APPROVED: Reza Mirshams, Major Professor Seifollah Nasrazadani, Committee Member Nourredine Boubekri, Committee Member Enrique Barbieri, Chair of the Department

of Engineering Technology Costas Tsatsoulis, Dean of the College of

Engineering Victor Prybutok, Vice Provost of the

Toulouse Graduate School

KNOWLEDGE BASED SYSTEM AND DECISION MAKING METHODOLOGIES IN MATERIALS

SELECTION FOR AIRCRAFT CABIN METALLIC STRUCTURES

Pashupati Raj Adhikari

Thesis Prepared for the Degree of

MASTER OF SCIENCE

UNIVERSITY OF NORTH TEXAS

August 2016

Adhikari, Pashupati Raj. Knowledge Based System and Decision Making Methodologies in

Materials Selection for Aircraft Cabin Metallic Structures. Master of Science (Engineering

Technology-Mechanical Systems), August 2016, 64 pp., 15 figures, 24 tables, 27 numbered

references.

Materials selection processes have been the most important aspects in product design

and development. Knowledge-based system (KBS) and some of the methodologies used in the

materials selection for the design of aircraft cabin metallic structures are discussed. Overall

aircraft weight reduction means substantially less fuel consumption. Part of the solution to this

problem is to find a way to reduce overall weight of metallic structures inside the cabin. Among

various methodologies of materials selection using Multi Criterion Decision Making (MCDM)

techniques, a few of them are demonstrated with examples and the results are compared with

those obtained using Ashby’s approach in materials selection. Pre-defined constraint values,

mainly mechanical properties, are employed as relevant attributes in the process. Aluminum

alloys with high strength-to-weight ratio have been second- to-none in most of the aircraft

parts manufacturing. Magnesium alloys that are much lighter in weight as alternatives to the

Al-alloys currently in use in the structures are tested using the methodologies and ranked

results are compared. Each material attribute considered in the design are categorized as

benefit and non-benefit attribute. Using Ashby’s approach, material indices that are required

to be maximized for an optimum performance are determined, and materials are ranked

based on the average of consolidated indices ranking. Ranking results are compared for any

disparity among the methodologies.

Copyright 2016

by

Pashupati Raj Adhikari

ii

ACKNOWLEDGEMENTS

There are a number of individuals that are involved with my graduate studies and

preparation of this work that I am indebted to, but two of them have to be thanked the most

before the rest. It was my wife, Aarti, who always insisted that I get a graduate degree. Despite

all the difficulties in life that we had to go through together, her encouragement always pushed

me through the process and helped me get to this point in my academic career. Secondly, I would

like to thank my advisor Professor Reza Mirshams for his endless guidance and patience

throughout this study. I should also mention that he not only treated me as his graduate student,

but also as a guardian and always comforted me during my difficult times while being away from

my family. To these individuals, I will always be thankful.

I am especially thankful to Professor Seifollah Nasrazadani for his great sense of humor

that always made me smile every time I visited his office. I would like to thank Professor

Nourredine Boubekri for all his time in my efforts. His critiques on my writing has made me think

on a higher level and helped me be a better student researcher. I would also like to thank the

entire administrative team in the department for their help whenever I needed it.

Finally, I would like to thank my sister, Gyanu, for her great support throughout my life.

Every stage of my life up until now, she has always helped me with everything I have asked for

and supported me unconditionally. At last, but not the least, I am grateful to my dearest son,

Aarush Raj Adhikari, for his sacrifice in his young age while he had to live away from me for a very

long time due to my studies. He is the charm of my life and every time I think of him, it makes me

jump a foot higher.

iii

TABLE OF CONTENTS

ACKNOWELDGEMENTS……………………………………………………………….……………..……………………..….......iii

LIST OF FIGURES ...........................................................................................................................................viii

LIST OF TABLES ............................................................................................................................................. vi

CHAPTER 1: INTRODUCTION ................................................................................................................. .......1

CHAPTER 2: BACKGROUND AND MOTIVATION .................................................................................... .........6

CHAPTER 3: MATERIAL SELECTION STRATEGIES ................................................................................ ...........9

3.1 Material Attributes ..................................................................................................................... 10

3.1.1 Density……………………………………………. ......................................................... 11

3.1.2 Young’s Modulus ............................................................................................................. 12

3.1.3 Fracture Toughness ........................................................................................................... 13

3.1.4 Tensile Strength ................................................................................................................ 14

3.1.5 Yield Strength ................................................................................................................... 15

3.1.6 Cost………………………………………. ...................................................................... 16

3.2 Material Information Sources ..................................................................................................... 17

CHAPTER 4: METAL ALLOYS AND THEIR CLASSIFICATIONS ............................................................... .........19

4.1 Aluminum and Al-Alloys .............................................................................................................. 20

4.2 Effects of Processes in Al-Alloys to Their Mechanical Properties ............................................... 21

4.2.1 Quenching ......................................................................................................................... 21

4.2.2 Solution Heat Treatment ................................................................................................... 22

4.2.3 Strain Hardening ............................................................................................................... 23

4.3 Magnesium and Mg-Alloys ......................................................................................................... 24

CHAPTER 5: LITERATURE REVIEW AND MATERIAL SELECTION STRATEGIES ....................................... .......26

5.1 Graph Theory and Matrix Representation .................................................................................. 26

5.2 Analytical Hierarchy Process (AHP) ............................................................................................. 28

5.2.1 AHP Process ..................................................................................................................... 29

5.3 Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) .............................. 32

5.4 Ashby’s Charts ............................................................................................................................. 35

iv

5.4.1 Material Indices ................................................................................................................ 37

CHAPTER 6: RESULTS AND DISCUSSION ..................................................................................................... 41

6.1 Analytical Hierarchy Process ....................................................................................................... 43

6.2 TOPSIS ......................................................................................................................................... 48

6.3 Ashby’s Approach ....................................................................................................................... 52

6.4 Summary of Results .................................................................................................................... 56

CHAPTER 7: CONCLUSION AND RECOMMENDATION FOR FUTURE WORKS ................................... ..........59

7.1 Recommendations for Future Works.......................................................................................... 60

v

REFERENCES.................................................................................................................................62

LIST OF TABLES

Table 2.1: Comparison of some of the relevant material properties and processing

characteristics of Al, Mg, and Ti, alloys ………………………………………………………………...8

Table 3.1: Relative prices of various materials used in aircraft cabin metallic

structures products ………………………………………………………………………….…………….....16

Table 4.1: Group designation of aluminum alloys indicating principal alloying element……...20

Table 4.2: Thermal solution heat treatment Al alloy designation numbers ..…………….………...22

Table 5.1: Pairwise comparison scale of attribute or alternatives in AHP..…………..…….….…….30

Table 5.2: RI Values for consistency check….…………………………………………………………….………...31

Table-6.1: Table showing all the alternative material and relevant attributes for the

design along with numerical values of each attributes in non-normalized

standard units …………………………………………………………………………………………………....41

Table 6.2: Chemical composition of short-listed materials in material selection of

aircraft cabin metallic structures .…………………………….…………………………………………42

Table 6.3: Pairwise comparison matrix of all the attributes in the design along with

sum of each column………………………………………………………………………………………….…43

Table 6.4: Normalized comparison matrix with sum of each rows yielding Criteria

Weight matrix ……………………………………………………………………………………………..……..44

Table 6.5: Calculated values of Ws, W and {Cons} required to calculate CR….……………………...45

Table 6.6 Pairwise comparison matrix of all the alternatives with respect to density …………46

Table 6.7: Normalized comparison matrix with sum of each rows to showing the

priority each vector {Pi} of alternative material with respect to density….….….……46

vi

Table 6.8: Table showing the Final Rating Matrix with priority vector (Pi) of each

alternative material and criteria weights of each attribute ……………….………….….…47

Table 6.9: Material Suitability Index values of each alternative material and their

respective ranking …..……………………………………………………………………………………….…47

Table 6.10: Decision matrix with weighted values from 1 to 9 of each attribute for each

alternative………………………………………………………………………………………………………..…49

Table 6.11: Relative importance of attributes in the design of aircraft cabin metallic

structures………………………………………………………………………………………………………...…49

Table 6.12: Table showing the findings of positive ideal solution and negative ideal

solution……………………………………………………………………………………………………………....50

Table 6.13: Table showing the calculated separation measure values …………………………………..51

Table 6.14: Relative closeness values to the ideal solution of each alternative materials ….....51

Table 6.15: Table showing material index values of each indices and their individual

ranking yielding an ultimate average ranking……………………………………………….….….54

Table 6.16: Ranking of individual material based on each of each of the material indices....….55

Table 6.17: Table showing the ultimate ranking of materials using Ashby’s approach.…………..51

Table 6.18: Table comparing ranking of materials using Ashby’s approach,

TOPSIS, and AHP………………………………………………………..…………………………………….….55

vii

LIST OF FIGURES

Figure 1.1: Structure of the knowledge-based system [4] ........................................................... 1

Figure 1.2: A hierarchical structure for material classification with a schematic

of materials’ attribute records [6] ............................................................................. 4

Figure 3.1: Interrelations of design, materials, and processing to produce a product [12] ........ 9

Figure 3.2: Strength vs density plot showing strength-to-weight ratio for structural

material [26]............................................................................................................. 11

Figure 3.3: Stress-Strain curve with deformation taking place on a material ........................... 12

Figure 3.4: Three different modes of crack propagation and failure due to stress…………………14

Figure 3.5: A glimpse of GRANTA CES Edupack material selection tool showing Young’s s

modulus plotted against density. ............................................................................ 17

Figure 5.1: Material selection attributes graph [adapted from [15] ......................................... 27

Figure 5.2: Ashby's chart - Young's modulus (E) plotted against density (ρ) highlighting

alloy family [18] ........................................................................................................ 36

Figure 5.3: Ashby’s chart with Young’s modulus, E, plotted against cost, C, highlighting

alloy family and few other metal elements [18]…………………………………………………..37

Figure 5.4: Chart showing material index E/ρ describing the objective of stiffness at

minimum weight [6]................................................................................................. 39

Figure 6.1: A plot showing the AHP ranking of materials using based on their Material

Suitability Index values .......................................................................................... 48

Figure 6.2: Plot showing the ranking of materials based on their relative closeness to

ideal solution……………….. ......................................................................................... 52

Figure 6.3: A plot showing material ranking using new Optimized Ashby’s Method ................ 56

Figure 6.4: Plot showing rankings of alternative material compare with each other ............... 57

viii

CHAPTER 1

INTRODUCTION

In simple engineering designs, a design engineer can select materials easily from a

materials handbook. However, selecting materials for complex designs with respect to the

material properties using this approach alone is almost impossible. There has been significant

work done in developing a systematic procedure in material selection referred to as knowledge-

based system (KBS). KBS is one of the most important tools in material selection process in

engineering design, without a complete understanding of which it is impossible even to think of

a design. A knowledge base consists of rules and techniques for representing knowledge in the

structure. KBS is developed by collectively employing data and knowledge, where data is the

results of measurements and knowledge is connection between items of data [20], and is vital in

the process of materials selection. A general structure of KBS illustrated in Figure 1.1 explains

how users are interfaced with KBS to acquire enough knowledge about data to help select

materials in engineering design.

Figure 1.1: Structure of the knowledge-based system [adapted from 4]

1

Any engineering design problem always has more than one solution and the first one is

not always the best [11]. How the best of several feasible designs could be selected is a big

question. There may be multiple answers to this question, but optimization could probably be

the best. Optimization is the process of maximizing a desired quantity or outcome and minimizing

an undesired one. In another word, optimization is the process of finding the best answer to a

problem which is inherent in the design process. Optimization has been explained for decades by

various mathematical models. Dieter [11] explained how a simple model could be expressed for

an objective function which defines the value of the design in terms of independent variables.

For example, if x1, x2, x3… xn are n objective functions in a design which typically are the

constraints such as physical properties, cost, limitations, and other characteristics of materials

that are used, then Equation 1.1 gives the value of ‘U’, which is the function value to the

optimization problem.

),.....,,,( 321 nxxxxUU ------------------------------------------------------ (1.1)

These objective functions are subject to some constraints that come from physical laws,

limitations, and compatibility conditions on individual variables. Functional constraints Ψ, also

called equality constraints, specify relations as given in Equation 1.2 that must exist between the

variables.

)2.1(0),......,,,(

.

.

.

0),......,,,(

0),......,,,(

0),......,,,(

321

32133

32122

32111

nnn

n

n

n

xxxx

xxxx

xxxx

xxxx

2

A type of regional constraint that arises naturally in design situations is based on

specifications. Specifications are points of interaction with other parts of the system. Often a

specification results from an arbitrary decision to carry out a sub-optimization of the system.

According to J. N. Siddal [21], there are four methods of optimization:

(a) Optimization by evolution - An attempt to improve an existing design over time by

modifications of resulting variations is evolutionary optimization. This evolution could either

be technological or biological. Today’s aircrafts, automobiles, electronics, computing, and

very much everything is the result of this kind of optimization.

(b) Optimization by intuition - Intuition means the ability to understand something immediately,

without the need for conscious reasoning. Knowing what to do without knowing why one

does it is the perfect example of this method of optimization. Many optimized designs by

intuition are history. However, intuition still continues to play an important role in

optimization.

(c) Optimization by trial-and-error method - In this modeling, various design methods are

exercised for few iterations in the hope of finding an improved design. This method is the

direct result of an engineering assumption that the first design is not always the best. This

may not really be an optimization.

(d) Optimization by Numerical algorithm - Current active development in which mathematically

based strategies and tools are used to search for optimum results. This is the best and the

latest optimization method. Significant progress has been made under this methodology by

developing software tools and creating database collectively known as the knowledge-base.

3

While designing a product, one of the most intriguing challenges design engineers have

to come across is to get into thousands and thousands of materials to choose from that are

available. It is estimated that there are around 100,000 engineering materials [12]. Even with a

systematic algorithm of short-listing materials, the choices would still be enormous. It all starts

with a complete understanding of the material universe. A hierarchical structure for material

classification with a schematic of materials’ attribute records is given in Figure 1.2. Material

universe highlights family, class, sub-class, member, and attributes of materials. Metal family is

highlighted in the figure. Metal family has classes of metal that are either ferrous or non-ferrous

metals or their alloys such as aluminum alloys. Each aluminum alloy is further divided into sub-

class such as designated aluminum alloy group of 6xxx. This group is further divided into members

based on alloying element content and processing. At this point it is much easier to see the entire

attribute of this particular aluminum alloy coming all the way down from the enormous material

universe and decide on whether or not the attributes satisfy the design requirements.

Figure 1.2: A hierarchical structure for material classification with a schematic of materials’ attribute records [adapted from 6]

4

A similar hierarchical structure is also available that is based on material process rather

than material attributes. It may be easily noticed that no matter how much we talk about the

material world and its hierarchical structure, KBS comes into play everywhere, every time in

materials selection.

With often-changing demands from the airline companies with respect to low-cost and

higher efficiency, and FAA mandated safety challenges altogether add up to be great challenges

in design of aircraft cabin metallic structures. One main resource while selecting materials in a

design is to use a material property data table and narrow down the list of all feasible materials.

This process can only be executed efficiently and as desired with KBS in place.

5

CHAPTER 2

BACKGROUND AND MOTIVATION

During the ancient times, trial and error approaches were used to select materials in

engineering design and manufacturing processes. In the modern engineering world, with the

rapid increase in manufacturing and advancement in technology, specific algorithms and

methodologies are developed for material selection in product design and development.

Understanding of various physical, chemical, mechanical, and other properties that play a

significant role in materials selection process in a product design is highly essential.

Within the last several years, magnesium alloys have been considered as an alternative

to the use of aluminum alloys for some of the aircraft components. Currently most aircraft

components are made of aluminum alloys because of its superior quality and lower cost.

However, some manufacturers have gradually started to use some magnesium alloys in various

parts of aircraft components to reduce weight while maintaining strength-to-weight ratio. In

some cases, in recent years even composite materials have taken some space in the aircraft

components manufacturing. However, since composite materials are complex and there are

many uncertainties in mechanical properties for aerospace structural applications, FAA

certification has not yet been completely developed [19]. In particular, FAA and industries have

started testing different magnesium alloys in aircraft cabin structures to determine the feasibility

of its use in its parts manufacturing. The material selection process in designing and developing

aircraft cabin metallic structures is crucial in terms of fuel efficiency, flight efficiency, safety, and

environmental impact. As an example relevant to the aircraft cabin metallic structures, a typical

6

first class aircraft seat weighs about 24 pounds, or up to 44 pounds when it comes to business

class seat. Reducing seat weights even by a pound or two adds up to a great deal of aircraft weight

reduction, hence contributing in significant fuel cost saving. Aluminum, magnesium, and titanium

alloys are the lightest metal alloys. By developing a model to perfectly fit in the process of

materials selection for aircraft cabin metallic structures and implementing the use of these alloys

by optimization, the ultimate solution to the problem in this area could be achieved.

A number of techniques and algorithms have been developed and are in place to help

select materials for engineering design and manufacturing processes, the implementation of

which selection of right material is possible. Cost is a very important factor in this process.

Companies are constantly competing with one another towards reducing manufacturing cost

while maintaining quality and reliability of the product. A KBS is necessary in this process.

Computerized database of properties and KBS together with a proper optimization methodology

can be optimal in materials selection process.

A quick overview of a few feasible materials as alternatives to the currently used materials

in the aircraft cabin metallic structures is presented in Table 2.1. Young’s modulus, unit cost, and

density of three different possible candidate materials in the aircraft cabin metallic structures are

listed. Young’s modulus identifies how tough the material is and what kind of stress it can

withstand, unit cost determines the overall cost impact on the product, and density describes the

weight aspect of materials.

Magnesium is the lightest alloy, but its lower Young’s modulus and stiffness indicate its

low strength. Another shortfall of the magnesium alloys is that they are highly flammable in the

7

Table 2.1: Comparison of some of the relevant material properties and processing characteristics

of Al, Mg, and Ti alloys

case of fire in the cabin. In terms of strength-to-weight ratio, titanium alloys have the best

strength and stiffness, but their higher cost and more than doubled weight of the other two

makes it less desirable in the application.

8

CHAPTER 3

MATERIAL SELECTION STRATEGIES

Over the years, recognizing the significance of materials selection in engineering design,

researchers and engineers have constantly made extensive progress in developing tools that help

select the best materials for any given engineering design. Concurrent engineering is a team

based approach in which all aspects of the product development process are represented by a

closely communicating team [12]. This approach has been greatly facilitated by computer aided

engineering such as CAD and materials database.

Figure 3.1: Interrelations of design, materials, and processing to produce a product [adapted from 12]

Selecting the best material for a part requires more than choosing both a material that

has the properties to provide necessary performance in service and the processing method used

to create the finished part [12]. Figure 3.1 shows how materials, processing and design are

9

interrelated with each other. Faced with the large number of combinations of materials and

processes from which to choose, the materials selection task can only be done effectively by

applying simplification and systemization [12]. As design proceeds from concept design, to

configuration and parametric design also called embodiment design, and to detail design, the

materials and process selection becomes more detailed. At the concept level of design,

essentially all materials and processes are considered in broad detail. The materials selection

charts and methodology are highly appropriate at this stage. In the materials selection process,

design, materials, and processing go hand-in-hand. The right design leads to selecting the right

materials and the right materials help execute the right process. This cycle is valid in either

direction.

3.1 Material Attributes

In the materials selection process, the most important constraints are the material

attributes that are most desirable for a particular design. Material attributes say everything about

a particular material. Knowing different attribute values and how each value affects design

requirements, material selection process becomes much easier and effective. Any engineering

components have one or more functions to carry: to support a load, to contain a pressure, to

transmit heat and so forth [6]. For a component that requires light weight but high strength, a

material with low density and high tensile strength is considered. A material that has all the

desired characteristics but a single but highly unfavorable characteristic has to be easily

eliminated. Based on these tradeoffs, a design engineer must exercise optimization and use all

the techniques that can best provide the optimum outcome.

10

In the process of materials selection for any aircraft cabin metallic structures, design

engineers must comply with all the regulations that FAA has put in place. As given in appendix C

[19] and as part of the design requirement considered in this study, the following material

attributes are explained.

3.1.1 Density

The density of a material is given by its amount of mass per unit volume as represented

in Equation 3.1. Density of a material can differ with varying temperature and atmospheric

pressure.

ρ = m/V……………………………………...……………………………………………………. (3.1)

Where, m is mass of the material and V is the total volume. In aircraft cabin metallic structures,

unless unavoidable, materials with lower density are desired. In accordance with density of a

material, its strength is measured and a relative measurement between these two attributes are

used to calculate the strength-to-weight ratio. As a primary requirement among many others,

the objective in the design is to select materials with the highest strength-to-weight ratio.

Figure 3.2: Strength vs density plot showing strength-to-weight ratio for structural material [adapted from [26]

11

Strengths of potential structural materials for the aircraft cabin metallic structures with

different densities are shown in Figure 3.2. The best material for the design can be read from the

plot, and that is Al-alloys.

3.1.2 Young’s Modulus

Young's modulus, also known as elastic modulus, is a measure of the stiffness of an elastic

material and is a quantity used to characterize materials’ stiffness. It is defined as the ratio of the

stress (F/A-force per unit area) along an axis to the strain (∆L/L - ratio of deformation over initial

length) along that axis in the range of stress. A material with a higher Young’s modulus is stiffer

than a material with a lower Young’s modulus and resists deformation by bending or twisting to

a greater extent. Figure 3.3 shows the stress vs strain curve with various activities occurring

during the tensile test to measure Young’s modulus.

Figure 3.3: Stress-Strain curve with deformation taking place on a material due to stress [Adapted from 27]

Every material has a certain degree of elasticity. It is easier to see in elastic material but

rather hard in metals. This simply means that elastic materials have much less Young’s modulus

12

than hard metals. When a material is under stress, it starts deforming elastically. Once elastic

deformation region is complete, it deforms plastically. The point where this transition takes place

is called yield point and the stress is called yield strength. Strain is proportional to stress within

the elastic zone and that changes later. Among the materials used in the aircraft components,

some steel alloys and titanium alloys are used where maximum stiffness is required. However,

because of their higher density, use of aluminum alloys are preferred everywhere possible.

3.1.3 Fracture Toughness

Fracture toughness is a property which describes the ability of a material containing a

crack to resist fracture and is one of the most important properties of any material for many

design applications [12]. Engineering components are loaded under repeated loading conditions.

Under such conditions, also called fatigue loading, a crack nucleates, propagates, and cultivates

to a point where the material fails. To understand the mechanics behind it, it is useful to discuss

stress intensity factor given in Equation 3.2.

𝐾=𝑌𝜎√𝜋𝑎 ………………………………………………………………….. (3.2)

Where, K is the stress intensity factor, σ is the stress, and a is the crack length, while Y depends

on the geometry of the material. If we recall the point in stress-strain curve right before the

failure happens, where the stress intensity factor becomes critical, K becomes KC. This point also

gives materials fracture strength as well as the stress that the material was able to withstand

right before failure. Critical stress intensity factor, KC, in plain strain fracture is called fracture

toughness, K1C. In plain strain, fracture toughness is measured in three different modes of crack

propagation as given in Figure 3.4.

13

Between aluminum and magnesium alloys, aluminum alloys have higher fracture

toughness because of their higher stiffness. Titanium alloys have much higher fracture toughness

but are not often used in aircraft parts due to their higher density and exceedingly high cost.

Figure 3.4: Three different modes of crack propagation and failure [27]

3.1.4 Tensile Strength

The maximum stress a material withstands before failing is its ultimate tensile strength.

Ultimate tensile strength (UTS), often shortened to tensile strength (TS) or ultimate strength, is

the maximum stress that a material can withstand while being stretched or pulled before failing

or breaking. In the stress-strain curve, when a load is applied on a material, it is deformed

elastically and beyond yield point, and the material elongates uniformly and plastically. Upon

further cyclic loading on the material, it reaches a point where it can no longer withstand the

load and fails. The point where the material starts to enter in the failure region is in fact the

tensile strength of the material. One main difference between yield strength and tensile strength

14

is that yield strength is in the elastic region and tensile strength is in the plastic region before

failure.

Not surprisingly, materials used in aircraft components have high tensile strength.

Similarly as in the case of yield strength and fracture toughness, materials with higher yield

strength and higher fracture toughness are most likely to have higher tensile strength. Aluminum

alloys have very good tensile strength also compared to magnesium alloys. Titanium alloys have

much higher tensile strength than both aluminum and magnesium alloys, but due to cost and

density issues, those are not preferred.

3.1.5 Yield Strength

Yield strength or yield point of a material under stress is the point at which a material

begins to deform plastically. Prior to the yield point the material will deform elastically and will

return to its original shape when the applied stress is removed. In the stress-strain curve, when

a load is applied on a material, it stretches or compresses uniformly and suddenly starts to curve.

At this point, the material is said to have deformed plastically and the stress at transition between

elastic and plastic regions determine the yield strength of the material.

Materials used in aircraft components have high yield points. Materials with higher

stiffness and higher fracture toughness are most likely to have higher yield strength. Aluminum

alloys have very good yield strength compared to magnesium alloys and are superior in aircraft

part design. Titanium alloys have exceedingly high yield strength, but as mentioned earlier, they

are too costly and add unwanted weight in the aircraft. For that reason, titanium alloys are rarely

15

used in aircrafts unless unavoidable. Strain hardening as well as cold work is done on materials

to increase yield strength.

3.1.6 Cost

Cost is a critical factor in material selection. Although product design at an optimum level

with all the required characteristics is crucial, cost criteria cannot be left behind. Design engineers

should always find the material that is most cost effective keeping all the other requirements

non-negotiable. However, it is never a good exercise to select cheaper materials and compromise

other important characteristics directly related to safety and longevity. Market prices of

materials change very often. These changes are not often reflected in the standard material

database. That is why vendor quote is the ultimate accurate cost for that particular material.

Table 3.1: Relative prices of various material used in aircraft cabin metallic structures products

Cost information of materials is usually cross-referenced with normalized cost comparing one

with the unit cost of another. Price relative one material relative to another is helpful in

identifying the best candidate material with respect to cost. Price of a material compared to itself

is always one. Table 3.1 gives an overview of this cost comparison.

16

3.2 Material Information Sources

American Society for Metals (ASM) publishes volumes of materials information

periodically. This database is also available for students online through university libraries. These

handbooks are also called ASM handbooks and are available in different volumes. ASM

handbooks are the most reliable sources to obtain any information on engineering materials that

are widely used. Information provided in ASM hand books include each and every material’s

universal identifier called Unified Numbering System (UNS) number, complete chemical

composition with plots showing engineering application, mechanical properties, physical

properties, electrical properties, and fabrication characteristics.

Figure 3.5: A glimpse of GRANTA CES Edu pack material selection tool showing Young’s modulus plotted against density. All the material that lie on the line have the same strength-to-weight ratio [adapted from 27]

17

GRANTA Material Intelligence is a UK-based company founded by Michael F. Ashby in

collaboration with ASM. GRANTA has developed a material selection software with an entire ASM

handbook database. This software is applicable to all engineering areas such as aerospace,

manufacturing, automobile, and more. The secondary source of information on materials is the

material producing companies. This source of information is more accurate than ASM since they

have up-to-date cost information that ASM cannot update often. A glimpse of the software used

for the purpose of this study adapted from GRANTA website given in Figure 3.5 shows a glimpse

of this software with ready access data.

18

CHAPTER 4

METAL ALLOYS AND THEIR CLASSIFICATIONS

Metals are primarily classified as ferrous and non-ferrous. Ferrous metals contain iron

and are magnetic, while non-ferrous are free of iron content and are non-magnetic. Pure metals

in their original form are usually soft and cannot be used in engineering structures. When a

certain percentage of various metals are mixed with a primary metal, the form an alloy of that

metal. Properties of an alloy depend on the percentages of alloying elements added and

processes they undergo such as tempering, annealing, cold rolling, and others. Aluminum alloys,

stainless steel alloys, titanium alloys, and other metal alloys are used in various aircraft parts

depending on the performance need.

Metal alloys that are light weight and stiff are always preferred. Aluminum alloys are

mostly used in the aircraft parts including cabin metallic structures. Magnesium is the lightest

structural metal and abundantly available in nature, probably more than any other metal.

Magnesium has much less density than other metals but less stiffness. In terms of strength-to-

weight ratio, magnesium alloys compare almost equally to aluminum alloys. Use of magnesium

in the aircraft parts replacing Al alloys is still in discussion due to few unfavorable properties such

as flammability. Details on how aluminum alloys are classified and how their mechanical and

other properties differ with varying grade number in the alloy is given below. Some of the

magnesium alloys and their classification are also explained.

19

4.1 Aluminum and Al-Alloys

Commercially pure aluminum is a white lustrous metal which stands second in the scale

of malleability, sixth in ductility, and ranks high in its resistance to corrosion. Principal alloying

elements in aluminum alloys are copper, manganese, silicon, magnesium, and zinc, among which

copper shows more susceptibility to corrosion.

As a standard, aluminum alloys are designated with a 4-digit number. In the 2xxx to 8xxx

groups that are mostly used structurally, the first digit indicates the principal alloying element.

The second digit indicates specific alloy modification in terms of impurities. The last two digits in

the designation identify the different alloys in the group. Table 4.1 gives the summary of this

classification. In the 2xxx through 8xxx alloy groups, if the second digit is zero, it indicates the

original alloy, while digits 1 through 9 indicate alloy modifications with respect to impurities.

Table 4.1: Group designation of aluminum alloys indicating principal alloying element

Groups Principal alloying element

1xxx Al 99 percent or greater

2xxx Copper, Cu

3xxx Manganese, Mn

4xxx Silicon, Si

5xxx Magnesium, Mg

6xxx Magnesium and Silicon

7xxx Zinc, Zn

8xxx Other elements

9xxx Unused series

20

4.2 Effects of Processes in Al Alloys to Their Mechanical Properties

Aluminum can be obtained either in wrought or cast forms. Wrought aluminum alloys

suitable for rolling, drawing, or forging, while cast aluminum alloys are suitable for sand casting,

permanent mold, or die casting. In the wrought form, commercially pure aluminum is known as

1100 aluminum. It has a high degree of corrosion, is relatively low in strength, and does not have

properties that are required in aircraft parts manufacturing. While alloying gives the aluminum

some strength and improves properties, they must undergo different processes such as various

heat treatments, aging, and cold work. Nitriding is a process of diffusing nitrogen particles into

the alloy while heating in a furnace at about 10000F and adds significant strength to the alloy.

Some of the other heat treatment processes that are significant to give alloys the strength and

other properties that are required are outlined below.

4.2.1 Quenching

Aluminum alloys are heated at a critical temperature of about 10000F. The alloy is

quenched to prevent immediate re-precipitation. The quenching medium could vary depending

on part, alloy, and other properties desired. Some of the quenching methods are: cold water

quenching, hot water quenching, and spray quenching. In cold water quenching, the heated alloy

is suddenly dropped in room temperature water not exceeding 850F that keeps the temperature

rise under 200F ensuring maximum corrosion resistance. Hot water quenching minimizes

distortions and alleviates cracking which may be produced by the unequal temperatures

obtained during the quench. High velocity spray quench also minimizes distortions, but it also

increases resistance to corrosion.

21

4.2.2 Solution Heat Treatment

Alloys are heated at different temperatures and brought to solution treatment known as

solution heat treatment. Depending on the various characteristics requirement, they are either

artificially aged, naturally aged, cold worked, or sometimes a combination of them. Aluminum

alloys that are solution heat treated are designated with additional numbers followed by the

letter ‘T’ separated from the actual alloy designation number. For example, Al 2024-T4 means

2024 aluminum alloy that is solution heat treated and naturally aged.

Table 4.2. Thermal solution heat treatment Al alloy designation numbers

Thermal Treatment designation

Solution treatment

T651 Solution heat treated, stress relieved by stretching and artificially aged

T4 Solution heat-treated and naturally aged to a substantially stable condition

T6 Solution heat treated and artificially aged

T81 Solution heat treated, cold worked, and artificially aged

Different T numbers mean different types of thermal treatment. Some of the relevant

aluminum alloy thermal treatment designation are given with a description of solution heat

treatment in Table 4.2. In addition, T1 to T4 are designated for natural aging. T5, T6 and T9 are

designated for artificial aging. Similarly, T7 is designated for solution heat treated then stabilized.

T8 is for solution heat treated, cold worked, and artificially aged. Finally, T10 is designated for

22

cooled from an elevated temperature, artificially aged, and then cold worked. While T651 is for

stress relieved by stretching, T652 is for stress relieved by compressing.

4.2.3 Strain Hardening

Strain hardening, work hardening, or strengthening of metal is a process by which an alloy

is deformed plastically. When a material is under stress, it goes through two types of

deformation. The first is called elastic deformation in which the material under stress returns to

its original shape after the load is removed. When a force is applied on the material at a certain

direction, the atoms in the crystal are moved from their normal position to that direction. When

the force is removed, the atoms return back to their original position. This phenomenon is called

elastic deformation and no property changes occur on the material. Unlike elastic deformation,

if the force is constantly applied beyond elastic deformation, the material yield, and cannot

return to its original shape. This phenomenon is called plastic deformation and material

properties change significantly. Basic understanding of these phenomena can be explained by

using Figure 3.3.

Properties such as tensile strength cause material hardness to increase significantly,

giving metal a much better strength for structural applications. Strain hardening involves

processes such as hammering, bending, stretching, and deformation upon applied force. Results

from strain hardening are often comparable to that from heat treatments. Therefore, it is cost

effective to apply this method to process alloys for better performances.

23

4.3 Magnesium and Mg-Alloys

Magnesium is the world’s lightest structural metal. It is a silvery white in color and weighs

roughly two-thirds as much as aluminum. Magnesium does not possess sufficient stiffness for

structural application, but when alloyed with zinc, aluminum, and manganese it produces an alloy

having almost a similar strength-to-weight ratio to that of most of the aluminum alloys. Another

positive side of this metal is that it is abundantly found in nature. Despite long-going discussion

on Mg-alloy application in aircraft parts, some of today’s aircrafts use a significant amount of mg-

alloys in their structures such as nose wheel doors, flap cover skin, flooring, and more

contributing huge weight reduction of the aircraft.

Magnesium alloys are grouped and identified much differently than aluminum alloys.

However, there is not a specific standard in designating magnesium-alloys. Different magnesium

alloys producing companies set their own standard for various alloys. Normally, the first letters

followed by Mg represent symbols of alloying elements and numbers that follow represent

percentage of each of the alloying elements respectively. Anything after is designated for various

heat and cold treatment processes similar to that applied in aluminum alloys. For example, Mg

AZ31B represents magnesium alloy with three percent of aluminum and one percent of zinc. The

letter B that follows represents other characteristics of the alloy set by the producing company.

Magnesium alloys are processed to alter properties for better performance using

methods such as annealing, quenching solution heat treatment, aging, and stabilizing, most of

which have already been discussed in the previous section. Sheet and plate magnesium are

annealed at the rolling mill. The solution heat treatment is used to put as much of the alloying

24

ingredients as possible into a solid solution, which results in high tensile strength and maximum

ductility. Aging is applied to casting following heat treatment, where maximum hardness and

yield strength are desired.

Magnesium alloys embody fire hazards of an unpredictable nature. When in large

sections, its high thermal conductivity makes it difficult to ignite and prevents it from burning. It

will not burn until it reaches 12040F. However, Mg chips and fine dust are ignited easily. These

are some of the reasons why there is still discussion among FAA regulators, engineers, scientists,

and of course industries.

25

CHAPTER 5

LITERATURE REVIEW AND MATERIAL SELECTION STRATEGIES

Design engineers and decision makers use various methodologies available to decide

which material to choose among a number of feasible alternatives. In the course of engineering

research, engineers have developed quite a few new methodologies in the last several years.

Analytical Hierarchy Process (AHP) is widely used to make a pairwise comparison in decision

making. This technique was first developed by T.L. Satty [3] in 1980.

Selection of materials is always governed by its attributes and manufacturing processes

[12]. There are two different approaches to material selection. First is the material first approach.

In this approach the design engineer selects materials based on material class and narrows it

down as previously described. Second is the process-first approach. In this approach the design

engineer selects materials based on the manufacturing process. At the end, regardless of the

type of approach, the material selection process ends at the same conclusion. Material first

approach is used for the purpose of this study. Materials are short-listed based on their attribute

rather than their processing governance. The following sub-sections discuss various literatures

reviewed in the course of this study, mostly in the area of material selection and decision making

and step-by-step explanation of some of the methodologies that follow.

5.1 Graph Theory and Matrix Representation

A graph is a nonempty finite set of nodes V along with a set D of 2 - element subsets of V.

The elements of V are called vertices and elements of D are called edges. Study of such graphs to

26

solve mathematical problems is graph theory. Graph theory is a logical and systematic approach.

The advanced theory of graphs and its applications is widely used in mathematics. Material

selection factors graph models the material selection factors and their interrelationship. Rao [15]

explains that this graph consists of a set of nodes V = {vi}, with i=1, 2, . . ., N and a set of directed

edges D= {dij}. A node ni represents ith material selection factors, and edges represent the relative

importance among the factors. The number of nodes N considered is equal to the number of

material selection factors considered. If a node ‘i’ has relative importance over another node ‘j’

in the material selection, then a directed edge or an arrow is drawn from node i to node j

represented by dij. If ‘j’ has relative importance over ‘i’, then a directed edge or arrow is drawn

from node j to node i represented by dji. A visual representation of this theory is given in Figure

5.1 and considers six attributes to compare.

Figure 5.1: Material selection attributes graph [adapted from 15]

27

While comparing one attribute to the other, design engineers make their best judgement

to decide the relative importance of one attribute to the other. In the real world each attribute

is somehow important to the other, and therefore arrows are drawn from each node to the other

for all. The fact is that if relative importance of node 1 to 6 is dij, the relative importance of node

6 to 1 is 1/dij. When the number of attributes represented in nodes increases, it is harder to follow

this technique. In such a case, similar representation is translated into matrix representation. In

this matrix of size MxM where M is the number of attributes to be represented, a pairwise

comparison is performed. This process will later be explained in Section - 5.2.1 with reference to

Equation 5.1.

5.2 Analytical Hierarchy Process (AHP)

AHP is a problem solving methodology for making a choice from a set of feasible

alternatives when the selection criteria represent multiple objectives. This method is widely used

in multiple areas to solve decision making problems. An AHP hierarchy can have as many levels

as needed to fully characterize a particular decision situation. A number of functional

characteristics make AHP a useful methodology. These include the ability to handle decision

situations involving subjective judgements, multiple decision makers, and the ability to provide

measures of consistency of preferences [7]. AHP is built on principles and axioms such as top-

down decomposition and reciprocity of paired comparisons that enforces consistency

throughout an entire set of alternative comparisons [12]. This method is based on matrix theory

where a pairwise comparison of an attribute or an alternative is made by creating a square

28

matrix. An important property of these matrices is that the principle eigenvector of these

matrices can generate legitimate weighting factors [12].

5.2.1 AHP Process

AHP leads a design team through the calculation of weighing factors for decision criteria

for one level of the hierarchy at a time. AHP also defines a pairwise comparison-based method

for determining relative ratings for the degree to which each of a set of options fulfills each of

the criteria [2]. AHP’s application to the engineering design selection task requires that the

decision maker first create a hierarchy of the selection criteria. This process starts with creating

a matrix A of size MxM where M is the number of attributes or the alternatives depending on

what is being compared. The size of this matrix increases with the increase in the number of

attributes as well as the number of alternatives. Each element in the matrix is denoted by rij,

which means that attribute i is compared with attribute j. An attribute compared to itself is 1.

That is if rij = 1 when i=j and rji = 1/rij. For example, if the importance of attribute i to j is p, then

the importance of attribute j to i is its reciprocal, 1/p. The overview of the matrix A of size MxM

is given in Equation 5.1 [8].

29

In this matrix, values of all the diagonal elements are 1 and the rest are either rij or 1/rji.

Table 5.1 presents the relative importance scale used in AHP. If the number of attributes are

large, values in between can also be assigned. This definition of degree of importance varies from

one literature to another. Some of researchers have considered decimal values from 0.115 to

0.895 and numbers in between with equal intervals. The following steps are taken to complete

the AHP process:

Table 5.1: Pairwise comparison scale of attribute or alternatives in AHP

Step-1: A criteria comparison matrix [C] is created using ratings from Table 5.1.

Step-2: Matrix [C] is normalized by dividing each element in the matrix by sum of each column.

This gives a new matrix [Norm C].

Step-3: Each row of [Norm C] is averaged. This gives criteria weight vector {W}.

Step-4: A consistency check on comparison matrix [C] is performed by calculating the Consistency

Ratio (CR). CR checks the consistency of the comparison matrix values assigned by the decision

maker. If this value is within a limit, the criteria comparison matrix [C] is considered consistent

and criteria weight {W} is valid. Otherwise, the decision maker has to go back to [C] and adjust

the values.

Additional steps to perform the consistency check by calculating CR are given as follows [12]:

a) Calculate the weighted sum vector, {Ws} = [C] x {W}.

Definition

Equally Important

Moderately more Important

Strongly more important

Very strongly important

extremely important

Degree of Importance

1

3

5

7

9

30

b) Calculate the consistency vector, {Cons} = {Ws} / {W}.

c) Estimate Eigen value λ of the unit matrix given by [C]. This is the average value of {Cons}. In

matrix theory, the Eigen values are a set of scaler quantities associated with a linear system of

a matrix equation also known as characteristic roots. For any nth order polynomial, there are

n number of characteristic roots. The largest of these roots is called the maximum Eigen value

of the matrix and is represented with λmax. In AHP this value is the average of consistency

vector {Cons}.

d) Evaluate the consistency index value. Equation 5.2 is used to calculate the CI value.

𝐶𝐼 =(𝜆−𝑛)

(𝑛−1) ; -------------------------------------------------------------------- (5.2)

Where n is the number of attributes or alternatives compared.

e) Determine the Random Index (RI) value. The RI values are the consistency index values for

randomly generated versions of [C]. These values for different n are given in Table 5.2. This

table was first developed by S. L. Satty [3].

Table 5.2: RI Values for Consistency Check

1.57

1.49

12

13

14

15

1.51

1.54

1.56

1.57

11

0.00

0.00

0.52

0.89

1.11

1.25

1.35

1.40

1.45

5

6

7

8

9

10

Number of Criteria RI Values

1

2

3

4

31

f) Calculate the CR = CI / RI. This value must be within 10 percent of the total index of 1 to ensure

that the comparison matrix [C] constructed by the decision maker is more consistent than the

randomly populated matrix with values from 1 to 9. CR value under 0.1 is a green signal to

proceed with the AHP process and criteria weights {W} for the attributes are accounted.

This process is repeated for each alternative with respect to each attribute. Size of the

alternative comparison matrix is based on the number of alternatives. Since one alternative is

compared with respect to each attribute, this becomes a lengthy process and yet relatively

simple. Each comparison matrix corresponding to each attribute gives design alternative priority

vector {Pi}. Design alternative priority vector with respect to each attribute gives a matrix called

final rating matrix [FRating]. [FRating] is transposed and matrix multiplication between [FRating]T

and criteria weight vector {W} is performed. This multiplication results into consolidated scores

for each of the alternatives called material suitability index (MSI). The material with the highest

MSI is the best material.

5.3 Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS)

Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is a Multi

Criteria Decision Making problem solving technique and was first developed by Hwang and Yoon

[1]. This method is based on the concept that the best alternative to a problem from a set of

available options will have the shortest Euclidean distance from the positive ideal solution (PIS)

and farthest from the negative ideal solution (NIS). Euclidean distance between two points p and

q is defined as the length of the line segment connecting the points. In two dimensional

measurement, this distance between the points is the absolute value of their numerical

32

difference. However, if the number of dimension for Euclidean space is n, then Equation 5.3 can

be used to calculate the distance.

𝑑 = √(𝑝1 − 𝑞1)2 + (𝑝2 − 𝑞2)2 + (𝑝3 − 𝑞3)2 + ⋯ … … + (𝑝𝑛 − 𝑞𝑛)2 -------------------- (5.3)

The PIS is the hypothetical solution for which all attribute values correspond to the

maximum attribute values comprising the satisfying solution, and NIS is the hypothetical solution

for which all attribute values correspond to the minimum attribute values comprising the

satisfying solution. TOPSIS thus gives a solution that is not only closest to the hypothetically best,

but also farthest from the hypothetically worst [2].

The basic steps in TOPSIS that are taken for the selection of the best material from the

set of short-listed materials are given as follows:

Step-1: Material selection attributes for the given engineering application are

determined, and materials are short-listed on the basis of the identified attributes satisfying the

requirements. Weighted decision matrix is created by assigning weights in the scale from 1 to 9

with only odd numbers to each of the materials with respect to each attribute based on a

material’s actual property value. For a benefit criteria, material with the highest attribute value

receives the highest rating and material with the least attribute value receives the lowest rating.

The opposite is true for the cost criteria. A matrix based table of size i x j where i is the number

of short-listed materials and j is the number of attributes is created with corresponding values of

each attribute for each alternative. Each element mij in the table represents the weighted value

of jth attribute for the ith alternative. It is important to recognize that the rating system can vary

33

from one decision maker to another. Some consider whole even numbers from 2 to 10 and some

even consider decimal values from 0.115 to 0.955.

Step-2: Euclidean distance from each of the elements in the rows to the origin is

calculated using Equation 5.3. Normalized decision matrix Rij is obtained using Equation (5.4). The

term in the denominator is simpy the Euclidean distance that has already been calculated.

𝑅𝑖𝑗 =𝑚𝑖𝑗

[∑ 𝑚𝑖𝑗2𝑚

𝑗=1 ]1/2 -------------------------------------------------------- (5.4)

Step-3: Next, weights of each attributes for the given application wj, are determined using

AHP. In this assignment, either actual weighted values from AHP or corresponding even numbers

from 2 to 10 can be used. A weighted normalized matrix Vij is obtained by multiplying wj by Rij.

This allows to determine the Positive Ideal Solution (PIS) and negative Ideal Solution (NIS) to the

given problem. The PIS is a set of the highest values for each attributes in the weighted

normalized matrix and NIS is a set of the smallest values of each attributes in the weighted

normalized matrix. These sets of values are represented by the expression given in Equation 5.5.

Vi+ = {V1

+, V2+, V3

+, ………., VM+}

Vi- = {V1

-, V2-, V3

- , ……..…, VM-} ----------------------------------------- (5.5)

It may be added that PIS is a set of the smallest values of cost criteria and highest values

of benefit criteria in the weighted normalized matrix. In the case of NIS, that would be just the

opposite.

34

Step-4: Once the positive and negative ideal solutions are obtained, positive separation

measure (Si+) and negative separation measure (Si

-) are calculated for each alternatives, once

again using Euclidean distance as expressed by Equation 5.6.

𝑆𝑖+ = {∑ (𝑉𝑖𝑗 − 𝑉𝑗

+)2𝑀

𝑗=1 }(

1

2)

, 𝑖 = 1,2,3, … , 𝑁

𝑆𝑖− = {∑ (𝑉𝑖𝑗 − 𝑉𝑗

−)2𝑀

𝑗=1 }(

1

2)

, 𝑖 = 1,2,3, … , 𝑁 -------------------------------------- (5.6)

Step-5: Finally, the relative closeness of a particular alternative to the ideal solution, Pi is

calculated using the expression given in equation 5.7.

𝑃𝑖 =𝑆𝑖

−

(𝑆𝑖++ 𝑆𝑖

−) -------------------------------------------------------------------------------- (5.7)

All the values of Pi are ranked in descending order: the alternative on the top is the best material

and the value at the bottom is the worst material among the ones short-listed for the application.

Pi value is sometimes also referred to as the performance score of alternative Ai.

5.4 Ashby’s Charts

Materials selection in engineering design is solely governed by material properties that

we consider for the design. Materials are selected based on how each material performs with

respect to their relevant properties satisfying the design requirements. It is seldom the case that

performance of a component depends on just one property. It is almost always a combination of

properties that matter [5]. This gives an idea of plotting one property against the other in a chart

for a range of materials. Michael F. Ashby [5, 6, 18] created such charts, which are called Ashby’s

charts after his name. These charts include range of materials in the material universe and

35

contain a large body of information and correlate one property to the other for any material of

interest.

Figure 5.2 shows an example of Ashby’s chart showing Young’s modulus, E, plotted

against density, ρ [18]. As mentioned earlier in the introduction section, metal alloys of

magnesium, aluminum, and titanium are highlighted in the figure and Young’s modulus of each

is compared with their density. It is visually clear that magnesium alloy is the lightest of the three

but has the least stiffness, while titanium has the most stiffness but is the heaviest of the three.

It could be very much appreciated from the plot alone that aluminum alloy could be the optimum

metal alloy for a design that needs to be lighter and at the same time has a very good stiffness.

Figure 5.2: Ashby's chart - Young's modulus (E) plotted against density (ρ) highlighting [adapted from 18]

36

Another similar plot is presented in Figure 5.3, comparing Young’s modulus against

material cost [18]. While selecting materials, cost is one of the critical factors since companies

are always looking to cut overall production cost without compensating other important factors.

Referring back to the Table 2.1, comparison among magnesium, aluminum, and titanium alloys

this time with respect to cost, it is clear that aluminum costs the least of all. In this regard,

combination of such plots involving all relevant material properties satisfying the design

requirements can very well predict the best material alternative among the short-listed

materials.

Figure 5.3: Ashby’s chart with Young’s modulus, E, plotted against cost, C, highlighting alloy [adapted from 18]

5.4.1 Material Indices

A material index is a combination of material properties which characterizes the

performance of a material in a given application [5]. The design of a structural element is

37

specified by three things: the functional requirements, the geometry, and the properties of the

material of which it is made. The performance of the element is described by an expression of

the form given in Equation 5.8.

𝑝 = 𝑓 [

(𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡𝑠, 𝐹),(𝐺𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟𝑠, 𝐺),

(𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝑃𝑟𝑜𝑝𝑒𝑟𝑡𝑖𝑒𝑠, 𝑀)]

𝑝 = 𝑓(𝑓, 𝐺, 𝑀) ---------------------------------------------------------------- (5.8)

Where, 𝑃 describes some aspect of the performance of the component: its mass, or volume, or

cost, of life for example; and f means a function of optimum design. Therefore the above

equation can be further written in the form given in Equation 5.9.

𝑝 = 𝑓1(𝐹)𝑓2(𝐺)𝑓3(𝑀) ---------------------------------------------------------- (5.9)

Where, 𝑓1, 𝑓2, 𝑓3 are separate functions which are simply multiplied together.

In an engineering design, a material property alone does not explicitly explain the

performance of a component. It is often a combination of two or even more that best describe

the performance, hence allowing the design engineer to best select the material meeting the

requirements. Among material attributes that are considered for the design, a higher value of

some of them is desired, and therefore such attributes are called benefit attributes. On the other

hand, a smaller value of some of the attributes is desired, and therefore such attributes are called

non-benefit attributes. For a design that requires a material with lighter weight and higher

strength, a material with higher strength-to-weight ratio, that is a material with lower density

and higher Young’s modulus is preferred. Since smaller value of density is desired, it called a non-

benefit attribute. Similarly, since a higher value of Young’s modulus is desired, it is called benefit

attribute. Together both Young’s modulus, E, and density, ρ, yield a material index for that

38

particular material given as E/ρ. Any particular index for a given material is a constant number as

given in Equation 5.10. Maximizing the value of this index maximizes stiffness at a minimum

weight as an objective for the design. For a particular material,

𝐸

𝜌= 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 (𝐶) … … … … … … … … … … … … … … … … … … … … (5.10)

Taking logs on both sides, Equation 5.10 can be written in the form of expression given in

Equation 5.11.

log(𝐸) = log(𝜌) + log (𝐶) … … … … … … … … … . … … … … … … … (5.11)

Figure 5.4: Chart showing material index E/ρ describing the objective of stiffness at minimum weight [adapted from 6]

39

This is an equation of a straight line of slope one on a plot of log(𝐸) against log(𝜌). Figure 5.4

shows a plot of E against ρ in log-log scale describing the objective of stiffness at a minimum

weight at a different level.

A grid of lines corresponding to values of E/ρ from 0.1 to 10 in units of GPa / (Mg.m-3) are

shown in the figure. It is now easy to read the subset of materials that maximize performances,

meaning that they have the highest values of E/ρ. All the materials that lie on a line of constant

E/ρ perform equally well as light, stiff components, those above the line perform better, and

those below the line perform less. A material with the value of E/ρ = 10 in these units gives a

component with one tenth the weight for a given stiffness of a material with the value of E/ρ = 1.

40

CHAPTER 6

RESULTS AND DISCUSSION

After reviewing previous works carried out in the area of materials selection as part of the

literature review, several methodologies of materials selection are taken into consideration for

the application. Some of the methodologies reviewed were: compromised ranking method

proposed by Rao [17], graph theory and matrix approach proposed by Rao [15], analytical

hierarchical process (AHP) proposed by Satty [3], and technique for order of preference by

similarity to ideal solution (TOPSIS) proposed by Hwang and Yoon [1]. Most of these

methodologies have been briefly discussed in the literature review section of this report. Two of

the methodologies studied, AHP and TOPSIS, are used to perform MCDM on a set of short-listed

materials in the design of certain aircraft cabin metallic structure. These materials are given in

Table 6.1 with their respective attribute values that are also considered in the design as

requirements.

Table 6.1: Table showing all the alternative materials and relevant attributes for the design along with numerical values of each attributes in non-normalized standard units

41

Among the materials short-listed, Al 7075-T651 and Al 2024-T4 are currently being used

by industries in aircraft cabin metallic structures. Al 2024-T6 and Al 2024-T81 are short-listed as

alternative materials to potentially replace the ones currently in use. Pair of magnesium alloys,

Mg AZ31B and Mg AZ61A are short-listed based on their high strength-to-weight ratio,

competitive Young’s modulus, and much lower density. Magnesium alloys are short-listed also

because of the fact that there has been a long-going discussion regarding use of these alloys in

the aircraft parts as part of the overall aircraft weight reduction agenda. It would be interesting

to see where in the ranking these materials would stand and if in fact there is any feasibility of

these alloys to substitute the use of aluminum alloys.

In addition to the attribute values of each material short-listed for the study, their

chemical composition are given in Table 6.2. How metal alloys are designated with a group and

sub-group and what each letter means at the end of the alloy numbers has been discussed in the

previous chapter.

Table 6.2: Chemical composition of short-listed materials in the materials selection of aircraft cabin metallic structure

Besides, Al 7075-T651 is solution heat treated, artificially aged with stress relieved by

stretching. Al 2024-T4 is solution heat treated and naturally aged. Al 2024-T6 is solution heat

treated and artificially aged. Al 2024-T81 is solution heat treated, cold worked, and artificially

Al Cr Cu Fe Mg Mn Si Ti Zn Zr Ni Ca Others

Al 7075-T651 89.750 0.230 1.100 0.250 1.250 0.150 0.200 0.100 5.600 0.025 x x 0.075

Al 2024-T4 92.700 0.050 4.350 0.250 0.750 0.600 0.250 0.075 0.125 0.025 x x 0.075

Al 2024-T6 92.700 0.050 4.350 0.250 0.750 0.600 0.250 0.075 0.125 0.025 x x 0.075

Al 2024-T81 92.700 0.050 4.350 0.250 0.750 0.600 0.250 0.075 0.125 0.025 x x 0.075

Mg AZ31B 3.000 x 0.025 0.003 95.150 0.600 0.050 x 0.100 x 0.003 0.020 0.150

Mg AZ61A 6.500 x 0.003 0.003 92.000 0.325 0.050 x 0.950 x 0.003 x 0.150

MaterialsChemical composition by percentage

42

aged. Mg AZ31B is solution heat treated, stress relieved at 149oC form 30 minutes, and air cooled.

Finally, Mg AZ61A is solution heat treated and artificially aged.

6.1 Analytical Hierarchy Process

Analytical Hierarchy Process (AHP) is used to select material. The basic requirements are

that the materials must be light weight and cost effective as cost criteria. Unlike cost criteria,

materials must have high Young’s modulus, high yield strength, high tensile strength, and high

fracture strength as benefit criteria. Table 6.1 displays the non-normalized numerical values with

respective units of all the attributes for short-listed materials

A pairwise comparison between one attribute to another is performed. Weights are

assigned on the basis of degree of relative importance scale given in Table 5.1, and a criteria

comparison matrix [C] is created as given in Table 6.3. An attribute compared to itself is always

one. Yield strength compared to density is given slightly more importance. Even though density

is an important attribute in the design, yield strength of the material cannot be compromised for

the lighter weight due to components’ safety reasons. A similar argument applies to the cost. No

matter how important it is to reduce production cost, it can never be compromised with

mechanical properties whose higher values are always desired.

Table 6.3: Pairwise comparison matrix of all the attributes in the design with sum of each column.

43

It is sometimes harder to perform pairwise comparison among the mechanical properties

of the materials. In such situations, one has to decide whether the components require a better

fracture toughness or tensile strength and so forth.

Criteria comparison matrix is normalized by dividing each element in the matrix with its

respective column total called normalized weighted matrix [Norm C] and is given in Table 6.4.

The average of each rows gives the criteria weight vector {W} for each attribute in the design.

According to {W}, Young’s modulus is the most important criterion. Fracture toughness, Yield

strength, tensile strength, and density follow Young’s modulus in the order, while cost turns out

to be the least important.

Table 6.4: Normalized comparison matrix with sum of each rows yielding Criteria Weight Vector

Criteria weight vector {W} describes the individual weights of each attribute affecting the

design. A consistency check is performed to ensure the consistency in pairwise comparison in the

criteria comparison matrix [C]. This process has been explained in the previous chapter and

results are given below.

Weighted sum vector is calculated as {Ws} = [C] {W}. To do this, a vector multiplication

between the criteria comparison matrix [C] and criteria weight matrix {W} is performed. This is

44

the sum of the product of each row in [C] and column in {W}. This provides the weight sum vector

{Ws}. Consistency vector {Cons} is determined by multiplying {Ws} with the reciprocal of {W}.

Combined results of these calculations are given in Table 6.5. Average value of the consistency

vector {Cons} is calculated to be 6.53 and is called the Eigen value of the matrix. Consistency

Index (CI) is calculated using Equation 5.2 and is 0.106793, where n is the number of attributes.

Random Index (RI) value of 1.25 for n = 6 is obtained from Table 5.2. Finally CR is calculated to be

0.0854, which is less than 0.1, meaning the consistency is greater than 90 percent and is

acceptable for the process. This indicates the pairwise comparison weights assigned by the

decision maker are consistent, and the process may proceed. Once CR in the matrix is checked

for consistency, the criteria weights vector {W} for the attributes is finalized.

Table 6.5: Calculated values of Ws, W and {Cons} required to calculate CR

This process is repeated for each alternative material with respect to each attribute. This

is called alternative comparison with respect to each individual attribute. Since there are six

attributes, six additional such comparison matrices are created based on each material’s actual

attribute values. Each alternative material’s priority vectors {Pi} are obtained. As an illustration,

material-to-material comparison is performed with respect to density as given in Table 6.6.

Symbols Ws W Consistency

ρ 0.3474 0.06 6.20

σy 0.9580 0.14 6.68

σF 0.5647 0.09 6.17

E 3.1357 0.46 6.83

Fracture Toughness (MPa√m) K1C 1.5769 0.22 7.16

C 0.1821 0.03 6.16

Yield Strength (MPa)

Tensile Strength (MPa)

Young's Modulus (MPa)

Price (USD/Kg)

Attributes

Density (gm/c^3)

45

Table 6.6: Pairwise alternatives comparison matrix with respect to density

Using a similar approach as in the criteria comparison, the above matrix is normalized by

dividing each element by column total. Average of each row is the material alternative priority

vector {Pi} with respect to density. Calculation of priority vector with respect to density is given

in Table 6.7. Similar priority vectors for each alternative with respect to each attribute are

calculated, and a new Final Rating Matrix [FRating] is produced. As a precaution, consistency

check was performed on each of the alternative materials and verified that the CRs in each of the

comparisons was below 0.1, allowing the AHP process to continue.

Table 6.7: Normalized comparison matrix with sum of each rows to showing the priority vector {Pi} of each

alternative material with respect to density

Final Rating Matrix [FRating] for each alternative material with respect to every attribute

is given in Table 6.8. Matrix multiplication between final rating matrix, [FRating] and criteria

46

weight vector {W} is performed. This multiplication results in individual consolidated scores for

each alternative material called material suitability index (MSI). Material with the highest MSI is

the best material. Matrix multiplication resulting into MSI is given in Table 6.9. Each material is

ranked based on MSI, and the result is presented in a plot given in Figure 6.1.

Table 6.8: Table showing the Final Rating Matrix with priority vector (Pi) of each alternative material and criteria

weight vector of each attribute previously calculated

Table 6.9: Material Suitability Index values of each alternative

material and their respective ranking

Materials Material Suitability Index Ranking

AL 7075-T651 0.1375 4

AL 2024-T4 0.2481 2

AL 2024-T6 0.2431 3

AL 2024-T81 0.2524 1

Mg AZ31B 0.0628 5

Mg AZ61A 0.0561 6

47

Figure 6.1: A plot showing the AHP ranking of materials using based on their material suitability index

Using AHP, it is determined that Al 2024-T81 is the best material of all. It is also evident

that regardless of their much lighter weight, both magnesium alloys are not suitable for the

design. Results that are so far produced and illustrated in this study could slightly vary from one

decision maker to another.

6.2 TOPSIS

Weighted decision matrix is created by weighing the materials given in Table 6.1 in the

scale of 1 to 9. Lower values of cost criteria receive higher ratings, and lower values of benefit

criteria receive lower ratings. Rating Scale can vary from one decision maker to another.

Euclidean distance is calculated from each element in the rows to the origin using Equation 5.3.

Weighted decision matrix with each attribute’s Euclidean distance to the origin with respect to

alternative materials is given in Table 6.10.

0

1

2

3

4

5

6

7

AL 7075-T651 AL 2024-T4 AL 2024-T6 AL 2024-T81 Mg AZ31B Mg AZ61A

Ran

kin

g

Material

Material Ranking - AHP

48

Table 6.10: Decision matrix with weighted values from 1 to 9 of each attribute for each alternative

Weighted decision matrix is normalized by dividing each of its element by respective

Euclidean distances using Equation 5.4. At this time, each attribute needs to be given weight

based on their respective importance in the design. To execute this assignment, each attribute is

weighted in the scale from 2 to 10 with only even numbers. In order to be consistent with

weighing on attributes, AHP can be exercised to determine the weight. Criteria weight vector {W}

that was calculated in the previous section is used for this purpose. Based on the actual weights

in {W}, ratings from 2 to 10 could be assigned. It is critical to know that this rating scale could

very well be different from one decision maker to another.

Table 6.11: Table showing summary of normalized matrix with weighted attributes based on criteria

weight vector obtained from AHP

49

It might sometimes be confusing to see different norms in rating scale. However, as long

as a single set of rating scale is used to weigh a matrix, results should remain the same. Since

Young’s modulus has the most weight in {W}, it receives 10, while cost receives only 2 for its poor

weight in the vector {W}. A table with summary of normalized matrix with weighted attributes is

given in Table 6.11.

Each element in the normalized decision matrix is multiplied with the rated weighted

attributes. This results in weighted normalized decision matrix. Weighted normalized decision

matrix is given in Table 6.12. A set of lower values of cost criteria and higher values of benefit

criteria from each row gives the PIS. Similarly, a set of higher values of cost criteria and lower

values of benefit criteria from each row gives the NIS. Table 6.12 also summarizes the PIS and the

NIS.

Table 6.12: Weighted normalized decision matrix showing the findings of PIS and NIS

Using Equation 5.6, both positive and negative separation measures from weighted

normalized decision matrix are calculated. The sum of positive separation measures gives the

total positive separation measure Si+, and the sum of negative separation measures gives the

total negative separation measure Si-. Both measures are added together, and relative closeness

50

to the ideal solution Pi are calculated using Equation 5.7. Material with the highest Pi value is the

best material according to this methodology. A summary of this calculation is given in Table 6.13.

Table 6.13: Table showing the calculated separation measure values

Ranking of materials along with calculated values of relative closeness to PIS using this

methodology is given in Table 6.14. According to this methodology, Al 2024-T81 is the best

material for the given design which agrees with the result from AHP. Both of the magnesium

alloys perform poorly again in this methodology. Rest of the ranking do not agree very well with

that from AHP.

Table 6.14: Relative closeness values to the ideal solution of each alternative materials

Materials Relative Closeness to

Ideal Solution (Pi) Ranking

AL 7075-T651 0.6338 4

AL 2024-T4 0.6539 3

AL 2024-T6 0.8265 2

AL 2024-T81 0.8636 1

Mg AZ31B 0.0904 6

Mg AZ61A 0.1744 5

51

Figure 6.2: Plot showing the ranking of materials based on their relative closeness to the ideal solution using TOPSIS.

Ranking results obtained using AHP do not quite match with the one obtained in this

method. However, overall ratings between these MCDM methodologies do not differ much

either. This approach of MCDM using TOPSIS has been very promising and is widely used to solve

decision making problems. This is a fairly short process, easy to understand, and can handle a

number of attributes and alternatives without any complexity. A plot showing ranking results

obtained using TOPSIS is given in Figure 6.2 above.

6.3 Ashby’s Approach

Under Ashby’s approach, which as has been discussed, involves the significance of benefit

and non-benefit attributes in the design, it is important to recognize the differences between

attributes while determining the material indices. The objective is always to maximize the value

of benefit criteria and minimize that of non-benefit criteria. Among six attributes considered,

density and cost are identified as non-benefit attributes and the rest of the attributes are

identified as benefit attributes. Based on the classification of attributes in terms of what needs

0

1

2

3

4

5

6

7

AL 7075-T651 AL 2024-T4 AL 2024-T6 AL 2024-T81 Mg AZ31B Mg AZ61A

Ran

kin

g

Material

Material Ranking - TOPSIS

52

to be minimized or maximized, the following material indices are identified and maximized.

Maximum value of each of the indices listed below will perform at an optimum level by a

component in a given aircraft cabin metallic structures:

Young’s modulus against density (E/ρ)

Young’s modulus against cost (E/C)

Yield strength against density (σy /ρ)

Yield strength against cost (σy /C)

Tensile strength against density (σF /ρ)

Tensile strength against cost (σF /C)

Fracture toughness against density (K1C /ρ)

Fracture toughness against cost (K1C /C)

If Ashby’s charts are created for each of the indices by plotting one attribute versus the

other, materials that perform equally well with respect to each of the indices could be located.

For each index plot, precisely focusing in the region where aluminum and magnesium alloys are

located, and if indeed short-listed material in this study are found in the same location, it would

be fair to say that ranking based on the performance of individual material index values gives the

best material for the design. In addition, as described in Section 5.4.1 with respect to Figure 5.4,

a grid of lines could be drawn parallel to each of the straight lines produced by individual indices

in a log-log scale and an attempt could be made to locate magnesium and aluminum alloys in the

region at close proximity to the grid lines. This would be another attempt to locate material

matching the short-listed materials that are used in this study. Obviously, without using a

53

material selection software that incorporates Ashby’s charts such as GRANTA CES Edupak, this

task would be very difficult to execute.

Each of the material indices listed above give different values for different short-listed

materials. Since the maximum value of each of the index is desired, the material with the highest

index value in each category is the best material. For example, while maximizing E/ρ, Al 2024-T4

would be the best material, but maximizing E/C would make Al 7075-T651 the best material. If

all the materials are ranked based on individual index values, different materials would perform

differently. In order to identify a single best material for the design with respect to all the indices,

their individual ranking could be averaged. Since the best material receives a ranking of one, the

material with the least average ranking could be identified as the best material. This approach

has been applied to the short-listed materials in this study and results are summarized below in

Table 6.15.

Table 6.15: Individual material indices values for each of the short-listed materials

Each of the index values are ranked individually. Since each of the indices is to be

maximized, material with the highest index value is the best material. This ranking is given in

Table 6.16, and their average is calculated at the end of the table

54

Table 6.16: Ranking of individual material based on each of the material indices with their average

From the table, it is apparent that different materials rank differently with respect to

individual material index. Mg AZ61A ranks as the best material with respect to tensile strength

versus density. That means if a design requires high tensile strength and low density material,

Mg AZ61A would be the best material given no other constraints remain active and that is not

very likely in any design. According to this approach and based on the average of each of the

indices ranking, Al 2024-T81 is the best material. This outcome perfectly agrees with the results

obtained using TOPSIS as well as AHP methods. It should also be mentioned that ranking using

this approach, both Al 2024-T6 and Al 2024-T81 rank similarly. In either case, AL 2024-T81 can

very well be selected as the best material for the design. A summary of average of the individual

ranking and resulting ultimate ranking in the material selection for aircraft cabin metallic

structure is given in Table 6.17. A plot of the ranking using this approach is given in Figure 6.3.

Table 6.17: Table showing the ultimate ranking of material using Ashby’s approach

55

Figure 6.3: A plot showing material ranking using new Optimized Ashby’s Method

6.4 Summary of Results

Two different methodologies: AHP and TOPSIS, were used to perform multiple criteria

decision making (MCDM) to select materials for aircraft cabin metallic structures. In addition,

Ashby’s approach was also used to make a material selection decision for the same purpose.

Interestingly enough, the best material using all three approach appeared to be Al 2024-T81.

However, while the rest of the results from AHP do not quite agree with those from TOPSIS and

Ashby’s to a degree that is agreeable, TOPSIS and Ashby’s results agree almost perfectly. TOPSIS

is widely used as a promising method in material selection and decision making. Since results

from Ashby’s approach almost perfectly align with those from TOPSIS, Ashby’s approach as a new

methodology could be satisfactorily used in material selection for aircraft cabin metallic

structures. Ashby’s approach is simple and can accommodate a large number of alternative

materials to choose from with an unrestricted number of attributes to consider. A summary of

0

1

2

3

4

5

6

7

AL 7075-T651 AL 2024-T4 AL 2024-T6 AL 2024-T81 Mg AZ31B Mg AZ61A

Ran

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Materials

Material Ranking - Ashby's Approach

56

ranking of materials using all three different methodologies is given in Table 6.18. It is easier to

compare the ranking using this table. For visual interpretation, all the rankings are incorporated

together in a plot given in Figure 6.4.

Table 6.18: Table comparing ranking of materials using Ashby’s approach, TOPSIS, and AHP

Materials AHP TOPSIS Ashby's

AL 7075-T651 4 4 3

AL 2024-T4 2 3 4

AL 2024-T6 3 2 2

AL 2024-T81 1 1 1

Mg AZ31B 5 6 6

Mg AZ61A 6 5 5

Figure 6.4: Plot showing how ranking of each alternative material determined using different methodologies compare with each other.

0

1

2

3

4

5

6

7

AL 7075-T651 AL 2024-T4 AL 2024-T6 AL 2024-T81 Mg AZ31B Mg AZ61A

Ran

kin

gs

Materials

Materials Ranking ComparisionAHP TOPSIS Ashby's

57

From the plot it is easier to see how ranking from each of the three material selection

methodologies compare with each other. Ranking using Ashby’s approach and that from TOPSIS

method align very well and AHP does not so much.

As mentioned earlier, because of the lengthy process, AHP could easily have some form

of inconsistency and results can vary from one decision maker to another. AHP, however, ranks

similarly to TOPSIS for Al 7075-T651 and similarly to both TOPSIS and Ashby’s for Al 2024-T81 as

observed in the plot.

58

CHAPTER 7

CONCLUSION AND RECOMMENDATION FOR FUTURE WORKS

Understanding of KBS and its implementation in materials selection for aircraft cabin

metallic structures using various existing methodologies remained the focus in this study. Much

literature in the area of material selection and engineering materials was reviewed. Material

attributes as data and the information in the data about the material collectively known as KBS

was accepted as an integral part in the study. It was critical to identify the most relevant

attributes to satisfy the design for any aircraft cabin metallic structures. Short-listing of materials

was done based on two materials from aluminum alloy group known to have been used by

industries to design the components for aircraft cabin metallic structures and another four with

attributes very close to the reference materials. The effect of various processing on materials

towards mechanical and other structural properties of the materials was studied. It was found

that processing on materials has a significant effect on their properties. A different application in

the design requires different material characteristics, and that is achieved by such processes on

materials.

Numbering systems of various metal alloys were found to have interesting implications

on what each combination of numbers and letters mean in terms of materials’ chemical

composition and characteristics. Solution heat treatment, artificial and natural aging, cold work,

and strain hardening are some of the popular methods to process metal alloys that are used in

aircraft parts both interior and exterior. Upon having an overview of the material world and

59

strategies to carry out material selection process for optimum results, two existing

methodologies, AHP and TOPSIS, were used to select materials for aircraft cabin metallic

structures. Ranking results from the methodologies did not agree very well but did agree on the

best material. AHP was a very lengthy process and ranking could have varied from one decision

maker to the other. That could be one of the reasons for the inconsistency. TOPSIS on the other

hand is believed to have produced favorable ranking results as it has been used for years in

various decision making problems. In addition, TOPSIS was fairly a short step process, and there

was much less chance for errors compared to that in the AHP process.

As a contribution in these efforts, a new methodology in materials selection for aircraft

cabin metallic structures using Ashby’s approach was formulated. Six different materials as

described previously were used as short-listed materials to implement the new methodology.

Materials were ranked using this new approach and results were highly satisfactory, matching

almost perfectly to those from TOPSIS. Since results from Ashby’s approach almost perfectly align

with those from TOPSIS, this approach as a new methodology could be satisfactorily used in

material selection for aircraft cabin metallic structures. Ashby’s approach is simple and can

accommodate a large number of alternative materials to choose from with an unrestricted

number of attributes to consider. Further tests and analysis are still required to verify that the

new methodology works in material selection for aircraft cabin metallic structures with no flaws.

7.1 Recommendations for Future Works

Material selection in engineering design is a very big world. Properly selected materials in

a design give optimum performance and save cost and efforts. Any scientific and engineering

60

contribution in the study of material selection is always helpful but never enough. This study was

limited to material selection for random component in aircraft cabin metallic structure. There

are many different metallic parts inside the aircraft that have different performance

requirements. In addition, there was no joint effort between the researcher and the companies

who actually design and build these components. As a continuation of this research, it is

recommended to find such companies and work in collaboration. This gives the researcher a

complete overview of what the end user, the airliners, look for in such products. Design is at its

best when the designer has an absolute idea of the end user requirements.

61

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