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Question 1

The Bloodhound Supersonic Car (Figure 1a) is a land vehicle that is being designed to achieve 1000 MPH and break the current speed record. The  design of the wheels is not easy, they need to withstand the enormous centrifugal forces turning at very high speed. A normal racing car  wheel will just burst. The approach is to make them of a solid machined metal (Figure 1b).

a) Show that given a traveling speed (1000 MPH = 447 m/s) the maximum stress of the wheel does not depend on the radius of the wheel. Explain why.

b) Derive a material index for the selection of a material for this application. Use suitable mechanical properties to do so. The table catalogues the requirements.

The Strait of Gibraltar crossing is a hypothetical bridge or tunnel spanning the Strait of Gibraltar (about 14 km or 9 miles at its narrowest point)  that would connect Europe and Africa. There have been many studies about the feasibility and cost of the tunnel since 1979. In 2021 the UK,  Spain and Morocco have announced plans to return to the project (Figure 2).

You are requested to select a material for the walls of the tunnel following the method that we have seen in the lectures. It is going to be built  with a tunnel boring machine. It is surrounded by high pressure deposits. It needs to withstand an external pressure without failure. It also  needs to be as cheap as possible since the main burden is the cost of the infrastructure.

You need to follow the selection of materials process  seen in the lectures and you will need to define constraints, free variables, objective, function… Note that not everything is given in the text above and you will need to make your own documented decisions.

You have to document the whole selection process.

(a) Using the above information and your own assumption (if applicable), translate the problem

(b) From your translation, derive the performance index. [Hint] Pending on your own assumptions, you may have more than one performance index

(c) Use Granta Edupack 2021 software to create a graph representing the material index and identify the region of the chart with the cheapest  materials for the tunnel. [Hint] Pending on your own assumptions, you may have more than one performance index

(d) Select one of the suitable material highlighted in you material selection and compare your material choice with actual materials used in similar tunnels.

## Question 2

A crack with a depth of 2 cm is found in a cast iron rod of an old steam engine. Every weekend the machine is used for 8 hours for  demonstration purposes, during which it is run at 15 rpm and the load in the rod varies from +6.4×104 N to -6.4×104 N. It may be assumed  that the crack is completely closed under compressive load but that under tensile load crack closure is negligible.

The Paris relation is sufficiently accurate until failure.

To answer the following questions, you have been given the following:

Kc = 16 MPa m0.5

?Kth = 5 MPa m0.5

cross section rod = 0.04 m2

factor in the Paris relation: C = 4.3×10-8 m(MPam0.5)-4

KI = 1.12 σ (πa) 0.5

a) Using the above information, justify if it is safe to use this machine for demonstrations and if so for how long?

b) If the load varies from +0.92 MN to -0.92 MN, would it be safe to use the machine and for how long

a) Using appropriate drawings, examples and references justify the following statement: “ Creep mechanism “bulk diffusion” is highly dependent with stress”.

b) Using appropriate drawings, examples and references justify the following statement: “Creep mechanism “bulk diffusion” is highly dependent on grain size”.

c) Using suitable examples and references explain what mechanism of creep can be prevented using a single crystal part.

d) Using suitable examples and references explain what mechanism of creep can be accentuated with alloying elements.

Blackpool Tower has developed problems of corrosion as seen in Figure 3. The corroded parts must de replaced by new parts made of the same  material as the original parts. Suggest two strategies that can be used to prevent or reduce the corrosion of Blackpool Tower after the  replacement of the corroded components.. You need to justify your choice with ee xamples and discuss their advantages and disadvantages.

a) Modern bicycle frames are made with aluminium ALU 6061, which tend to crack after years of use. Whereas steel frames may last decades  and never fail. Contrast the behaviour of aluminium versus steel subjected to many cycles of stress.

b) Using the information seen in class and suitable examples or references, contrast Aluminium grade 6061T0 with Aluminium grade 6061T6

c) Explain the process to transform Aluminium 6061T0 into aluminium 6061T6

d) Bike users, often ask ,if their cracked aluminium frames can be repaired. Commonly, cracks appear on the weldments (Figure 4). Peter suggested that it would be easy to weld again by grinding the crack, expose new base material and weld again on the new material. However,   Peter’s approach is never advised. Discuss one reason why this is advised against from the structural point of view.

e) Aluminium grade 6061 T6 is shown in Figure 5, indicate three features that are clearly seen in the picture.

f) Make a drawing of the microstructure of aluminium of the previous question after being subjected to a heat treatment to reach microstructural phase equilibrium.