Question 1

A composite material consists of 35% parallel carbon fibres of Young's modulus 420GPa in a matrix of epoxy resin with a Young's modulus of 3GPa.

Calculate the Young's modulus of the composite in the directions parallel and perpendicular to the direction of the fibres.

Start writing down the value of your unique data for the cabon fibre Young's modulus.

Question 2

Aluminium 6061 is widely used in the aircraft industry and high tech industry. With the suitable heat treatment can be used in welded structures as bicycle frames. In the laboratory some probes of Aluminium 6061T6 are going to be tested against fatigue failure. Two experiments have been performed already, the probe have failed after 10⁷ cycles and 10⁵ cycles at 92 MPa and 113 MPa stress range respectively.

a) Applying Basquin's law, estimate the stress range that will make the probe fail at 10⁴ cycles.

b) Applying Goodman's rule, estimate the stress range that will make the probe fail at 10⁷ cycles if the probe is subjected to a mean continuous tensile stress of 70 MPa. (σ_TS=0.25 GPa)

Start writing down the unique data for your stress ranges.

Question 3

Explain, with aid of a diagram, the physical failure of a bolt under, evaluate the accuracy of the assumptions you take for the calculations:

a) Single shear where the forces are parallel and opposing and applied atright angles to the longest axis.

b) Double shear where the forces are parallel and opposing and applied at right angles to the longest axis.

[Hint] You will need to understand engineering drawings, top view, front view, side view. You will need to assume and estimate the area of all possible failed sections.

Question 4

A bearing pad, shown in Figure 2.3 and consisting of two steel plates bonded to an artificial rubber, is subjected to a shear force F = 12kNduring a static test. The pad has dimensions of a =170 mm and b = 250 mm and the artificial rubber has a thickness t = 50 mm. When the force F equals 12kN, the top plate is found to have moved laterally by 8 mm with respect to the bottom plate. What is the shear modulus of elasticity, G, of the artificial rubber?

Start writing down the unique data for the shear force.

Question 5

The figure below shows the copper-antimony Cu-Sb phase diagram.

Figure: copper-antimony Cu-Sb phase diagram

a) Find the chemical formula for the compound marked X (atomic weights of Cu and Sb are 63.54 and 121.75 respectively).

b) The Cu-Sb system contains 2 eutectics, 1 eutectoid, 1 peritectic and 1 peritectoid. Mark them all on the figure, write down the temperature and composition of each point, and identify the phases involved in each reaction, on cooling.

c) An alloy containing 53wt% Sb is cooled slowly to room temperature from the melt. Explain the phase changes that occur during cooling, using schematic sketches of the microstructure at key temperatures to illustrate your answer. Start writing down the unique data for weight percentage of Sb.

d) Sketch a temperature-time curve for the 95 wt% Sb alloy over the range 650 to 450oC and account for the shape of the curve.

Question 6.

a) Brass (CW614N - CZ121) has a Young's modulus of 92 GPa and a Poisson's ratio of 0.34. Calculate the effective modulus at the interface when two brass plates are loaded together. Start writing down your unique data for Young's modulus.

b) Copper has a modulus of 120GPa and a hardness of 150 MPa. Estimate the elastic strain in copper at the yield stress. Start writing down your unique data for Young's modulus.

Question 7.

A steel shaft with a Ra value of 0.4μm is rotating in a brass bush with a Ra value in its inner diameter of 0.7μm. The shaft and bush are immersed in oil and, during operation, an oil film thickness of 1.8 μm is developed. In which lubrication regime is the sliding interface operating? Your answer should be supported by a suitable example where this regime is often found. Start writing down the unique data for the oil film thickness.

Question 8.

It is found that a polymer-based bearing supporting a rotating steel shaft has a depth wear rate of 0.25mm in 1000 hours both at a bearing pressure of 10MPa and speed of 10^-1 ms^-1, and at a pressure of 1 MPa and a speed of 1ms^-1.

(a) Show that the bearing is operating in the range where the specific wear rate is constant.

(b) Calculate the time taken to reach a wear depth of 0.25mm if the pressure and speed were 2 MPa and 0.2 ms^-1.

(c) Given this information, decide if you could safely calculate the wear rate at a pressure of 10MPa and a speed of 1ms-1, and give reasons for your decision.

(d) The test results were obtained using a polished steel shaft in a laboratory environment and at room temperature. Suggest changes in these conditions that could cause the specific wear rate to be different.

Question 9.

"To reduce wear on a steel component, a hard wear resistant ceramic coating is applied"

(a) Explain using suitable examples, what is meant by this statement.

why using ceramic coatings on steel

(b) With the aid of diagrams, illustrate three different techniques by which this could be done. Explain how a ceramic coating can be applied and discuss the advantages of the three techniques. You may use appropriate examples and references.

Question 10.

A Tungsten carbide ball 12 mm in diameter is loaded under an increasing normal force against a stainless steel plate with a hardness of 2000 MPa, as shown below.

a) At what force does the material of the plate first yield?;
b) What is the corresponding contact width?;
c) What are the mean and maximum pressures in the contact zone?;
d) What are the magnitude and the location of the maximum shear stress?

The relevant Hertz equations for this contact are:

Radius of the circle of contact, a = (3PR/4E*)^1/3 (equation 1)

Maximum pressure, p₀ = 3P/2πa²= (6PE*²/π³R²)^1/3 (equation 2)

Where P is the normal load, R is the radius of the ball and E* is the composite modulus at the contact.

Start writing down the unique data for the diameter.