University of Cape Town
Mechanical Engineering Department
MEC3060F - Materials under stress
May / June Examination 2013
INTERNAL EXAMINER/S: Dr. S. George
EXTERNAL EXAMINER: Dr. Hein Moller
DURATION:
2 Hours
MARKS:
96
INSTRUCTIONS
ANSWER ALL QUESTIONS. TOTAL MARKS 4 x 24 = 96
Take note of the mark allocations for each question and use them as a guide in your
answer.
Answer in clear sentences and use diagrams to illustrate your answers where appropriate.
Additional equations supplied on last page.
MEC3060F - EXAM
Page 1 of 6
31/05/2013
QUESTION 1 – SHORT ANSWERS:
(a) Discuss each of the following terms:
i.
The Schmid factor
ii.
Dislocation line
iii.
Stress intensity factor
iv.
Pearlite
v.
Homogeneous solid solution
[5 x 3 = 15]
(b) Discuss how you would determine the following mechanical properties:
i.
Yield strength in aluminium
ii.
Work hardening co-efficient
iii.
Ductile to brittle transition temperature (DBTT)
[3 x 3 = 9]
TOTAL MARKS = 24
MEC3060F - EXAM
Page 2 of 6
31/05/2013
QUESTION 2 – MANUFACTURING WITH MATERIALS:
Indent 1
Indent 2
Indent 4
Indent 5
SHEET A
SHEET B
Indent 3
Figure 1: Section through the welded sheets.
Two sheets of EN8 (0.4%C steel) must be butt welded together. The one sheet (A) is from the store
room and is in the annealed condition, the other sheet (B) of exactly the same alloy composition, has
been bought especially for the job. The materials’ property information for Sheet A and Sheet B are
shown below (Table 1):
Table 1: Table of mechanical properties of Sheet A and Sheet B.
Young’s Modulus (GPa)
UTS (MPa)
Elongation (%)
Hardness (HV)
(a)
Sheet A
210
410
30
140
Sheet B
210
590
2.5
230
Describe the annealing processes of Recovery and Recrystallisation.
[6]
(b) The hardness of this material is related to the yield strength in the following way: HV = 0.4 x σ y.
The hardness at Indent 1(shown in Figure 1) is given as 140HV. Indent 2 is just out of range of
the heat affected zone (HAZ) and the hardness is measured as 136HV. Microstructural
investigations showed that the grain size of the parent material of Sheet A is 160µm, and the
grain size at Indent 2 is 213 µm.
I. Determine the constants σo and k (in MPa√m).
II. What is the average grain size of the parent metal in Sheet B at indent 5? Does this value
represent the true grain size of this material?
[6]
(c) Indents 3 and 4 are in the heat affected zone (HAZ) of sheet B. The hardness value at indent 3
is 150HV and at indent 4 is 165HV. Discuss the strengthening mechanism that explains this
difference. Show calculations to support your answer
[4]
(d) The welding process is completed with ease by a welder. But the part fails in service and a
failure analysis investigation is performed. The investigator looks at the microstructure and
performs hardness indentation tests across the weld from sheet A to sheet B, along the dotted
line in the figure. Describe the results he would have obtained, in terms of microstructure and
mechanical properties from sheet A, across the HAZ of A, the weld itself, the HAZ of B into the
parent metal of B.
[8]
TOTAL MARKS = 24
MEC3060F - EXAM
Page 3 of 6
31/05/2013
QUESTION 3 – THE IRON-CARBON PHASE DIAGRAM:
(a)
(b)
Figure 2: (a) Schematic diagram of a samurai sword, (b) Cross-section through the thickness
of the sword, showing the two different alloys making up the sword
The cross section of a Samurai sword is shown above. The centre material has a carbon content of
0.4wt%C, and the outer layer has a carbon content of 0.85wt%C. The material/alloy selection and the
heat treatment of the sword blade are very specific.
(a) One alloy is hyper-eutectoid and the other is hypo-eutectoid. Discuss the microstructure
formation of each under equilibrium cooling conditions from the austenite region. Make use of a
phase diagram to discuss your answer.
[8]
(b) What is the effect of increasing the cooling rate from the austenite region on the microstructure of
the 0.4wt%C steel alloy? And what effect does this have on the mechanical properties?
[2]
(c) Describe the heat treatment that is necessary to maximize the hardness of the sword edge and
the mechanism by which this occurs. Will this heat treatment affect the whole sword in the same
way?
[6]
(d) The KIC value for 0.8wt%C steel of the outer layer is 12MPa.m1/2 and in the fully martensitic
condition the UTS is 2010MPa.
I. Calculate the critical crack length.
II. What implications does this value have on the manufacture and final production of the sword?
(Y = 1.12)
III. Could you suggest an improvement to the heat treatment procedure?
[6]
(e) Describe how the carbon content affects the fracture toughness of steel in the normalised
condition. Can you use the microstructure as a guide to deduce this?
[2]
TOTAL MARKS = 24
MEC3060F - EXAM
Page 4 of 6
31/05/2013
QUESTION 4 – MATERIALS IN SERVICE:
A large (1600 ton) press is used for the extrusion of high strength aluminium alloys into various
sections. The die mounting block and main piston are effectively restrained by four large bolts
(200mm in diameter, 10meter length). The bolts are subject to cyclic fatigue in tension. Cracks in the
bolts may be modelled as transverse edge cracks in tension, therefore Y is 1.12.
Because of constraints on the rest of the extrusion press, the diameter of the bolts cannot be
changed, and, under normal operating conditions, the maximum and minimum stresses are to
continue at their previous levels of 250MPa and 112MPa respectively. There is typically one
extrusion every 10 minutes, and the machine operates for 24 hours a day, 6 days per week, 50 weeks
per year.
There are two types of NDT evaluation methods available to detect cracks in the system (Table 2):
Table 2: NDT methods for crack length inspection.
NDT method
Ultrasonic testing
Magnetic particle
testing
Conditions during testing
Parts can be evaluated in situ,
with machine on
Machine must be off, and all bolts
are removed for evaluation
Type of crack
Surface and
internal cracks
Surface and
internal cracks
Minimum detectable
crack length
7.5mm
5mm
Table 3: Fracture and fatigue properties of materials for the bolt material selection.
Material
Ferritic-pearlitic steel
Martensitic steel
Fracture toughness (MPa.√m)
100
Paris equation (m/cycle)
145
(a) Two choices of material for the bolt are available in such sizes as shown in Table 3. Determine
the critical crack lengths for the edge cracks of the bolt for both materials.
[4]
(b) The part is required to have minimum life of 100 000 cycles. Calculate the fatigue life for both
NDT detection methods for BOTH materials. Which material-and-detection method combinations
meet the minimum fatigue life requirements? Determine an inspection interval for each case.
[12]
(c) Which material is best suited for the manufacture of new bolts for this press? Justify your answer
by referring to the values seen in the calculations.
[4]
(d) Describe the key features you would look for on a fracture surface, if you were asked to perform
a failure analysis investigation on a failed square section, steel beam. Mention both macroscopic
and microscopic features.
[4]
TOTAL MARKS = 24
--------------------------------------------------------- END --------------------------------------------------------------------MEC3060F - EXAM
Page 5 of 6
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Additional equations:
 y o 
k
d
SAsphere  4r 2 for the surface area of a sphere
4
Vsphere  r 3 for the volume of a sphere
3
Pr
2t
Pr
h 
t
t 
for a cylindrical pressure vessel
K IC  Y ac
K  Y a
da
 C (K ) m
dN
da
Nf  
ao
C (Y ac ) m
ac
  A e
n


m
m 
 ac (1 2 )  ao (1 2 ) 
Nf 


m
m
m
m 

2
(
1

)
CY  ( )
2


1
Q
RT
Indefinite integrals:
dx
 ln x
x
dx x1n
 xn  1 n

MEC3060F - EXAM
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31/05/2013