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Obtain a material index for the elastic bending of a simply supported beam with uniform distributed load for the entire length of the beam for a circular cross section, d (where d – diameter of the beam). Both the length and stiffness of the beam are fixed by the design. The beam should not deflect more than � under the bending load, F and the selected material should be as cheap as possible. The mid-point deflection, � of an elastic beam of length, L loaded inthree-point bending by a central load, F is given by:

[Hint] Translation of the problem – 4 marks and derivation of the material index – 6 marks.

QUESTION A2

Boeing aerospace manufacture company is interested in analysing the failure of aircrafts due to fatigue. Boeing company has developed the in-house laboratory facility to test the aerospace materials for fatigue related failures. A group of designer engineer of the Boeing company planned to perform a series of fatigue test for a component made up of a steel. The fracture toughness of steel material under investigation was Kc = 90 MPa√m. In the process of fatigue testing, non-destructive testing technique by ultrasonic methods was followed. A crack of 2.6 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

The constants of the Paris equations were estimated to be A = 5 x 10−12 and m = 4, where σ is in MPa. Under the laboratory test condition, the steel component is subjected to an alternating Page 4 of 11 stress of range, ∆σ = 220 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?

(ii) Estimate the number of cycles to failure.

(iii) Estimate the number of cycles to failure if the alternating stress range of the component is changed from ∆σ = 220 MPa to ∆σ = 250 MPa. All other parameters are kept constant.

QUESTION A3

(i) 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 polymer laboratory in the universities. In the process of setting up the injection moulding machine in UCLAN a trial experiment was conducted on the thermosetting plastics. A force, F will inject a given weight of an epoxy thermosetting polymer into intricate mould of the injection moulding machine in two different time and temperature scale, i.e., 30 s at 180 degrees Celsius and in 85 s at 162 degrees Celsius. If the viscosity of the epoxy thermosetting polymer follows an Arrhenius law of diffusion, with a rate of process proportional to calculate how long the process will take at 237 degrees Celsius.

(ii) Discuss the possible behaviour of this material in relation to creep and compare it with the possible behaviour of a thermoplastic taking into consideration the main polymer structure characteristic of both. Compare the equation to model the injection with the equation to model creep.

Give you answers with no more than 3 decimal places.

Phase diagram is a graphical representation of the physical states of a substance and it summarise the equilibrium constitution of an alloy system. A binary phase diagram of the copper-zinc system including brass is shown in the Figure Q – A4. Using the binary phase diagram of the Cu – Zn system list out the salient features by answering the following questions:

(i) List out the compositions and temperatures of the eutectoid point, and five peritectic points present in the binary Cu – Zn system.

(ii) What distinguishes the two alloys (70/30 brass and 60/40 brass) in the binary Cu – Zn system?

(iii) What roughly is the melting point of 70/30 brass in the binary Cu – Zn system?