Problem Sheet 12

The numbers in square brackets refer to the number of the problem in your textbook.

1. [E13.1] The self-diffusion constants for aluminium are Do = 1.7 X 10-4 m2/s and Dd = 142 kJ/mol. What is the diffusion coefficient in aluminium at 400oC?
2. [E13.2] A steel component is nickel plated to give corrosion protection. To increase the strength of the bond between the steel and the nickel, the component is heated for 4 hours at 1000oC. If the diffusion parameters for nickel in iron are Do = 1.9 x 10-4 m2/s and Qd = 284 kJ/mol, how far would you expect nickel to diffuse into the steel in this time?
3. [E13.3] The diffusion coefficient at the melting point for materials is approximately constant, with the value D = 10-12 m2/s. What is the diffusion distance if a material is held for 12 hours at just below its melting temperature? (This distance gives an idea of the maximum distance over which concentration gradients can be smoothed by diffusion).
4. [E13.5] Pipework with a radius of 20 mm and a wall thickness of 4 mm made of 2 1/4 Cr Mo steel contains a hot fluid under pressure. The pressure is 10 MPa at a temperature of 600oC. The creep constants for this steel are as follows: Reference strain rate $\dot{\epsilon}$ = 3.48 x 1010 /second. Reference stress $\sigma_0$ = 169 MPa. Rupture exponent, m = 7.5 and Activation energy Qc is 280 kJ/mol. Calculate the creep rate of the pipe wall, assuming steady-state power-law creep.
5. [E13.6] There is concern that the pipework described in the previous problem might rupture in less than the design life of 1 year. If the Monkman-Grant constant for 2 1/4 Cr Mo steel is 0.06, how long will it last before it ruptures?
6. [E13.7] If the creep rate of a component made of 2 1/4 Cr Mo steel must not exceed 10-8/second at 500oC, what is the greatest stress that it can safely carry? Use the data listed in the previous two examples.
7. [E13.8] A stainless steel suspension cable in a furnace is subjected to a stress of 100 MPa at 700oC. Its creep rate is found to be unacceptably high. By what mechanism is creep occurring? What action would you suggest to tackle the problem? The deformation mechanism map for the material is shown in the figure on p. 306 of your textbook.
8. [E13.9] The wall of a pipe of the same stainless steel as that of the previous excercise carries a stress of 3 MPa at the very high temperature of 1000oC. In this application it, too, creeps at a rate that is unacceptably high. By what mechanism is creep occurring? What action would you suggest to tackle the problem?
9. [E13.10] It is proposed to make a shelf for a hot-air drying system from acrylic sheet. The shelf is simply supported (see the diagram on p. 307 of your textbook), and has a width w = 500 mm, a thickness t = 8 mm and a depth b = 200 mm. It must carry a distributed load of 50 N at 60oC with a design life of 800 hours (about a year0 of continuous use. Use the creep modulus plotted in Figure 13.17 (p. 294 of your textbook) and the solution to the appropriate elastic problem (Chapter 5 of your textbook) to find out how much it will sag in time.
10. What causes rise in temperature of the aircraft skin at speeds above Mach 1? If outside temperature is -50oC, and the Mac number is 3, how much would be the skin temperature? Why is it that sustained flight may be limited to speeds below Mach 3.5?
11. Derive an expression that describes the stress relaxation (reduction in stress as a function of time) by creep. (pp. 302-304 of your textbook).
12. Consider pipework in a steam-turbine power-generating station. Pipes in a typical 600 MW unit carry steam at 650oC and a pressure of 15 MPa. Suppose you have been asked to recommend a pipe required as a temporary fix while modifications are made to the plant. Space is constrained: the pipe cannot be more than 300 mm in diameter, The design life is 6 months. A little creep does not matter, but the pipe must not rupture. Type 304 stainless steel pipe with a diameter of 300 mm and a wall thickness of 10 mm is available. Will it function safely for the design life?
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