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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
kin
g
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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