fatigue analysis of an aluminium radial impeller - lth€¦ · fatigue analysis of an aluminium...

Fatigue Analysis of an

Aluminium Radial Impeller

AUTHOR: DAVID JIMÉNEZ GARCIA

SUPERVISORS: SRINIVASAN IYENGAR, LTH

LARS LUNDIN, VOLVO POWERTRAIN AB

EXAMINER: SOLVEIG MELIN

ISRN

MASTER THESIS

DEPARTMENT OF MECHANICAL ENGINEERING

DIVISION OF MATERIAL’S ENGINEERING

LUND UNIVERSITY

SPRING 2011

Fatigue Analysis of an Aluminium Radial Impeller David Jiménez Garcia

-I-

Abstract

High cycle and low cycle fatigue properties have been determined for Al2618-

T8511. HCF testing has been performed with stress control and LCF with strain

control. Both types of fatigue test were performed at 200ºC. With strain-lifespan

data points, cyclic stress-strain curve is obtained.

Fatigue data has been scaled to other temperatures and used to redesign the

back-disc of a radial impeller of a turbocharger of a truck. Lifespan of the

impeller depends on the type of use. If the truck is driven at high altitude the

impeller can only withstand 10421 cycles. When the truck is driven at sea level,

the cycles that the impeller can withstand vary from 85406 (maximum

requirements) to more than 10 Million cycles (normal-low requirements).

Due to trade secret, stress, strain and temperature scales have been removed

from the results.


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Acknowledgements

I would like to address a few kind words of thanks to the following people for

aiding me throughout the process of this Master Thesis.

Srinivasan Iyengar from LTH, who supported me throughout the Master

Thesis process and encouraged me to persevere when everything seemed

to go wrong and slow with some troubles.

Lars Lundin from VOLVO Powertrain AB, who provided me with the

opportunity to do this Master Thesis, in addition to helping me with the

simulations and furnishing me with all the useful information and data he

could.

Zivorad Zivkovic from LTH, who helped me with all the material testing

experiments and provides me with assistance in solving the problems I

encountered while executing them.

Håkan Torstensson from VOLVO Powertrain AB, who helped me with the

simulations by showing me how to introduce the temperature field.

Ulf Karlsson from SIMULIA Scandinavia [19], who let me use a free-of-

charge special license of ABAQUS 6.10 CAE to run the simulations.

Antonio and Marta, my parents, who made this happen by encouraging me

throughout my entire life to study hard, financing my education and this

year abroad.

Lauren Scamuffa, who helped me to proofread and edit this report any

time I asked.

Sergio, Raquel, Juanjo and friends who had a constant concern about this

Master Thesis, making sure to constantly ask me where I was in the

process while encouraging and supporting me to complete it swiftly and

promptly.


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List of figures

Figure 1: Wohler’s curve. ............................................................................................................ 3

Figure 2. Ultimate tensile strength variation with temperature. ............................................... 8

Figure 3. Yield tensile strength variation with temperature. ..................................................... 9

Figure 4. Elongation at break variation with temperature. εbreak(T) ....................................... 10

Figure 5. Modulus of elasticity variation with temperature. E(T). ........................................... 10

Figure 6: Schematic diagram of a turbocharger. ..................................................................... 11

Figure 7: Dimensions of the sample used for fatigue testing. .................................................. 13

Figure 8: General view of fatigue experimental facilities......................................................... 14

Figure 9: View of mounting the sample’s process. ................................................................... 15

Figure 10: View of the machine ready to heat the sample and perform the test. ................... 15

Figure 11: View of the ready heater controller. ....................................................................... 16

Figure 12: View of grips hydraulic pressure controller. ............................................................ 16

Figure 13: Left: Hydraulic press controller. Right: Detail of the controlling panel. .................. 17

Figure 14: Rockwell B hardness testing equipment. ................................................................ 19

Figure 15: Struers Rotopol-2. .................................................................................................... 21

Figure 16: XL 30 ESEM microscope. .......................................................................................... 22

Figure 17: Stress level versus cycles. All obtained points’ data. ............................................... 24

Figure 18: Stress level versus cycles. No run-outs obtained points’ data. ................................ 25

Figure 19: Stress level versus cycles. Used obtained points’ data. ........................................... 26

Figure 20: Total, plastic and elastic strain amplitude versus reversals. ................................... 27

Figure 21: Plastic strain amplitude versus reversals. ............................................................... 28

Figure 22: Stress amplitude versus reversals. .......................................................................... 29


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Figure 23: Strain versus reversals with plastic and elastic straight lines. ................................ 30

Figure 24: Cyclic stress-strain. Comparison between experimental and used data. ............... 32

Figure 25: LCF. Comparison between strain and strain&load-controlled curves. .................... 33

Figure 26: Cyclic stress-strain. Scaling at different temperatures............................................ 34

Figure 27: LCF Curve. Scaling at different temperatures. ......................................................... 35

Figure 28: Tensile test’s graph at room temperature. ............................................................. 36

Figure 29: Tensile test’s graph at 200ºC. ................................................................................. 36

Figure 30: Comparison between the 2 tensile tests’ graphs. ................................................... 37

Figure 31: Zoom of the comparison between the 2 tensile tests’ graphs. ............................... 37

Figure 32: Microstructure at different magnification factors. ................................................. 40

Figure 33: Microstructure at 2000X magnification factor. ..................................................... 41

Figure 34: Surface of a HCF tested sample at different magnification factors. ....................... 42

Figure 35: Surface of a LCF tested sample at different magnification factors. ........................ 43

Figure 36: Spectrum of the matrix phase. ................................................................................ 45

Figure 37: Spectrum of the precipitate phase. ......................................................................... 45

Figure 38: Worst impeller’s back-disc design regarding centrifugal forces. ............................ 47

Figure 39: Best impeller’s back-disc design regarding centrifugal forces. ............................... 47

Figure 40: Temperature field of the impeller. .......................................................................... 48

Figure 41: Stress distribution caused by only the temperature. .............................................. 49

Figure 42: Stress distribution of the impeller used at high altitude. ........................................ 50

Figure 43: Log(life) distribution of the impeller used at high altitude. .................................... 51

Figure 44: Impeller’s stress distribution used at sea level with normal-low requirements. .... 52

Figure 45: Impeller’s log(life) distribution used at sea level with normal-low requirements. . 53


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Figure 46: Impeller’s stress distribution used at sea level with maximum requirements. ....... 54

Figure 47: Impeller’s log(life) distribution used at sea level with maximum requirements. .... 55


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List of tables

Table 1. Composition of AL2618-T851 ....................................................................................... 5

Table 2. Main properties at room temperature ......................................................................... 7

Table 3. Keller’s etch composition. ........................................................................................... 21

Table 4. Rm and Re values. ....................................................................................................... 38

Table 5. Hardness values. ......................................................................................................... 39

Table 6. Weight percentage of each element in the matrix phase. ......................................... 44

Table 7. Weight percentage of each element in the precipitate phase. .................................. 44

Table 8. Simulation’s results depending on the use assembled together. ............................ 56


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Table of Contents

1 Introduction ............................................................................................................... 1

1.1 Background ................................................................................................................... 1

1.2 Problem Description ...................................................................................................... 1

1.3 Objectives ..................................................................................................................... 1

1.4 Limitations .................................................................................................................... 1

2 Theoretical Work ....................................................................................................... 2

2.1 Fatigue .......................................................................................................................... 2

2.2 AL2618-T8511 ................................................................................................................ 5

2.2.1 General Description........................................................................................................................... 5

2.2.2 Composition ...................................................................................................................................... 5

2.2.3 Thermo-Mechanical Treatments ....................................................................................................... 6

2.2.4 Properties .......................................................................................................................................... 6

2.3 Turbocharger ............................................................................................................... 11

3 Experimental Work .................................................................................................. 13

3.1 Fatigue Testing ............................................................................................................ 13

3.1.1 Sample Used .................................................................................................................................... 13

3.1.2 Testing Process and Facilities Used ................................................................................................. 14

3.2 Tensile Test ................................................................................................................. 18

3.3 Hardness Testing ......................................................................................................... 19

3.4 Microscope .................................................................................................................. 20

3.4.1 Bare Sample’s Preparation .............................................................................................................. 20

3.4.2 Microstructure analysis ................................................................................................................... 22

3.4.3 Fractography ................................................................................................................................... 23

3.4.4 Energy Dispersive Spectroscopy (EDS) ............................................................................................ 23


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4 Results ..................................................................................................................... 24

4.1 Fatigue Testing ............................................................................................................ 24

4.1.1 HCF. Load-Controlled ...................................................................................................................... 24

4.1.2 LCF. Strain-Controlled ..................................................................................................................... 27

4.1.3 Data for Fatigue Simulations ........................................................................................................... 28

4.1.3.1 Scaling at different temperatures .......................................................................................... 34

4.2 Tensile Tests ................................................................................................................ 36

4.3 Hardness Testing ......................................................................................................... 39

4.4 Microscope .................................................................................................................. 40

4.4.1 Microstructure Analysis .................................................................................................................. 40

4.4.2 Fractography ................................................................................................................................... 42

4.4.3 EDS .................................................................................................................................................. 44

5 Impeller Design Process ............................................................................................ 46

5.1 Design Steps ................................................................................................................ 46

5.1.1 Optimizing the Design Regarding Centrifugal Forces ...................................................................... 46

5.1.2 Introducing the Temperature Field ................................................................................................. 48

5.1.3 Regarding Life (Fatigue Analysis) ..................................................................................................... 49

5.2 Optimized Design ........................................................................................................ 50

5.2.1 From 30% to 100% of Top Speed .................................................................................................... 50

5.2.2 From 30% to 75% of Top Speed ...................................................................................................... 52

5.2.3 From 30% to 90% of Top Speed ...................................................................................................... 54

5.2.4 Results Assembled Together ........................................................................................................... 56

6 Conclusions .............................................................................................................. 57

7 References ............................................................................................................... 58


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1 Introduction This Master Thesis comes from VOLVO’s desire to minimize the cost of a

turbocharger in a diesel engine.

1.1 Background

Currently, titanium alloys are used to build the impellers of the turbochargers.

High mechanical and corrosion resistance are well known as being properties of

titanium. However, a huge cost is attached to using titanium.

Nowadays, aluminium alloys are being used more frequently in a wide range of

engineering mechanisms. Aluminium alloys are replacing expensive materials,

yet still maintaining the capability to withstand forces at a much cheaper price.

1.2 Problem Description

All of these elements have made VOLVO consider using an aluminium alloy

instead of the currently used titanium alloy. The issue that VOLVO faces is the

lack of fatigue data at high temperatures.

1.3 Objectives

This Master Thesis is about redesigning the back-disc of an impeller regarding

the fatigue data of an aluminium alloy, which has been derived from material

testing.

1.4 Limitations

The main limitations of this Master Thesis are the time availability of the fatigue

testing machine, as well as, the short Master Thesis duration.


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2 Theoretical Work As one can read in the title of this Master Thesis, the three main topics that will

be discussed are: what exactly does fatigue mean, the aluminium alloy and the

turbochargers.

2.1 Fatigue

Security factors are used to avoid reaching, among other properties, the yield

tensile strength of the material of an element and avoid the situation that the

mechanic limit is exceeded. However, that is not the only property to be

considered.

Fatigue is highly important especially when dynamic cyclic loads are applied.

Actually, around the 90% of failures in metallic elements are caused by fatigue.

Fatigue is shown up as a fracture. At the beginning it can only be a microscopic

fracture, but once it has appeared, it starts to grow until it can be perceived by

human eye. The fracture is propagated until the breakage is reached. The

breakage of one element of a machine can be the cause of the breakage of other

components of the machine or even the cause of an accident involving human

beings. Ref. [8]

Then, it is clear that being the main cause of a machine failure and being able to

cause unexpected dangerous accidents make fatigue knowledge be of high

importance in the engineering area.

Fatigue appears on a material when a load is repeatedly applied. The most

dangerous effect is that a dynamic cyclic load can make the failure appear below

the yield tensile strength of the material. This kind of failure is completely

unexpected if fatigue has not been taken into account in the design process.

Stress and strain are the two different approaches regarding fatigue life that can

be used when designing. Stress-approach is more often used because more data

can be found and experiments are easier and cheaper to perform because no

extensometer is needed.


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The main way to take fatigue into account when designing is to know the

Wohler’s curve (Figure 1) of the material used.

Figure 1: Wohler’s curve, Ref. [6]

As Norman E. Dowling says in [12] Stress-life curves are assumed to follow the

power relationship expressed in equation 11.

arσ = σ’f·(2·Nf)b (1)

Where arσ is stress amplitude and Nf is cycles to failure.

Wohler’s curve is also known as S-N curve. It is a graph where Stress (S) and

Number of cycles to failure (N) are related. It is useful to calculate how long life

an element will have depending on how high stress has to withstand, in other

words, how many times a stress can be applied before fatigue breakage occurs.

1 Basquin, 1910.


-4-

In Wohler’s curve two different regions are noticeable: High Cycle Fatigue (HCF)

and Low Cycle Fatigue (LCF). On one hand, HCF corresponds to the right region

which is about low stress levels and elastic deformation and, therefore, a high

number of cycles of life. On the other hand, LCF corresponds to the left region

which is about high stress levels and plastic deformation and, therefore, a low

number of cycles of life.

Although strain-approach is not as commonly used as stress-approach, in this

Master Thesis, the redesign of the back-disk of the impeller is performed using

strain-approach.

Strain-approach (Ref. [9-12]) consists on splitting the plastic deformation from

the elastic deformation to be able to calculate an accurate strain-life curve that

fits both HCF and LCF. Different regressions, equations and corrections have to

be used during this data evaluating process2.

2 Further explanation can be found in section 4.1.


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2.2 AL2618-T8511

The alloy to be analysed is the AL2618-T8511. The following remarks provide

useful information regarding this alloy.

2.2.1 General Description

AL2618-T8511 is wrought aluminium, which contains copper and magnesium. It

is age-hardenable and commonly used for pistons, large rotating aircraft engines

components and compressor blades. Until 315°C, it has good elevated

temperature properties.

2.2.2 Composition

The chemical composition ranges for each element of the alloy can be seen in the

Table 13.

Table 1. Composition of AL2618-T851,Ref.[4-5]

3 Percentages can vary depending on the source. Averages are shown in this Table 1.

Element Minimum [%] Maximum [%]

Aluminium [Al] Balance

Cooper [Cu] 1.90 2.70

Magnesium [Mg] 1.30 1.80

Iron [Fe] 0.90 1.30

Nickel [Ni] 0.90 1.20

Silicon [Si] - 0.25

Titanium [Ti] 0.04 0.10

Manganese [Mn] - 0.20

Zinc [Zn] - 0.10

Other - 0.15

Each - 0.05


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2.2.3 Thermo-Mechanical Treatments

Certain treatments are performed over the alloy in order to obtain its final

properties, Ref. [3-4].

Essentially, a solution heat treatment is executed at 529°C for a period as long

as 24 hours. In addition, an age hardening heat treatment is performed at 199°C

varying from 5 to 20 hours depending on the section. A stretching to relieve

stress is performed in between both processes.

Apart from that, additional treatments can be applied to get some different as

well as improved properties.

2.2.4 Properties

To understand why this alloy is used for aircraft engines, it is important to

discuss its properties, Ref. [1-5].

Physical, mechanical and thermal properties have a lot of significance when a

fatigue analysis is wanted.

In Table 2 the main properties at room temperature are shown.


-7-

Table 2. Main properties at room temperature, Ref. [2, 5]

Property Value

Ph

ysic

al

Density (ρ) 2.77g/cm3

Mec

han

ical

pro

per

ties

Hardness, Brinell 115HB

Hardness, Rockwell B 72 HRB

Ultimate Tensile Strength (Rm) 432MPa

Yield Tensile Strength (Re) 345MPa

Elongation at break (εbreak) 10%

Modulus of elasticity (E) 71GPa

Compressive Strength 370MPa

Shear Strength (τ) 262MPa

Modulus of Rigidity (G) 27GPa

Poisson ratio 0,30

Ther

mal

Linear Coefficient of Thermal Expansion 22.3 µm/m·°C

Specific Heat Capacity 0.875J/g·°C

Thermal Conductivity >146W/m·K

Melting point >510°C

The main purpose of this Master Thesis is to determine the fatigue behaviour at

high temperatures; however, it is also important to understand how the

mechanical properties change with temperature. In the following figures some of

them are shown.


-8-

Figure 2. Ultimate tensile strength variation with temperature. Rm(T), Ref. [5]

As it is explained in [2.1], the ultimate tensile strength (UTS) is the maximum

value of tension that a material can withstand before considerably decreasing its

cross-section. It is measured as a force per unit area [N/m2].

UTS is usually measured performing a tensile test. Testing temperature, sample’s

surface, preparation and, of course, material may vary the results. On the other

hand, results are independent of the size of the sample.


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Figure 3. Yield tensile strength variation with temperature. Re(T), Ref. [5]

Yield tensile strength, also known as yield point, is the stress level point from

which a material starts to deform plastically; it other words, without recovering

its initial shape. It is the stress level that a material can withstand before

suffering a permanent deformation. Ref. [7]

In engineering, plastically deformation means that the material has a permanent

deformation of 0.2% of the original dimension.


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Figure 4. Elongation at break variation with temperature. εbreak(T), Ref. [5]

Figure 5. Modulus of elasticity variation with temperature. E(T). Ref. [2]


-11-

2.3 Turbocharger

As authors said in [14] and [15], the purpose of a turbocharger is to recover part

of the waste energy from an engine’s exhaust gases and use it to compress air

and push it into the engine.

Once the air pushed into an engine is compressed, more air can be squeezed.

More air inside the cylinders means more fuel allowed inside. Once the engine

burns the air-fuel mixture, power is generated. The more mixture used, the more

powerful engine. In addition, the efficiency of the combustion is improved.

A turbocharger consists of a turbine and a compressor connected by a common

shaft supported on a bearing system. Extracted from [14].

Figure 6: Schematic diagram of a turbocharger. Ref. [16]


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The turbine recovers the waste energy. The exhaust gases are collected in the

turbine housing and guided into the turbine wheel. The gases make the turbine

wheel spin by pushing its blades in an adiabatic expansion. The speed of the

gases is decreased and they leave the turbine housing via the exhaust outlet

area.

As the turbine wheel spins, so does the impeller. Air is guided through the

compressor housing to the impeller, which converts the low-pressure airstream

into a high-pressure airstream. Compressing air means making its temperature

rise. In fact, air leaves the compressor housing at temperatures up to 200ºC4.

The bearing system is lubricated by oil from the engine, which also acts as a

coolant. This is another important function due to the high temperatures reached

in the turbine and impeller.

To conclude, turbochargers give some benefits such as increased engine power

output and improved fuel consumption. However, turbochargers also improve the

engine’s emissions due to the fact that they use exhaust gas to compress air in

order to augment the mixture without having to burn extra fuel.

4 As a reminder, material testing of an alloy for an impeller is done at this temperature in

this thesis.


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3 Experimental Work Although fatigue data is the most important part for the goal of this Master

Thesis, other testing has been performed.

The following paragraphs explain how fatigue, tensile test, hardness and

microstructure data have been obtained.

3.1 Fatigue Testing

In this Master Thesis two different types of fatigue have been studied. For both

high cycle fatigue (HCF) and low cycle fatigue (LCF) the same samples and

experimental facilities were used.

The only facility difference when testing HCF or LCF is the controlled variable:

load and strain, respectively. This difference makes it necessary to additionally

use an extensometer for the strain-controlled LCF.

3.1.1 Sample Used

The initial sample for testing was a piece of AL2618-T8511 with the dimensions

shown in Figure 7.

Figure 7: Dimensions of the sample used for fatigue testing.


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However, when running the experiments [13], it was observed that the said

dimensions caused some problems: samples did not break in the thin section,

but in the down base.

After several trials, it was decided to shorten the bases and decrease the

medium diameter around 1 mm. This decision resulted in having different

dimensions on each experiment, but all of them had a diameter between 6.42

and 7.02mm5.

3.1.2 Testing Process and Facilities Used

For performing the fatigue testing at 200ºC, a hydraulic press and a heater are

the most important machines. However, controlling items are also important. In

the following picture, a general view of fatigue experimental facilities is shown.

Figure 8: General view of fatigue experimental facilities.

5 Exact diameter of each experiment is shown in Results section.


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Before starting the experiments, the sample has to be mounted, in other words,

fixed inside the grips of the press as shown in the picture below.

Figure 9: View of mounting the sample’s process.

Once the sample is fixed, the heater is closed around the press and the heating

process can start.

Figure 10: View of the machine ready to heat the sample and perform the test.


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For the sample to reach the target temperature of 200ºC, the heater must reach

234ºC. The heater ready to perform the fatigue testing is shown in the following

picture.

Figure 11: View of the ready heater controller.

Before starting the experiments, pressure has to be given to the grips to grab

the sample correctly and strongly. This is done with the pressure controller

shown below.

Figure 12: View of grips hydraulic pressure controller.


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For both the HCF and LCF testing, the process up to this point is done. The

difference lies on how to start the experiment.

HCF testing is controlled with the hydraulic press controller shown in the

following picture. It is only necessary to introduce the desired load cyclic

waveform, run the experiment and read the total number of cycles when it is

finished.

Figure 13: Left: Hydraulic press controller. Right: Detail of the controlling panel.

LCF testing is controlled with the help of an extensometer, which is attached to

the sample and connected to the hydraulic press controller. In addition, a

computer is also connected to the controller and the desired strain waveform is

introduced through it. When the experiment is over, load waveform data used to

calculate the stress level, is taken from the stored data in the computer.


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3.2 Tensile Test

With the aim of confirming that the AL2618-T8511 was the suspected alloy, 3

tensile tests6 were carried out: two tensile tests at room temperature and one

test at 200ºC. In addition, they provided useful data for starting the fatigue

experiments.

Tensile tests were done with the same facilities as the fatigue testing; in fact,

using the same than with LCF (the extensometer was obviously needed). The

only difference between tensile tests and fatigue experiments is that the load is

not cyclic. In that case, samples are pulled until it breaks.

6 Tensile test graphs can be found in Results section.


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3.3 Hardness Testing

Rockwell B hardness test was also used to confirm that the AL2618-T8511 was

the suspected alloy.

As described in [17] and [18], the hardness test performed consists of indenting

a 1/16 inches ball with a load of 100kgf using the equipment shown in the

following picture.

Figure 14: Rockwell B hardness testing equipment.

Three different experiments were carried out and its mean value was used for

being compared to the Rockwell B hardness data7.

7 Rockwell B hardness result can be found in Results section.


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3.4 Microscope

When analysing the microstructure8, it is important to obtain a high quality

surface in order to investigate it with precision.

The surface of the bare sample does not show enough quality to look at its

microstructure. That makes it compulsory to prepare the sample before using the

microscope.

3.4.1 Bare Sample’s Preparation

The goal of preparing the bare sample is to have a well-polished surface that

facilitates the picture taking process of the microstructure.

First of all, rugosity has to be decreased. To do that, two different grinding

processes are performed with two different grinding discs. The first one leaves

the sample ground at a rugosity of 4000 µm and the second one at a rugosity of

1000 µm.

After being ground, the sample needs to be as good polished as possible. For this

process, a 3 µm diamond particles’ suspension disc is used.

Both grinding and polishing are performed using the equipment, shown in the

figure X, Struers Rotopol-2. It works by spinning a grinding or polishing disc and

the sample must be manually pressed against the disc in order to receive the

desired result.

8 Microstructure analysis can be found in Results section.


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Figure 15: Struers Rotopol-2.

After getting the smooth surface, etching is used to reveal the grains, size,

shape, and the morphology phase when looking it through the microscope.

The etching consists on immersing the sample around 15 seconds in a Keller’s

etch, whose composition is shown in the following table.

Table 3. Keller’s etch composition.

Compound Quantity [ml]

HF 1.0

HCL 1.5

HNO3 2.5

H2O 95.0


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3.4.2 Microstructure analysis

Microstructure pictures were taken using the XL 30 ESEM microscope shown in

the picture below.

Figure 16: XL 30 ESEM microscope.

To take the pictures, the polished sample is introduced into the enclosure and its

door is closed. Then, the air inside the enclosure is evacuated and the pressure is

decreased to less than 1.3mbar.

Microstructure pictures9 have been taken at a magnification of 125X, 250X,

500X, 1000X and 2000X.

9 Microstructure pictures can be seen in Results section.


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3.4.3 Fractography

Fractography was also analysed in both HCF and LCF tested samples.

Pictures of the fracture’s surface have been taken at a magnification of 125X,

250X, 500X and 1000X.

3.4.4 Energy Dispersive Spectroscopy (EDS)

Apart from taking pictures of the surface, a spot analysis and an energy

dispersive spectroscopy (EDS) was also carried out to determine the spectrum

and percentage in weight of the main elements of both phases.


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4 Results In this section, all the results obtained while performing this Master Thesis are

presented.

4.1 Fatigue Testing

For better understanding of how and why each result been used, it is necessary

to split this section into three subsections: data from the HCF, data from the LCF

tests and data obtained for the fatigue simulations.

Due to trade secret, scales are removed from the graphs in this section.

4.1.1 HCF. Load-Controlled

Due to the problems described in section 3.1.1 and the previously mentioned

time limitations only eight “stress-cycles points” were obtained from the HCF

load-controlled testing. In figure 17, these points and their potential regression

are shown.

Figure 17: Stress level versus cycles. All obtained points’ data.


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Once the potential regression is analysed, it is easily seen that it does not make

sense. It should show that the less the stress level, the more number of cycles.

Instead, it shows the less the stress level, the less number of cycles. The reason

is that among these points, there is one run-out test, which is the upper-right

point. It is decided to remove this point in order to analyze the data. Figure 18

shows the obtained points once the run-out point is removed.

Figure 18: Stress level versus cycles. No run-outs obtained points’ data.

Although without the run-out point, the potential regression looks reasonable; it

is observed that all the points except one (the upper point) are very close to the

regression.

It is decided to remove the upper point and analyze the regression of the six

remaining points. As it can be seen in figure 19, the left points fit the new

regression line more accurately; therefore, these six points will be used

afterwards in order to get the rest of the results.


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Figure 19: Stress level versus cycles. Used obtained points’ data.

Both HCF and LCF data have to be used together afterwards and they have to be

obtained with the same R-value, which is the relation between the minimum and

maximum stress levels.

HCF-tests were performed with an R-value of almost 0. However, LCF-tests were

performed with an R-value of 0.85.

Therefore, Smith Watson Topper mean stress correction factor (Equation 2) has

to be used to calculate the needed data.

σR=-0.8 =

R

R

−

=

12

0σ (2)

Using an R of -0.85 in equation 2, HCF correspondent data at an R-value of 0.85

is obtained. Figure 19 shows that data.


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4.1.2 LCF. Strain-Controlled

From LCF strain-controlled testing, eight “strain amplitude-reversals points” were

obtained. In this case, there were no run-outs and all of the points were useful.

Using equations 3 and 4, the total strain amplitude can be split up into plastic

and elastic strain amplitudes.

2ee∆ =

E2σ∆

(3)

2pe∆ =

2e∆

-E2σ∆

=2e∆

-2

ee∆ (4)

Total, plastic and elastic strain amplitudes are shown in figure 20, as well as its

potential regression.

Figure 20: Total, plastic and elastic strain amplitude versus reversals.


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4.1.3 Data for Fatigue Simulations

To run the fatigue simulations with CUMFAT5810, it is necessary to introduce

strain-life and cyclic stress-strain points. To get more of these points, more data

is needed. This section deals with the data needed for fatigue simulations.

Once the parameters from the potential regression of the plastic strain amplitude

versus the reversals (equation 5) are known, it is necessary to know the

equivalent parameters from the regression of the stress amplitude versus the

reversals (equation 6). Figures 21 and 22 show the graphs of these regressions.

Figure 21: Plastic strain amplitude versus reversals.

2pe∆ = ε’f·(2·Nf)c (5)

10 A program from VOLVO. See appendix to know more.


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Figure 22: Stress amplitude versus reversals.

2σ∆

= σ’f·(2·Nf)b (6)

Knowing the parameters of both potential regressions, it is possible to calculate

the total strain versus the reversals using the equation 7.

2e∆

= E

f'σ· (2Nf)b + ε’ f·(2Nf)c (7)

Figure 23 shows the graph of the total strain versus reversals, as well as the

plastic and elastic straight lines whose sum results in the total strain plot.


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Figure 23: Strain versus reversals with plastic and elastic straight lines11.

To calculate the reversals where the strain changes from being mostly plastic

into mostly elastic (Nt), equation 8 is used.

Nt = cb

f

f E −

1

'·'

σe

= 291.8 (8)

Apart from mathematically, Nt can be calculated using the graph. Nt corresponds

to the number of reversals in which plastic and elastic straight lines cross. The

graphical solution does not have a high precision due to both the logarithmic

scale of the graph and human eye’s precision. However in the graph Nt seems to

be around 300 reversals and mathematically it is 291.8 reversals, as it can be

seen in equation 8.

11 Logarithmic scales in both axes.


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With the parameters from the potential regressions of the plastic strain

amplitude versus the reversals and the stress amplitude versus the reversals, it

is also possible to calculate the cyclic stress-strain points.

First of all cyclic strain hardening exponent (n’) and cyclic strength coefficient

(K’) have to be calculated using equations 9 and 10.

n’ = cb

(9)

K’ = ( ) ''

'n

f

f

e

σ (10)

Then, using equation 11, cyclic stress-strain is calculated.

εt = Eσ +

'1

'n

K

σ (11)

Cyclic stress-strain has been calculated using the regressions from the LCF data

(called “Strain based” in figure 24), as well as, the regression using LCF stress

data and HCF stress data altogether (called “Strain&Load based” in figure 24).

Then, both plots are compared to the data from other alloys that VOLVO is using

nowadays (2024-T4 and 7075-T6).

Figure 24 shows the four plots in the same graph. It can be noticed that the

“Strain&Load based” plot is between the nowadays used data and the “Strain

based” plot, with a shape more similar to the nowadays used data than to the

“Strain based” data.


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Figure 24: Cyclic stress-strain. Comparison between experimental and nowadays

used data.

Due to the cyclic stress-strain comparison, using data from HCF and LCF tests

altogether has to be taken into account.

Another comparison is done to decide which data will be used as an input for the

fatigue simulation program, the “strain” or the “strain&load” based data. In this

case, the LCF curve is compared as it can be seen in figure 25.


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Figure 25: LCF. Comparison between strain and strain&load-controlled curves.

Due to the little difference between the strain-controlled and the “strain&load”

controlled data LCF curve, and that literature says that strain-controlled data has

to be used; it is decided to discard the “strain&load” based data and use the

strain-controlled data.


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4.1.3.1 Scaling at different temperatures

Once the input data needed for the fatigue simulations program is calculated

from the experimental data, it is important to have data at other temperatures12.

More data introduced at other temperatures means more reliable results.

This extra data has been scaled down due to the lack of time to perform more

experiments at different temperatures. There were many different options to

scale it; however, the final decision was to use the ultimate tensile strength

value of each new temperature divided by the value of 200ºC (equation 12). The

scaling gives the data shown at figures 26 and 27.

Scaling factor = Cm

m

RR

º200

(12)

Figure 26: Cyclic stress-strain. Scaling at different temperatures.

12 Due to trade secret, temperatures’ values are not included in this report.


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Figure 27: LCF Curve. Scaling at different temperatures.

To verify that the scaled data can be supposed as good data, scaled data at room

temperature is compared to data from the literature at room temperature. As an

example, for a lifespan of a million of reversals, the difference between literature

and scaled data is of only 4 MPa. Once it is compared, it can be presumed as

acceptable data.


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4.2 Tensile Tests

The 2 tensile tests carried out at room temperature each produced the same

graph. Shown in the following pictures are the tensile test graph conducted at

room temperature, the tensile test graph conducted at 200ºC and two graphs

representing the comparison between the two.

Figure 28: Tensile test’s graph at room temperature.

Figure 29: Tensile test’s graph at 200ºC.


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Figure 30: Comparison between the 2 tensile tests’ graphs.

Figure 31: Zoom of the comparison between the 2 tensile tests’ graphs.


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The Rm and Re values were derived from the graphs; they are shown in the

following table and they are compared to literature data at room temperature in

the following table.

Table 4. Rm and Re values.

Literature Room temperature 200ºC

Rm [MPa] 432 435 327

Re [MPa] 345 350 258

Rm and Re values at room temperature confirmed that the tested alloy is the

suspected alloy.


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4.3 Hardness Testing

Shown in the following table are the results from the three hardness tests carried

out with medium derived from all three tests as well as the literature data.

Table 5. Hardness values.

Source Hardness, Rockwell B [HRB]

Literature 72

Experiment 1 73,9

73,93 Experiment 2 73,6

Experiment 3 74,3

Experimental hardness is similar to literature data; therefore, samples material is

accepted as the suspected alloy.


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4.4 Microscope

In this section, the results obtained with the microscope are shown.

4.4.1 Microstructure Analysis

Pictures regarding the sample’s microstructure are shown in the following figure.

Although up to a magnification of 250X, grains’ edges do not start to be

noticeable, at a magnification of 125X, the precipitate’s phase and some holes

are easily located. Beyond a magnification of 500X, the grains, holes and

precipitate’s phase are perfectly distinguishable.

Figure 32: Microstructure at different magnification factors.

All the particles different from the matrix phase seem to be part of the

precipitate. However, by analyzing figure 33 which shows a magnification of

2000X other possibilities come to mind.


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Figure 33: Microstructure at 2000X magnification factor.

There are little precipitate particles (less than 4 µm length) which could possibly

be diamond particles coming from the diamond polishing disc’s suspension.


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4.4.2 Fractography

Fracture pictures of both HCF and LCF tested samples are shown in this section.

In the both of the following pictures, a deformation before breakage is

noticeable. No matter what type of fatigue is tested, the fracture is always

ductile. Ref. [3.2]

Figure 34: Surface of a HCF tested sample at different magnification factors.


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Figure 35: Surface of a LCF tested sample at different magnification factors.


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4.4.3 EDS

Energy dispersive spectroscopy results are shown in the following pages for both

the matrix and the precipitate phase.

Table 6. Weight percentage of each element in the matrix phase.

Element Wt [%]

CuL 2.24

MgK 2.88

AlK 94.88

Total 100.00

As AL2618-T8511 is an aluminium alloy, it’s normal that the matrix consists on

such high percentage of aluminium.

Table 7. Weight percentage of each element in the precipitate phase.

Element Wt [%]

CuL 6.23

MgK 2.34

AlK 80.87

FeK 10.56

Total 100.00

As the hardness is the result of a precipitate hardness process, it’s normal that

the precipitate phase it’s similar to the matrix with a high percentage of

aluminium as well.


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Figure 36: Spectrum of the matrix phase.

Figure 37: Spectrum of the precipitate phase.

The idea was to identify where each element was located. However, due to the

fact that the composition of the matrix and the phase were similar, it was

decided that it was neither interesting nor useful.


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5 Impeller Design Process The design process consists of an iterative process in which the sketch of the

shape of the back-disc is changed at every simulation. The goal of the iterations

is to see how stress distribution changes, as well as, its maximum value to be

able to define the most optimized design. The program used to perform the

simulations is ABAQUS 6.10 CAE. [19]

5.1 Design Steps

The design process consists of different steps in which different aspects are

regarded. The design steps are explained in this section.

5.1.1 Optimizing the Design Regarding Centrifugal Forces

The first design step is done regarding the maximum principal stress level

generated when the impeller spins at the top speed, which is the worst case.

The optimization process is started regarding the centrifugal forces because the

majority of the stresses in the impeller are caused by the high spinning speed.

In this step, the following observations are detected:

• The more material at the back-disc of the impeller, the higher the

maximum principal stress value.

• The more material in the outer region, the less stress level on that region,

but the more stress level at the centre hole.

• The more curved the back-disc of the impeller, the more concentrated

stress at this region with the more maximum principal stress value.

• The less the impeller’s length, the more the maximum principal stress

value.

The mesh is more refined in the regions prone to have more stress level. It is

changed while first designs are simulated.

A lot of different sketches are simulated but only the worst (figure 38) and the

best (figure 39) stress distribution designs are shown.


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The worst design gives a maximum value of 740 MPa while the best design gives

a value of 357 MPa. Note that colour scales are different on each figure.

Figure 38: Worst impeller’s back-disc design regarding centrifugal forces.

Figure 39: Best impeller’s back-disc design regarding centrifugal forces.


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5.1.2 Introducing the Temperature Field

Once the optimized back-disc design regarding centrifugal forces is reached, it is

decided to introduce the temperature field.

There is no exact data regarding the temperature distribution. However, the

temperature field shown in figure 40 is supposed to be quite a good

approximation. Scale is removed due to trade secret, but it goes from blue

(lowest temperature) up to red (highest temperature).

Figure 40: Temperature field of the impeller.

Due to the temperature, some stresses appear on the impeller. It makes all the

different designs regarding the centrifugal forces increase their maximum stress

level to around 10 MPa. Compared to stress caused by centrifugal forces, it is

visible that it is as important as previously thought. This has also been taken into

account.


-49-

It is then decided to study the stress caused by only the temperature. Its

distribution is shown in figure 41 and its maximum value is 9.49 MPa.

Figure 41: Stress distribution caused by only the temperature.

5.1.3 Regarding Life (Fatigue Analysis)

Final design step consists of using CUMFAT58 with all the data for fatigue

simulations13.

It is observed that best results are obtained with the best impeller’s back-disc

design regarding centrifugal forces with the temperature field included. This step

has not been of use to further optimize the design.

13 See section 4.1.3 to read about it.


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5.2 Optimized Design

Up to this point, simulations of the optimized design have been performed as if

the impeller was constantly spinning at its top speed. A further study was

performed analyzing three different types of use that can have the impeller.

These three situations are explained in this section. All of them have a similar

stress distribution, with the maximum principal stress value located in the

medium region. The differences among them is the stress scale and impeller’s

lifespan.

5.2.1 From 30% to 100% of Top Speed

When a truck is driven at high altitude, the impeller of its turbochargers spins at

a speed from 30% to 100% of its top speed. This is the worst situation regarding

fatigue because the impeller’s lifespan may decrease due to these big changes in

speed.

When these simulations are performed, the results obtained say that 380 MPa is

the maximum principal stress level as it can be seen in figure 42.

Figure 42: Stress distribution of the impeller used at high altitude.


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In regarding to lifespan, the impeller can only withstand 10421 cycles, being the

centre hole the worst region. Log(life) has been plotted in figure 43 for an

improved distinction between regions’ lifespan. The red coloured the region

signifies the region prone to fail and break the first, in other words, withstanding

the less number of cycles.

Figure 43: Log(life) distribution of the impeller used at high altitude.


-52-


Normal use of the impeller is when the truck is driven at sea level. In this case,

the impeller spins at a speed from 30% to 75% of its top speed. This is a

situation where the impeller is not forced and its requirements are quite low.

The results obtained with these simulations say that 212 MPa is the maximum

principal stress level as it can be seen in figure 44.

Figure 44: Stress distribution of the impeller used at sea level with normal-low

requirements.


-53-

In regard to lifespan, the impeller can only withstand 10729630 cycles, with the

centre hole again being the worst region. Log(life) is shown in figure 45.

Figure 45: Log(life) distribution of all the impeller used at sea level with

normal-low requirements.


-54-


Instead of analysing the normal-low requirements at sea level driven truck’s

impeller, it is also both interesting and useful to perform a simulation with the

maximum requirements of an impeller when the truck is driven at sea level. This

is a situation that occurs very often. In this case, the impeller spins at a speed

from 30% to 90% of its top speed.

The results obtained with these simulations say that 301 MPa is the maximum

principal stress level as it can be seen in figure 46.

Figure 46: Stress distribution of the impeller used at sea level with maximum

requirements.


-55-

In regard to lifespan, the impeller can only withstand 85406 cycles, with the

centre hole being again the worst region. Log(life) is shown in figure 47.

Figure 47: Log(life) distribution of all the impeller used at sea level with

maximum requirements.


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5.2.4 Results Assembled Together

After all the simulations, it is noticed that optimizing the design is a never-ending

process and that even a small decrease in stress improves the impeller’s lifespan

significantly.

The following table shows all the simulation’s results assembled together with the

approximated number of cycles shown for a faster comparison.

Table 8. Simulation’s results depending on the use assembled together.

% of Top Speed Type of use Max. Principal

Stress # Cycles

30% 100% High altitude 380 MPa 10421

30% 75% Normal-Low 212 MPa 1.07·107

30% 90% Maximum at sea level 301 MPa 8.54·104


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6 Conclusions In this Master Thesis material testing of AL2618-T8511 has been performed to

obtain the fatigue data. With this data, some graphs have been obtained and

more data has been calculated with a scaling factor. This collected data has been

used to redesign the back disc of a radial impeller. The following conclusions

have been reached:

• The lifespan of the impeller is affected by fatigue failure at high

temperatures

• AL2618 has reasonably good mechanical properties at 200ºC

• Optimized design of the back-disc of the impeller is essential for long

lifespan

• Even a small decrease in stress improves the impeller’s lifespan

significantly

• Life of the impeller is also affected by type of use (Table 8).

Future work could be performed using the lower 2-σ or 3-σ design curve in order

to redesign the back disc of the radial impeller. These curves consist of shifting

the median S-N curve in logarithmic coordinates to the left by 2 or 3 times the

standard deviation. In addition, statistical studies would be needed.


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7 References

[1] J. Gilbert Kaufman, 1999, Properties of Aluminum Alloys: Tensile, Creep and

Fatigue Data at High and Low Temperatures, ASM International, pages 88-93.

[2] MIL-HDBK-5H, 1 December 1998.

[3] Engineers Edge, Aluminum Tempers. Retrieved from the internet April 2011.

http://www.engineersedge.com/aluminum_tempers.htm

[4] Metal Suppliers Online, 2618 Aluminum Material Property Data Sheet.

Retrieved from the internet February 2011.

http://www.suppliersonline.com/propertypages/2618.asp

[5] MatWeb Material Property Data, Aluminium 2618-T61. Retrieved from the

internet February 2011.

http://www.matweb.com/search/DataSheet.aspx?MatGUID=f6d0bebbfc72488

38243b7fa141431ba

[6] Wohler’s curve drawing. Retrieved from the internet February 2011.

http://www.cad-cae.com/images2/022.jpg()

[7] DOE-HDBK-1017, January 1993, Properties of Metals, Physical Properties. Retrieved

from the internet February 2011.

http://www.tpub.com/content/doe/h1017v1/css/h1017v1_73.htm

[8] Shawn M. Kelly, April 1997, Fatigue. Retrieved from the internet March 2011.

http://www.sv.vt.edu/classes/MSE2094_NoteBook/97ClassProj/anal/kelly/fati

gue.html

[9] Cavaliere, Nobile, Panella, Squillace, 2005, Mechanical and microstructural

behaviour of 2024-7075 Aluminium Alloy sheets joined by friction stir

welding. International Journal of Machine Tools & Manufacture. Pages 592 –

593.

[10] S. Suresh, 1998, Fatigue of materials, 2nd ed, Cambridge University Press,

London, UK. Chapter 8.

http://www.engineersedge.com/aluminum_tempers.htm

http://www.sv.vt.edu/classes/MSE2094_NoteBook/HomeWork/STD_HomePage/fld1/fld2/97/corrected/kelly.html


-59-

[11] Bannantine, Comer, Handrock, Fundamentals of Metal Fatigue Analysis,

Prentice Hall, Englewood Cliffs, N. J. 07632.

[12] Norman E. Dowling, Mechanical Behaviour of Materials. Engineering

Methods for Deformation, Fracture, and Fatigue. Third Edition. Upper Saddle

River, New Jersey 07458. Chapter 14.

[13] Mechanical Testing and Evaluation, Volume 8 of ASM Handbook.

[14] Cummins Turbo Technologies, How a Turbocharger Works. Retrieved from

the internet March 2011. http://www.holset.co.uk/mainsite/files/2_3_1-

how%20a%20turbocharger%20works.php

[15] Floyd G. West, Turbocharger System, US Patent 3576102, April 1971.

[16] Turbocharger scheme. Retrieved from internet March 2011.

http://www.cap-ny153.org/Turbocharger%2002.jpg

[17] S.P. Rockwell, Hardness-Testing Machine, US Patent 1516207, Nov 1924.

[18] ASTM test method E 18.

[19] Abaqus 6.10 CAE and tutorials. http://www.simulia.com

http://www.holset.co.uk/mainsite/files/2_3_1-how%20a%20turbocharger%20works.php

http://www.holset.co.uk/mainsite/files/2_3_1-how%20a%20turbocharger%20works.php

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