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s ME301 1/10 SCHOOL OF ENGINEERING MODULAR HONOURS DEGREE LEVEL 3 SEMESTER 1 2004/05 MATERIALS ENGINEERING Examiners: Dr M Philip/Dr E Sazhina Attempt FIVE questions only Time allowed: 3 hours Total number of questions = 8 All questions carry equal marks. The figures in brackets indicate the relative weightings of parts of a question. The following charts, tables and other special requirements are supplied: Equations List Graph paper ME301 2/10 1) A circular saw blade is manufactured as a thin disc of outer radius R2 = 100 mm. It is attached on a shaft of radius R1 =20 mm rotating at a constant angular speed of 6000 revolutions per minute. It can be assumed that the shaft does not exert any pressure on the blade, so that the radial stress is zero at inner and outer radius of the blade. The blade rotates with the same angular velocity as the shaft. For the material of the blade (hardened steel), assume that density ρ =7800 kg m-3 and ν = 0.33. Hoop and radial stress at any radius, r, in a rotating disc with a central hole, R1 < r < R2 (see Fig Q1) are given by the expressions: Disc with a central hole with inner radius R1 and outer radius R2 (3 ) 2 R12 R2 r [ R1 R2 2 r 2 ] 2 2 2 8 r 2 R12 R22 H [(3 )( R12 R2 2 2 ) (1 3 )r 2 ] 8 r Fig.Q1 R1 R2 a) Briefly outline the main stages of the derivation of the stresses in a disc in rotation. What is the main difference in the derivation between the thin disc and thick cylinder approximation? (5) b) Calculate the value of hoop stress at the inner edge of the disc indicating the 2 units of in the process of calculation. Sketch Mohr’s circle of stress and 8 calculate maximum shear stress at the inner edge (6) c) Calculate the value of hoop stress at the outer edge of the disc. (3) d) Determine the location and the value of maximum radial stress in the disc. (6) ME301 3/10 2) The state of stress at an element A on a rotor shaft under pure torsion is given by σ x xy xz xyσ y zy the tensor: xz zy σ z where xy 90MPa , XZ 0 and XY 0 A while all the diagonal values are zero: σx 0 , σy 0 , σz 0 a) Determine the magnitude of the normal and shear stress at the point A, on a 1 plane whose normal is defined by the direction cosines, l m , by using 2 the 3D stress transformation equations (5) Px = x + xym +xzn Py = xy + ym +yzn Pz = xz + yzm +zn n = x 2 + ym2 +zn2 + xy m + 2yzmn +2xzn n P2 n 2 b) Find principal stresses by solving the characteristic equation. (4) c) Calculate the Safety Factor using von Mises theory. (3) d) Calculate Octahedral normal and shear stress for this stress system (4) e) Show that the Safety Factor obtained using the Octahedral shear stress for this stress system, is the same as that calculated from principal stresses in part c) (4) ME301 4/10 3) A thin-walled tube of non-circular cross-section as shown in Fig. Q3.1, is designed to withstand torsion loading. The thickness of the walls varies between tmin = 10mm to tmax = 20 mm, with inner radius r = 0.85 m. The area enclosed by the median line in the cross-section of the tube is A = 2.31 m2. 20mm 10mm Fig Q3.1 a) Explain the concept of shear flow. Identify the location of maximum and minimum shear stresses in the tube. Calculate the ratio of maximum shear stress to minimum shear stress. (5) b) Calculate the maximum torque that the tube can withstand assuming that the shear stress in the walls should not exceed 50 MPa. (5) QUESTION 3 CONTINUED ON PAGE 5/10 ME301 5/10 c) A tube with open cross-section is considered as a further modification to the design. The dimensions are the same as for closed-section in Fig Q3.1, but a small gap is introduced for an open-section tube. 20mm 10mm Fig Q3.2 Calculate the maximum torque that the open-section tube can withstand assuming that the shear stress in the walls should not exceed 50 MPa. (5) d) Is the open-section design as shown in Fig. Q3.2 preferable to the design shown in Fig Q3.1? Explain your answer by sketching shear stresses in the cross- section for both designs. (5) ME301 6/10 4) a) Briefly describe how the Larson-Miller method is used for predicting the long- term creep behaviour of a metal from data obtained over relatively short periods of time. (6) b) A component of a gas turbine is made from a creep resistant alloy. The component is intended to be loaded during service for the following lengths of time and under the conditions given in Table 4. Using the Larson-Miller equation and Fig. Q4, attached determine the lifetimes for each level of stress, given that, P1 = T (20 + log10tr) (6) c) Prove that the component will survive. For how many more hours could the component continue in service at 1050 K and 230 MPa before creep rupture occurred? (8) Time (h) Stress (MNm-2) Temperature (K) 1200 41 1200 1100 150 1100 1500 230 1050 Table 4: Loading History for a given alloy 5) a) Explain how the Galvanic Series (Table Q5) can be used when selecting materials for environments such as on the coast at Brighton. (4) b) Describe two different approaches to cathodic protection and state their advantages and disadvantages. (12) c) Explain how a buried steel pipeline in the centre of Brighton may be protected from corrosion, identifying the environmental factors that need to be considered. (4) ME301 7/10 6) a) Explain in terms of metallurgical features, why body-centred cubic metals have a yield point and are prone to brittle fracture. (8) b) Explain the mechanism by which a metal may deform and fail under creep conditions. (6) c) Briefly describe two metallurgical techniques that can be used to increase the resistance of alloys to creep failure? (6) 7) Figure Q7 is an idealised Pourbaix diagram describing the change in electrical potential with pH for the iron-water system. A given steel is found to be in the corrosion zone (II) at a position indicated by the asterisk (*). It is however possible to change the condition and to reduce the corrosion rate by following either path “a” or path “b” on the diagram. a) Briefly describe the use of each method, giving an example in each case. (6) b) Explain the phenomenon of passivation that occurs in zone III using the example of stainless steel. (8) c) Describe the circumstances under which the corrosion resistance of stainless steel can be lost. (6) Potential (E) III II a * b I pH Figure Q7. Electropotential - pH diagram for the Fe - H2O system ME301 8/10 8) a) Explain what is meant by the Fatigue Limit and the Endurance Limit and show how they are used when designing for environments where fatigue is likely. (4) b) Explain the mechanism of crack initiation and propagation leading to fatigue failure in a metal. (10) c) Describe how the resistance to fatigue failure may be improved in a steel drive shaft. (6) ME301 9/10 Fig. Q4 Data for Larson-Miller Parameter 590 570 550 530 510 490 470 450 430 410 390 370 350 Stress, (MNm-2) 330 310 290 270 250 230 210 190 170 150 130 110 90 70 50 30 10 23000 24000 25000 26000 27000 28000 29000 30000 31000 32000 Larson-Miller Parameter, P1 ME301 10/10 Table 5 Galvanic Series in Sea Water Graphite Stainless steel (passive) Monel metal (70 % nickel, 30 % copper) Nickel (passive) Bronze Copper Aluminium bronze Nickel Brass Tin Lead Stainless steel (active) Cast iron Plain carbon steel Aluminium and its alloys Cadmium Zinc Magnesium and its alloys

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