SECTION A ANSWER ALL QUESTIONS

QUESTION A1
Boeing aerospace manufacture company is interested in analysing the failure of aircrafts due to fatigue and fast fracture related failure mechanism. In order to analysis the failure of aircrafts Boeing company has developed an in-house laboratory test facility comprising both testing and material characterization using non-destructive techniques of the aerospace materials. A group of designer engineer of the Boeing company planned to perform a series of fatigue test for a component made up of a high strength steel. The toughness and fracture toughness of steel
material under investigation was Gc = 75 kJ/m2 and Kc respectively. In the process of fatigue testing, non-destructive testing technique by ultrasonic methods was followed. A central crack of 3 mm deep was observed by non-destructive testing. The crack growth rate under cyclic loading in the laboratory test condition was given by Paris relation
da = m
A (∆K) dN
The constants of the Paris equations were estimated to be A = 6 x 10−12 and m = 4, where σ is in MPa. Under the laboratory test condition, the steel component is subjected to an alternating stress of range, ∆σ = 250 MPa about a mean tensile stress of ∆σ/2. Geometry factor in the fracture toughness expression, Y = 1.05 is assumed.
(i) At what critical length will fast fracture occur?
(2 marks)

(ii) Estimate the number of cycles to failure.
(3 marks)

(iii) Explain and justify with supporting evidence what would happen to the fatigue life of the component if the initial central crack length is changed from 3 to 5 mm deep while keeping all other parameters same. Suggest a way to increase the fatigue life of the component.
(5 marks)

(Total: 10 marks)

QUESTION A2
(i) Using suitable material example of your choice, explain the term diffusion creep? Discuss how the rate of diffusion creep depend on the stress, temperature, and grain size of the material?
(4 marks)

(ii) The British Plastics Federation (BPF) is the world’s longest running plastics trade association, established in 1933 to represent the UK industry. BSF want to support the education institution along with the industrial partner to support the setting up the material testing laboratory in the universities. In the process of setting up the material testing laboratory in UCLAN a trial experiment was conducted on the creep behaviour of the alloy tie bar. An alloy tie bar has been designed to withstand a stress, 𝜎 of 30 MPa at 650 ℃. Creep tests were carried out on 5 samples of the alloy under a steady state creep rate, ε̇ of 7.71 x 10−12 s−1. The stress and temperature of the alloy was increased to 35 MPa and 680 ℃ in service for 40% of the running time. Calculate the average creep rate under service conditions. The alloy can be considered to creep according to the equation:
𝑑𝜀 5𝑒− 𝑅𝑇𝑄
= 𝐴𝜎
𝑑𝑡
where A and Q are constants, R is the universal gas constant and T is the absolute temperature. The activation energy is 180 kJ/mol.
(6 marks)

[Hint] Give you answers with no more than 3 decimal places.
(Total: 10 marks)

QUESTION A3

CASE STUDY ANALYSIS

Critically assess the outputs, techniques and reported failures on these three case studies (1000 words maximum):
1. Evaluation of microstructural degradation in a failed gas turbine blade due to overheating, X. Guo, W. Zheng, C. Xiao, L. Li, S. Antonov, Y. Zheng, Q. Feng, Engineering
Failure Analysis, Volume 103, 2019, Pages 308-318, ISSN 1350-6307, https://doi.org/10.1016/j.engfailanal.2019.04.021.
(http://www.sciencedirect.com/science/article/pii/S1350630718316601)

2. Failure analysis of gas turbine first stage blade made of nickel-based superalloy,
A.M. Kolagar, N. Tabrizi, M. Cheraghzadeh, M.S. Shahriari, Case Studies in Engineering
Failure Analysis, Volume 8, 2017, Pages 61-68, ISSN 2213-2902, https://doi.org/10.1016/j.csefa.2017.04.002.
(http://www.sciencedirect.com/science/article/pii/S2213290217300093)

3. Identification of failure mechanisms in nickel base superalloy turbine blades through microstructural study, M. Sujata, M. Madan, K. Raghavendra, M.A. Venkataswamy, S.K. Bhaumik, Engineering Failure Analysis, Volume 17, Issue 6, 2010, Pages 1436-1446, ISSN 1350-6307, https://doi.org/10.1016/j.engfailanal.2010.05.004.
(http://www.sciencedirect.com/science/article/pii/S1350630710000968)

[Hint 1]: In order to do this task successfully, you will need to read other case studies from the same journal and from books and investigate the techniques, structures and failures named in the articles but not explained, as it is assumed the reader already knows about them.

[Hint 2]: In order to understand the articles, you will need to find out the meaning of the technical terms used. You will be expected to use suitable technical terms as part of your analysis.

[Hint 3]: You can discuss for example failure modes or materials phases. You may discuss alternative techniques to be used in order to verify the outcomes of the authors. Is there any other technique could have been considered not currently included in the article? What could have been the benefit? Why do you think those techniques have been used in the article? [Hint 4]: Was it possible to anticipate the failures in the process design? Might a good Finite Element Method analysis have predicted the failures?

[Hint 5]: Use references, examples and/or your own experience appropriately.

(20 Marks)

SECTION B

ANSWER ALL QUESTIONS

QUESTION B1

MATERIAL SELECTION FOR A FLYWHEEL

A flywheel is a mechanical device specifically designed to efficiently store energy. An efficient flywheel stores as much energy per unit weight as possible without failure (Figure 1). As the flywheel is spun up, increasing its angular velocity ω, it stores more energy. But if the centrifugal stress exceeds the tensile strength of the flywheel, it flies apart. So strength sets an upper limit on the energy that can be stored. Consider a flywheel as a solid disk of radius, R and thickness, t rotating with angular velocity, ω.

Figure 1: Flywheel

You will need to find out the necessary equations to solve the energy stored in the flywheel per unit mass. The flywheel should not fail by fast fracture and it should not burst.

(i) Translate the problem indicating function, objective, constraints and free variables.
(5 marks)

(ii) Derive the performance index and select the material graphically using GRANTA EduPack material selection software.
(15 marks)

(Total: 20 marks)

QUESTION B2

MATERIAL SELECTION FOR A SPLINE SHAFT OF AN AEROENGINES

A spline shaft in an aeroengine consists of external and internal splines and are made up of high strength steel materials of a hollow circular cross section. Spline shafts in an aeroengines are subjected to an axial, bending and torsion loading during operation. As a design engineer of the Boeing Aerospace Company you have been assigned a task of selecting a new high strength alloy steel material which has a superior property of the current materials with minimum weight and as cheap as possible. The maximum load applied on the spline shaft under bending and torsion is fixed by the designer. The external diameter, 𝟐𝑹 and length, L of the spline shaft is fixed. The wall thickness, 𝒕 of the spline shaft is not defined. The selected shaft material should not fail by yielding and fast fracture in torsion and bending.

(i) Translate the problem indicating function, objective, constraints and free variables.
(6 marks)

(ii) Derive the performance index based on torsion and select the material graphically using GRANTA EduPack material selection software.
(15 marks)

(iii) Discuss the implication of two performance index for the selection of one material based on torsion. Find the coupling line by making equal the cost calculated with the two indexes.
(4 marks)

(iv) Derive the performance index based on bending and select the material graphically using GRANTA EduPack material selection software.
(15 marks)

TORSION EQUATION
𝐓 𝝉 𝐆𝜽 = =
𝐉 𝐑 𝐋
T – Applied torque in Nm
J – Polar moment of inertia (m4) = ∬ 𝑦2 𝑑𝐴
𝜏 – Shear stress (Pa)
R – Radius (m) G – Shear modulus (Pa) θ – Twist angle (rad) L – Length of the shaft (m) Assume the thickness is much smaller than the diameter of the shaft. Therefore:
𝐽 𝜋𝑅𝑡
Area of the shaft,
𝐴 𝜋𝑅𝑡
Maximum shear stress theory,
𝜎
𝜏 =
2
Fast fracture condition,
𝐾𝑐 = 𝜏 (𝜋𝑎𝑐)1/2

Figure 2: Torsion of shaft

BENDING MOMENT EQUATION
𝐌 = 𝝈𝒃 = 𝐄
𝐈 𝐲 𝐑

M – Bending moment in Nm
I – Moment of inertia (m4) = 𝑑𝐴
𝜎𝑏 – Bending stress (Pa)
R – Radius of curvature (m) E – Youngs modulus (Pa) θ – Twist angle (rad) L – Length of the shaft (m)

Assume the thickness is much smaller than the diameter of the shaft. Therefore:
𝐼 𝜋𝑅𝑡

Area of the shaft,
𝐴 𝜋𝑅𝑡
Fast fracture condition,
𝐾𝑐 = 𝜎 (𝜋𝑎𝑐)1/2
(Total: 40 marks)

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