Abstract
In this paper, an approach for selection of materials in metal additive manufacturing based on three-way decision-making is proposed. The process of this approach is divided into three stages. First, a decision matrix for a material selection problem in metal additive manufacturing is established based on the basic components of the problem and normalised via a ratio model and a unified rule. Second, the summary loss function, conditional probability, and expected losses of each alternative material are calculated according to the weighted averaging operator, grey relational analysis, and the three-way decision theory, respectively. Third, the three-way decision-making results for the problem are generated according to the developed generation rules and the best material for the problem is selected based on the generated results. The application of the approach is illustrated via a material selection example in metal additive manufacturing. The effectiveness of the approach is demonstrated via a quantitative comparison with several existing approaches. The demonstration results suggest that the proposed approach is as effective as the existing approaches and is more flexible and advantageous in solving a material selection problem in metal additive manufacturing.
Similar content being viewed by others
Avoid common mistakes on your manuscript.
1 Introduction
Metal additive manufacturing (AM) is a set of processes that join metal materials layer upon layer to build metal components directly from their three-dimensional model data [1,2,3,4]. Representative metal AM technologies include direct metal laser sintering, selective laser melting, electron beam melting, and direct metal deposition [5,6,7]. The research and application of metal AM processes are gaining importance and popularity because of their attractive advantages over conventional subtractive manufacturing technologies, which mainly include flexible geometric design, no extra cost to achieve geometric complexity, eliminating costs on waste material, tooling, and non-essential assembly, and reducing the production time [8].
Application of a metal AM technology to manufacture a component includes a set of activities, where material selection is a critical one [9, 10]. In this activity, a material that can simultaneously optimise certain key factors for a specific application, such as the quality, property, manufacturability, and cost of the component, is selected from a certain number of available materials. Currently, nearly 1500 materials for metal AM have been developed and sold on the market [11]. How to select appropriate materials to build a component satisfying certain requirements is not easy [12]. There are two main reasons for this. First, the selection needs a comprehensive understanding of the utilities, performance, strengths, and limitations of all alternative materials and the influence of materials on the property and quality of the component, which is difficult to achieve. Second, different materials might belong to the same material type and have considerable overlap in utilities, performance, properties, metallurgical incompatibilities, and limitations [13, 14], which increases the difficulty in actual selection.
To assist selection of materials in AM, many approaches have been developed in the literature [15]. For example, a knowledge-based system for AM material selection integrated with an existing computer-aided design (CAD) environment was developed in [16]; an AM process and material selection approach based on CAD feature analysis was presented in [17]; a targeted material selection process for polymers in laser sintering was introduced in [18]; An integrated decision-making model for multi-criterion decision-making (MCDM) problems in design for AM based on an aggregation of deviation and similarity models was developed in [19]; an integrated AM material and process selection method based on analytical hierarchy process and simple additive weighting was presented in [20]; A heuristic and analytical algorithm for AM material selection based on analytical hierarchy process was developed in [21]; an integrated AM material-design-process selection methodology based on analytical hierarchy process was developed in [22]; a multi-criterion evaluation system for AM process and resource selection based on analytical hierarchy process was developed in [23]; an AM machine and material selection approach based on best-worst method was presented in [24]; a generic method for MCDM problems in design for AM based on a fuzzy power weighted Maclaurin symmetric mean operator was developed in [25]; four MCDM methods including SAW (simple additive weighting), MOORA (multi-objective optimisation based on ratio analysis), TOPSIS (technique for order performance by similarity to ideal solution), and VIKOR (abbreviation of a term in Serbian that means multi-criterion optimisation and compromise solution) were applied to sustainable AM material selection in [26]; a material selection approach for biomedical AM based on TOPSIS was developed in [27]; a metal AM material selection approach based on information entropy method and CODAS (combinative distance-based assessment) was presented in [28].
The selection of AM materials is usually associated with the selection of AM processes/machines, since the materials supported by different processes/machines are usually different. In practice, to fabricate a part or a group of parts, an AM process/machine to be used is generally determined first, and then a material satisfying certain requirements is selected from among those supported by the process/machine and also available on the market [20]. An AM process/machine selection approach might also be applied to AM material selection. Currently, there are also many AM process/machine selection approaches in the literature [29]. For example, an AM process selection method based on graph theory and matrix approach was developed in [30]; an approach for selection of AM techniques based on an adaptive analytical hierarchy process was presented in [31]; six MCDM methods including TOPSIS, graph theory and matrix approach, analytical hierarchy process, multiplicative analytical hierarchy process, simple pair analysis, and Verein Deutscher Ingenieure were applied to selection of AM technologies in [32]; an AM process selection approach based on analytical hierarchy process and the technical specifications of a part was presented in [33]; a decision-making methodology to facilitate AM process selection and assist product/part design based on analytical hierarchy process was developed in [34]; an AM process selection method based on fuzzy logic was proposed in [35]; An experimental design approach for the selection of AM processes based on TOPSIS was developed in [36]; a decision support method for AM process selection based on knowledge value measuring was proposed in [37]; a decision support system for AM process selection based on fuzzy set was developed in [38]; a weighted rough set based fuzzy axiomatic design approach for AM process selection was presented in [39]; an integration of fuzzy analytical hierarchy process and fuzzy TOPSIS was applied to prioritise AM processes for micro-fabrication in [40]; a decision support system for AM process selection based on a hybrid of analytical hierarchy process and a modified TOPSIS was developed in [41]; an approach to evaluate the AM machine selection problem for healthcare applications based on an integration of fuzzy analytic hierarchy process and TOPSIS was presented in [42]; an AM machine selection approach based on fuzzy power weighted Bonferroni aggregation operators was proposed in [43]; an MCDM method for AM process selection based on stepwise weight assessment ratio analysis and complex proportional assessment was presented in [44].
Each of the AM material/process/machine selection approaches above can work well in its specific context, but they lack flexibility and could generate undesirable results when prior knowledge for selection is insufficient or the cost of improper decisions is high, because they are all based on two-way decision model (2WDM). 2WDM is a granular computing technique commonly used in MCDM. As the name suggests, there are two decisions on an alternative in 2WDM. They are acceptance and rejection, which mean that an alternative is either accepted or rejected. 2WDM is simple and direct and has certain advantages when prior knowledge for decision-making is sufficient or replacement of improper decisions does not require a high cost. However, there is yet no evidence that a comprehensive knowledge base for selection of materials in metal AM has been established. Further, many metal AM processes are widely known for their high machine, material, and processing costs [45, 46].
In this paper, three-way decision model (3WDM) is introduced to propose a new approach for selection of materials in metal AM. 3WDM is another granular computing technique used in MCDM [47]. Compared to 2WDM, 3WDM has an additional decision called abstaining. This makes the model more flexible and advantageous than 2WDM since it effectively prevents premature classification of the alternatives at the edge of acceptance and rejection. Because of such feature, 3WDM is more suitable for the decision-making problems where there is not enough prior knowledge or replacement of inappropriate decisions is costly [48]. Here a real-life decision-making example cited from [49] is introduced to intuitively compare the two models. A woman was going to make an omelette with only six eggs left in her kitchen. After she had beaten five eggs in a bowl, her husband arrived to assist with the last egg. He appreciates decision-making theory. Two thoughts crossed his mind as he picked up the last egg: Was this egg a good one? Which decision-making model was most suitable for the current circumstance? If he adopts 2WDM, there will be two options for him. One option is beating the egg to the bowl and the other is discarding it. The benefits and possible costs associated with these options are shown in Fig. 1. Naturally, if he is confident that the last egg is a good egg, then the first option is more suitable; Otherwise, the second option is better. However, if it is difficult for him to judge whether the last egg is good or bad, then neither option seems to be suitable. In other words, it appears that 2WDM is not suited for this circumstance. If the man adopts 3WDM, an additional option, beating the egg to a new bowl to have a check, will be available for him. The benefits and possible costs associated with this option are also shown in Fig. 1. It can be seen that 3WDM is more suitable than 2WDM under the circumstance.
The remainder of the paper is organised as follows: Section 2 describes the details of the proposed approach. An illustration of the application of the approach and a demonstration of the effectiveness of the approach are documented in Section 3. Section 4 draws a conclusion of the paper.
2 The proposed approach
In this section, the proposed approach for selection of materials in metal AM is described in detail. A general flow of this approach is delineated in Fig. 2. The proposed approach takes as input a set of alternative materials, certain selection criteria, value of each selection criterion of each alternative material, and weight of each selection criterion and outputs three-way decision-making results together with the best material for a material selection problem in metal AM. Its main process is divided into three stages: initialisation, calculation, and determination. In the initialisation stage, a decision matrix for the problem is first established and then normalised. In the calculation stage, the summary loss function, conditional probability, and expected losses of each alternative material are successively calculated. In the determination stage, the three-way decision-making results for the problem are generated and the best material for the problem is selected. The details of these three stages are explained below.
2.1 Initialisation stage
There are two steps in the initialisation stage. The first step is to establish a decision matrix for a material selection problem in metal AM. Formally, the basic components of this problem include m alternative materials M1,M2,...,Mm, n selection criteria C1,C2,...,Cn, value of each selection criterion (Cj) of each alternative material (Mi) xi,j (i = 1,2,...,m;j = 1,2,...,n), and weight of each selection criterion (Cj) wj (0 ≤ wj ≤ 1 and \({\Sigma }_{j=1}^{n} w_{j} = 1\)). The alternative materials can be screened from current material types available for metal AM, which mainly include stainless steel, tool steel, titanium alloy, aluminium alloy, inconel, nickel alloy, and copper alloy [11]. The selection criteria are generally identified according to the specific requirements of the component to be built, in which the properties of alternative materials (e.g. density, melting point, tensile strength, hardness, thermal conductivity), the predicted properties of the built component (e.g. predicted tensile strength, predicted hardness, predicted elongation, predicted surface roughness), and the predicted cost to build the component may be considered [50]. The values of selection criteria of alternative materials can be acquired from vendor documents and benchmark data, prediction based on theoretical models, simulations, or experiments, or evaluation based on expert experience [29]. Based on these components, a decision matrix is established as A = [xi,j]m×n.
The second step is to normalise the established decision matrix. The values of different criteria usually have different ranges, which cause inconvenience to subsequent calculations. To this end, each criterion value is converted into a number in [0, 1] using the following ratio model [51]:
Further, there are generally two types of criteria in an MCDM problem. They are positive and negative criteria. The value of a positive criterion is positively correlated with the decision-making results, while the value of a negative criterion is the opposite. For example, the hardness and price of a material respectively belong to a positive criterion and a negative criterion in a material selection problem in metal AM, since the greater the hardness and the lower the price, the better the decision-making results. To unify the effect of different types of criteria, the following unified rule is applied to each converted criterion value:
Through the conversion and unification, a normalised decision matrix is obtained as B = [zi,j]m×n.
2.2 Calculation stage
The calculation stage consists of two parallel steps and a subsequent step. The first step is to calculate the summary loss function of each alternative material. Let Sj and ¬Sj be two states that respectively stand for the alternative material Mi meets the selection criterion Cj and Mi does not meet Cj. Each state corresponds to the three decisions acceptance (denoted as DACC), abstaining (denoted as DABS), and rejection (denoted as DREJ) in 3WDM. Inspired by the relative loss functions developed in [52,53,54], a relative loss function derived from the normalised criterion value zi,j is established in Table 1, where 0 ≤ λj ≤ 1 is a risk avoidance coefficient that corresponds to Cj.
This relative loss function is explained as follows: The cost of correct decisions is 0; The cost of rejection is zi,j when Mi meet Cj; The cost of acceptance is 1 − zi,j when Mi does not meet Cj; The cost of abstaining in each state lies between the cost of acceptance and the cost of rejection in this state. According to the relative loss function in Table 1, each normalised criterion value zi,j is converted into a relative loss function:
Using the weighted averaging operator, the relative loss functions of each alternative material (i.e. the n relative loss functions f(zi,1),f(zi,2),...,f(zi,n)) are aggregated into a summary loss function:
The second step is to calculate the conditional probability of each alternative material. One of the crucial elements of 3WDM is the conditional probability. In some applications of 3WDM, the conditional probabilities are assigned an identical fixed value. However, the conditional probabilities of the alternatives in an MCDM problem are typically different and generally need to be determined according to the values of criteria of alternatives. In [55], TOPSIS is used to determine the conditional probabilities. The two states of a criterion are referred to as the positive and negative ideal solutions. The conditional probabilities of alternatives are implied by the final relative closeness degrees. This method, which uses distance as a scale, can only reflect how the data curves are positioned in relation to one another and cannot convey the significance of alternatives through the trend in a data sequence. Grey relational analysis [56], a technique for assessing the degree of relationship between data sequences, was found to provide an effective measure for the trend difference of data sequences and the similarity between data curves [53]. To this end, grey relational analysis is applied to calculate the conditional probability of each alternative material. Firstly, the grey relational coefficients between the alternative material Mi and \(\max \limits _{j=1}^{n}\{z_{i,j}\}\) and between Mi and \(\min \limits _{j=1}^{n}\{z_{i,j}\}\) are calculated as
Then, the grey relational degrees of Mi with respect to \(\max \limits _{j=1}^{n}\{z_{i,j}\}\) and of Mi with respect to \(\min \limits _{j=1}^{n}\{z_{i,j}\}\) are calculated as
Finally, the conditional probability of Mi is computed as the relative closeness of the grey relation of Mi
where S is a state that stands for the alternative material Mi meets an aggregation of all n criteria.
The third step is to calculate the expected losses of each alternative material. Let ¬S be a state that stands for the alternative material Mi does not meet an aggregation of all n criteria. If P(S|[Mi]) + P(¬S|[Mi]) = 1, according to the three-way decision theory [47], the summary loss function in Eq. (4), and the conditional probability in Eq. (9), the expected losses of Mi when making the decision D∗ (∗ = ACC, ABS, REJ) are calculated as
2.3 Determination stage
There are two steps in the determination stage. The first step is to generate three-way decision-making results for the material selection problem. According to the Bayesian decision theory, the decision with the lowest cost is the best one [47]. Based on this, three decision rules are developed as follows:
-
(1)
If L(DACC|[Mi]) ≤ L(DABS|[Mi]) and L(DACC|[Mi]) ≤ L(DREJ|[Mi]), then make the decision DACC for Mi;
-
(2)
If L(DABS|[Mi]) ≤ L(DACC|[Mi]) and L(DABS| [Mi]) ≤ L(DREJ|[Mi]), then make the decision DABS for Mi;
-
(3)
If L(DREJ|[Mi]) ≤ L(DACC|[Mi]) and L(DREJ |[Mi]) ≤ L(DABS|[Mi]), then make the decision DREJ for Mi.
On the basis of these decision rules, the three-way decision-making results can be generated according to the following rules: If the decision DACC is made for Mi, then classify Mi to an acceptance set MACC; If the decision DABS is made for Mi, then classify Mi to an abstaining set MABS; If the decision DREJ is made for Mi, then classify Mi to a rejection set MREJ.
The second step is to select the best material. According to the three-way decision theory [47] and the generated three-way decision-making results, the best material is selected from the acceptance set MACC if this set is non-empty. Otherwise, it is selected from the abstaining set MABS.
3 Application and demonstration
In this section, the application of the proposed approach is first illustrated via a material selection example in metal AM [28]. Then a quantitative comparison between the proposed approach and several existing approaches is carried out to demonstrate the effectiveness of the approach.
3.1 Application of the proposed approach
A user needs to select a material from eight alternative materials to build a component using a metal AM process. The eight alternative materials are 316L stainless steel (M1), H13 tool steel (M2), Ti6Al4V titanium alloy (M3), AlSi10Mg aluminium alloy (M4), AlSi12Cu2Fe aluminium alloy (M5), Inconel 718 (M6), Hastelloy X nickel alloy (M7), and CuSn10 copper alloy (M8). The selection criteria of these materials are identified as price (C1), density (C2), tensile strength (yield) (C3), elastic modulus (C4), Brinell hardness (C5), and electrical resistivity (C6). The values of these criteria of the eight alternative materials are cited from [28] and listed in Table 2. The weights of the selection criteria are assumed to be 0.3, 0.1, 0.3, 0.1, 0.1, and 0.1, respectively.
Using the proposed approach, the material selection problem above can be solved according to the following steps:
(1) Establish a decision matrix. Based on the eight alternative materials, six selection criteria, and values of the six selection criteria of the eight alternative materials, a decision matrix for the material selection problem is established as A = [xi,j]8×6, where the values of xi,j are listed in Table 2.
(2) Normalise the decision matrix. According to Eq. (1), each criterion value in A (i.e. xi,j) is converted into a number in [0, 1] (i.e. yi,j). Further, among the six selection criteria, price is a negative criterion, while the remaining ones are positive criteria. Based on this, the converted criterion values (i.e. [yi,j]8×6) are normalised according to Eq. (2) and a normalised decision matrix is obtained as
(3) Calculate the summary loss functions. According to Eq. (3), each normalised criterion value in B (i.e. zi,j) is converted into a relative loss function (i.e. f(zi,j)), in which the risk avoidance coefficients of the six selection criteria take the same value 0.35. Then according to Eq. (4) and the given weights, the relative loss functions of each alternative material (i.e. f(zi,1),f(zi,2),...,f(zi,9)) are aggregated into a summary loss function (i.e. f(zi)), as listed in Table 3.
(4) Calculate the conditional probabilities. According to Eqs. (5)–(9), the conditional probability of each alternative material (i.e. P(S|[Mi])) is respectively calculated, as listed in Table 4.
(5) Calculate the expected losses. According to Eqs. (10)–(12), the expected losses of each alternative material when making the decision D∗ (∗ = ACC, ABS, REJ) are respectively calculated, as listed in Table 5.
(6) Generate three-way decision-making results. According to the developed decision and classification rules, the three-way decision-making results for the material selection problem are obtained as MACC = {M2}, MABS = {M1,M3,M6}, and MREJ = {M4,M5,M7,M8}.
(7) Select the best material. Based on the generated three-way decision-making results, M2 (i.e. H13 tool steel) is selected as the best material for the material selection problem.
3.2 Demonstration of effectiveness
As reviewed in the introduction, most of the existing AM material/process/machine selection approaches are based on certain MCDM methods, which mainly include analytical hierarchy process, best-worst method, fuzzy power weighted Bonferroni aggregation operators (FPWBAOs), fuzzy power weighted Maclaurin symmetric mean operator (FPWMSMO), SAW, MOORA, TOPSIS, VIKOR, and CODAS. To demonstrate the effectiveness of the proposed approach, a quantitative comparison between it and the existing approaches based on FPWBAOs [43], FPWMSMO [25], SAW [26], MOORA [26], TOPSIS [26], VIKOR [26], and CODAS [28] is carried out. In this comparison, each approach is applied to solve the material selection problem above. Each value in Table 2 is converted into a number in [0, 1] using the ratio model in Eq. (1). The converted results together with the given criterion weights are taken as the input of the existing approaches. It is worth noting that the existing approaches based on analytical hierarchy process and best-worst method are not included in the comparison, because these two methods are based on pairwise comparison of criteria and require specific pairwise comparison matrices as input, while there are not such matrices in the material selection problem. When adapting the FPWMSMO, both of the controlling parameters of Maclaurin symmetric mean and Hamacher t-norm and t-conorm are set to 3. When adapting the FPWBAOs, both of the controlling parameters of Bonferroni mean and geometric Bonferroni mean are set to 1 and 2; The controlling parameter of Hamacher t-norm and t-conorm is set to 3; The risk attitude factor is set to 0.5. The results of the comparison are listed in Table 6.
As can be seen from Table 6, M2 is the alternative material in the first position of each order, M3 and M1 or M3 and M6 are the alternative materials in the second and third positions, and the remaining alternative materials are in the following positions. Such results are fully consistent with the three-way decision-making results generated by the proposed approach: M2 is recommended, M4, M5, M7, and M8 are not recommended, and the remaining alternative materials require more prior knowledge to make further decisions. This validates the proposed approach in solving a material selection problem in metal AM.
The quantitative comparison above has demonstrated that the proposed approach is as effective as several existing approaches from the perspective of generated decision-making results. As the proposed approach comes from a combination of 3WDM and MCDM, it has a significant advantage over these existing approaches. The existing approaches are based on conventional 2WDM, while the proposed approach is based on 3WDM. As illustrated in the introduction, 3WDM is more flexible than 2WDM since it can effectively avoid hasty classification of the alternatives in a state of hesitation. Benefiting from this feature, 3WDM is more suitable for a decision-making problem in which there is not sufficient prior knowledge or replacement of improper decisions requires a high cost. There is not a comprehensive knowledge base for material selection in metal AM and many metal AM processes are widely known for their high costs. From these two aspects, the proposed approach may be more advantageous than the existing approaches.
4 Conclusion
In this paper, an approach for selection of materials in metal AM based on three-way decision-making is presented. The main process of this approach consists of an initialisation stage, a calculation stage, and a determination stage. In the initialisation stage, a decision matrix for a material selection problem in metal AM is established and normalised. The summary loss function, conditional probability, and expected losses of each alternative material are successively calculated in the calculation stage. In the determination stage, the three-way decision-making results for the problem are produced and the best material for the problem is determined. The paper also introduces a material selection example in metal AM to illustrate the application of the presented approach and demonstrates the effectiveness of the approach via a quantitative comparison with several existing approaches. The demonstration results suggest that the presented approach is as effective as the existing approaches and is more flexible than them in solving a material selection problem in metal AM.
Future work will aim especially at studying the application of three-way decision-making in solving other MCDM problems in the field of AM. For example, three-way decision-making would be applied to determine the optimal AM part design variant from a set of candidate design variants, choose the best AM machine to fabricate a specific component from several available machines, find the optimal orientation to build an AM part from a certain number of alternative orientations, select the best combination of process parameters to build an AM part or a group of AM parts from some possible combinations, and schedule AM component batches to a network of AM machines.
References
Gibson I, Rosen D, Stucker B, Khorasani M (2021) Additive manufacturing technologies. Springer, Cham
Cooke S, Ahmadi K, Willerth S, Herring R (2020) Metal additive manufacturing: technology, metallurgy and modelling. J Manuf Process 57:978–1003
Cam G (2022) Prospects of producing aluminum parts by wire arc additive manufacturing (WAAM). Materials Today: Proceedings 62(1):77–85
Xiong Y, Tang Y, Zhou Q, Ma Y, Rosen DW (2022) Intelligent additive manufacturing and design state of the art and future perspectives. Addit Manuf 59:103139
Ramalho A, Santos TG, Bevans B, Smoqi Z, Rao P, Oliveira JP (2022) Effect of contaminations on the acoustic emissions during wire and arc additive manufacturing of 316L stainless steel. Addit Manuf 51:102585
Li B, Wang L, Wang B, Li D, Oliveira JP, Cui R, Yu J, Luo L, Chen R, Su Y, Guo J, Fu H (2022) Electron beam freeform fabrication of NiTi shape memory alloys: crystallography, martensitic transformation, and functional response. Materials Science and Engineering: A 843:143135
Zuo X, Zhang W, Chen Y, Oliveira JP, Zeng Z, Li Y, Luo Z, Ao S (2022) Wire-based Directed Energy Deposition of NiTiTa shape memory alloys: microstructure, phase transformation, electrochemistry, X-ray visibility and mechanical properties. Addit Manuf 59:103115
Gu D, Shi X, Poprawe R, Bourell DL, Setchi R, Zhu J (2021) Material-structure-performance integrated laser-metal additive manufacturing. Science 372(6545):eabg1487
Thompson MK, Moroni G, Vaneker T, Fadel G, Campbell RI, Gibson I, Bernard A, Schulz J, Graf P, Ahuja B, Martina F (2016) Design for Additive Manufacturing: trends, opportunities, considerations, and constraints. CIRP Ann 65(2):737–760
Vaneker T, Bernard A, Moroni G, Gibson I, Zhang Y (2020) Design for additive manufacturing: Framework and methodology. CIRP Ann 69(2):578–599
Senvol LLC (2022) Senvol database: Industrial additive manufacturing machines and materials–materials search. http://senvol.com/material-search/ Accessed 6 Aug 2022
Bourell D, Kruth JP, Leu M, Levy G, Rosen D, Beese AM, Clare A (2017) Materials for additive manufacturing. CIRP Ann 66(2):659–681
Rodrigues TA, Farias FWC, Zhang K, Shamsolhodaei A, Shen J, Zhou N, Schell N, Capek J, Polatidis E, Santos TG, Oliveira JP (2022a) Wire and arc additive manufacturing of 316L stainless steel/Inconel 625 functionally graded material: development and characterization. J Market Res 21:237–251
Rodrigues TA, Bairrao N, Farias FWC, Shamsolhodaei A, Shen J, Zhou N, Maawad E, Schell N, Santos TG, Oliveira JP (2022b) Steel-copper functionally graded material produced by twin-wire and arc additive manufacturing (T-WAAM). Materials & Design 213:110270
Rahim AAA, Musa SN, Ramesh S, Lim MK (2020) A systematic review on material selection methods. Proceedings of the Institution of Mechanical Engineers Part L: J Mater: Des Appl 234(7):1032–1059
Smith PC, Rennie AEW (2010) Computer aided material selection for additive manufacturing materials. Virtual Phys Prototyp 5(4):209–213
Smith PC, Lupeanu ME, Rennie AEW (2012) Additive manufacturing technology and material selection for direct manufacture of products based on computer aided design geometric feature analysis. Int J Mater Struct Integr 6(2-4):96–110
Vasquez GM, Majewski CE, Haworth B, Hopkinson N (2014) A targeted material selection process for polymers in laser sintering. Addit Manuf 1:127–138
Zhang Y, Bernard A (2014) An integrated decision-making model for multi-attributes decision-making (madm) problems in additive manufacturing process planning. Rapid Prototyp J 20(5):377– 389
Uz Zaman UK, Rivette M, Siadat A, Mousavi SM (2018) Integrated product-process design: Material and manufacturing process selection for additive manufacturing using multi-criteria decision making. Robot Comput Integr Manuf 51:169–180
Alghamdy M, Ahmad R, Alsayyed B (2019) Material selection methodology for additive manufacturing applications. Procedia CIRP 84:486–490
Hodonou C, Balazinski M, Brochu M, Mascle C (2019) Material-design-process selection methodology for aircraft structural components: application to additive vs subtractive manufacturing processes. Int J Adv Manuf Technol 103(1):1509–1517
Kadkhoda-Ahmadi S, Hassan A, Asadollahi-Yazdi E (2019) Process and resource selection methodology in design for additive manufacturing. Int J Adv Manuf Technol 104(5):2013–2029
Palanisamy M, Pugalendhi A, Ranganathan R (2020) Selection of suitable additive manufacturing machine and materials through best–worst method (BWM). Int J Adv Manuf Technol 107(5):2345–2362
Huang M, Chen L, Zhong Y, Qin Y (2021) A generic method for multi-criterion decision-making problems in design for additive manufacturing. Int J Adv Manuf Technol 115(7):2083–2095
Agrawal R (2021) Sustainable material selection for additive manufacturing technologies: a critical analysis of rank reversal approach. J Clean Prod 296:126500
Jha MK, Gupta S, Chaudhary V, Gupta P (2022) Material selection for biomedical application in additive manufacturing using TOPSIS approach. Materials Today: Proceedings 62(3):1452–1457
Malaga AK, Agrawal R, Wankhede VA (2022) Material selection for metal additive manufacturing process. Materials Today: Proceedings 66(4):1744–1749
Wang Y, Blache R, Xu X (2017) Selection of additive manufacturing processes. Rapid Prototyp J 23(2):434–447
Rao RV, Padmanabhan KK (2007) Rapid prototyping process selection using graph theory and matrix approach. J Mater Process Technol 194(1-3):81–88
Armillotta A (2008) Selection of layered manufacturing techniques by an adaptive AHP decision model. Robot Comput Integr Manuf 24(3):450–461
Borille A, Gomes J, Meyer R, Grote K (2010) Applying decision methods to select rapid prototyping technologies. Rapid Prototyp J 16(1):50–62
Mancanares CG, de S Zancul E, Cavalcante da Silva J, Cauchick Miguel PA (2015) Additive manufacturing process selection based on parts’ selection criteria. The International Journal of Advanced Manufacturing Technology 80(5):1007–1014
Liu W, Zhu Z, Ye S (2020) A decision-making methodology integrated in product design for additive manufacturing process selection. Rapid Prototyp J 26(5):895–909
Khrais S, Al-Hawari T, Al-Araidah O (2011) A fuzzy logic application for selecting layered manufacturing techniques. Expert Syst Appl 38(8):10286–10291
Ic YT (2012) An experimental design approach using TOPSIS method for the selection of computer-integrated manufacturing technologies. Robot Comput Integr Manuf 28(2):245–256
Zhang Y, Xu Y, Bernard A (2014) A new decision support method for the selection of rp process: Knowledge value measuring. Int J Comput Integr Manuf 27(8):747–758
Vimal KEK, Vinodh S, Brajesh P, Muralidharan R (2016) Rapid prototyping process selection using multi criteria decision making considering environmental criteria and its decision support system. Rapid Prototyp J 22(2):225–250
Zheng P, Wang Y, Xu X, Xie SQ (2017) A weighted rough set based fuzzy axiomatic design approach for the selection of AM processes. The International Journal of Advanced Manufacturing Technology 91(5):1977–1990
Anand MB, Vinodh S (2018) Application of fuzzy AHP–TOPSIS for ranking additive manufacturing processes for microfabrication. Rapid Prototyp J 24(2):424–435
Wang Y, Zhong RY, Xu X (2018) A decision support system for additive manufacturing process selection using a hybrid multiple criteria decision-making method. Rapid Prototyp J 24(9):1544–1553
Ransikarbum K, Khamhong P (2021) Integrated fuzzy analytic hierarchy process and technique for order of preference by similarity to ideal solution for additive manufacturing printer selection. J Mater Eng Perform 30(9):6481–6492
Qin Y, Qi Q, Scott PJ, Jiang X (2020) An additive manufacturing process selection approach based on fuzzy Archimedean weighted power Bonferroni aggregation operators. Robot Comput Integr Manuf 64:101926
Chandra M, Shahab F, Vimal K, Rajak S (2022) Selection for additive manufacturing using hybrid MCDM technique considering sustainable concepts. Rapid Prototyp J 28(7):1297–1311
Baumers M, Tuck C, Wildman R, Ashcroft I, Rosamond E, Hague R (2013) Transparency built-in: Energy consumption and cost estimation for additive manufacturing. J Ind Ecol 17(3):418– 431
Baumers M, Dickens P, Tuck C, Hague R (2016) The cost of additive manufacturing: machine productivity, economies of scale and technology-push. Technol Forecast Soc Chang 102:193– 201
Yao Y (2010) Three-way decisions with probabilistic rough sets. Inf Sci 180(3):341–353
Yao Y (2011) The superiority of three-way decisions in probabilistic rough set models. Inf Sci 181(6):1080–1096
Yao Y (2012) Three-way decisions. In: Jia X, Shang L, Zhou X, Liang J, Miao D, Wang G, Li T, Zhang Y (eds) Theory and Application of Three-Way Decisions. Nanjing University Press, pp 1–16
Seifi M, Salem A, Beuth J, Harrysson O, Lewandowski JJ (2016) Overview of materials qualification needs for metal additive manufacturing. Jom 68(3):747–764
Brauers WKM, Zavadskas EK, Peldschus F, Turskis Z (2008) Multi-objective decision-making for road design. Transport 23(3):183–193
Jia F, Liu P (2019) A novel three-way decision model under multiple-criteria environment. Inf Sci 471:29–51
Liu P, Wang Y, Jia F, Fujita H (2020) A multiple attribute decision making three-way model for intuitionistic fuzzy numbers. Int J Approx Reason 119:177–203
Qin Y, Qi Q, Shi P, Scott PJ, Jiang X (2022) A multi-criterion three-way decision-making method under linguistic interval-valued intuitionistic fuzzy environment. Journal of Ambient Intelligence and Humanized Computing. https://doi.org/10.1007/s12652-022-04102-6
Liang D, Xu Z, Liu D, Wu Y (2018) Method for three-way decisions using ideal TOPSIS solutions at Pythagorean fuzzy information. Inf Sci 435:282–295
Deng J (1989) Introduction to grey system theory. J Grey Syst 1(1):1–24
Acknowledgements
The authors are very grateful to the three anonymous reviewers for their insightful comments for the improvement of the paper.
Funding
This study was supported by the EPSRC UKRI Innovation Fellowship (Ref. EP/S001328/1), the EPSRC Fellowship in Manufacturing (Ref. EP/R024162/1), and the EPSRC Future Advanced Metrology Hub (Ref. EP/P006930/1).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Ethical approval
This paper does not contain any studies with human participants or animals performed by any of the authors.
Consent to participate
Not applicable
Consent for publication
Not applicable
Conflict of interest
The authors declare no competing interests.
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Qin, Y., Qi, Q., Shi, P. et al. Selection of materials in metal additive manufacturing via three-way decision-making. Int J Adv Manuf Technol 126, 1293–1302 (2023). https://doi.org/10.1007/s00170-023-10966-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-023-10966-5