Final Year 2009 - University of Glasgowuserweb.eng.gla.ac.uk/philip.harrison/Teaching/2009 Sandeep... · Final Year 2009 A Materials ... I would like to take this opportunity to express

Final Year

2009

A Materials Selection Case Study

Sandeep Kumar Pavuluri 0809466

Masters in Mechanical Engineering and Management

Supervisor: Dr. Phil Harrison

Department of Mechanical Engineering

University of Glasgow


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SANDEEP KUMAR PAVULURI - 0809466

Acknowledgement

This thesis presents the written result of my project for the degree, Master of Science

in Mechanical Engineering and Management at the Department of Mechanical

Engineering, University of Glasgow. I would like to take this opportunity to express

my thanks to many people who gave me great support during my study and project.

Dr. Phil Harrison, for being my project supervisor. Thank you for giving me this great

opportunity and your full support during my project. Thank you for guiding me in the

right direction and moreover letting me work independently.

Dr Ron Thomson, for being the co-ordinator of MSc Projects.

Dr Safa hashim, for being my advisor in the University.

Last but not least, I would like to thank my family and friends for their continued

encouragement during my studies and my project.


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Abstract

For designing a panel, the objectives taken in this case were minimum cost and minimum

weight and the constraints which limited the final design were minimum deflection and

maximum strength. Using material property charts (young’s modulus vs density, yield

strength vs. density, young’s modulus vs. (price * density), yield strength vs. (price *

density)), a list of 40 materials which are as good as self-reinforced composites were found.

By using ranking methods, materials which meet the desired attribute profile were filtered

from the previous finalised list of 40 and from the considered self-reinforced composites. The

first ranking method is Index method and the material found from it as the best choice was

Balsa (Ochroma spp.) (0.09-0.11) (I) and by using another ranking method called trade-off

strategies (Pareto and penalty), the material found as the best compromise was Redwood

(Sequoia sempervirens (young)) (I). By exploring through the properties of the above 2

materials, the best choice found was Redwood (Sequoia sempervirens (young)) (I). By

adding the mouldability feature, the resulted list of materials from Material property charts

was reduced to 24 materials and by using ranking methods again for these 24 materials

along with the self-reinforced composite materials, 5 materials were finalised. By using Index

method, PEEK/IM Carbon Fiber, UD Composite 00Lamina was found as best choice and by

using Trade-off strategies (Pareto and Penalty), the materials found as the best compromise

were Wrought magnesium alloy (EA55RS), PP (42% Directionalized Glass Mat – Parallel,

Homopolymer), Armordon, Pure and tegris. By exploring through their properties, the best

choice was found as Wrought magnesium alloy (EA55RS).So without adding the

mouldability feature, the best choice was Redwood (Sequoia sempervirens (young)) (I) and

by adding the mouldability feature the best choice was Wrought magnesium alloy (EA55RS).


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Contents

Abstract................................................................................................................................. 3

List of Figures ....................................................................................................................... 5

List of Tables ........................................................................................................................ 5

1. INTRODUCTION: ............................................................................................................. 6

2. OBJECTIVES: .................................................................................................................. 6

3. LITERATURE REVIEW: ................................................................................................... 7

4. MATERIAL SELECTION PROCESS: ............................................................................... 9

4.1 Translation:................................................................................................................ 10

4.2 Screening & Ranking: ................................................................................................ 11

4.2.1 Indices on charts: ................................................................................................... 11

4.2.2. Graphical Method: ................................................................................................. 19

4.2.3 Trade-off strategies: ............................................................................................ 24

4.2.3 (a) Strategy 1(Pareto method):............................................................................ 25

4.2.3 (b) Strategy 2 (Penalty Functions):...................................................................... 28

4.3 Supporting Information: ............................................................................................. 29

4.4 Screening & Ranking: ................................................................................................ 30

4.4.1. Graphical Method:.............................................................................................. 31

4.4.2 Trade-off strategies: ............................................................................................ 33

4.4.2(a) Strategy 1(Pareto method):............................................................................. 33

4.4.2 (b) Strategy 2 (Penalty Functions):...................................................................... 36

4.5 Supporting Information: ............................................................................................. 37

5. CONCLUSION AND RECOMMENDATIONS: ................................................................ 37

6. BIBLIOGRAPHY: ........................................................................................................... 38


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List of Figures

Figure 1 Young’s modulus vs. Density (Granta Design Limited, 2009) ................................ 13

Figure 2 Yield strength vs. Density (Granta Design Limited, 2009)...................................... 14

Figure 3 Young’s modulus vs. (Price*Density) (Granta Design Limited, 2009) .................... 15

Figure 4 Yield strength vs. (Price*Density) .......................................................................... 16

Figure 5 Deflection of beams and panels (Ashby, 1992) ..................................................... 19

Figure 6 Failure of Beams (Ashby, 1992)............................................................................ 21

Figure 7 Index Chart (1) ...................................................................................................... 24

Figure 8 Pareto Curve (1) ................................................................................................... 27

Figure 9 Penalty Function (1) .............................................................................................. 29

Figure 10 Index Chart (2) .................................................................................................... 33

Figure 11 Pareto Curve (2) ................................................................................................. 35

Figure 12 Penalty Function (2) ............................................................................................ 36

List of Tables

Table 1 Material Index table (1) (Granta Design Limited, 2009) .......................................... 22

Table 2 Cost and Mass Table (1) (Granta Design Limited, 2009)........................................ 25

Table 3 Material Index table (2) (Granta Design Limited, 2009) .......................................... 32

Table 4 Cost and Mass table (2) (Granta Design Limited, 2009) ......................................... 34


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1. INTRODUCTION:

For designing a panel, selecting materials by comparing them with Self-reinforced

composites will have so many advantages. The final selected material will be light in weight

with good impact strength and will retain good mechanical performance. Thus comparing

with self-reinforced composites is the preferred choice in designing a light, stiff panel. This

case study deals with comparison of materials with self-reinforced composites which are as

good as them and ranking the final resulted materials.

First of all, all bulk materials will be considered under selection so that every material will be

considered and there is no scope for any mistake of losing any good material for selection.

The next is to filter all those materials to find the desired material for the design. To do that,

different methods are to be used like Material Index method, Pareto curve and Penalty

function. Before that, the first thing to do is to find the materials which are as good as self-

reinforced composites and this can be done with the help of Cambridge Engineering

Selector (CES).By plotting graphs using CES helps to identify the materials which are as

good as self-reinforced composites. After identifying those materials, the other methods will

be used to filter those materials even more and finally the desired material will be found and

selected for the design.

2. OBJECTIVES:

This report is a case study which involves comparison of SRC materials with other

competing materials to find the best material for designing a panel which is as cheap as

possible and as light as possible. So the objectives are:

• Minimum cost

• Minimum weight

And the constraints which have to be considered for the selection of the material are:

• Minimum deflection

• Maximum strength


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3. LITERATURE REVIEW:

Materials play a crucial role in engineering design (Y.-M. Deng and K.L. Edwards, 2005). So

identifying a material for selection is also very important as it affects the performance of the

final design. “There are approximately 40000 to 80000 materials which can be considered

for selection” (Ashby, Brechet, Cebon and Salvo, 2003). So it is hard for a designer to select

the desired material (Ashby, Brechet, Cebon and Salvo, 2003). Wrong selection of material

will yield problems like increase in cost and often leads to product failure. So the designer

needs to find the appropriate material for design without any mistake (Prasenjit Chatterjee,

Vijay Manikrao Athawale and Shankar Chakraborty, 2009).As there are many different

choices for selection and different criteria which affect the material selection, a more precise

approach would be required for the selection (Dehghan-Manshadi, Mahmudi, Abedian and

Mahmudi, 2005).Design and material engineers normally uses Materials selection process.

The aim of materials selection process is to identify the materials which meet the desired

attribute profile and this can be done by going through appropriate manufacturing operations

(S. M. Sapuan, 21 July 2000) ( Ashby, Brechet, Cebon and Salvo, 2003). Designer needs

to find the material which can be used to maximize the performance of the required system

of design (Y.-M. Deng and K.L. Edwards, 2005).To go through the selection process,

thousands of data would be needed to rank all the materials with respect to the desired

properties profile.There are so many selection methods available for the design engineers to

choose the most suitable materials.The method basically used is to look at tables of material

properties in data books to find the best match but this is not a perfect method to do as once

published, data books are difficult to update and hence it is not recommendable. In recent

years, data regarding properties of materials is stored in a computer system as a

database.By doing that, it is easy to access and retrieve the data from the computer

database in order to select a material for a design. This computerised system may not

necessarily be considered as material selection system as it provides access to materials

data but accesing to data will help in material selection(S. M. Sapuan, 21 July 2000) (

Ashby, Brechet, Cebon and Salvo, 2003).. So therefore computerised database will help

design engineers in a better way to access through it and in turn will help to find the best

material for selection.

A number of database systems are developed for material selection in mechanical design.

These systems are used to search a better solution which is already stored in database. A

large number of factors have to be taken into account for materials selection in mechanical

design which include considering the mechanical properties of the materials like strength,

stiffness, toughness, hardness, density and creep resistance. First step in selection process


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is to specify the performance requirements of the final design and accordingly certain

materials will be eliminated and others can be considered for the design (Dehghan-

Manshadi, Mahmudi, Abedian and Mahmudi, 2005). In Ashby’s selection method, after

finding the materials which meet the desired attribute profile, one property should be plotted

against another in order to rank the best material among them. Ashby provided a

comprehensive review of strategies for selection (Ashby, 1992). Ashby proposed another

method called multi-objective optimization in materials design and selection using ‘utility’

functions. Though this second method is very simple but is not efficient. A fuzzy logic

approach for material selection can be used and in this, there is no need for scaling of the

materials properties. (Sarfaraz Khabbaz, B. Dehghan Manshadi, Abedian and R. Mahmudi,

2008). The other methods used for materials selection are A novel method for materials

selection in mechanical design: Combination of non-linear normalization and a modified

digital logic method (B. Dehghan-Manshadi, H. Mahmudi, A. Abedian and R. Mahmudi

,2005), A decision making methodology for material selection using an improved

compromise ranking method (Venkata Rao, 2007), Selection of materials using compromise

ranking and outranking method (Prasenjit Chatterjee, Vijay Manikrao Athawale and Shankar

Chakraborty,2009). But Ashby’s first selection method of using strategies for selection is

preferable as the above mentioned fuzzy logic approach for materials selection involves lot

of computation (R. Venkata Rao, 2007) and the other methods are unreliable and involves

more computation as well compared to Ashby’s method called Selection strategies

for materials and processes (M. F. Ashby, Y. J. M. Bréchet, D. Cebon and L. Salvo,

2003)But every method needs to check the properties of the materials to proceed further and

therefore the computer based database is essential in every method.

Self-reinforced composites are said to be a new class of thermoplastic composite. In the

self-reinforced composite materials, the matrix and fibers are composed of same polymer or

with almost identical polymers. Due to better interfacial bonding between fiber and matrix,

Self-reinforced composites will have good mechanical performance and are recyclable which

in turn good for the environment. Self-reinforced composites are better when compared to

traditional, glass and carbon fiber reinforced composites due to their light weight and good

impact strength (Kyoung Ju Kim, Woong-Ryeol Yu and Philip Harrison, 2008). The act of

self-reinforcing modifies the composite structure. It improves the performance of the

properties of the composites which results in increasing the performance of the function in

which the material is used (Tiiu Niemela, Henna Niiranen and Minna Kelloma, 2007). Self

reinforced composites can be produced by various different methods but the methods

commonly used are hot compaction and co-extrusion. They can be manufactured according


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to the desired output and can be used for the specified applications (Ju Kim, Woong-Ryeol

Yu and Philip Harrison, 2008). They can be used for different applications, for example self-

reinforced bioabsorbable polymers can be used for treating the traumas of skeletal system.

The bioabsorbable polymer composites will gain strength in their properties after self-

reinforcing and hence will increase the performance in treating the traumas of skeletal

system (T. Niemela, H. Niiranen, M. Kellomaki and P. Tormala, 2004). One more example is

that of using cellulose fibers as reinforcement agents in composite materials is widely used

which help in increasing the mechanical properties of the composite materials(Aparecido

Junior de Menezes, Daniel Pasquini, Antonio Aprígio da Silva Curvelo and Alessandro G,

2008). Self-reinforced composites which are biodegradable will have good mechanical

properties and can be used in surgeries (P. Tormala, 2004).Like this self-reinforced

composites are more preferable when compared to other composites due to their high

performance and high reliability. They are used in material section process also to compare

the other competing materials with them which help the designer to find the best choice for

the required function.

4. MATERIAL SELECTION PROCESS:

The process of material selection as explained in section 1 (introduction), consists of the

following methods which are explained below (Ashby, 1992)

1. Material selection charts

a) Young’s modulus vs. Density

b) Yield strength vs. Density

c) Young’s modulus vs. (Price*Density)

d) Yield strength vs. (Price*Density)

2. Graphical method (using Indices)

3. Trade-off Strategies

a) Strategy 1 (Pareto method)

b) Strategy 2 (Penalty function method)

The main task can be stated in two points which are as follows (Ashby, 1992)

1) identify the desired attribute profile


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2) comparing it with real engineering materials to find the best match

In this case, self-reinforced composite materials and glass materials are considered to

compare with the materials which will meet the desired attribute profile in order to find the

best match. The self-reinforced composites considered in this case are Armordon, Pure,

Curv, Tegris and the glass materials are Twintex PP 1/1 60 fibre volume fraction and

Twintex PP 4/1 60 fibre volume fraction.

Every material is characterized by a set of attributes which are nothing but its properties

(Ashby, 1992). Selection method involves in finding the best by analysing the property-

profiles of the materials according to the requirement of the design. First of all, examining the

design requirements will give the constraints for the choice of material and in this case the

constraints are deflection and strength. By screening- out the materials that cannot meet the

constraints will help to reduce a wide range of materials for selection. This method is called

screening. To filter the materials even more in order to find the best possible choice out of

the resulted materials from screening process can be done by ranking the materials by their

ability to maximize the performance and this can be done by identifying the material indices.

This method is called ranking. So therefore screening separates the materials which meet

the desired attribute profile and ranking identifies the materials among the resulted list that

can do the job best (Ashby, 1992).

The selection procedure can be stated in three steps. They are

1. Translation

2. Screening & Ranking

• Indices on charts

• Graphical Method (using indices)

• Trade-off strategies

3. Supporting information

• Explore the resulted materials to find the best choice

By applying these steps for this case will give the following procedure

4.1 Translation:

The property or Property group that maximizes performance for a given design is called its

material index (Ashby, 1992). The material attributes that are constrained by the design has


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to be identified in order to optimize the performance. The material indices can be identified

by considering the function, objective and constraints for the required design. The

constraints in this case are stiffness and strength, the objectives are minimum weight and

minimum cost and the function is panel. So therefore the material indices in this case are

identified as follows (Ashby, 1992):

• Panel, Minimum weight, stiffness prescribed - (E1/2)/ρ

• Panel, Minimum weight, strength prescribed - (σy2/3)/ρ

• Panel, Minimum cost, stiffness prescribed - (E1/2)/(Cm*ρ)

• Panel, Minimum Cost, Strength prescribed - (σy2/3)/(Cm*ρ)

Where,

E = Young’s Modulus

σy= Elastic Limit

ρ = Density

Cm = Cost/kg

4.2 Screening & Ranking:

With the help of the material indices which are identified above, the considered self-

reinforced composite materials are plotted on the graph and a slope line will be drawn under

the self-reinforced composite group with a calculated slope. The materials which lie on the

upper side of the index line will be considered as the competing materials with self-

reinforced composites.

4.2.1 Indices on charts:

The slope of the line can be calculated as follows:

The material indices E1/2/ρ and σy2/3 are used to plot the graphs. The first condition

E1/2/ρ = C (Ashby, 1992)

Taking logs,

Log (E) = 2 Log (ρ) + 2 Log (C) (Ashby, 1992)

is a family of straight parallel lines of slope 2 on a plot of Log (E) against Log (ρ) each line

corresponding to a value of the constant C.


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The other condition is σy2/3 = C

Taking logs again,

2/3 Log (σy) = Log (ρ) + Log (C) (Ashby, 1992)

Log (σy) = 3/2 Log (ρ) +3/2 Log (C) (Ashby, 1992)

This gives another set, with a slope 3/2

By using those slopes, the following graphs have to be plotted in order to find the competing

materials with self-reinforced composite materials.

• Young’s modulus vs. Density graph

• Yield strength vs. Density graph

• Young’s modulus vs. (Price*Density)

• Yield strength vs. (Price*Density)

The graphs have to be plotted by using Cambridge Engineering Selector (CES) and are

shown as follows:


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Figure 1 Young’s modulus vs. Density (Granta Design Limited, 2009)


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Figure 2 Yield strength vs. Density (Granta Design Limited, 2009)


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Figure 3 Young’s modulus vs. (Price*Density) (Grant a Design Limited, 2009)


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Figure 4 Yield strength vs. (Price*Density)


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The material selection charts (graphs) which are shown above identifies the materials which

are as good as considered SRC materials. With the help of Cambridge engineering selector,

the materials which passed all the four stages can be found. The materials that resulted in

this case are 40 and are shown as follows:

Mtrl 1 - Ash (Fraxinus nigra) (I)

Mtrl 2 - Balsa (Ochroma spp.) (0.09-0.11) (I)



Mtrl 5 - Balsa (I) (Id)

Mtrl 6 - Cedar (Libocedrus decurrens) (I)

Mtrl 7 - Douglas Fir (Pseudotsuga menziesii (Northern)) (I)

Mtrl 8 - Fir (Abies procera) (I)

Mtrl 9 - Larch (Larix deciduas) (I)

Mtrl 10 - Mahogany (Swietenia macrophylla) (I)

Mtrl11 - Pine (Pinus spp.) (I)

Mtrl 12 - Redwood (Sequoia sempervirens (young)) (I)

Mtrl 13 - Spruce (Picea abies) (I)

Mtrl 14 - Spruce (Picea rubens) (I)

Mtrl 15 - Walnut (Juglans regia) (I)

Mtrl 16 - Willow (Salix alba) (I)

Mtrl 17 - BMI/HS carbon Fiber, UD Composite, 00Lamina

Mtrl 18 - Epoxy SMC (Carbon Fiber)

Mtrl 19 - Epoxy/Aramid Fiber, UD Composite, 00Lamina

Mtrl 20 - Epoxy/E-Glass Fiber, Woven Fabric Composite, Biaxial Lamina

Mtrl 21 - Epoxy/ HS carbon Fiber, UD Composite, 00Lamina


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Mtrl 22 - Epoxy/ HS carbon Fiber, UD Composite, Quasi-isotropic Laminate

Mtrl 23 - Epoxy/ HS carbon Fiber, Woven Fabric Composite, Biaxial Lamina

Mtrl 24 - Epoxy/ HS carbon Fiber, Woven Fabric Composite, QI Laminate

Mtrl 25 - Epoxy/S-Glass Fiber, UD Composite, 00Lamina

Mtrl 26 - Glass/Epoxy Unidirectional Composite

Mtrl 27 - Mg-12%SiC (p)

Mtrl 28 - Molybdenum high speed steel, AISI M47

Mtrl 29 - PA (Type 6, 30% PAN Carbon Fiber)


Mtrl 31 - PA (Type 66, 30-33% Glass Fiber)


Mtrl 33 - PEEK/IM Carbon Fiber, UD Composite, 00Lamina

Mtrl 34 - PP (42% Directionalized Glass Mat – Parallel, Homopolymer)

Mtrl 35 - Phenolic/E-Glass Fiber, Woven Fabric Composite, Biaxial Lamina

Mtrl36 - Phenolic/E-Glass Fiber, Woven Fabric Composite, Quasi-isotropic Laminate

Mtrl 37 - Silicon Nitride (hot pressed) (5%MgO)

Mtrl 38 - Wrought aluminum alloy, 7055, T77511


Mtrl 40 - Wrought magnesium alloy (EA55RS)

Each and every material is denoted by their number with the name Mtrl in order to use them

further in the report and the considered self-reinforced composite materials are also denoted

as follows

Mtrl 41 - Armordon

Mtrl 42 - Pure

Mtrl 43 - Curv


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Mtrl 44 - Tegris

After filtering the materials, the following methods will be introduced in order to find the best

material for the selection. The methods are:

1. Graphical method

2. Trade-off strategies

• Pareto curve method

• Penalty function method

4.2.2. Graphical Method:

As the material selection is over constrained here (stiffness and strength), the method to

follow is ‘single objective but limited by more than one constraint’. The following procedure

will give material indices which are required to plot the graph (Ashby, 1992).

Considering the stiffness constraint, one material index can be derived

S = (C1EI)/L3 ------------------------ (1)

Where,

S = stiffness constraint

I = moment of inertia

E = young’s modulus

L = length

Figure 5 Deflection of beams and panels (Ashby, 199 2)

From Figure 5,

Moment of Inertia for a panel, I = (b*t3)/12


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Therefore Equation (1) becomes

S = (C1Ebt3)/ (12L3)

Writing the equation in terms of t gives

t3 = (12SL3)/ (C1Eb)

t = ((12SL3)/ (C1Eb)) 1/3 -------------------- (2)

The mass m of the panel has to be minimized and for that the objective function is

m1= A*L* ρ

= (b*t)*L* ρ (Area of panel = b*t)

Writing the above equation in terms of t gives

t = m1/ (b*L* ρ) --------------------- (3)

Equating equations (2) and (3) gives

((12SL3)/ (C1Eb)) 1/3 = m1/ (b*L* ρ)

That gives

m1= b*L* ρ*((12SL3)/ (C1Eb)) 1/3

m1 = b*(12S/C1b) 1/3 *L2 (ρ/E1/3) ---------------- (4)

This gives the material index,

M1 = ρ/E1/3

Now, consider the strength constraint

σf = M*ym/I --------------------------------- (5)

Where

σf = strength constraint

M = bending moment


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ym = perpendicular distance from the neutral axis to the outer surface of the panel

Figure 6 Failure of Beams (Ashby, 1992)

From Figure 6,

Moment of Inertia for a panel, I = (b*t3)/12

And ym = t/2

Therefore (5) becomes

σf = (M*(t/2)) / (bt3/12)

This gives

t = (6M/b σf) 1/2 ----------------------- (6)

The mass m of the panel has to be minimized and for that the objective function is

m2 = A*L* ρ

= (b*t)*L* ρ (Area of panel = b*t)

Writing the above equation in terms of t gives

t = m2/ (b*L* ρ) ---------------------- (7)

Equating both the equations (6) and (7) gives

(6M/b σf) 1/2 = m2/ (b*L* ρ)

That gives m2 = (b*L* ρ) * (6M/b σf) 1/2


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m2= L * (6Mb) 1/2 * (ρ/ σf1/2) -------------- (8)

This gives the material index,

M2 = ρ/σf1/2

By equating both the performance equations (4) and (8), we get

m1 = m2

b*(12S/C1b) 1/3 *L2 * (ρ/E1/3) = L * (6Mb) 1/2 * (ρ/ σf1/2)

(b*(12S/C1b) 1/3 *L2 ) * M1 = L * (6Mb) 1/2 * M2

M2 = (((12S/C1b)) 1/3 * L*b) * M1

Or on logarithmic scales

Log (M2) = Log (M1) + log (((12S/C1b)) 1/3 * L*b)

This gives a slope of 1, in a position that depends on the value of (((12S/C1b)) 1/3 * L*b) and

this line is called coupling line and (((12S/C1b)) 1/3 * L*b) is called the coupling constant and

its symbol is Cc

So therefore coupling constant, Cc = ((12S/C1b)) 1/3 * L*b)

To plot the graph, calculate the material index M1 and M2 for all the 40 materials and for the

SRC materials which are considered in this case. The results are shown in the following

Table 1:

Table 1 Material Index table (1) (Granta Design Limited, 2009 )

Material M 1 M2

Mtrl 1 237.1 82.54

Mtrl 2 75.96 41.88

Mtrl 3 89.49 43.09

Mtrl 4 114.01 53.31

Mtrl 5 135.93 63.63

Mtrl 6 209.81 68.92

Mtrl 7 226.36 77.58

Mtrl 8 186.58 68.52

Mtrl 9 245.4 79.97

Mtrl 10 231.02 77.46


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Mtrl 11 234.33 76.33

Mtrl 12 193.6 65.64

Mtrl 13 204.9 74.03

Mtrl 14 194.92 71.34

Mtrl 15 295.22 87.87

Mtrl 16 174.42 66.21

Mtrl 17 327.58 38.29

Mtrl 18 328.6 98.34

Mtrl 19 339.62 39.18

Mtrl 20 631.51 88.1

Mtrl 21 305.21 35.39

Mtrl 22 417.3 90.01

Mtrl 23 395.8 56.81

Mtrl 24 444.57 67.2

Mtrl 25 532.08 45.84

Mtrl 26 525.43 74.67

Mtrl 27 510.83 104.35

Mtrl 28 1328.69 156.43

Mtrl 29 476.28 94.87

Mtrl 30 483.2 103.19

Mtrl 31 606.22 97.07

Mtrl 32 454.24 95.22

Mtrl 33 300.17 31.71

Mtrl 34 572.65 81.2

Mtrl 35 581.78 96.35

Mtrl 36 635.35 109.88

Mtrl 37 474.36 122.57

Mtrl 38 712.15 119.12

Mtrl 39 682.61 121.7

Mtrl 40 551.79 96.88

Mtrl 41 657.59 61.86

Mtrl 42 444.4 55.15

Mtrl 43 572.94 83.98

Mtrl 44 444.4 55.15


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With the help of the material indices found from the Table 1, plot the graph using logarithmic

scales and the resulted graph will be as follows

Figure 7 Index Chart (1)

The material which is at the bottom left of the graph will have both smaller M1 and M2 and is

considered as the best choice. Therefore, the best choice in this case is Mtrl 2 - Balsa

(Ochroma spp.) (0.09-0.11) (I) and is marked in the above table.

4.2.3 Trade-off strategies:

Materials selection generally requires that a compromise be reached between the conflicting

objectives. The general objectives are (Ashby, 1992)

• Minimizing mass

• Minimizing volume

• Minimizing cost

• Minimizing environmental impact

There are so many objectives which are specific to certain applications but all those

objectives are same as the above mentioned objectives but they are expressed in different

words. So therefore there happens to be only four objectives overall and each one is


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characterized by a performance metric. In designing any product, more than one objective

will be involved. But the problem will be the choice that optimizes one objective will not do

the same for the other objective. So therefore the best choice has to be the compromise

between the objectives. There happens to be another problem which is how one objective

will be compared against another objective as each objective will be measured in different

units. In this kind of problem, trade-off strategies have to be followed.

In the Trade-off strategies method, one objective will be plotted against another objective. By

considering the desired profile, the solutions which meet all the constraints are defined and

these solutions are placed on the graph.

4.2.3 (a) Strategy 1(Pareto method):

If the choice of the material is to minimize two performance metrics, P1 and P2 in addition to

meet a set of constraints, a solution has to be defined which meets all the constraints but not

necessarily optimal by any one of the objectives. By plotting P1 against P2 will give

alternative solutions. The solutions which minimize P1 do not minimize P2 and the solutions

which maximize P1 do not maximize P2. Some solutions are far from desired and these are

called as dominated solutions which will have lower values of both the objectives. The

remaining solutions are called non-dominated solutions as they do not have lower values of

both the objectives. The line or surface on which the non-dominated solutions lie is called

the non- dominated or optimal trade-off surface. The solutions which are on or near the

trade-off surface offer the best compromise and the remaining solutions can be rejected and

this result in a short list of materials which can be proceeded to third step which is supporting

information and the final material is selected by ranking the resulted materials. (Ashby, 1992)

Table 2 Cost and Mass Table (1) (Granta Design Limi ted, 2009)

Material Price/kg Total

Price

Mass =

Density * unit vol

Mtrl 1 1.84 993.6 540

Mtrl 2 6.85 685 100

Mtrl 3 6.85 890.5 130

Mtrl 4 6.85 1301.5 190

Mtrl 5 6.85 1849.5 270

Mtrl 6 1.84 763.6 415

Mtrl 7 0.79 422.65 535

Mtrl 8 0.79 343.65 435

Mtrl 9 0.79 458.2 580


26



Mtrl 10 6.85 3527.75 515

Mtrl 11 0.79 387.1 490

Mtrl 12 0.79 308.1 390

Mtrl 13 0.79 402.9 510

Mtrl 14 0.79 351.55 445

Mtrl 15 6.85 4726.5 690

Mtrl 16 1.84 634.8 345

Mtrl 17 67.46 107261.4 1590

Mtrl 18 10.76 16678 1550

Mtrl 19 32.19 44422.2 1380

Mtrl 20 18.7 34782 1860

Mtrl 21 21 32865 1565

Mtrl 22 21 32865 1565

Mtrl 23 28.31 44588.25 1575

Mtrl 24 28.31 44588.25 1575

Mtrl 25 13.07 24898.35 1905

Mtrl 26 10.17 18051.75 1775

Mtrl 27 13.71 27557.1 2010

Mtrl 28 3.607 28711.72 7960

Mtrl 29 6.27 8025.6 1280

Mtrl 30 6.35 8604.25 1355

Mtrl 31 2.25 2868.75 1275

Mtrl 32 8.82 12171.6 1380

Mtrl 33 62.72 97843.2 1560

Mtrl 34 1.8 2178 1210

Mtrl 35 15.93 29470.5 1850

Mtrl 36 15.93 29470.5 1850

Mtrl 37 22.68 71442 3150

Mtrl 38 1.03 2966.4 2880

Mtrl 39 1.34 3782.82 2823

Mtrl 40 1.09 2120.05 1945

Mtrl 41 5 4150 830

Mtrl 42 15 11700 780

Mtrl 43 17 15640 920

Mtrl 44 20 15600 780


27



The objectives for the selection of material in this case are to minimize the mass and cost

along with the constraints stiffness and strength .Therefore with the help of Table 2, cost

(P1) will be plotted against mass (P2) and some solutions will be developed on the graph as

shown in the Figure 8 below.

Figure 8 Pareto Curve (1)

The dominated solution is Mtrl 30 and non-dominated solution is Mtrl 2 and both are marked

on the Figure 8.The best choice here is Mtrl 2 - (Balsa (Ochroma spp.) (0.09-0.11) (I)). The

solutions on or near the trade-off surface are considered as the best compromise. So the

best materials are

Mtrl 2 - (Balsa (Ochroma spp.) (0.09-0.11) (I)) and

Mtrl 12 - (Redwood (Sequoia sempervirens (young)) (I))


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4.2.3 (b) Strategy 2 (Penalty Functions):

The trade-off surface identifies the solutions which are best compromise between the

objectives but ultimately a single solution has to be found. This can be done by adding all the

objectives and including it into a single objective function. The minimum of these can be

identified as the best possible solution. To do this, a linear penalty function Z is needed and

is defined as follows (Ashby, 1992)

Z = α1P1 + α2P2 + α3P3 +.....

The smallest value of Z gives the best choice. The α’s are exchange constants which

converts the units of performance into the units of penalty function, Z. The performance

Metric P2 in this case is mass m, and then α2 is the change in Z associated with unit

increase in m. The other objective is to minimize the cost, C, so that performance metric, P1

= C. Therefore penalty has to be measured in terms of cost. With this choice, unit change in

C gives unit change in Z, and with α1 =1, the above equation becomes (Ashby, 1992)

Z = C + (α*m) (Ashby, 1992)

Or

m = (-1/ α)*C + (1/ α)*Z (Ashby, 1992)

Plot mass against cost using the values of table 2 and the value of Penalty function Z

decreases towards the bottom left. So the best choice lies at the bottom left. The optimum

solution will have the lowest value of Z which is the one nearest to the point at which a

penalty line is tangential to the trade-off surface.


29



Figure 9 Penalty Function (1)

So the optimum solution here is Mtrl 2 - (Balsa (Ochroma spp.) (0.09-0.11) (I)) as shown in

Figure 9. But taking one material as the best choice at this stage is not recommended

because there is one more step for selecting the final material. So take the subset of

solutions that lie closest to the tangent-point. So the materials which lie closest to the

tangent-point are

Mtrl 2 - Balsa (Ochroma spp.) (0.09-0.11) (I) and

Mtrl 12 - Redwood (Sequoia sempervirens (young)) (I)

4.3 Supporting Information:

From the above three steps, the materials identified as the best choice are Mtrl 2 and Mtrl

12.By exploring through their properties which maximizes the performance of the function

can gives the best from the two. As cost and mass are two main objectives, these two

materials are analysed based on those objectives. On analysing, it was found that cost of

Mtrl 12 is 10 times lesser than Mtrl 2. But mass of Mtrl 12 is more than 2 times of Mtrl 2.On


30



comparing these, Mtrl 12 is the preferred because it has lesser cost with reasonable weight

and also it has good impact strength, fatigue strength and fracture toughness. So the best

choice for designing the panel is Mtrl 12 - Redwood (Sequoia sempervirens (young)) (I )

4.4 Screening & Ranking:

If the desired material for selection should be mouldable, then remove the materials which

do not have the mouldability feature. The woods are not mouldable, so just remove them

from the list and check whether any other material is unmouldable. The resulted list is as

follows:

Mtrl 17 - BMI/HS carbon Fiber, UD Composite, 00Lamina

Mtrl 18 - Epoxy SMC (Carbon Fiber)

Mtrl 19 - Epoxy/Aramid Fiber, UD Composite, 00Lamina

Mtrl 20 - Epoxy/E-Glass Fiber, Woven Fabric Composite, Biaxial Lamina

Mtrl 21 - Epoxy/ HS carbon Fiber, UD Composite, 00Lamina

Mtrl 22 - Epoxy/ HS carbon Fiber, UD Composite, Quasi-isotropic Laminate

Mtrl 23 - Epoxy/ HS carbon Fiber, Woven Fabric Composite, Biaxial Lamina

Mtrl 24 - Epoxy/ HS carbon Fiber, Woven Fabric Composite, QI Laminate

Mtrl 25 - Epoxy/S-Glass Fiber, UD Composite, 00Laminav

Mtrl 26 - Glass/Epoxy Unidirectional Composite

Mtrl 27 - Mg-12%SiC (p)

Mtrl 28 - Molybdenum high speed steel, AISI M47



Mtrl 31 - PA (Type 66, 30-33% Glass Fiber)


Mtrl 33 - PEEK/IM Carbon Fiber, UD Composite, 00Lamina

Mtrl 34 - PP (42% Directionalized Glass Mat – Parallel, Homopolymer)


31



Mtrl 35 - Phenolic/E-Glass Fiber, Woven Fabric Composite, Biaxial Lamina

Mtrl 36 - Phenolic/E-Glass Fiber, Woven Fabric Composite, Quasi-isotropic Laminate

Mtrl 37 - Silicon Nitride (hot pressed) (5%MgO)



Mtrl 40 - Wrought magnesium ally (EA55RS)

And the self-reinforced composite materials are denoted as follows

Mtrl 41 - Armordon

Mtrl 42 - Pure

Mtrl 43 - Curv

Mtrl 44 - Tegris

The following methods are to be followed again in order to select the best material out of

these mouldable materials.

1. Graphical method

2. Trade-off strategies

• Pareto curve method

• Penalty function method

4.4.1. Graphical Method:

As the material selection is over constrained here (stiffness and strength), the method to

follow is ‘single objective but limited by more than one constraint’.

The process and equations are same as calculated above but here in this case, but only

mouldable materials are considered. The material indices for the 24 mouldable materials

along with SRCs are shown in the following Table 3


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Table 3 Material Index table (2) (Granta Design Lim ited, 2009)

M1 M2

Mtrl 17 327.58 38.29

Mtrl 18 328.6 98.34

Mtrl 19 339.62 39.18

Mtrl 20 631.51 88.1

Mtrl 21 305.21 35.39

Mtrl 22 417.3 90.01

Mtrl 23 395.8 56.81

Mtrl 24 444.57 67.2

Mtrl 25 532.08 45.84

Mtrl 26 525.43 74.67

Mtrl 27 510.83 104.35

Mtrl 28 1328.69 156.43

Mtrl 29 476.28 94.87

Mtrl 30 483.2 103.19

Mtrl 31 606.22 97.07

Mtrl 32 454.24 95.22

Mtrl 33 300.17 31.71

Mtrl 34 572.65 81.2

Mtrl 35 581.78 96.35

Mtrl 36 635.35 109.88

Mtrl 37 474.36 122.57

Mtrl 38 712.15 119.12

Mtrl 39 682.61 121.7

Mtrl 40 551.79 96.88

Mtrl 41 657.59 61.86

Mtrl 42 444.4 55.15

Mtrl 43 572.94 83.98

Mtrl 44 444.4 55.15

With the help of the material indices which are found from the Table 3, plot the graph using

logarithmic scales and the resulted graph is shown in Figure 10.


33



Figure 10 Index Chart (2)

The material which is at the bottom left of the graph will have both smaller M1 and M2 and is

considered as the best choice. Therefore, the best choice in this case is Mtrl 33 - PEEK/IM

Carbon Fiber, UD Composite, 0 0Lamina and is marked in the above table.

4.4.2 Trade-off strategies:

4.4.2(a) Strategy 1(Pareto method):

The objectives for the selection of material in this case are to minimize the mass and cost

along with the constraints stiffness and strength .Therefore cost (p1) will be plotted against

mass (p2) and some solutions will be developed on the graph as shown in the figure below.

By knowing density of all the materials, mass and cost can be calculated by taking volume

as constant and therefore the following Table 4 gives the values of mass and cost which are

plotted on the Figure 11.


34



Table 4 Cost and Mass table (2) (Granta Design Limited, 2009)

Material Price/kg Total price Mass/unit vol

Mtrl 17 67.46 107261.4 1590

Mtrl 18 10.76 16678 1550

Mtrl 19 32.19 44422.2 1380

Mtrl 20 18.7 34782 1860

Mtrl 21 21 32865 1565

Mtrl 22 21 32865 1565

Mtrl 23 28.31 44588.25 1575

Mtrl 24 28.31 44588.25 1575

Mtrl 25 13.07 24898.35 1905

Mtrl 26 10.17 18051.75 1775

Mtrl 27 13.71 27557.1 2010

Mtrl 28 3.607 28711.72 7960

Mtrl 29 6.27 8025.6 1280

Mtrl 30 6.35 8604.25 1355

Mtrl 31 2.25 2868.75 1275

Mtrl 32 8.82 12171.6 1380

Mtrl 33 62.72 97843.2 1560

Mtrl 34 1.8 2178 1210

Mtrl 35 15.93 29470.5 1850

Mtrl 36 15.93 29470.5 1850

Mtrl 37 22.68 71442 3150

Mtrl 38 1.03 2966.4 2880

Mtrl 39 1.34 3782.82 2823

Mtrl 40 1.09 2120.05 1945

Mtrl 41 5 4150 830

Mtrl 42 15 11700 780

Mtrl 43 17 15640 920

Mtrl 44 20 15600 780


35



Figure 11 Pareto Curve (2)

The dominated solution is Mtrl 30 (PA (Type 66, 30% PAN Carbon Fiber)) and non-

dominated solution is Mtrl 41 (Armordon) and both are marked in the figure. The material

which lies on the bottom left will be considered as the best choice and here it is Armordon

but taking single material as the best choice is not ideal as there is one more step to be

completed for the selection. So the materials on or near the trade-off surface can be taken

as best compromise. So the best materials here are

Mtrl 40 - (Wrought magnesium alloy (EA55RS))

Mtrl 34 - (PP (42% Directionalized Glass Mat – Parallel, Homopolymer))

Mtrl 41 - (Armordon)

Mtrl 42 - (Pure)

Mtrl 44 - (tegris)


36



4.4.2 (b) Strategy 2 (Penalty Functions):

The performance Metric P2 in this case is mass m and then α2 is the change in Z associated

with unit increase in m. The other objective to be minimized is Cost, C, so that P1 = C.

Therefore penalty has to be measured in terms of currency. With this choice, Unit change in

C gives unit change in Z, with the result that α1 =1 and above equation becomes

Z = C + (α*m) (Ashby, 1992)

Or

M = (-1/ α)*C + (1/ α) Z (Ashby, 1992)

Figure 12 Penalty Function (2)

So the optimum solution here is Mtrl 41 - (Armordon) as shown in the figure above.


37



4.5 Supporting Information:

From the above three methods, the materials identified as the best choice are Mtrl 33, Mtrl

34, Mtrl 40, Mtrl 42 and Mtrl 44.By exploring through their properties which maximizes the

performance of the function will give the best one out of these materials. On analysing, Mtrl

40 has less cost with reasonable mass compared to the other materials. Also on comparing

low cost materials (Mtrl 40 and Mtrl 34), Mtrl 40 has good impact strength, fatigue strength

and fracture toughness. So therefore the best choice for designing the panel is Mtrl 40 -

Wrought magnesium alloy (EA55RS).

5. CONCLUSION AND RECOMMENDATIONS

As it can be seen, for designing a panel there are many methods to be followed in order

to select the best material. The methods used in this report were Index method, Pareto

method and Penalty function method and along with them material property charts were also

used. It was understood by following these methods, lots of study has to be made on the

properties of the materials in order choose the final choice. This study has to be made in

order to reduce the risk of investing more on the unnecessary materials. A thorough

selection method has to be followed in order to find the best material which can be used for

the design.

In the Index method, the best material was found from the graph which has low values of M1

and M2 but this result can be improved by calculating the minimum and maximum coupling

constants along with the slopes.


38



6. BIBLIOGRAPHY:

• Aparecido Junior de Menezes, Daniel Pasquini, Antonio Aprígio da Silva Curvelo and

Alessandro G (2008), Self-reinforced composites obtained by the partial oxypropylation

of cellulose fibers. 1. Characterization of the materials obtained with different types of

fibers, 8 October 2008

• B.Dehghan-Manshadi, H. Mahmudi, A. Abedian and R. Mahmudi (2005), A novel method

for materials selection in mechanical design: Combination of non-linear normalization

and a modified digital logic method, 30 March 2005

• Kyoung Ju Kim, Woong-Ryeol Yu and Philip Harrison (2008), Optimum consolidation

of self-reinforced polypropylene composite and its time-dependent deformation

behaviour, 27 April 2008

• M .F. Ashby, Y.J.M. Breche, D.Cebon and L.Salvo (2003), Selection strategies

for materials and processes, 18 February 2003

• Michael F.Ashby (1992), Material Selection in Mechanical Design

• P. Tormala (2004), Biodegradable self-reinforced composite materials; Manufacturing

structure and mechanical properties, 10 April 2004

• Prasenjit Chatterjee (2009), Vijay Manikrao Athawale and Shankar Chakraborty,

Selection of materials using compromise ranking and outranking method, 23 February

2009

• R. Sarfaraz Khabbaz, B. Dehghan Manshadi, A. Abedian and R. Mahmudi (2008),A

simplified fuzzy logic approach for materials selection in mechanical engineering design,

9 February 2008

• R. Venkata Rao (2007), A decision making methodology for material selection using an

improved compromise ranking method, 24 August 2007

• S .M. Sapuan (2000), A knowledge-based system for materials selection in mechanical

engineering design, 21 July 2000

• Tiiu Niemela (2007), Henna Niiranen and Minna Kelloma, Self-reinforced composites of

bioabsorbable polymer and bioactive glass with different bioactive glass contents. Part II:

In vitro degradation,15 January 2007

• Y .-M. Deng and K.L.Edwards (2005), The role of materials identification and election in

engineering design, 9 February 2005

• Granta Design Limited (2009), Cambridge Engineering Selector

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