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8/18/2019 Past Exams Lefm and Solns 1516
1/35
Dr David R Gordon, LEFM, Level 4, 2015/16
Dr David R Gordon, ED&A4 Trimester 1 Session 2015 -16 1/35
ENGINEERING DESIGN &
ANALYSIS 4
Past Exam Questions & Solutions
Jan ’09 - Jan’15
LEFM
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Dr David R Gordon, LEFM, Level 4, 2015/16
Dr David R Gordon, ED&A4 Trimester 1 Session 2015 -16 2/35
January 2015 (14-15)
Q.2 A simple ratchet mechanism for an industrial tool consists of a self springing
lever which only allows rotation of the serrated wheel axis in one direction and
provides a locking operation as shown schematically in Figure Q.2.
a)
Determine the maximum exerted load, and corresponding maximumnominal bending stress on the lever when the mechanism is being rotated;
[6]
b) The lever has been found to have incurred some suspected fatigue damage
resulting in a crack-like defect of 0.01mm deep as indicated in section A-A of
Figure Q.2. Ignoring crack tip plasticity effects, Determine:
(i) whether this crack is growing due to a fatigue mechanism;
[5]
(ii)
the critical crack size between 2mm and 3mm deep which wouldlead to fracture of the lever;
[8]
(iii) the number of additional ratchet operations required for fracture
to occur.
[6]
DATA: 2/3/3 m MN K IC 2/3/1.0 m MN K th E = 3 GN/m
2
Deflection of an end loaded cantilever beam, WL
EI
3
3
Paris Law 5.38.102 K xdN da m/cycle
Geometric Crack Geometry Correction Factor ‘F’ can be
Obtained from DATASHEET Q.2
Lever deflection = 1mm
CrackA
A
Figure Q.2
Crack
Depth
0.01mm
12mm
5 mm
View on A-A30 mm
Lever
Serrated Wheel
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Dr David R Gordon, LEFM, Level 4, 2015/16
Dr David R Gordon, ED&A4 Trimester 1 Session 2015 -16 3/35
DATASHEET Q.2
w
W
W/2 W/2
wL/2 wL/2
-wL2/12
wL2/12
WL/8-WL/8
W
-Wab2/L
2 Wa
2 b/L
2
Wb/(a+b) Wa/(a+b)
F
BA2
1F
ABMM
A B
M2EI
L2
3
LM
AB 1 2 AB
F
2W
aa
Curve 6
aW
Curve 7 Curve 8
Wa
2
2a 2a
Curve 1
Curve
Ligament
breaks Curve 3
2a
2
2W
Curve 4
2a
2WCurve 5
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Dr David R Gordon, LEFM, Level 4, 2015/16
Dr David R Gordon, ED&A4 Trimester 1 Session 2015 -16 4/35
January 2014 (13-14)
Q.2 (a) Distinguish between the engineering terms ‘Stress Concentration Factor’
(SCF) and ‘Stress Intensity Factor ’ (SIF) and explain how each is used when
assessing the integrity and failure of components.
[6]
(b) A garden chemical pressure sprayer is moulded from a polymeric material.
Fracture tests on this polymer revealed a Fracture Toughness (K IC) of 1.6
MN/m3/2 and fatigue crack growth tests gave the results shown in table Q.2b)
below. The manufacturing process involved for the garden chemical sprayer
was found to induce ‘total’ defects of approximately 0.4mm in length from
crack tip to crack tip. The garden chemical sprayer dimensions can be
considered to be very large with respect to the defect length and as such the
Stress Intensity Factor geometric correction function ‘F’ can be assumed as
unity. Determine:
(i) the empirical constants ‘C’ and ‘m’ in the so-called ‘Paris Law’ for
predicting crack growth due to fatigue;
[6]
(ii) the maximum static tensile stress that can be applied to the garden
chemical sprayer whilst providing a factor of safety of 4 against sudden
failure due to brittle fracture;
[6]
(iii) the number of cycles ‘N’ to cause fatigue failure given that the garden
chemical sprayer is pressurised ON-OFF to produce a maximum tensile
stress of 2 MN/m2 and given an initial defect as described above.
[7]
Paris Law: m
K C dN
da).(
dN
da (m/cycle)
K (MN/m3/2)
4x10-7
0.53
11x10-7 0.79
Table Q.2(b)
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Dr David R Gordon, ED&A4 Trimester 1 Session 2015 -16 5/35
December 2012 (12-13)
Q.2 (a) Describe the three main applications of Fracture Mechanics and explain how it
could be used in each case.
[9]
(b) An industrial chain drive mechanism has suffered a fractured tooth as shown inFigure Q.2(b). The geometry and fractured surface information is as shown. The
tooth experiences a bending moment arising from chain tooth forces and this
induces a nominal bending stress in the crack location of 100MN/m2 for each
revolution of the chain wheel. Neglecting crack tip plasticity corrections,
consider only mode I loading. Use can be made of the DATA provided:
i) Determine whether the machine was operating to specification at the
time of the fracture.
[6]
ii) If the source of the cracking is deemed to originate from a 0.3 mm
crack-like surface scratch extending across the full breadth of the tooth
induced at the time of manufacture, determine whether such a defect
would be problematic and estimate the number of cycles to failure.
[10]
DATA:
Fracture Toughness, 2/3/60 m MN K IC
Threshold Stress Intensity Range,2/3
/3 m MN K th Geometric Correction Factor F(a/W), from DATASHEET Q.2(b)
Paris Law Equation: cyclem K dN
da/105.0
311
10mm
fractured
surface
20mm
14mm
chain drive
tooth profile fatigue
surface
Bending Moment
Figure Q.2(b)
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Dr David R Gordon, ED&A4 Trimester 1 Session 2015 -16 6/35
DATASHEET Q.2 (b)
Geometric Correction Factor
F(a/W) versus (a/W) for edge crack in Bending
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Dr David R Gordon, ED&A4 Trimester 1 Session 2015 -16 7/35
December 2011 (11-12)
Q.2 (a) Describe briefly, with the aid of sketches, the THREE classical Fracture
Mechanics crack face deformation modes and the problems associated with the
assessment of structural integrity in situations where components are subject to
‘mixed mode’ loading.
[8]
(b) The closed thin cylinder shown in Figure Q.2(b) has a diameter of 1.5m and a
wall thickness of 100mm. The working internal pressure is 15MN/m2 and the
cylinder contains a defect of length ‘2a’ which may be inclined at an angle ‘θ’
to the longitudinal axis. Assume crack tip plasticity effects can be ignored.
i) For a defect orientation such that ‘θ’ is approximately 45° describe,
without calculation, how this arrangement produces mixed mode
behaviour and suggest the value of ‘θ’ which would provide for the
worst case scenario.[6]
ii) Determine the critical through thickness total defect length for the worst
case condition described in (b)-i) above.
[5]
iii) Evaluate the number of ON-OFF pressurisation cycles that the cylinder
can withstand based on the value obtained in (b)-ii) above and assuming
an initial total defect length of 4mm exists in the cylinder.
[6]
p
θ
Figure Q.2(b)
2a
Data: )..( F a K cyclem K dN
da/.103
8.312
2/3/40 m MN K Ic
t
pD
2
t
pD L
4 Geometric Correction Factor ‘F’ = 1.2
for any crack length ‘a’
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Dr David R Gordon, LEFM, Level 4, 2015/16
Dr David R Gordon, ED&A4 Trimester 1 Session 2015 -16 8/35
December 2010 (10-11)
Q.4 The railway geometry indicated in Figure Q.4(a) consists of a continuous rail, with the cross section and properties as shown in Figure Q.4(b). The rail is supported
between periodic railway ‘sleeper’ supports. Fatigue crack growth with crack tip fronts
at depths of atop and a bottom have the potential to exist within either of two particular
regions ‘A’ or ‘B’ as illustrated below.
The rolling axle load is assumed to induce an ON/OFF bending moment of 30kNm.
The material properties data for the continuous rail section are as given below and use
can be made of DATASHEET Q.4.
Consider only Mode I loading and ignore crack tip plasticity effects.
(a) Explain briefly why these specific crack tip fronts would be expected to occur
in the locations A and B as illustrated.[6]
(b) If a crack is found to occur at point B, use engineering judgement to estimate
the critical crack size ac.
[9]
(c) A microscopic examination of the rail reveals surface damage at B which could
be assumed to be similar to an initial defect of 2 mm. Determine whether this
defect will propagate to the critical level found in (b)-above, and the
corresponding theoretical number of cycles to failure based upon a Fracture
Mechanics approach. Comment on the result.
[10]
DATA:
K IC = 70 MN/m3/2 ΔK th = 3 MN/m
3/2 311 )(102 K dN
da
m/cycle
I XX
= 10.75x106 mm4
e y =69.4 mm
X X
e y
crack tip front at ‘A’
140mm
atop
a bottom
a bottom atop
railway ‘sleeper’ supports
rolling axle load
Figure Q.4(a) Figure Q.4(b)
fatigue cracks
A
B
crack tip front at ‘B’
continuous rail
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Dr David R Gordon, LEFM, Level 4, 2015/16
Dr David R Gordon, ED&A4 Trimester 1 Session 2015 -16 9/35
DATASHEET Q.4
φ
5.1)](1[
..
ba
b I
F
F a K
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Dr David R Gordon, LEFM, Level 4, 2015/16
Dr David R Gordon, ED&A4 Trimester 1 Session 2015 -16 10/35
January 2010 (09-10)
Q.4 (a) Explain what is meant by the so-called ‘leak before break’ philosophy as
referenced within Fracture Mechanics applications, giving examples of its
suitability to pressurised components and when it may be dangerous to rely
upon it. Your solution should include sketches as appropriate.
[8]
(b) A schematic drawing of a cutting knife is shown in Figure Q.4(b). The blade is
20mm wide and 2mm thick, and is partitioned into segments by means of a
series of parallel oblique 60° ‘grooves’. These grooves are sharp edged and
have depth ‘a’ measured from one surface into the thickness which allows each
segment to be broken off through a bending action. The applied bending
moment ‘M’ supplied by the user is to be not larger than 80% of the moment
required to cause initial yielding (MY) for an un-cracked cross section of the
blade. Ignoring crack-tip plasticity effects and making use of DATASHEETQ.4(b), and the Data provided below, determine:
i) the minimum depth ‘a’ of each groove to break a segment in one single
bending action; [8]
ii) the number of repeated ON-OFF bending actions if the groove is
0.13mm deep and comment on your result.
[9]
Data: Yield strength ‘σ Y ’ = 600 MN/m2
Fracture Toughness ‘K IC ’ = 10MN/m3/2.
Paris Law cyclem K dN
da/)(106.0
410
M20mm
60°
Groove de th2mm thick
Blade extends to
reveal next se ment
Blade segments
Bending the
Segment along
the groove line
breaks it off
Figure Q.4(b)
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Dr David R Gordon, LEFM, Level 4, 2015/16
Dr David R Gordon, ED&A4 Trimester 1 Session 2015 -16 11/35
DATASHEET Q.4(b)
Geometric Correction Factor ‘F’ for Stress Intensity Factor F a K I
F
W
a
M MaW
B
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Dr David R Gordon, LEFM, Level 4, 2015/16
Dr David R Gordon, ED&A4 Trimester 1 Session 2015 -16 12/35
JAN 2009 (08-09)
Q.4 (a) Computer CD and DVD drives are being continually driven faster with
the demand for increasing data transfer rates. For example a ‘40X’ drive
operates at 8000 rev/min, and the latest ‘52X’ drives operate at 10,500 rev/min.
Such high speed components could be subject to catastrophic brittle fracture ifcracks are present, particularly in regions of high stress. The relevant properties
of a typical CD/DVD disc are as given below. Determine, using the supplied
Data and the stress distribution results provided graphically in DATASHEET
Q.4:
(i) the location and orientation (radial or tangential hoop) of any potentially
critical crack. Your solution should include both an explanation and a
sketch as appropriate;
[4]
(ii)
the critical crack size ‘ac’ for both the ‘40X’ and ‘52X’ drives describedabove including crack tip plasticity effects;
[8]
(iii) the number of read/write cycles remaining in a 52X CD/DVD disc
which has been discovered to have an initial crack size of 2mm,
excluding crack tip plasticity effects.
[7]
(a) A CD/DVD disc will simply fail to operate (read/write) when a crack
enters the ‘Index Track’ which is located at a radius of 20mm.
Explain briefly, based upon the results obtained in (a)-ii) above whether a ‘Fail
safe’ philosophy (such as the Leak Before Break philosophy used in pressurised
components) might apply to a cracked CD/DVD disc operating at ‘40X’ and‘52X’ speeds.
[6]
DATA:
Inside radius, r i = 7.5 mm outer radius, r o = 60mm thickness, t =1mm
K IC = 1 MN/m3/2, σY = 60 MN/m
2, da/dN = 0.5x10-7.ΔK 3.5 m/cycle.
aY K ..
The Geometric Stress Intensity Correction Factor, Y = 1.12 for any small crack
size relative to disc outer radius (a
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Dr David R Gordon, ED&A4 Trimester 1 Session 2015 -16 13/35
DATASHEET Q.4
VARIATION IN THE STRESS IN A ROTATING CD/DVD DISC
Ref: Report for Research Machines, RM plc, Prof. David Nowell, Aug. 2001
2
Typical CD/DVD Geometry
rr
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Dr David R Gordon, ED&A4 Trimester 1 Session 2015 -16 14/35
JAN 2015
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Dr David R Gordon, ED&A4 Trimester 1 Session 2015 -16 15/35
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JAN 2014
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DEC 2012
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DEC 2011
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DEC 2010
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JAN 2010
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JAN 2009
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