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Case Studies of Using Materials Ranking
CHAPTER
5
Case Studies of Using Materials Ranking 5.1 RATIONALE FOR CASE STUDIES It has already been explained that there are a very large number of materials, and associated materials processes, available to the designer. To select suitable materials for a particular application necessitates the simultaneous consideration of many conflicting criteria. Apart from the simplest of products this is normally a difficult problem-solving activity. The choice of materials is often restrained (by keeping to what you know) and assumptions made (because of restricted information) and approximations used (since the analysis is difficult) to achieve workable solutions. This stifles the uptake of different materials (to a particular designer) or new materials (for all designers), and when used are often based on experience only leading to inappropriate deployment, for example, anisotropic materials treated as if they are isotropic materials, leading to possible under utilization of the materials’ performance or premature failure of a component. The methods described in the preceding chapters have been developed to assist designers cope with complex (real-world) materials selection problems. However, to help understand and appreciate the capability of the methods, worked examples and case studies are invaluable. Recent publications demonstrate the issues pertaining to the optimal selection of materials by incorporating challenging case studies such as the design of bipolar plates for a polymer electrolyte membrane fuel cell [1], flywheel [2], cryogenic storage tank [3], spar for the wing of aircraft [4], and loaded thermal conductor [5]. These and other case studies have significant impact on the future development of improved decision support systems for materials selection. The detailed case studies that follow have been carefully chosen to demonstrate the scope and explain the materials selection methods described in the preceding chapters.
5.2 MATERIALS SELECTION FOR BIOMEDICAL IMPLANTS Biomaterials are artificial or natural materials that replace diseased or damaged organic systems to provide a pain-free life for patients.
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Multi-criteria Decision Analysis for Supporting the Selection of Engineering Materials
Biomaterials are used in different parts of the human body such as artificial valves in the heart, stents in blood vessels, replacement implants in shoulders, knees, hips, elbows, ears, and orodental structures [6,7]. In the case of biomedical implants, the increasingly ageing population is continually raising the expectations and demands for creating new and improved products, economically and in high volumes. As a consequence, developing new and improved biomedical implants is seen as a complex design problem-solving activity and, in conjunction with demanding manufacturing constraints, utilizing the most appropriate materials (and materials combinations) presents many unique challenges.
5.2.1 Hip Prosthesis A hip prosthesis comprises three main components: (1) femoral component, (2) acetabular cup, and (3) acetabular interface. The femoral component is a rigid metal pin (manufactured as a precision machined forging in cobalt chrome or titanium alloy but previously also in stainless steel, with either an integral ground and polished head or separately attached ceramic ball head) is implanted into the hollowed out shaft of the femur, replacing the natural femoral head. The hip socket (acetabulum) is inserted with an acetabular cup; a soft polymer molding (a variety of materials have been used in the past but is now predominantly in polypropylene), which is fixed to the ilium. The acetabular interface is placed between the femoral component and the acetabular cup and comes in variety of material combinations (metal on polypropylene, ceramic on ceramic, and metal on metal) to reduce wear debris generated by friction. Figure 5.1 shows typical form and position of hip joint prosthesis. The compressive strength of compact bone is about 140 MPa and the elastic modulus is about 14 GPa in the longitudinal direction and about 1/3 of that in the radial direction. These values of strength and modulus for bone are modest compared to most engineering materials. However, live healthy bone is self-healing and has a great resistance to fatigue loading. The pin and cup are fixed to the surrounding bone structure by adhesive bone cement and perform different functions. In this example, the material for the pin has been considered whose requirements are tissue tolerance, corrosion resistance, mechanical behavior, elastic compatibility, weight, and cost. Table 5.1 shows the pin’s candidate materials, criteria, objectives of the designer, and
Case Studies of Using Materials Ranking
85
Figure 5.1 Typical form and position of hip joint prosthesis.
subjective weightings [3,8]. C1, C2 are ordinal data or categorical data where there is a logical ordering to the categories that have been used for description of nonnumeric attributes, C3, C4, C7, and C8 are numeric attributes that represent absolute measure of material properties, and finally C5, C6, and C9 are ratio values. The correlation of criteria for materials selection of the hip joint prosthesis and final weighting of dependency are demonstrated in Table 5.2. Table 5.3 shows normalized values of hip joint prosthesis materials for all criteria. The subjective weightings are the same as those considered by Farag [3,8]. Table 5.4 shows objective weightings that have been extracted from Table 5.3. Table 5.5 is a summary of the weightings, including the objective weighting, weighting of dependency, and finally subjective weighting. Also, the final weighting using different levels of importance for three types of weighting is shown in Table 5.5. In this case, with regard to the type and number of criteria, the new version of both TOPSIS [9] and VIKOR [10] methods can fit as well for ranking the materials. Table 5.5 shows ranking orders of materials using different weightings and ranking methods. When the data is obtained using the comprehensive VIKOR, with λ 5 1 that means only subjective weighting, were compared with the extended TOPSIS model, only materials 5 and 8 changed places (rank 2 and 3). With λ 5 0.4, material 6 is the best one in extended TOPSIS, while with the same value of λ in the comprehensive VIKOR, material 8 is in the top rank. However, most of the time for both methods, the top ranking belongs to material 6. When tracking the ranking of material 5, it shows that decreasing λ in extended TOPSIS causes a change in ranking of this material from 3 to 6 and in the comprehensive VIKOR from 2 to 10.
Table 5.1 Decision Matrix for Hip Joint Prosthesis Materials Selection Objectives of Design
Max
Max
Max
Max
Max
Max
Target Value
Target Value
Min
Criteria
C1
C2
C3
C4
C5
C6
C7
C8
C9
Tissue
Corrosion
Tensile
Fatigue
Relative
Relative Wear
Elastic
Specific
Cost
Tolerance
Resistance
Strength
Strength
Toughness
Resistance
Modulus
Gravity (g/cc)
(MPa)
(MPa)
(GPa)
Stainless steels 316
10
7
517
350
8
8
200
8
1
Stainless steels 317
9
7
630
415
10
8.5
200
8
1.1
Stainless steels 321
9
7
610
410
10
8
200
7.9
1.1
Stainless steels 347
9
7
650
430
10
8.4
200
8
1.2
CoCr alloysCast alloy (1)
10
9
655
425
2
10
238
8.3
3.7
CoCr alloysWrought alloy (2)
10
9
896
600
10
10
242
9.1
4
Unalloyed titanium
8
10
550
315
7
8
110
4.5
1.7
Ti6Al4V
8
10
985
490
7
8.3
124
4.4
1.9
Composites (fabric reinforced)Epoxy-70% glass
7
7
680
200
3
7
22
2.1
3
Composites (fabric reinforced)Epoxy-63% carbon
7
7
560
170
3
7.5
56
1.6
10
Composites (fabric reinforced)Epoxy-62% aramid
7
7
430
130
3
7.5
29
1.4
5
Table 5.2 Correlation of Criteria and Weighting of Dependency for a Hip Joint Prosthesis C6
C7
C8
C9
Rjk
Wc
C1
C2
C3
C4
C5
C1
1.00
0.16
0.23
0.78
0.53
0.79
20.97
20.96
0.48
6.96
0.102
C2
0.16
1.00
0.57
0.48
20.01
0.48
20.18
20.05
0.13
6.42
0.095
C3
0.23
0.57
1.00
0.73
0.29
0.46
20.30
20.21
0.16
6.07
0.089
C4
0.78
0.48
0.73
1.00
0.68
0.79
20.85
20.80
0.49
5.70
0.084
C5
0.53
20.01
0.29
0.68
1.00
0.25
20.62
20.67
0.62
6.93
0.102
C6
0.79
0.48
0.46
0.79
0.25
1.00
20.81
20.76
0.13
6.66
0.098
C7
20.97
20.18
20.30
20.85
20.62
20.81
1.00
0.99
20.47
11.21
0.165
C8
20.96
20.05
20.21
20.80
20.67
20.76
0.99
1.00
20.51
10.97
0.162
C9
0.48
0.13
0.16
0.49
0.62
0.13
20.47
20.51
1.00
6.97
0.103
Table 5.3 Normalizing of Hip Joint Prosthesis Materials Row
Materials
C1
C2
C3
C4
C5
C6
C7
C8
C9
1
Stainless steels 316
1.0000
0.0000
0.1568
0.4681
0.7500
0.3333
0.1842
0.2338
1.0000
2
Stainless steels 317
0.6667
0.0000
0.3604
0.6064
1.0000
0.5000
0.1842
0.2338
0.9889
3
Stainless steels 321
0.6667
0.0000
0.3243
0.5957
1.0000
0.3333
0.1842
0.2468
0.9889
4
Stainless steels 347
0.6667
0.0000
0.3964
0.6383
1.0000
0.4667
0.1842
0.2338
0.9778
5
CoCr alloysCast alloy (1)
1.0000
0.6667
0.4054
0.6277
0.0000
1.0000
0.0175
0.1948
0.7000
6
CoCr alloysWrought alloy (2)
1.0000
0.6667
0.8396
1.0000
1.0000
1.0000
0.0000
0.0909
0.6667
7
Unalloyed titanium
0.3333
1.0000
0.2162
0.3936
0.6250
0.3333
0.5789
0.6883
0.9222
8
Ti6Al4V
0.3333
1.0000
1.0000
0.7660
0.6250
0.4333
0.5175
0.7013
0.9000
9
Composites (fabric reinforced)Epoxy-70% glass
0.0000
0.0000
0.4505
0.1489
0.1250
0.0000
0.9649
1.0000
0.7778
10
Composites (fabric reinforced)Epoxy-63% carbon
0.0000
0.0000
0.2342
0.0851
0.1250
0.1667
0.8158
0.9351
0.0000
11
Composites (fabric reinforced)Epoxy-62% aramid
0.0000
0.0000
0.0000
0.0000
0.1250
0.1667
0.9342
0.9091
0.5556
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Case Studies of Using Materials Ranking
Table 5.4 Objective Weightings C1
C2
C3
C4
C5
C6
C7
C8
C9
Standard deviation
0.405
0.433
0.290
0.305
0.412
0.317
0.362
0.349
0.298
Objective weight
0.128
0.137
0.092
0.096
0.130
0.100
0.114
0.110
0.094
Table 5.5 Final Weightings Using Different Effect of Subjective, Objective, and Dependency Weightings C1
C2
C3
C4
C5
C6
C7
C8
C9
Subjective weight
0.200
0.200
0.080
0.120
0.080
0.080
0.080
0.080
0.080
Objective weight
0.128
0.137
0.092
0.096
0.130
0.100
0.114
0.110
0.094
Dependency weight
0.102
0.095
0.089
0.084
0.102
0.098
0.165
0.162
0.103
W(λ 5 0, (1 2 λ)/2 5 0.5)
0.115
0.116
0.090
0.090
0.116
0.099
0.140
0.136
0.098
W(λ 5 0.2, (1 2 λ)/2 5 0.4)
0.132
0.132
0.088
0.096
0.109
0.095
0.128
0.125
0.095
W(λ 5 0.4, (1 2 λ)/2 5 0.3)
0.149
0.149
0.086
0.102
0.102
0.091
0.116
0.114
0.091
W(λ 5 0.6, (1 2 λ)/2 5 0.2)
0.166
0.166
0.084
0.108
0.094
0.088
0.104
0.102
0.087
W(λ 5 0.8, (1 2 λ)/2 5 0.1)
0.183
0.183
0.082
0.114
0.087
0.084
0.092
0.091
0.084
W(λ 5 1, (1 2 λ)/2 5 0)
0.200
0.200
0.080
0.120
0.080
0.080
0.080
0.080
0.080
As a result, these rapid changes highlight the need for the aggregation technique [11] for the final optimum ranking that has been shown in Table 5.6. Figure 5.2 shows how a combination of tools and techniques can be used to select the optimum material for the hip prosthesis.
5.2.2 Knee Prosthesis Knee prostheses are implanted in the human body to relief pain and restore form and function. In order to match the performance of a natural knee, the materials of prosthesis are required to have several specific properties with values approaching those of natural biological materials (bone and tissue). In this example, metallic biomaterials (biologically compatible materials) that are currently used and newly developed metallic biomaterials that could potentially be used in the future for the femoral component of knee-joint implants (Figure 5.3) are considered as candidate materials [12,13]. For any knee implant to be successful it needs to have high wear resistance, an elastic modulus to minimize stress-shielding and biocompatibility (capability to integrate with the surrounding bone). The material property criteria considered include tensile strength, Young’s modulus, ductility, corrosion
90
Multi-criteria Decision Analysis for Supporting the Selection of Engineering Materials
Table 5.6 Aggregated Result and Individual Ranks of Hip Prosthesis Materials that Generated by Extended TOPSIS, and Comprehensive VIKOR with Different Weightings Materials
Ranking with Different Values of λ Extended TOPSIS
Aggregated Rank Comprehensive VIKOR
1
0.8
0.6
0.4
0.2
0
1
0.8
0.6
0.4
0.2
0
1
5
5
5
5
7
9
5
5
5
7
8
8
5
2
7
7
7
7
6
5
7
7
7
6
6
6
7
3
8
8
8
8
8
7
8
8
8
8
7
7
8
4
6
6
6
6
5
4
6
6
6
5
5
5
6
5
3
3
4
4
4
6
2
2
2
4
4
10
4
6
1
1
1
2
2
3
1
1
1
1
3
3
1
7
4
4
3
3
3
2
4
4
4
3
2
2
3
8
2
2
2
1
1
1
3
3
3
2
1
1
2
9
9
9
9
9
9
8
9
9
9
9
9
4
9
10
11
11
11
11
11
11
11
11
11
11
11
11
11
11
10
10
10
10
10
10
10
10
10
10
10
9
10
Determining the criteria and alternatives in format of decision matrix
Normalizing the decision matrix
Calculating the objective, subjective and dependency weightings
Ranking with different methods using different weightings
Selecting appropriate ranking method (targetbased)
Combining three types of weightings under uncertainty
Applying the aggregation method for optimum decisionmaking
Figure 5.2 The stages applied for hip prosthesis materials selection example.
Case Studies of Using Materials Ranking
91
Figure 5.3 The main components of a total knee replacement (Upper part: Femoral component, middle part: Tibial insert, lower part: Tibial tray).
resistance, wear resistance, and osseointegration ability. The metals currently used are stainless steels, CoCr alloys, titanium, and titanium alloys. The metals that could potentially be used in the future are NiTi shape memory alloys (SMA) including dense and porous NiTi. All of these materials adequately fulfill the mechanical and biological requirements. The candidate metallic materials are therefore stainless steel L316 (annealed), stainless steel L316 (cold worked), CoCr alloys (wrought CoNiCrMo), CoCr alloys (castable CoCrMo), Ti alloys (pure Ti), Ti alloys (Ti6Al4V), Ti6Al7Nb (IMI-367 wrought), Ti6Al7Nb (Protasul-100 hot-forged), NiTi SMA, and porous NiTi SMA. Table 5.7 shows the properties of these materials, 110, respectively. This case study includes interval data, incomplete data, linguistic terms, and target criteria. The fuzzy conversion scales [1416] systematically converts linguistic terms into their corresponding fuzzy numbers and used to assign the values of the attributes on a qualitative scale. An 11-point scale (Table 5.8) is used here for better understanding and representation of the qualitative attributes and converting linguistic terms into corresponding numbers (Table 5.9). The application of the interval-target based VIKOR that was described in Section 4.7 is illustrated in this case step by step as follows: Step 1: Determining the most favorable values for all criteria (Tj 5 1.3, 1240, 16, 54, 0.96, 0.96, 0.96). The target criteria are density and modulus of elasticity near to that of human bone and for all the other properties being the higher the better.
Table 5.7 Properties of Candidate Materials for Femur Component Materials Selection Objectives
Target
Max
Target
Max
Max
Max
Max
Material
Density (g/
Tensile Strength
Modulus of Elasticity
Elongation
Corrosion
Wear Resistance
Osseointegration
Number
cc)
(MPa)
(GPa)
(%)
Resistance
1
8
517
200
40
High
Above average
Above average
2
8
862
200
12
High
Very high
Above average
3
9.13
896
240
1030
Very high
Extremely high
High
4
8.3
655
240
1030
Very high
Extremely high
High
5
4.5
550
100
54
Exceptionally high
Above average
Very high
6
4.43
985
112
12
Exceptionally high
High
Very high
7
4.52
900
105120
10
Exceptionally high
High
Very high
8
4.52
10001100
110
1015
Exceptionally high
High
Very high
9
6.50
1240
48
12
Extremely high
Exceptionally high
Average
10
,4.3
1000
15
12
Very high
Exceptionally high
Exceptionally high
Case Studies of Using Materials Ranking
93
Table 5.8 Value of Materials Selection Factors in Format of 11-Point Scale Qualitative Measure of Material Selection Factor
Assigned Value
Exceptionally low
0.045
Extremely low
0.135
Very low
0.255
Low
0.335
Below average
0.410
Average
0.500
Above average
0.590
High
0.665
Very high
0.745
Extremely high
0.865
Exceptionally high
0.955
Step 2: Subjective weightings that have been calculated based on modified digital logic (MDL) [4]. In the MDL method, the scale of scores for the weighted factors is considered to be 1, 2, or, 3; one (1) for attributes that are less important, two (2) for attributes which are equally important, and three (3) for attributes that are more important. More specifically, for each pair of attributes the question asked is, which attribute (material property) is more important for the desired outcome of the end product, property A or property B? The total number of possible decisions (pair-wise comparisons), N, is N5
nðn 2 1Þ 2
where n is the number of properties/criteria under consideration. After each combination is compared and assigned a binary score, the results are put into a matrix form as shown in Table 5.10, and the number of positive decisions for each attribute (i.e., with a score of “1”) is summed and a weighting factor, Wj is calculated and normalized such that X Wj 5 1 j 5 1; . . .; n Step 3: Table 5.11 shows the required parameter for normalizing L the materials (Table 5.12). Computing valuesSiL ; SiU ; RLi ,RU i ; Qi , andQU i with v 5 0.5 is demonstrated in Table 5.13.
Table 5.9 Decision Matrix for Femur Materials Selection with Quantitative Data Material Number
Density (g/cc)
Tensile Strength (MPa)
Modulus of Elasticity (GPa)
Elongation (%)
Corrosion Resistance
Wear Resistance
Osseointegration
1
8
517
200
40
0.665
0.59
0.59
2
8
862
200
12
0.665
0.745
0.59
3
9.13
896
240
20
0.745
0.865
0.665
4
8.3
655
240
20
0.745
0.865
0.665
5
4.5
550
100
54
0.955
0.59
0.745
6
4.43
985
112
12
0.955
0.665
0.745
7
4.52
900
112.5
10
0.955
0.665
0.745
8
4.52
1050
110
12.5
0.955
0.665
0.745
9
6.5
1240
48
12
0.955
0.955
0.5
10
4.3
1000
15
12
0.745
0.955
0.955
Table 5.10 Determination of Relative Importance of Criteria Using MDL Method Criteria
Number of Possible Decisions [N 5 n(n 2 1)/2] 1
2
3
4
5
6
Density
1
1
1
1
1
1
Tensile strength
3
Modulus of elasticity Elongation Corrosion resistance Wear resistance Osseointegration
3
7
8
9
10
11
1
2
1
1
1
3 3
3 2
3
1
14
1
15
1
17
18
1
19
20
1 3
3
2
Weight
6
0.07
9
0.11
12
0.14
9
0.11
15
0.18
2
17
0.20
2
16
0.19
2
3 3
Sum 21
1
3 3
3
16
1
3 3
3
13
1 3
3
12
96
Multi-criteria Decision Analysis for Supporting the Selection of Engineering Materials
Table 5.11 Required Parameter for Normalization of Femur Materials Density
Tensile
Modulus of
Elongation
Corrosion
Wear
(g/cc)
Strength
Elasticity
(%)
Resistance
Resistance
(MPa)
(GPa)
Osseointegration
Tj
1.3
1240
16
54
0.955
0.955
0.955
max xU j
9.13
1240
240
54
0.955
0.955
0.955
xLmin j
4.3
517
15
10
0.665
0.59
0.5
Step 4: Table 5.13 shows details of calculations. According to the guideline of comparing interval data (Table 4.8), material 10 (porous NiTi SMA) has the minimum value of Qi½QLi ; QU i . The ranking of other materials is shown in Table 5.14. When considering only one criterion such as wear resistance makes CoCr alloys as the highest ranking in the currently used materials while it now has second ranking.
5.3 MATERIALS SELECTION FOR AIRCRAFT STRUCTURE REPAIR When aircraft reach the end of their service life, fatigue cracks are found to develop along rivet holes and other highly stressed regions of the airframe or structure. In order to extend the life of aircraft, repairs can be made to arrest the cracks. Three critical steps in implementing a repair are design, choice of materials, and application. Composite doublers or repair patches provide an innovative repair technique which can enhance the way in which aircraft are maintained. Bonded repair of metallic aircraft structure is used to extend the life of flawed or under-designed components at reasonable cost. Such repairs generally have one of three objectives: fatigue enhancement, crack patching, and corrosion repair. The repair of cracked structure may be performed by bonding an external patch to the structure, to either stop or slow crack growth. The selected material must be able to withstand the expected environmental conditions in the damaged area. The material selected for the patch will almost always be either metallic or composite and within these classes are many different materials with advantages and disadvantages associated with their use [17]. The processes by which the adhesive and patch materials are installed on the aircraft have a direct influence on the final properties and long-term durability
Table 5.12 Normalized Data for Femur Materials L Vi;C1
U Vi;C1
L Vi;C2
U Vi;C2
L Vi;C3
U Vi;C3
L Vi;C4
U Vi;C4
L Vi;C5
U Vi;C5
L Vi;C6
U Vi;C6
L Vi;C7
U Vi;C7
1
0.8557
0.8557
1
1
0.8178
0.8178
0.3182
0.3182
1.0172
1.0172
1.0137
1.0137
0.8132
0.8132
2
0.8557
0.8557
0.5228
0.5228
0.8178
0.8178
0.9545
0.9545
1.0172
1.0172
0.589
0.589
0.8132
0.8132
3
1
1
0.4758
0.4758
0.9956
0.9956
1
0.5455
0.7414
0.7414
0.2603
0.2603
0.6484
0.6484
4
0.894
0.894
0.8091
0.8091
0.9956
0.9956
1
0.5455
0.7414
0.7414
0.2603
0.2603
0.6484
0.6484
5
0.4087
0.4087
0.9544
0.9544
0.3733
0.3733
0
0
0.0172
0.0172
1.0137
1.0137
0.4725
0.4725
6
0.3997
0.3997
0.3527
0.3527
0.4267
0.4267
0.9545
0.9545
0.0172
0.0172
0.8082
0.8082
0.4725
0.4725
7
0.4112
0.4112
0.4703
0.4703
0.3956
0.4622
1
1
0.0172
0.0172
0.8082
0.8082
0.4725
0.4725
8
0.4112
0.4112
0.332
0.1936
0.4178
0.4178
1
0.8864
0.0172
0.0172
0.8082
0.8082
0.4725
0.4725
9
0.6641
0.6641
0
0
0.1422
0.1422
0.9545
0.9545
0.0172
0.0172
0.0137
0.0137
1.011
1.011
10
0.3831
0.3831
0.332
0.332
0.0044
0.0044
0.9545
0.9545
0.7414
0.7414
0.0137
0.0137
0.011
0.011
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Multi-criteria Decision Analysis for Supporting the Selection of Engineering Materials
Table 5.13 Interval Numbers for S, R, and Q for Femur Materials Materials Number
SL
SU
RL
RU
QL
QU
1
0.855
0.855
0.203
0.203
1.000
1.000
2
0.788
0.788
0.182
0.182
0.791
0.791
3
0.625
0.675
0.135
0.135
0.306
0.352
4
0.654
0.704
0.135
0.135
0.333
0.378
5
0.480
0.480
0.203
0.203
0.658
0.658
6
0.484
0.484
0.162
0.162
0.368
0.368
7
0.499
0.508
0.162
0.162
0.382
0.390
8
0.459
0.486
0.162
0.162
0.345
0.371
9
0.369
0.369
0.192
0.192
0.481
0.481
10
0.306
0.306
0.133
0.133
0.000
0.000
Table 5.14 Comparing Ranking Orders of Candidate Materials for Femur Component Material Number
Material Name
Interval-Target Based VIKOR
1
Stainless steel L316 (annealed)
10
2
Stainless steel L316 (cold worked)
9
3
CoCr alloys (wrought CoNiCrMo)
2
4
CoCr alloys (castable CoCrMo)
4
5
Ti alloys (pure Ti)
8
6
Ti alloys (Ti6Al4V)
5
7
Ti6Al7Nb (IMI-367 wrought)
6
8
Ti6Al7Nb (Protasul-100 hot-forged)
3
9
NiTi SMA
7
10
Porous NiTi SMA
1
of the repair. Adhesive bonding technology (Figure 5.4), particularly bonded composite repairs, has been successfully applied by several nations to extend the lives of aircraft by bridging cracks in metallic structure, reducing strain levels, and repairing areas thinned by corrosion. Bonded composite reinforcements are highly efficient and cost effective when compared to conventional mechanically fastened approaches. In some cases, bonded repair technology is the only alternative to retiring a component. The repairs can be broadly divided into nonpatch procedures for minor damage and patch (or reinforcement) procedures to restore structural capability. The technique of repairing cracked metallic aircraft structures using high-strength
Case Studies of Using Materials Ranking
99
Vacuum line to vacuum bag Thermocouples Aircraft repair
Repair patch
Power supply to heater mat
Vacuum bag Heater mat Figure 5.4 Composite bonded repair patch being applied to an aircraft structure [18].
advanced composite materials is commonly known as “crack patching” and was pioneered by the Aeronautical and Maritime Research Laboratories (AMRL), for the Royal Australian Air Force (RAAF). The composite reinforcement, also known as the patch, can be attached to a damaged or weakened structure either by a mechanical fastener or by adhesive bonding. The use of adhesively bonded composite patches as a method of repair has several advantages over mechanically fastened repair methods, which include reduced installation cost, increased strength and fatigue life and hence effective crack retardation, reduced repair down time, elimination of unnecessary fastener holes in an already weakened structure and stress concentrations at fasteners, corrosion resistance, high stiffness, and lightweight. In selection of a patch material criteria include stiffness, strength, thickness, conformability, service temperature, and product form. The repair materials may be conventional metals, fiber metal laminates, or composites. The factors that may dictate patch materials selection include thickness, weight, stiffness, thermal expansion coefficient, ability to inspect the damage through the patch, and operating temperature requirements. Thinner patches can be designed with higher modulus materials. Composite materials have higher stiffness to weight ratios. Metals and fiber metal laminates have thermal expansion coefficients more compatible with the metal structure being repaired and are more capable of enduring elevated temperatures [18].
Table 5.15 Candidate Materials, Weightings, and Objectives for Patch Repair [17,18,20,21] Objectives
Max
Min
Max
Max
Max
Min
Max
Subjective Weightings
0.179
0.071
0.179
0.214
0.131
0.095
0.131
No.
Materials
C1
C2
C3
C4
C5
C6
C7
Thermal Expansion
Approximate Relative
Young’s
Shear
Elongation
Density
Tensile
Coefficient ( C 3 1025)
Material Cost
Modulus (GPa)
Modulus
(%)
(g/cm3)
Strength (GPa)
18
2.78
0.483
(GPa) 1
Al 2024-T3
2.32
1
73
27
2
Al 7075-T6
2.3
1
72
27
11
2.81
0.572
3
Titanium alloy 6 AL/4V
0.9
12
110
41
14
4.5
0.95 2.9
4
Aramid/Epoxy
20.8
2
82.7
2.07
2.5
1.38
5
Glass/Epoxy
0.61
1
72.5
3.52
4.8
2.58
4.03
6
HM Carbon/Epoxy
21
18
390
7.1
1.8
1.81
6.9
7
Boron/Epoxy unidirectional
0.452.3
40
20208
7
0.8
2
3.4
8
Graphite/epoxy unidirectional
0.32.8
13
12148
5
1.3
1.6
2.17
9
Aluminum laminate ARALL
1.6
7
68
17
0.89
2.3
1.282
10
Aluminum laminate GLARE
2
5
65
14.72
0.52
2.5
0.717
11
Electroformed Nickel
1.31
2
207
76
30
8.88
0.317
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101
Table 5.16 Required Parameter for Normalization of Patch Repair Materials C1
C2
C3
C4
C5
C6
C7
Tj
2.8
1
390
76
30
1.38
6.9
max xU j
2.8
40
390
76
30
8.88
6.9
xLmin j
21
1
12
2.07
0.52
1.38
0.317
The application of existing materials selection methods is not popular in the aerospace environment [19]. This is in spite of selection processes being used in this field that involve a wide range of influential factors. This example presents the process of optimal materials selection for composite patch repairs in ageing metallic aircraft. The objective is to rank the candidate materials that can be used in patch repairs (Table 5.15). The material properties considered for design should take into account the effects of these processes such as the cure cycle (time/ temperature) and pressure application method used for bonding. The need is for high strength and stiffness, fatigue, and environmental durability and formability. Composites satisfy most of the requirements; however, the main disadvantage is low thermal expansion coefficient, which gives rise to undesirable residual tensile stresses in the area of the repair. Table 5.16 shows the required values for normalizing of data (Table 5.17). Table 5.18 presents other calculations and ranking of candidate materials. According to Table 5.18, metallic repairs are better choices to help simplifying the design process. However, there are also very good reasons to consider the use of composite materials. Composites make exceptionally good repair materials due to their resistance to fatigue stresses and corrosion. The main disadvantage of composites as patching materials results from their relatively low coefficient of thermal expansion compared to the parent material, which results in residual tensile mean stresses in the repaired component. It seems the fiber composites boron/epoxy, carbon/epoxy, and graphite/ epoxy are the three main options generally considered and used for patch repair materials in Australia, UK, and US [20].
Table 5.17 Normalized Values of Patch Repair Materials No.
L Vi;C1
U Vi;C1
L Vi;C2
U Vi;C2
L Vi;C3
U Vi;C3
L Vi;C4
U Vi;C4
L Vi;C5
U Vi;C5
L Vi;C6
U Vi;C6
L Vi;C7
U Vi;C7
1
0.1263
0.1263
0
0
0.8386
0.8386
0.6628
0.6628
0.4071
0.4071
0.1867
0.1867
0.9748
0.9748
2
0.1316
0.1316
0
0
0.8413
0.8413
0.6628
0.6628
0.6445
0.6445
0.1907
0.1907
0.9613
0.9613
3
0.5
0.5
0.2821
0.2821
0.7407
0.7407
0.4734
0.4734
0.5427
0.5427
0.416
0.416
0.9038
0.9038
4
0.9474
0.9474
0.0256
0.0256
0.813
0.813
1
1
0.9328
0.9328
0
0
0.6076
0.6076
5
0.5763
0.5763
0
0
0.8399
0.8399
0.9804
0.9804
0.8548
0.8548
0.16
0.16
0.436
0.436
6
1
1
0.4359
0.4359
0
0
0.932
0.932
0.9566
0.9566
0.0573
0.0573
0
0
7
0.6184
0.1316
1
1
0.9788
0.4815
0.9333
0.9333
0.9905
0.9905
0.0827
0.0827
0.5317
0.5317
8
0.8158
0
0.3077
0.3077
1
0.6402
0.9604
0.9604
0.9735
0.9735
0.0293
0.0293
0.7185
0.7185
9
0.3158
0.3158
0.1538
0.1538
0.8519
0.8519
0.7981
0.7981
0.9874
0.9874
0.1227
0.1227
0.8534
0.8534
10
0.2105
0.2105
0.1026
0.1026
0.8598
0.8598
0.8289
0.8289
1
1
0.1493
0.1493
0.9392
0.9392
11
0.3921
0.3921
0.0256
0.0256
0.4841
0.4841
0
0
0
0
1
1
1
1
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Case Studies of Using Materials Ranking
Table 5.18 Interval Numbers for S, R, and Q for Patch Repair Materials Materials
SL
SU
RL
RU
QL
QU
Rank
Al 2024-T3
0.513
0.513
0.150
0.150
0.279
0.279
3
Al 7075-T6
0.544
0.544
0.151
0.151
0.322
0.322
4
Titanium alloy 6 AL/4V
0.572
0.572
0.133
0.133
0.249
0.249
2
Aramid/Epoxy
0.733
0.733
0.214
0.214
0.944
0.944
11
Glass/Epoxy
0.648
0.648
0.210
0.210
0.810
0.810
9
HM Carbon/Epoxy
0.540
0.540
0.199
0.199
0.611
0.611
6
Boron/Epoxy unidirectional
0.588
0.764
0.200
0.200
0.673
0.898
8
Graphite/epoxy unidirectional
0.566
0.777
0.206
0.206
0.681
0.949
10
Aluminum laminate ARALL
0.644
0.644
0.171
0.171
0.570
0.570
5
Aluminum laminate GLARE
0.644
0.644
0.177
0.177
0.611
0.611
7
Electroformed Nickel
0.385
0.385
0.131
0.131
0.000
0.000
1
REVIEW QUESTIONS 1. What are the possible ways of obtaining objective and dependency weighting for interval data? 2. In the materials selection for a knee prosthesis case study: a. Calculate the objective weightings. b. Combine the objective and subjective weightings, with the assumption of uncertainty in importance of each type of weightings. c. Obtain the ranking order of materials for different weightings and interpret the final ranking of materials using a graph that shows frequency of each material to each rank (e.g., if you obtain the ranking of materials 10 times and Material 1 assigns to rank 8, 7 times; then you might interpret Material 1 has rank 8 with 70 % confidence). 3. In the materials selection for an aircraft patch repair case study: a. Obtain the weighting of dependency and objective. b. Combine the three types of weightings with the assumption of equal importance on each type of weightings and calculate the final ranking of materials. c. Using the middle value of interval data and weighting obtained in the last step; determine the ranking orders of materials by both comprehensive VIKOR method and target-based TOPSIS method. d. If it is applicable, obtain the optimum ranking of materials by the aggregation method. e. If a designer decides to consider only composite materials for the repair, do you think you should recalculate the ranking of materials and why?
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Multi-criteria Decision Analysis for Supporting the Selection of Engineering Materials
REFERENCES [1] Shanian A, Savadogo O. A non-compensatory compromised solution for material selection of bipolar plates for polymer electrolyte membrane fuel cell (PEMFC) using ELECTRE IV. Electrochim Acta 2006;51:530715. [2] Jee DH, Kang KJ. A method for optimal material selection aided with decision making theory. Mater Des 2000;21:199206. [3] Farag MM. Materials selection for engineering design. New York, NY: Prentice-Hall; 1997. [4] Dehghan-Manshadi B, Mahmudi H, Abedian A, Mahmudi R. A novel method for materials selection in mechanical design: combination of non-linear normalization and a modified digital logic method. Mater Des 2007;28:815. [5] Shanian A, Milani AS, Carson C, Abeyaratne RC. A new application of ELECTRE III and revised Simos’ procedure for group material selection under weighting uncertainty. Knowledge-Based Syst 2008;21:70920. [6] Ramakrishna S, Mayer J, Wintermantel E, Leong KW. Biomedical applications of polymercomposite materials: a review. Compos Sci Technol 2001;61:1189224. [7] Park JB, Bronzino JD. Biomaterials: principles and applications. Boca Roton, FL: CRC 2003. [8] Farag MM. Materials and process selection in engineering. London: Elsevier Science and Technology 1979. [9] Jahan A, Bahraminasab M, Edwards KL. A target-based normalization technique for materials selection. Mater Des 2012;35:64754. [10] Jahan A, Mustapha F, Ismail MY, Sapuan SM, Bahraminasab M. A comprehensive VIKOR method for material selection. Mater Des 2011;32:121521. [11] Jahan A, Ismail MY, Shuib S, Norfazidah D, Edwards KL. An aggregation technique for optimal decision-making in materials selection. Mater Des 2011;32:491824. [12] Bahraminasab M, Jahan A. Material selection for femoral component of total knee replacement using comprehensive VIKOR. Mater Des 2011;32:44717. [13] Jahan A, Edwards KL. VIKOR method for material selection problems with interval numbers and target-based criteria. Mater Des 2013;47:759–765. [14] Rao RV, Davim JP. A decision-making framework model for material selection using a combined multiple attribute decision-making method. Int J Adv Manuf Technol 2008;35:75160. [15] Rao RV. A material selection model using graph theory and matrix approach. Mater Sci Eng A 2006;431:24855. [16] Chen SJJ, Hwang CL, Beckmann MJ, Krelle W. Fuzzy multiple attribute decision making: methods and applications. Secaucus, NJ: Springer-Verlag 1992. [17] Baker AA, Rose LRF, Jones R. Advances in the bonded composite repair of metallic aircraft structure. Elsevier Science Ltd: Oxford, 2002. [18] Duong CN, Wang DCH. Composite repair: theory and design. Elsevier Science Ltd: Oxford, 2007. [19] Fayazbakhsh K, Abedian A. Materials selection for applications in space environment considering outgassing phenomenon. Adv Space Res 2009;45:7419. [20] Fouladi E, Fayazbakhsh K, Abedian A. Patch materials selection for ageing metallic aircraft structures using digital quantitative materials selection methods. 27th International Congress of the Aeronautical Sciences 2010, 19–24 September, Nice, France. [21] Wu G, Yang JM. The mechanical behavior of GLARE laminates for aircraft structures. JOM J Miner Met Mater Soc 2005;57:729.
5
Case Studies of Using Materials Ranking 5.1 RATIONALE FOR CASE STUDIES It has already been explained that there are a very large number of materials, and associated materials processes, available to the designer. To select suitable materials for a particular application necessitates the simultaneous consideration of many conflicting criteria. Apart from the simplest of products this is normally a difficult problem-solving activity. The choice of materials is often restrained (by keeping to what you know) and assumptions made (because of restricted information) and approximations used (since the analysis is difficult) to achieve workable solutions. This stifles the uptake of different materials (to a particular designer) or new materials (for all designers), and when used are often based on experience only leading to inappropriate deployment, for example, anisotropic materials treated as if they are isotropic materials, leading to possible under utilization of the materials’ performance or premature failure of a component. The methods described in the preceding chapters have been developed to assist designers cope with complex (real-world) materials selection problems. However, to help understand and appreciate the capability of the methods, worked examples and case studies are invaluable. Recent publications demonstrate the issues pertaining to the optimal selection of materials by incorporating challenging case studies such as the design of bipolar plates for a polymer electrolyte membrane fuel cell [1], flywheel [2], cryogenic storage tank [3], spar for the wing of aircraft [4], and loaded thermal conductor [5]. These and other case studies have significant impact on the future development of improved decision support systems for materials selection. The detailed case studies that follow have been carefully chosen to demonstrate the scope and explain the materials selection methods described in the preceding chapters.
5.2 MATERIALS SELECTION FOR BIOMEDICAL IMPLANTS Biomaterials are artificial or natural materials that replace diseased or damaged organic systems to provide a pain-free life for patients.
84
Multi-criteria Decision Analysis for Supporting the Selection of Engineering Materials
Biomaterials are used in different parts of the human body such as artificial valves in the heart, stents in blood vessels, replacement implants in shoulders, knees, hips, elbows, ears, and orodental structures [6,7]. In the case of biomedical implants, the increasingly ageing population is continually raising the expectations and demands for creating new and improved products, economically and in high volumes. As a consequence, developing new and improved biomedical implants is seen as a complex design problem-solving activity and, in conjunction with demanding manufacturing constraints, utilizing the most appropriate materials (and materials combinations) presents many unique challenges.
5.2.1 Hip Prosthesis A hip prosthesis comprises three main components: (1) femoral component, (2) acetabular cup, and (3) acetabular interface. The femoral component is a rigid metal pin (manufactured as a precision machined forging in cobalt chrome or titanium alloy but previously also in stainless steel, with either an integral ground and polished head or separately attached ceramic ball head) is implanted into the hollowed out shaft of the femur, replacing the natural femoral head. The hip socket (acetabulum) is inserted with an acetabular cup; a soft polymer molding (a variety of materials have been used in the past but is now predominantly in polypropylene), which is fixed to the ilium. The acetabular interface is placed between the femoral component and the acetabular cup and comes in variety of material combinations (metal on polypropylene, ceramic on ceramic, and metal on metal) to reduce wear debris generated by friction. Figure 5.1 shows typical form and position of hip joint prosthesis. The compressive strength of compact bone is about 140 MPa and the elastic modulus is about 14 GPa in the longitudinal direction and about 1/3 of that in the radial direction. These values of strength and modulus for bone are modest compared to most engineering materials. However, live healthy bone is self-healing and has a great resistance to fatigue loading. The pin and cup are fixed to the surrounding bone structure by adhesive bone cement and perform different functions. In this example, the material for the pin has been considered whose requirements are tissue tolerance, corrosion resistance, mechanical behavior, elastic compatibility, weight, and cost. Table 5.1 shows the pin’s candidate materials, criteria, objectives of the designer, and
Case Studies of Using Materials Ranking
85
Figure 5.1 Typical form and position of hip joint prosthesis.
subjective weightings [3,8]. C1, C2 are ordinal data or categorical data where there is a logical ordering to the categories that have been used for description of nonnumeric attributes, C3, C4, C7, and C8 are numeric attributes that represent absolute measure of material properties, and finally C5, C6, and C9 are ratio values. The correlation of criteria for materials selection of the hip joint prosthesis and final weighting of dependency are demonstrated in Table 5.2. Table 5.3 shows normalized values of hip joint prosthesis materials for all criteria. The subjective weightings are the same as those considered by Farag [3,8]. Table 5.4 shows objective weightings that have been extracted from Table 5.3. Table 5.5 is a summary of the weightings, including the objective weighting, weighting of dependency, and finally subjective weighting. Also, the final weighting using different levels of importance for three types of weighting is shown in Table 5.5. In this case, with regard to the type and number of criteria, the new version of both TOPSIS [9] and VIKOR [10] methods can fit as well for ranking the materials. Table 5.5 shows ranking orders of materials using different weightings and ranking methods. When the data is obtained using the comprehensive VIKOR, with λ 5 1 that means only subjective weighting, were compared with the extended TOPSIS model, only materials 5 and 8 changed places (rank 2 and 3). With λ 5 0.4, material 6 is the best one in extended TOPSIS, while with the same value of λ in the comprehensive VIKOR, material 8 is in the top rank. However, most of the time for both methods, the top ranking belongs to material 6. When tracking the ranking of material 5, it shows that decreasing λ in extended TOPSIS causes a change in ranking of this material from 3 to 6 and in the comprehensive VIKOR from 2 to 10.
Table 5.1 Decision Matrix for Hip Joint Prosthesis Materials Selection Objectives of Design
Max
Max
Max
Max
Max
Max
Target Value
Target Value
Min
Criteria
C1
C2
C3
C4
C5
C6
C7
C8
C9
Tissue
Corrosion
Tensile
Fatigue
Relative
Relative Wear
Elastic
Specific
Cost
Tolerance
Resistance
Strength
Strength
Toughness
Resistance
Modulus
Gravity (g/cc)
(MPa)
(MPa)
(GPa)
Stainless steels 316
10
7
517
350
8
8
200
8
1
Stainless steels 317
9
7
630
415
10
8.5
200
8
1.1
Stainless steels 321
9
7
610
410
10
8
200
7.9
1.1
Stainless steels 347
9
7
650
430
10
8.4
200
8
1.2
CoCr alloysCast alloy (1)
10
9
655
425
2
10
238
8.3
3.7
CoCr alloysWrought alloy (2)
10
9
896
600
10
10
242
9.1
4
Unalloyed titanium
8
10
550
315
7
8
110
4.5
1.7
Ti6Al4V
8
10
985
490
7
8.3
124
4.4
1.9
Composites (fabric reinforced)Epoxy-70% glass
7
7
680
200
3
7
22
2.1
3
Composites (fabric reinforced)Epoxy-63% carbon
7
7
560
170
3
7.5
56
1.6
10
Composites (fabric reinforced)Epoxy-62% aramid
7
7
430
130
3
7.5
29
1.4
5
Table 5.2 Correlation of Criteria and Weighting of Dependency for a Hip Joint Prosthesis C6
C7
C8
C9
Rjk
Wc
C1
C2
C3
C4
C5
C1
1.00
0.16
0.23
0.78
0.53
0.79
20.97
20.96
0.48
6.96
0.102
C2
0.16
1.00
0.57
0.48
20.01
0.48
20.18
20.05
0.13
6.42
0.095
C3
0.23
0.57
1.00
0.73
0.29
0.46
20.30
20.21
0.16
6.07
0.089
C4
0.78
0.48
0.73
1.00
0.68
0.79
20.85
20.80
0.49
5.70
0.084
C5
0.53
20.01
0.29
0.68
1.00
0.25
20.62
20.67
0.62
6.93
0.102
C6
0.79
0.48
0.46
0.79
0.25
1.00
20.81
20.76
0.13
6.66
0.098
C7
20.97
20.18
20.30
20.85
20.62
20.81
1.00
0.99
20.47
11.21
0.165
C8
20.96
20.05
20.21
20.80
20.67
20.76
0.99
1.00
20.51
10.97
0.162
C9
0.48
0.13
0.16
0.49
0.62
0.13
20.47
20.51
1.00
6.97
0.103
Table 5.3 Normalizing of Hip Joint Prosthesis Materials Row
Materials
C1
C2
C3
C4
C5
C6
C7
C8
C9
1
Stainless steels 316
1.0000
0.0000
0.1568
0.4681
0.7500
0.3333
0.1842
0.2338
1.0000
2
Stainless steels 317
0.6667
0.0000
0.3604
0.6064
1.0000
0.5000
0.1842
0.2338
0.9889
3
Stainless steels 321
0.6667
0.0000
0.3243
0.5957
1.0000
0.3333
0.1842
0.2468
0.9889
4
Stainless steels 347
0.6667
0.0000
0.3964
0.6383
1.0000
0.4667
0.1842
0.2338
0.9778
5
CoCr alloysCast alloy (1)
1.0000
0.6667
0.4054
0.6277
0.0000
1.0000
0.0175
0.1948
0.7000
6
CoCr alloysWrought alloy (2)
1.0000
0.6667
0.8396
1.0000
1.0000
1.0000
0.0000
0.0909
0.6667
7
Unalloyed titanium
0.3333
1.0000
0.2162
0.3936
0.6250
0.3333
0.5789
0.6883
0.9222
8
Ti6Al4V
0.3333
1.0000
1.0000
0.7660
0.6250
0.4333
0.5175
0.7013
0.9000
9
Composites (fabric reinforced)Epoxy-70% glass
0.0000
0.0000
0.4505
0.1489
0.1250
0.0000
0.9649
1.0000
0.7778
10
Composites (fabric reinforced)Epoxy-63% carbon
0.0000
0.0000
0.2342
0.0851
0.1250
0.1667
0.8158
0.9351
0.0000
11
Composites (fabric reinforced)Epoxy-62% aramid
0.0000
0.0000
0.0000
0.0000
0.1250
0.1667
0.9342
0.9091
0.5556
89
Case Studies of Using Materials Ranking
Table 5.4 Objective Weightings C1
C2
C3
C4
C5
C6
C7
C8
C9
Standard deviation
0.405
0.433
0.290
0.305
0.412
0.317
0.362
0.349
0.298
Objective weight
0.128
0.137
0.092
0.096
0.130
0.100
0.114
0.110
0.094
Table 5.5 Final Weightings Using Different Effect of Subjective, Objective, and Dependency Weightings C1
C2
C3
C4
C5
C6
C7
C8
C9
Subjective weight
0.200
0.200
0.080
0.120
0.080
0.080
0.080
0.080
0.080
Objective weight
0.128
0.137
0.092
0.096
0.130
0.100
0.114
0.110
0.094
Dependency weight
0.102
0.095
0.089
0.084
0.102
0.098
0.165
0.162
0.103
W(λ 5 0, (1 2 λ)/2 5 0.5)
0.115
0.116
0.090
0.090
0.116
0.099
0.140
0.136
0.098
W(λ 5 0.2, (1 2 λ)/2 5 0.4)
0.132
0.132
0.088
0.096
0.109
0.095
0.128
0.125
0.095
W(λ 5 0.4, (1 2 λ)/2 5 0.3)
0.149
0.149
0.086
0.102
0.102
0.091
0.116
0.114
0.091
W(λ 5 0.6, (1 2 λ)/2 5 0.2)
0.166
0.166
0.084
0.108
0.094
0.088
0.104
0.102
0.087
W(λ 5 0.8, (1 2 λ)/2 5 0.1)
0.183
0.183
0.082
0.114
0.087
0.084
0.092
0.091
0.084
W(λ 5 1, (1 2 λ)/2 5 0)
0.200
0.200
0.080
0.120
0.080
0.080
0.080
0.080
0.080
As a result, these rapid changes highlight the need for the aggregation technique [11] for the final optimum ranking that has been shown in Table 5.6. Figure 5.2 shows how a combination of tools and techniques can be used to select the optimum material for the hip prosthesis.
5.2.2 Knee Prosthesis Knee prostheses are implanted in the human body to relief pain and restore form and function. In order to match the performance of a natural knee, the materials of prosthesis are required to have several specific properties with values approaching those of natural biological materials (bone and tissue). In this example, metallic biomaterials (biologically compatible materials) that are currently used and newly developed metallic biomaterials that could potentially be used in the future for the femoral component of knee-joint implants (Figure 5.3) are considered as candidate materials [12,13]. For any knee implant to be successful it needs to have high wear resistance, an elastic modulus to minimize stress-shielding and biocompatibility (capability to integrate with the surrounding bone). The material property criteria considered include tensile strength, Young’s modulus, ductility, corrosion
90
Multi-criteria Decision Analysis for Supporting the Selection of Engineering Materials
Table 5.6 Aggregated Result and Individual Ranks of Hip Prosthesis Materials that Generated by Extended TOPSIS, and Comprehensive VIKOR with Different Weightings Materials
Ranking with Different Values of λ Extended TOPSIS
Aggregated Rank Comprehensive VIKOR
1
0.8
0.6
0.4
0.2
0
1
0.8
0.6
0.4
0.2
0
1
5
5
5
5
7
9
5
5
5
7
8
8
5
2
7
7
7
7
6
5
7
7
7
6
6
6
7
3
8
8
8
8
8
7
8
8
8
8
7
7
8
4
6
6
6
6
5
4
6
6
6
5
5
5
6
5
3
3
4
4
4
6
2
2
2
4
4
10
4
6
1
1
1
2
2
3
1
1
1
1
3
3
1
7
4
4
3
3
3
2
4
4
4
3
2
2
3
8
2
2
2
1
1
1
3
3
3
2
1
1
2
9
9
9
9
9
9
8
9
9
9
9
9
4
9
10
11
11
11
11
11
11
11
11
11
11
11
11
11
11
10
10
10
10
10
10
10
10
10
10
10
9
10
Determining the criteria and alternatives in format of decision matrix
Normalizing the decision matrix
Calculating the objective, subjective and dependency weightings
Ranking with different methods using different weightings
Selecting appropriate ranking method (targetbased)
Combining three types of weightings under uncertainty
Applying the aggregation method for optimum decisionmaking
Figure 5.2 The stages applied for hip prosthesis materials selection example.
Case Studies of Using Materials Ranking
91
Figure 5.3 The main components of a total knee replacement (Upper part: Femoral component, middle part: Tibial insert, lower part: Tibial tray).
resistance, wear resistance, and osseointegration ability. The metals currently used are stainless steels, CoCr alloys, titanium, and titanium alloys. The metals that could potentially be used in the future are NiTi shape memory alloys (SMA) including dense and porous NiTi. All of these materials adequately fulfill the mechanical and biological requirements. The candidate metallic materials are therefore stainless steel L316 (annealed), stainless steel L316 (cold worked), CoCr alloys (wrought CoNiCrMo), CoCr alloys (castable CoCrMo), Ti alloys (pure Ti), Ti alloys (Ti6Al4V), Ti6Al7Nb (IMI-367 wrought), Ti6Al7Nb (Protasul-100 hot-forged), NiTi SMA, and porous NiTi SMA. Table 5.7 shows the properties of these materials, 110, respectively. This case study includes interval data, incomplete data, linguistic terms, and target criteria. The fuzzy conversion scales [1416] systematically converts linguistic terms into their corresponding fuzzy numbers and used to assign the values of the attributes on a qualitative scale. An 11-point scale (Table 5.8) is used here for better understanding and representation of the qualitative attributes and converting linguistic terms into corresponding numbers (Table 5.9). The application of the interval-target based VIKOR that was described in Section 4.7 is illustrated in this case step by step as follows: Step 1: Determining the most favorable values for all criteria (Tj 5 1.3, 1240, 16, 54, 0.96, 0.96, 0.96). The target criteria are density and modulus of elasticity near to that of human bone and for all the other properties being the higher the better.
Table 5.7 Properties of Candidate Materials for Femur Component Materials Selection Objectives
Target
Max
Target
Max
Max
Max
Max
Material
Density (g/
Tensile Strength
Modulus of Elasticity
Elongation
Corrosion
Wear Resistance
Osseointegration
Number
cc)
(MPa)
(GPa)
(%)
Resistance
1
8
517
200
40
High
Above average
Above average
2
8
862
200
12
High
Very high
Above average
3
9.13
896
240
1030
Very high
Extremely high
High
4
8.3
655
240
1030
Very high
Extremely high
High
5
4.5
550
100
54
Exceptionally high
Above average
Very high
6
4.43
985
112
12
Exceptionally high
High
Very high
7
4.52
900
105120
10
Exceptionally high
High
Very high
8
4.52
10001100
110
1015
Exceptionally high
High
Very high
9
6.50
1240
48
12
Extremely high
Exceptionally high
Average
10
,4.3
1000
15
12
Very high
Exceptionally high
Exceptionally high
Case Studies of Using Materials Ranking
93
Table 5.8 Value of Materials Selection Factors in Format of 11-Point Scale Qualitative Measure of Material Selection Factor
Assigned Value
Exceptionally low
0.045
Extremely low
0.135
Very low
0.255
Low
0.335
Below average
0.410
Average
0.500
Above average
0.590
High
0.665
Very high
0.745
Extremely high
0.865
Exceptionally high
0.955
Step 2: Subjective weightings that have been calculated based on modified digital logic (MDL) [4]. In the MDL method, the scale of scores for the weighted factors is considered to be 1, 2, or, 3; one (1) for attributes that are less important, two (2) for attributes which are equally important, and three (3) for attributes that are more important. More specifically, for each pair of attributes the question asked is, which attribute (material property) is more important for the desired outcome of the end product, property A or property B? The total number of possible decisions (pair-wise comparisons), N, is N5
nðn 2 1Þ 2
where n is the number of properties/criteria under consideration. After each combination is compared and assigned a binary score, the results are put into a matrix form as shown in Table 5.10, and the number of positive decisions for each attribute (i.e., with a score of “1”) is summed and a weighting factor, Wj is calculated and normalized such that X Wj 5 1 j 5 1; . . .; n Step 3: Table 5.11 shows the required parameter for normalizing L the materials (Table 5.12). Computing valuesSiL ; SiU ; RLi ,RU i ; Qi , andQU i with v 5 0.5 is demonstrated in Table 5.13.
Table 5.9 Decision Matrix for Femur Materials Selection with Quantitative Data Material Number
Density (g/cc)
Tensile Strength (MPa)
Modulus of Elasticity (GPa)
Elongation (%)
Corrosion Resistance
Wear Resistance
Osseointegration
1
8
517
200
40
0.665
0.59
0.59
2
8
862
200
12
0.665
0.745
0.59
3
9.13
896
240
20
0.745
0.865
0.665
4
8.3
655
240
20
0.745
0.865
0.665
5
4.5
550
100
54
0.955
0.59
0.745
6
4.43
985
112
12
0.955
0.665
0.745
7
4.52
900
112.5
10
0.955
0.665
0.745
8
4.52
1050
110
12.5
0.955
0.665
0.745
9
6.5
1240
48
12
0.955
0.955
0.5
10
4.3
1000
15
12
0.745
0.955
0.955
Table 5.10 Determination of Relative Importance of Criteria Using MDL Method Criteria
Number of Possible Decisions [N 5 n(n 2 1)/2] 1
2
3
4
5
6
Density
1
1
1
1
1
1
Tensile strength
3
Modulus of elasticity Elongation Corrosion resistance Wear resistance Osseointegration
3
7
8
9
10
11
1
2
1
1
1
3 3
3 2
3
1
14
1
15
1
17
18
1
19
20
1 3
3
2
Weight
6
0.07
9
0.11
12
0.14
9
0.11
15
0.18
2
17
0.20
2
16
0.19
2
3 3
Sum 21
1
3 3
3
16
1
3 3
3
13
1 3
3
12
96
Multi-criteria Decision Analysis for Supporting the Selection of Engineering Materials
Table 5.11 Required Parameter for Normalization of Femur Materials Density
Tensile
Modulus of
Elongation
Corrosion
Wear
(g/cc)
Strength
Elasticity
(%)
Resistance
Resistance
(MPa)
(GPa)
Osseointegration
Tj
1.3
1240
16
54
0.955
0.955
0.955
max xU j
9.13
1240
240
54
0.955
0.955
0.955
xLmin j
4.3
517
15
10
0.665
0.59
0.5
Step 4: Table 5.13 shows details of calculations. According to the guideline of comparing interval data (Table 4.8), material 10 (porous NiTi SMA) has the minimum value of Qi½QLi ; QU i . The ranking of other materials is shown in Table 5.14. When considering only one criterion such as wear resistance makes CoCr alloys as the highest ranking in the currently used materials while it now has second ranking.
5.3 MATERIALS SELECTION FOR AIRCRAFT STRUCTURE REPAIR When aircraft reach the end of their service life, fatigue cracks are found to develop along rivet holes and other highly stressed regions of the airframe or structure. In order to extend the life of aircraft, repairs can be made to arrest the cracks. Three critical steps in implementing a repair are design, choice of materials, and application. Composite doublers or repair patches provide an innovative repair technique which can enhance the way in which aircraft are maintained. Bonded repair of metallic aircraft structure is used to extend the life of flawed or under-designed components at reasonable cost. Such repairs generally have one of three objectives: fatigue enhancement, crack patching, and corrosion repair. The repair of cracked structure may be performed by bonding an external patch to the structure, to either stop or slow crack growth. The selected material must be able to withstand the expected environmental conditions in the damaged area. The material selected for the patch will almost always be either metallic or composite and within these classes are many different materials with advantages and disadvantages associated with their use [17]. The processes by which the adhesive and patch materials are installed on the aircraft have a direct influence on the final properties and long-term durability
Table 5.12 Normalized Data for Femur Materials L Vi;C1
U Vi;C1
L Vi;C2
U Vi;C2
L Vi;C3
U Vi;C3
L Vi;C4
U Vi;C4
L Vi;C5
U Vi;C5
L Vi;C6
U Vi;C6
L Vi;C7
U Vi;C7
1
0.8557
0.8557
1
1
0.8178
0.8178
0.3182
0.3182
1.0172
1.0172
1.0137
1.0137
0.8132
0.8132
2
0.8557
0.8557
0.5228
0.5228
0.8178
0.8178
0.9545
0.9545
1.0172
1.0172
0.589
0.589
0.8132
0.8132
3
1
1
0.4758
0.4758
0.9956
0.9956
1
0.5455
0.7414
0.7414
0.2603
0.2603
0.6484
0.6484
4
0.894
0.894
0.8091
0.8091
0.9956
0.9956
1
0.5455
0.7414
0.7414
0.2603
0.2603
0.6484
0.6484
5
0.4087
0.4087
0.9544
0.9544
0.3733
0.3733
0
0
0.0172
0.0172
1.0137
1.0137
0.4725
0.4725
6
0.3997
0.3997
0.3527
0.3527
0.4267
0.4267
0.9545
0.9545
0.0172
0.0172
0.8082
0.8082
0.4725
0.4725
7
0.4112
0.4112
0.4703
0.4703
0.3956
0.4622
1
1
0.0172
0.0172
0.8082
0.8082
0.4725
0.4725
8
0.4112
0.4112
0.332
0.1936
0.4178
0.4178
1
0.8864
0.0172
0.0172
0.8082
0.8082
0.4725
0.4725
9
0.6641
0.6641
0
0
0.1422
0.1422
0.9545
0.9545
0.0172
0.0172
0.0137
0.0137
1.011
1.011
10
0.3831
0.3831
0.332
0.332
0.0044
0.0044
0.9545
0.9545
0.7414
0.7414
0.0137
0.0137
0.011
0.011
98
Multi-criteria Decision Analysis for Supporting the Selection of Engineering Materials
Table 5.13 Interval Numbers for S, R, and Q for Femur Materials Materials Number
SL
SU
RL
RU
QL
QU
1
0.855
0.855
0.203
0.203
1.000
1.000
2
0.788
0.788
0.182
0.182
0.791
0.791
3
0.625
0.675
0.135
0.135
0.306
0.352
4
0.654
0.704
0.135
0.135
0.333
0.378
5
0.480
0.480
0.203
0.203
0.658
0.658
6
0.484
0.484
0.162
0.162
0.368
0.368
7
0.499
0.508
0.162
0.162
0.382
0.390
8
0.459
0.486
0.162
0.162
0.345
0.371
9
0.369
0.369
0.192
0.192
0.481
0.481
10
0.306
0.306
0.133
0.133
0.000
0.000
Table 5.14 Comparing Ranking Orders of Candidate Materials for Femur Component Material Number
Material Name
Interval-Target Based VIKOR
1
Stainless steel L316 (annealed)
10
2
Stainless steel L316 (cold worked)
9
3
CoCr alloys (wrought CoNiCrMo)
2
4
CoCr alloys (castable CoCrMo)
4
5
Ti alloys (pure Ti)
8
6
Ti alloys (Ti6Al4V)
5
7
Ti6Al7Nb (IMI-367 wrought)
6
8
Ti6Al7Nb (Protasul-100 hot-forged)
3
9
NiTi SMA
7
10
Porous NiTi SMA
1
of the repair. Adhesive bonding technology (Figure 5.4), particularly bonded composite repairs, has been successfully applied by several nations to extend the lives of aircraft by bridging cracks in metallic structure, reducing strain levels, and repairing areas thinned by corrosion. Bonded composite reinforcements are highly efficient and cost effective when compared to conventional mechanically fastened approaches. In some cases, bonded repair technology is the only alternative to retiring a component. The repairs can be broadly divided into nonpatch procedures for minor damage and patch (or reinforcement) procedures to restore structural capability. The technique of repairing cracked metallic aircraft structures using high-strength
Case Studies of Using Materials Ranking
99
Vacuum line to vacuum bag Thermocouples Aircraft repair
Repair patch
Power supply to heater mat
Vacuum bag Heater mat Figure 5.4 Composite bonded repair patch being applied to an aircraft structure [18].
advanced composite materials is commonly known as “crack patching” and was pioneered by the Aeronautical and Maritime Research Laboratories (AMRL), for the Royal Australian Air Force (RAAF). The composite reinforcement, also known as the patch, can be attached to a damaged or weakened structure either by a mechanical fastener or by adhesive bonding. The use of adhesively bonded composite patches as a method of repair has several advantages over mechanically fastened repair methods, which include reduced installation cost, increased strength and fatigue life and hence effective crack retardation, reduced repair down time, elimination of unnecessary fastener holes in an already weakened structure and stress concentrations at fasteners, corrosion resistance, high stiffness, and lightweight. In selection of a patch material criteria include stiffness, strength, thickness, conformability, service temperature, and product form. The repair materials may be conventional metals, fiber metal laminates, or composites. The factors that may dictate patch materials selection include thickness, weight, stiffness, thermal expansion coefficient, ability to inspect the damage through the patch, and operating temperature requirements. Thinner patches can be designed with higher modulus materials. Composite materials have higher stiffness to weight ratios. Metals and fiber metal laminates have thermal expansion coefficients more compatible with the metal structure being repaired and are more capable of enduring elevated temperatures [18].
Table 5.15 Candidate Materials, Weightings, and Objectives for Patch Repair [17,18,20,21] Objectives
Max
Min
Max
Max
Max
Min
Max
Subjective Weightings
0.179
0.071
0.179
0.214
0.131
0.095
0.131
No.
Materials
C1
C2
C3
C4
C5
C6
C7
Thermal Expansion
Approximate Relative
Young’s
Shear
Elongation
Density
Tensile
Coefficient ( C 3 1025)
Material Cost
Modulus (GPa)
Modulus
(%)
(g/cm3)
Strength (GPa)
18
2.78
0.483
(GPa) 1
Al 2024-T3
2.32
1
73
27
2
Al 7075-T6
2.3
1
72
27
11
2.81
0.572
3
Titanium alloy 6 AL/4V
0.9
12
110
41
14
4.5
0.95 2.9
4
Aramid/Epoxy
20.8
2
82.7
2.07
2.5
1.38
5
Glass/Epoxy
0.61
1
72.5
3.52
4.8
2.58
4.03
6
HM Carbon/Epoxy
21
18
390
7.1
1.8
1.81
6.9
7
Boron/Epoxy unidirectional
0.452.3
40
20208
7
0.8
2
3.4
8
Graphite/epoxy unidirectional
0.32.8
13
12148
5
1.3
1.6
2.17
9
Aluminum laminate ARALL
1.6
7
68
17
0.89
2.3
1.282
10
Aluminum laminate GLARE
2
5
65
14.72
0.52
2.5
0.717
11
Electroformed Nickel
1.31
2
207
76
30
8.88
0.317
Case Studies of Using Materials Ranking
101
Table 5.16 Required Parameter for Normalization of Patch Repair Materials C1
C2
C3
C4
C5
C6
C7
Tj
2.8
1
390
76
30
1.38
6.9
max xU j
2.8
40
390
76
30
8.88
6.9
xLmin j
21
1
12
2.07
0.52
1.38
0.317
The application of existing materials selection methods is not popular in the aerospace environment [19]. This is in spite of selection processes being used in this field that involve a wide range of influential factors. This example presents the process of optimal materials selection for composite patch repairs in ageing metallic aircraft. The objective is to rank the candidate materials that can be used in patch repairs (Table 5.15). The material properties considered for design should take into account the effects of these processes such as the cure cycle (time/ temperature) and pressure application method used for bonding. The need is for high strength and stiffness, fatigue, and environmental durability and formability. Composites satisfy most of the requirements; however, the main disadvantage is low thermal expansion coefficient, which gives rise to undesirable residual tensile stresses in the area of the repair. Table 5.16 shows the required values for normalizing of data (Table 5.17). Table 5.18 presents other calculations and ranking of candidate materials. According to Table 5.18, metallic repairs are better choices to help simplifying the design process. However, there are also very good reasons to consider the use of composite materials. Composites make exceptionally good repair materials due to their resistance to fatigue stresses and corrosion. The main disadvantage of composites as patching materials results from their relatively low coefficient of thermal expansion compared to the parent material, which results in residual tensile mean stresses in the repaired component. It seems the fiber composites boron/epoxy, carbon/epoxy, and graphite/ epoxy are the three main options generally considered and used for patch repair materials in Australia, UK, and US [20].
Table 5.17 Normalized Values of Patch Repair Materials No.
L Vi;C1
U Vi;C1
L Vi;C2
U Vi;C2
L Vi;C3
U Vi;C3
L Vi;C4
U Vi;C4
L Vi;C5
U Vi;C5
L Vi;C6
U Vi;C6
L Vi;C7
U Vi;C7
1
0.1263
0.1263
0
0
0.8386
0.8386
0.6628
0.6628
0.4071
0.4071
0.1867
0.1867
0.9748
0.9748
2
0.1316
0.1316
0
0
0.8413
0.8413
0.6628
0.6628
0.6445
0.6445
0.1907
0.1907
0.9613
0.9613
3
0.5
0.5
0.2821
0.2821
0.7407
0.7407
0.4734
0.4734
0.5427
0.5427
0.416
0.416
0.9038
0.9038
4
0.9474
0.9474
0.0256
0.0256
0.813
0.813
1
1
0.9328
0.9328
0
0
0.6076
0.6076
5
0.5763
0.5763
0
0
0.8399
0.8399
0.9804
0.9804
0.8548
0.8548
0.16
0.16
0.436
0.436
6
1
1
0.4359
0.4359
0
0
0.932
0.932
0.9566
0.9566
0.0573
0.0573
0
0
7
0.6184
0.1316
1
1
0.9788
0.4815
0.9333
0.9333
0.9905
0.9905
0.0827
0.0827
0.5317
0.5317
8
0.8158
0
0.3077
0.3077
1
0.6402
0.9604
0.9604
0.9735
0.9735
0.0293
0.0293
0.7185
0.7185
9
0.3158
0.3158
0.1538
0.1538
0.8519
0.8519
0.7981
0.7981
0.9874
0.9874
0.1227
0.1227
0.8534
0.8534
10
0.2105
0.2105
0.1026
0.1026
0.8598
0.8598
0.8289
0.8289
1
1
0.1493
0.1493
0.9392
0.9392
11
0.3921
0.3921
0.0256
0.0256
0.4841
0.4841
0
0
0
0
1
1
1
1
103
Case Studies of Using Materials Ranking
Table 5.18 Interval Numbers for S, R, and Q for Patch Repair Materials Materials
SL
SU
RL
RU
QL
QU
Rank
Al 2024-T3
0.513
0.513
0.150
0.150
0.279
0.279
3
Al 7075-T6
0.544
0.544
0.151
0.151
0.322
0.322
4
Titanium alloy 6 AL/4V
0.572
0.572
0.133
0.133
0.249
0.249
2
Aramid/Epoxy
0.733
0.733
0.214
0.214
0.944
0.944
11
Glass/Epoxy
0.648
0.648
0.210
0.210
0.810
0.810
9
HM Carbon/Epoxy
0.540
0.540
0.199
0.199
0.611
0.611
6
Boron/Epoxy unidirectional
0.588
0.764
0.200
0.200
0.673
0.898
8
Graphite/epoxy unidirectional
0.566
0.777
0.206
0.206
0.681
0.949
10
Aluminum laminate ARALL
0.644
0.644
0.171
0.171
0.570
0.570
5
Aluminum laminate GLARE
0.644
0.644
0.177
0.177
0.611
0.611
7
Electroformed Nickel
0.385
0.385
0.131
0.131
0.000
0.000
1
REVIEW QUESTIONS 1. What are the possible ways of obtaining objective and dependency weighting for interval data? 2. In the materials selection for a knee prosthesis case study: a. Calculate the objective weightings. b. Combine the objective and subjective weightings, with the assumption of uncertainty in importance of each type of weightings. c. Obtain the ranking order of materials for different weightings and interpret the final ranking of materials using a graph that shows frequency of each material to each rank (e.g., if you obtain the ranking of materials 10 times and Material 1 assigns to rank 8, 7 times; then you might interpret Material 1 has rank 8 with 70 % confidence). 3. In the materials selection for an aircraft patch repair case study: a. Obtain the weighting of dependency and objective. b. Combine the three types of weightings with the assumption of equal importance on each type of weightings and calculate the final ranking of materials. c. Using the middle value of interval data and weighting obtained in the last step; determine the ranking orders of materials by both comprehensive VIKOR method and target-based TOPSIS method. d. If it is applicable, obtain the optimum ranking of materials by the aggregation method. e. If a designer decides to consider only composite materials for the repair, do you think you should recalculate the ranking of materials and why?
104
Multi-criteria Decision Analysis for Supporting the Selection of Engineering Materials
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