# SCHOOL OF ENGINEERING (DOC)

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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 + 2yzmn +2xzn

 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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