Answer all the questions-
Q1. a) Explain why there may be considerable scatter in the results of a fatigue test and distinguish between what is meant by "endurance limit" and "fatigue limit" of materials.
The "S/N" curves in Fig Q1A gives the fatigue data for both mild steel and aluminium alloy. Redraw the graph and use the sketch to identify each of the materials to explain your answer.
b) An aluminium cantilever switching device of rectangular cross section 30 mm wide and 200 mm long is required to accept a displacement of ± 2.7 mm at its free end. (see Fig Q1 B).
Find the required depth of section "d", in order to avoid fatigue failure in bending up to 100, 000 cycles. [Use the graph provided in Fig Q1 A to find the allowable fatigue stress and take a factor of safety of 5]
Use the bending equation and take the deflection at the free end of a cantilever to be δ = WL3/3EI,
Given: E aluminium = 79 GN/m2
Q2. a) The Comet Airliner was withdrawn from service after a series of crashes.
Discuss factors in the design, development and manufacture of the plane that contributed to these accidents.
b) Outline the important ethical issues that were highlighted by the Comet failures, and explain how a "whistleblower" may have helped to prevent the tragedy.
c) Describe the ethical situation that VW faces with regards to the recent diesel engine emissions scandal and explain,
1) How it could be allowed to happen?
2) Who do you think is to blame in the Company?
3) Suggest ways in which VW can address the problems and difficulties that have arisen?
Q3. Bending tests were undertaken on a lightweight aluminium tube, 23 mm outside diameter and 1 mm wall thickness to determine the mode of failure.
It was simply supported and loaded centrally, (Fig Q3)
The results of a load deflection test were as follows:
|
Mass (kg)
|
Deflection (mm)
|
|
5
|
4.0
|
|
9
|
7.5
|
|
13
|
11.0
|
|
17
|
15.0
|
|
21
|
19.0
|
|
25
|
25.0
|
|
29
|
35.0
|
|
31
|
45.0
|
Plot a graph of load versus deflection.
a) On the graph, show the yield point and calculate the yield stress. [Use the bending equation, use I = ∏(D4-d4)/64 and ignore the weight of the tube]
b) Find the maximum bending stress at 31 kg mass.
c) Describe 2 ways in which the tube may deform in bending and explain the effect that a notch may have on the mode of failure. Use sketches to illustrate your answer.
d) If after testing, the permanent "set" in the tube was 25 mm, use Pythagoras to derive an expression for the radius of curvature "R" Hence find the value of "R" over the 1 meter span. [State any assumptions used in your analysis]
Q4. a) Use an x-y plot to demonstrate and explain the empirical relationships between the Alternating Stress (σa) and the Mean Stress (σm) in cyclical loading, according to the:
Modified Goodman Equation σa = σf [1- σm/σu]
Soderberg Equation σa = σf [1- σm/σy]
Where σf is the fatigue limit σy is the yield stress and σu is the ultimate tensile stress.
b) The stepped shaft shown in Fig Q 4 was subjected to a steady axial force of 100 kN and an alternating bending moment ± M. (Nm)
1) Find the mean axial stress at the fillet radius.
2) Use the bending equation to find an expression for the alternating stress.
3) Determine the fatigue strength reduction factor, if the stress concentration factor kt for the fillet radius is 1.55 and the notch sensitivity factor q is 0.9.
4) If the yield strength of the rotor was 300 MN/m2, the ultimate tensile strength400 MN/m2 and the fatigue limit in reversed bending was 200 MN/m2, calculate the maximum value of M by using both the Soderberg and Modified Goodman equations given above, to avoid fatigue failure in the rotor.
Q5. a) Define what is meant by stress concentration and illustrate the concept by considering the fluid flow analogy for:
1) A strut in compression
2) Two types of geometrical discontinuity.
b) The steel test piece in Fig Q 5 was mounted on 8 mm diameter pins and subjected to an axial cyclic load of ± P kN
If the stress concentration factor kt for the hole = 2.2 and for the fillet radius kt = 2.4, with a notch sensitivity factor q = 0.9 for both, determine:
1) The fatigue strength reduction factor kf for the hole and fillet.
2) The safe working axial load "P" up to 107 cycles, if the fatigue limit is 320 N/mm2.
3) If the corner radius is increased from 3 mm to 5 mm, such that kt for the radius is reduced to 2.2, does the safe working load change and where will failure be likely to occur?
Q6. Increasingly adhesives are being used to replace traditional methods of fastening.
a) Describe six benefits of using adhesives.
b) Describe three bonded joint designs and with the aid of sketches comment on their relative performance.
c) Compare the strength and performance of one adhesive joint design with a mechanical joint that performs the same function, with particular reference to design and engineering failure.
Attachment:- Figures.rar