (suggested length of answer ~ 300-350
words, you should use specific examples from your lecture notes, no referencing required)
[8 marks]
(b) Discuss the advantages of nickel base superalloy over stainless steel when being used in the
high temperature section of the aeroengine. Subsequently, explain the role of the various alloying
elements in the nickel base superalloy in providing the performance benefits discussed in MQ1(a)
and compare the effect these same alloying elements have in stainless steels (suggested length
of answer ~ 200-250 words)
[5 marks]
(c) What problems might you find in welding an austenitic stainless steel, and what alloying
decisions might you make to avoid these
[3 marks]
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(d) Creep lives to 1% strain for a directionally solidified nickel base superalloy, CM247L can be
seen in Table MQ1d. The times to reach a strain level of 1% have been determined at a range of
stresses at a constant temperature of 750oC
Stress (MPa) 190 250 400 525 600
Time to 1% e (h) 28695 5530 330 64.5 28.9
Table MQ1d – Life to 1% e at varying stress levels at 750oC
(i) If a turbine blade of this material is held at a constant temperature of 750oC but
experiences different stresses for different periods of time, how can you estimate the
creep lifetime
[1 mark]
(ii) The turbine blade is held at 750oC for 500 hours at 250 MPa, then the stress reduces
to 210 MPa for another 5000 hours. If the stress then increases to 475 MPa how
many more hours would you predict it could withstand (at this same temperature)
before it reaches 1% strain. Explain your assumptions and working fully.
[4 marks]
Copyright 2022 University of Southampton Page 4 of 10
MQ2
(a) A high strength low alloy (HSLA) steel has been chosen for a nuclear reactor pressure
vessel. During operation it is maintained at a temperature of 300oC but it is periodically
cooled down and depressurised in a controlled manner to room temperature to allow for
reactor rod changes and an accompanying structural integrity inspection of the pressure
vessel. The HSLA steel used in the reactor pressure vessel has a KIC of 73 MPa√m (±3
MPa√m) at room temperature. The thermal strains from the planned temperature and
depressurisation cycling have been estimated through FEA to cause a stress change of 350
MPa in the pressure vessel. During one of the routine structural integrity inspections a
surface crack of 1.4 mm depth (with ±10% estimated error) is found. The planned
temperature and depressurisation cycle occurs twice a week. Fatigue crack growth rate
data has also been gathered for this alloy: the Paris law constant, A = 2.45 x 10-11 and the
Paris law exponent, m = 3.2.
You are asked to consider a safety case for the system, whereby a loss of coolant accident
would require a sudden flooding of the pressure vessel with room temperature water to stop
the nuclear reaction. This will apply a maximum tensile stress of 550 MPa. You can assume
the shape factor Q = 1.2, K is in MPa√m and a (crack length) is in m for the Paris law
constants quoted.
(i) How deep a crack can the pressure vessel safely withstand
[3 marks]
(ii) Based on that assessment, how much longer (in years) would you recommend the
pressure vessel is kept in service, and subjected to the standard (controlled) thermal
cycling
[9 marks]
Explain your reasoning and justify your recommendations.
FEEG2005W1
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(b) You are choosing a chassis material for an electric car, so you want to optimise both
stiffness and strength at as low a weight as possible. Based on your knowledge of the
course and the data given below, identify a suitable materials system to manufacture a
sheet that can withstand a tensile load of 50 kN. The sheet should be no thicker than 4mm
with dimensions of 0.7 m by 1.2 m and is loaded in uniaxial tension as shown in Figure
MQ2b. It should not extend by more than 1 mm under the expected service loads.
Figure MQ2b Sheet dimensions
and loading

(i) First define the maximum strain allowed for this geometry and express this in terms
of the stress, and material stiffness (also known as Young’s Modulus) E, noting
that thickness, t is a variable (with an upper limit of 4 mm). Now specify t in terms of
E
[1 mark]
(ii) Assume that 75% of UTS is a safe loading, now define the sheet thickness, t, allowed
in terms of this safe proportion of UTS.
[1 mark]
(iii) Table MQ2d (overleaf) compares some materials properties. Consider all three
materials systems in turn, taking the volume fraction of C fibres in any composite
system to be no more than 30%. Comparing between the three materials systems,
comment on each system in terms of how they perform, initially considering only the
loading and geometry constraints identified in parts (i) and (ii)) and identifying which
system can safely have the lowest weight and still perform mechanically as required.
State all your assumptions clearly
[7 marks]
Copyright 2022 University of Southampton Page 6 of 10
Material r (kg/m3) E (GPa) UTS (MPa)
Mg alloy 1770 42 262
Al alloy 2710 70 470
Carbon-fibres 1750 550 3200
Epoxy matrix 1200 3.1 70
Table MQ2d – Materials property comparison
(iv) If the loading were to become biaxial (along both edges of the sheet) – would you
change your recommendation and why Discuss also any potential manufacturing
considerations you might want to bring into the selection process
[4 marks]
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Copyright 2022 University of Southampton Page 7 of 10
SQ3
A cantilever beam with 2 m length, is fully fixed at one end and is loaded by a point force F
= 1 kN acting in the y-z plane orientated at 30° from a line parallel to the y-axis at the other
end, as shown in Figure SQ3-1. The beam is made out of aluminium with a Young’s modulus
E = 70 GPa, Poisson’s ratio n = 0.3 and tensile and compressive allowable stress of 300
MPa. The beam is made from two 100 mm wide aluminium plates with 5 mm and 2 mm
thickness and has an asymmetric T shape section as shown in Figure SQ3-2. This figure
also shows the oblique concentrated point force F applied to the mid-line at the tip of the
top plate.
Figure SQ3-1 – A 2 m cantilever beam under point force
Figure SQ3-2 – Details of the beam section and the loading applied to the end of the beam
Copyright 2022 University of Southampton Page 8 of 10
(a) Show that the second moments of area are: !! = 5.615 × 10″ mm# , $$ =
4.739 × 10″mm# and $! = 1.500 × 10″mm#.
[5 marks]
(b) Find the largest tensile and compressive axial stresses in the beam and identify the
location on the beam and on the section where the tensile and compressive stresses
are the largest. Indicate the location of the points with drawing schematics. Please note
that “largest compressive axial stress” refers to compressive stresses with the largest
magnitude, ignoring the negative sign of the compressive stresses.
[14 marks]
(c) Identify the location of the shear centre of the section. Find the distribution of shear
stress through the thickness at the middle of each wall of the section, indicated by A
and B in Figure SQ3-2 and draw separate diagrams to show how the shear stress varies
through the thickness at these locations. Please include all the details of your
calculations and indicate in each diagram the maximum/minimum shear stresses and
their direction. Please note that you only need to find the shear stress variation across
the thickness at the specific locations labelled by A and B in the figure, and not over the
whole section.
[17 marks]
(d) Can you suggest a quick method to find a rough estimate of the maximum magnitude
of shear stress (regardless of its sign) in this beam Please explain which parameters,
loading scenarios or inputs, are important and which ones are not so important. What is
your estimated maximum shear stress if you use this approach What is the error of this
method in percentage
[3 marks]
(e) Draw a schematic showing how the section at the end of the beam is displaced, both
before and after the load F is applied. Show schematically this movement with respect
to the direction of the applied load.
[2 marks]
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(f) If the force F shown in Figure SQ3-1 and SQ3-2 is removed from the beam and a pure
compressive force perfectly aligned with the axis of the beam is applied to the centre of
gravity of the beam section at the free end, calculate the maximum compressive load
that this beam can theoretically sustain. In your calculation, assume that the beam may
only buckle in the x-y or x-z planes and ignore the asymmetry of the section.
[4 marks]
(g) Similar to the previous part (f) of this question, imagine that the force F shown in figure
SQ3-1 and SQ3-2 is removed from the beam. Additionally, assume the boundary
conditions of both ends of the beam are now changed to pin support on both ends. For
a known compressive load of F = 75 kN, calculate what is the largest initial curvature
amplitude the beam may have without failing due to the applied load.
[5 marks]
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END OF PAPER