Past Exams Lefm and Solns 1516

8/18/2019 Past Exams Lefm and Solns 1516

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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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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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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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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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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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DATASHEET Q.2 (b)

Geometric Correction Factor

F(a/W) versus (a/W) for edge crack in Bending


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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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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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DATASHEET Q.4

φ

5.1)](1[

..

ba

b I

F

F a K


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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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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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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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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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JAN 2015


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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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Past Exams Lefm and Solns 1516

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