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Abstract

In this research work, friction stir welding of aluminium alloy AA5083-H321 is performed for optimization of the process parameters for maximum joint strength. Taguchi’s L₉ orthogonal array has been used for three parameters – tool rotational speed, traverse speed and tool tilt angle. Multi-response optimization has been carried out through Taguchi-based grey relational analysis. The grey relational grade has been calculated for all three responses – ultimate tensile strength, percentage elongation and micro-hardness. Analysis of variance is the tool used for obtaining grey relational grade to find out the significant process parameters. Tool rotational speed and traverse speed are the two most significant parameters which influence most of the quality characteristics of friction stir welded joint. Validation of the predicted values done through confirmation experiments at optimum setting shows a good agreement with the experimental values.

Keywords

Friction stir welding grey relational analysis orthogonal array grey relational grade analysis of variance ultimate tensile strength micro-hardness

Introduction

Friction stir welding (FSW) was used for the first time in 1991 for laboratory research work at TWI, United Kingdom. But the process of joining two aluminium sheets through FSW was so revolutionary that it captured the instant focus of the welding experts and industrialists. FSW provided the best key solution for all the experts who were facing difficulty for joining aluminium and its alloys at higher temperature.¹ Aerospace industry and modern automobile industry got new opportunities to have a relook for better use of the most available metal on earth. Nowadays, flow of expertise in FSW and maximum use of resources with minimum waste make FSW process more valuable and more automatic joining process.²

In FSW, a rotation tool with a pin is inserted in the weld line until the tool shoulder touches the upper surface of the plates. Frictional heat is induced between the tool shoulder and the welding plates which increase the temperature up to recrystallization temperature and the inserted pin intermixes the plasticize material to make solid-state welding. The used welded sheets may be of same or dissimilar materials. The mechanism of FSW process is shown in Figure 1. There are two sides of the welding; during clockwise rotation of the tool and forward feed, the left side is called the advancing side and the right side is called the retreating side. During welding joint, zones are formed named as (a) nugget zone (NZ), (b) thermo-mechanical-affected zone (TMAZ), (c) heat-affected zone and (d) base material which are represented in Figure 2. The central zone is the NZ where intermixing of the material is taken place. TMAZ is a zone of maximum deformation without intermixing. Heat-affected zone experiences the temperature variation without any deformation.

Figure 1.

A schematic diagram of friction stir welding process.

Figure 2.

Welding zone of FSW: (a) nugget zone, (b) thermo-mechanical-affected zone, (c) heat-affected zone and (d) base material.

The solid-state welding produces welded joint without melting of the material sheets; therefore, a number of defects, for example, porosity, cracking and blow holes which appear during conventional fusion welding process, are avoided.^1,3–7 In FSW, high temperature below the melting point is attained through friction between the tool shoulder and the joining sheets as well as frictional heat produced by the tool pin and the semi-solid material through the plastic flow of the materials under the tool shoulder.

The effect of different parameters on the welding joint strength has been investigated by many researchers.^8–11 Taguchi with grey relational analysis (GRA) has been used by many researchers in their respective fields for optimization of processes.^12–18 Taguchi technique has been used,¹⁹ but GRA for FSW has been used rarely, as the process has been used in aviation industry and marine industry; therefore, optimization of the process is very essential for having good factor of safety at different applications. Through this article, an attempt has been made to find out the valuable results for FSW experimentation and improved joint strength.

Experimental set-up

A non-consumable tool with a concave shoulder and a flat face cylindrical pin has been used for the FSW. Two sheets of aluminium alloy AA5083-H321 have been welded through FSW process. The used material AA5083 consists of main alloying elements, that is, 4.3% Mg, 0.63% Mn, 0.076% Si, 0.11% Cr–Zn–V and remaining aluminium. Each sheet’s dimensions are 150 mm × 75 mm × 4.5 mm and the edges of each sheet have been properly cleaned and made distortion free for the proper alignment of the two mating edges. Tool steel H-13 material has been used for the welding tool. It consists of concave shoulder with diameter of 18 mm and tool pin dimensions – diameter of 6 mm and length of 4.3 mm. The tool penetration depth has been fixed at 4.46 mm from the upper touch point. Three parameters – tool rotational speed (TRS), traverse speed (TS) and tool tilt angle (TTA) – have been selected for investigation based on the review of literature and some pilot study. The selected process parameters with their three levels are given in Table 1. Input force, initial tool feed time and some other parameters have been kept constant during experimentation.

Table 1.

Input process parameters and their levels.

S. no.	Input process parameters	Process parameters’ level
S. no.	Input process parameters	−1	0	+1
1.	TRS (r/min)	500	950	1400
2.	TS (mm/min)	16	28	40
3.	TTA (°)	1	2	3

TRS: tool rotational speed; TS: traverse speed; TTA: tool tilt angle.

Taguchi-based GRA has been used through selection of L₉ orthogonal array. Ultimate tensile strength (UTS), hardness and percentage elongation are the most important measures to ascertain the quality of the butt welded joint. GRA has been used to get the maximum values of the output variables. Orthogonal array L₉ experiments are given in Table 2.

Table 2.

Average response values of different responses.

Ex. no.	Input process parameters			Responses (avg.)
Ex. no.	TRS (r/min)	TS (mm/min)	TTA (°)	UTS (MPa)	% EL	Micro-hardness (HV)
1	500	16	1	232	2.75	69
2	500	28	2	298	3.10	71
3	500	40	3	257	3.70	73
4	950	16	2	242	5.00	79
5	950	28	3	315	5.20	78
6	950	40	1	269	5.80	77
7	1400	16	3	241	6.38	76
8	1400	28	1	293	6.10	73
9	1400	40	2	253	6.70	77

TRS: tool rotational speed; TS: traverse speed; TTA: tool tilt angle; UTS: ultimate tensile strength; EL: elongation.

The experiments have been conducted on a suitably modified vertical milling machine of Bharat Fritz Werner make. A fixture has been fabricated for proper holding of the workpiece on the milling machine table. FSW components and the arrangement of the plates have been shown in Figure 3.

Figure 3.

Experimental set-up.

For the testing of FSW butt welded joint, tensile test specimens were prepared in transverse direction as per ASTM E8M-04 module. The prepared tensile test specimens are shown in Figure 4. All the samples are tested at room temperature at a 40-kN universal testing machine. UTS test results are presented in Table 2. Micro-hardness is an important response which also helps to predict joint quality. The NZ or stirred zone has been selected due to well intermixing of the materials. Vickers’s hardness tests have been performed for better micro-hardness. Indentation load 10 kgf has been applied for 15 s. Percentage elongation and Vickers’s hardness (HV) testing results are also given in Table 2.

Figure 4.

Prepared tensile test specimens as per ASTM-E8.

Taguchi approach and GRA

Many researchers have used different statistical tools for optimization study of FSW process. Taguchi approach is one of the most useful techniques for single-response optimization studies used for a number of engineering problems.^15,20–23 In the present scenario of rapid manufacturing and cost reducing with maximum utilization, complex processes have several quality characteristics. In such situations, several multi-response optimization techniques are needed and the Taguchi-based GRA has been used in this work.

GRA was developed in 1982 by Deng Ju-Long.²⁴ Grey system works like a black box concept where the known and unknown factors are put together to get optimized responses. GRA uses normalization of data to calculate grey relational coefficients (GRCs) and grey relational grades (GRGs). It calculates the optimum arrangement, and the analysis of variance (ANOVA) is applied for the prediction of optimum GRGs as given by Flow chart 1.

Flow chart 1.

Steps for grey relational analysis.

UTS, micro-hardness and percentage elongation of FSWed joint are very important quality factors. All these characteristics are of ‘larger-the-better’ type and their maximum values are sought simultaneously.

The first step is to create grey relational generation with values between 0 and 1. This generation is achieved for all the three quality characteristics – smaller-the-better, larger-the-better and nominal the best. For this investigation, all the selected quality characteristics are of the type larger-the-better, and grey relational generation is calculated by equation (1)^24–26

x_{i}^{*} (k) = \frac{x_{i}^{o} (k) - min x_{i}^{o} (k)}{max x_{i}^{o} (k) - min x_{i}^{o} (k)}

(1)

where $x_{i}^{o} (k)$ is the reference series or sequence; $max x_{i}^{o} (k)$ and $min x_{i}^{o} (k)$ are the maximum and minimum values in the sequence, respectively; $x_{i}^{*} (k)$ is the sequence generated after data processing. i = 1, 2, 3,…, m; k = 1, 2, 3,…, n; m is the number of experiments, and n is the number of experimental data.

Now GRCs have been calculated with the respective deviation calculations as given in equations (2) and (3)^24,26

Δ_{oi} (k) = | x_{o}^{*} (k) - x_{i}^{o} (k) |

(2)

ζ_{i} (k) = \frac{Δ_{\min} + ζ \cdot Δ_{max}}{Δ_{oi} (k) + ζ \cdot Δ_{\max}}

(3)

where $Δ_{oi} (k)$ is the deviation series of reference series $x_{o}^{*} (k)$ and compatibility series $x_{i}^{o} (k)$ ; ζ is the identification coefficient, which is generally taken 0.5 when the parameters are given equal weightage.

GRC for each experiment of L₉ orthogonal array has been calculated through equation (3). The final step of calculation of GRG is performed for calculating the relationship strength between the reference series and the compatibility series. Its value varies between 0 and 1. Higher value of GRG shows better relationship and it is considered as an ideal case. GRG is the average summation of GRCs. It is calculated by the following equation (4)

γ_{i} = \frac{1}{n} \sum_{k = 1}^{n} ζ_{i} (k)

(4)

where $γ_{i}$ is a GRG of ith experiment and n is the number of performance characteristics.

Larger value of GRG indicates that the corresponding experimental results are closer to the ideal value or normalized value.

Results and discussion

Calculation of signal-to-noise ratio

The average values of all the responses have been reported in Table 2 with the input parameter settings. In the first part of the analysis, signal-to-noise (S/N) ratios for all three responses have been calculated. As mentioned earlier, higher values of UTS, HV and percentage elongation give better welding performance; therefore, equation (5) was used for the calculation of S/N ratio. Three iterations of the responses have been performed through mechanical testing. The FSW joint testing results with S/N ratios are given in Table 3

Signal - to - noise ratio (k) = - 10 lo g_{10} (\frac{1}{n}) \sum_{i = 1}^{n} \frac{1}{y_{ijk}^{2}}

(5)

where n is the number of experiment replications and y_ijk is the response variable value of the ith performance characteristic in the jth experiment at the kth trial.

Table 3.

S/N ratios of different responses.

Ex. no.	Raw data for responses									S/N ratios
Ex. no.	U1	U2	U3	E1	E2	E3	V1	V2	V3	S/N_UTS	S/N_EL	S/N_HV
1	235	230	231	2.77	2.75	2.73	70	68	69	47.309	8.786	36.777
2	298	297	299	3.20	3.00	3.10	72	71	70	49.484	9.827	37.025
3	254	258	259	3.69	3.71	3.71	73	74	72	48.198	11.364	37.266
4	244	243	239	4.90	4.80	5.30	78	79	80	47.676	13.979	37.952
5	314	315	316	5.30	5.20	5.10	79	78	77	49.966	14.320	37.841
6	270	270	267	5.60	5.80	6.00	78	78	75	48.595	15.268	37.729
7	244	240	239	6.40	6.37	6.37	77	76	75	47.640	16.096	37.616
8	293	291	295	6.15	6.15	6.00	74	74	71	49.337	15.706	37.266
9	253	254	252	6.71	6.70	6.71	78	77	76	48.062	16.521	37.729

S/N: signal-to-noise.

Data processing and calculation of deviation sequence

The next part of the analysis is to normalize S/N ratio of each response using equation (1). The results are presented in Table 4. Calculations of Experiment 1 for UTS, EL and HV are given as follows

\begin{array}{l} x_{i U T S}^{*} (1) = \frac{x_{i}^{o} (k) - \min x_{i}^{o} (k)}{\max x_{i}^{o} (k) - \min x_{i}^{o} (k)} = \frac{47.309 - 47.309}{49.966 - 47.309} = 0 \\ x_{i E L}^{*} (1) = \frac{x_{i}^{o} (k) - \min x_{i}^{o} (k)}{\max x_{i}^{o} (k) - \min x_{i}^{o} (k)} = \frac{8.786 - 8.786}{16.521 - 8.786} = 0 \\ x_{i H V}^{*} (1) = \frac{x_{i}^{o} (k) - \min x_{i}^{o} (k)}{\max x_{i}^{o} (k) - \min x_{i}^{o} (k)} = \frac{36.777 - 36.777}{37.952 - 36.777} = 0 \end{array}

Table 4.

Sequences of responses after data processing and deviation sequence.

Exp. no.	Ref. Seq.
	Sequences after data processing			Deviation sequence for each response
	UTS	EL	HV	UTS	EL	HV
	1.000	1.000	1.000	1.000	1.000	1.000
1	0	0	0	1	1	1
2	0.8185	0.1345	0.2110	0.1814	0.8654	0.7889
3	0.3345	0.3332	0.4161	0.6654	0.6667	0.5838
4	0.1381	0.6713	1	0.8618	0.3286	0
5	1	0.7154	0.9055	0	0.2845	0.0944
6	0.4840	0.8380	0.8102	0.5159	0.1619	0.1897
7	0.1245	0.9450	0.7140	0.8754	0.0549	0.2859
8	0.7632	0.8946	0.4161	0.2367	0.1053	0.5838
9	0.2834	1	0.8102	0.7165	0	0.1897

UTS: ultimate tensile strength; EL: elongation.

For calculating GRCs, the deviation sequences were determined, and the results are presented in Table 4. For Experiment 1, deviation sequence as determined from equation (2) is given as follows

\begin{matrix} Δ_{oiUTS} (1) = | x_{o}^{*} (k) - x_{i}^{o} (k) | = | 1 - 0 | = 1 \\ Δ_{oiEL} (1) = | x_{o}^{*} (k) - x_{i}^{o} (k) | = | 1 - 0 | = 1 \\ Δ_{oiHV} (1) = | x_{o}^{*} (k) - x_{i}^{o} (k) | = | 1 - 0 | = 1 \end{matrix}

Estimation of GRCs and grades

The deviation sequences as given in Table 4 were used for estimation of GRCs through equation (3). The distinguished coefficient (ζ) has been assigned a generalized value of 0.5 for all performance characteristics. For calculating GRCs, equation (3) has been used and the results have been reported in Table 5. The sample calculation for Experiment no. 1 is given as follows

\begin{matrix} ζ_{iUTS} (1) = \frac{Δ_{\min} + ζ \cdot Δ_{\max}}{Δ_{oi} (k) + ζ \cdot Δ_{\max}} = \frac{0 + 0.5 \times 1}{1 + 0.5 \times 1} = 0.333 \\ ζ_{iEL} (1) = \frac{Δ_{\min} + ζ \cdot Δ_{\max}}{Δ_{oi} (k) + ζ \cdot Δ_{\max}} = \frac{0 + 0.5 \times 1}{1 + 0.5 \times 1} = 0.333 \\ ζ_{iHV} (1) = \frac{Δ_{\min} + ζ \cdot Δ_{\max}}{Δ_{oi} (k) + ζ \cdot Δ_{\max}} = \frac{0 + 0.5 \times 1}{1 + 0.5 \times 1} = 0.333 \end{matrix}

Table 5.

Estimation of GRCs and GRGs.

Experiment no.	GRCs			GRGs	Order
Experiment no.	UTS	EL	HV	GRGs	Order
1	0.3333	0.3333	0.3333	0.1111	9
2	0.7338	0.3662	0.3879	0.1848	7
3	0.4290	0.4286	0.4613	0.1451	8
4	0.3671	0.6034	1.0000	0.1882	6
5	1.0000	0.6373	0.8411	0.2865	1
6	0.4921	0.7553	0.7249	0.2059	4
7	0.3635	0.9010	0.6362	0.1931	5
8	0.6787	0.8259	0.4613	0.2265	2
9	0.4110	1.0000	0.7249	0.2168	3

GRC: grey relational coefficient; GRG: grey relational grade; UTS: ultimate tensile strength; EL: elongation.

All the values of GRCs for all nine experiments have been calculated using equation (1). GRGs for all performance characteristics were determined using equation (4). Weightage for performance characteristics UTS, EL and HV is 0.5, 0.3 and 0.2, respectively, which has been decided according to the importance of the output parameter for practical application. GRG for Experiment 1 is calculated as

γ_{1} = \frac{1}{n} \sum_{k = 1}^{n} ζ_{i} (k) = \frac{1}{3} (0.5 \times 0.3333 + 0.3 \times 0.3333 + 0.2 \times 0.3333) = 0.1111

All nine experiments’ GRCs have been used for calculating GRGs through equation (4). All the values of GRGs randomly vary between 0 and 1. As the value of GRG reaches maximum, it represents strong relationship between the reference sequence and the comparability sequence.

This investigation of optimization of the complex multiple response characteristics of FSW has been transformed into simple optimization of single GRG. Taguchi approach is best suited for single-response optimization in the form of GRG. The GRG values corresponding to the three levels of the selected process parameters and the main effects in terms of GRG are reported in Table 6.

Table 6.

Grey relational grade for all three levels.

Process parameters	Symbol	Grey relational grade			Main effects
Process parameters	Symbol	L1	L2	L3	L2 − L1	L3 − L2
Tool rotational speed	TRS	0.1470	0.2268	0.2121	0.0898	−0.0147
Traverse speed	TS	0.1641	0.2326	0.1893	0.0685	−0.433
Tool tilt angle	TTA	0.1811	0.1966	0.2082	0.0271	0.0116

Estimation of optimum levels of input process parameters

After calculation of the average value of GRG for each level of the process parameters, the maximum value of GRG is selected for each process parameter. The bold values of GRG in Table 6 represent the maximum values among the three levels for each process parameter. These values correspond to TRS of 950 r/min, TS of tool of 28 mm/min and TTA of 3° for better performance characteristics as shown in Figure 5. It is revealed from Figure 6 that the optimum values of the process parameters give the maximum values of GRG.

Figure 5.

Plots of signal-to-noise ratio of quality characteristics.

Figure 6.

Plot of main effects of grey relational grade.

Implementation of ANOVA

ANOVA is implemented to establish the significance and contribution of each process parameter to the GRG value. Table 7 represents the ANOVA results and the percentage contribution of each factor.

Table 7.

ANOVA results for grey relational grade.

Process parameters	Degree of freedom	Sum of squares	Mean squares	F-ratio	% Contribution
TRS	2	0.010838	0.005419	21.676	55.18
TS	2	0.007197	0.003599	14.396	36.64
TTA	2	0.001106	0.000553	2.212	5.63
Error	2	0.000499	0.000250		2.54
Total	8	0.019641

TRS: tool rotational speed; TS: traverse speed; TTA: tool tilt angle.

The tabulated F-ratio at 95% confidence level is 3.2296. As seen from the ANOVA Table 7, there are two process parameters – TRS and TS – which have 55.18% and 36.64% contribution on GRG, respectively. TTA has an insignificant contribution of 5.63% on the GRG value.

The significant parameters and their optimal level selection indicate that the plastic flow of the material under the tool plays an important role for higher joint strength. Proper mixing of the materials makes FSW joint more efficient; in other words, heat generation is an important characteristic which is responsible for joint strength. During lower heat generation, two welded materials remain separate resulting in poor joint strength. The higher heat generation is also a reason for poor joint strength, because higher heat makes grain growth or second phase grains of larger size due to which the size of the heat-affected zone becomes large resulting in a decrease in tensile strength and micro-hardness. Higher tool TS also produces low-quality weld. These situations lead to different defects such as pinholes and cracks in the welding zone.^15,16

Optimal GRG value prediction and calculation of confidence interval

After calculation of the optimum value for each quality characteristic, optimal GRG value has been calculated using equation (5) for prediction and verification of improvement in GRG as given in equation (6)

γ_{e} = γ_{m} + \sum_{i = 1}^{q} ({\bar{γ}}_{i} - γ_{m})

(6)

The predicted optimum values are listed in Table 8. The value of $γ_{e}$ is calculated to be 0.2770 from the above equation. To check the reliability of the predicted GRG, confidence interval (CI) is also determined using equation (7)

CI = {(F_{α} (1, f_{e}) V_{e} [\frac{1}{n_{eef}} + \frac{1}{R}])}^{1 / 2}

(7)

where $F_{α} (1, f_{e})$ is the F-ratio at α% level of significance, R is the number of confirmation tests, V_e is the error mean squares and n_eef is the effective number of replications.

Here, R has a value of 3; total no. of experiments (N) = 9; $n_{eef} = 3 \times 9 = 27$ , for 95% confidence level $α = 0.05$ .

Table 8.

Actual and predicted values of grey relational grade.

Exp. no.	GRG
Exp. no.	Actual	Predicted	% Error
1	0.1111	0.1016	−8.52
2	0.1848	0.1855	0.40
3	0.1451	0.1538	6.02
4	0.1882	0.1969	4.64
5	0.2865	0.2770	−3.30
6	0.2059	0.2066	0.36
7	0.1931	0.1938	0.38
8	0.2265	0.2352	3.86
9	0.2168	0.2073	−4.37

GRG: grey relational grade.

The calculated $γ_{e}$ lies between 0.2270 and 0.3270. The comparison of the actual GRG and the predicted GRG has been depicted in Figure 7.

Figure 7.

Comparison between actual GRG and predicted GRG.

Confirmation experiments and GRG linear mathematical model

For the verification of the predicted GRG, a confirmation experiment was performed. The average values of UTS, %EL and micro-hardness are obtained as 314.3 MPa, 5.8% and 77 HV, respectively. The FSW joint at the optimized parameter setting is shown in Figure 8.

Figure 8.

Visual view of (a) FS welded joint’s front side and (b) back side of the FS welded joint.

Scanning electron microscopy (SEM) testing of the confirmation experiment reveals that high compactness of the small grains around the centre weld line provides higher strength. The microstructure of the advancing side and the retreating side of the NZ is shown in Figure 9.

Figure 9.

SEM microstructure images of advancing side (AS) and retreating side (RS).

During the FSW, the plastically deformed soften region has been replaced by the small equiaxed microstructure grains. The general linear model for GRG has been established through mathematical regression analysis of three parameters at three levels given in equation (8). A data set of the predicted GRG has been created through the developed linear model as reported in Table 8. The error difference between the actual and predicted values is −8.52 to 6.02. The adequacy of the developed mathematical model is tested using R² value which falls between 0 and 1

\begin{matrix} GRG = - 0.3201 + 0.000428 TRS + 0.02288 \\ + TS - 0.01106 TTA - 0.000001 TRS \times TRS \\ - 0.000416 TS \times TS + 0.003200 TTA \times TTA \\ + 0.000002 TRS \times TS + 0.000018 TRS \times TTA \dots \end{matrix}

(8)

The current mathematical model has R² value of 97.46% which is near to 1. Such a high value of R² indicates a good correlation between the actual values and the predicted values of GRG.

Conclusion

In this research study, Taguchi L₉ orthogonal array has been used for multi-response optimization through GRA. FSW process parameters have been optimized through Taguchi-grey relational approach using GRG. The following conclusions have been drawn from this study:

The research study reveals that the optimum values of the process parameters for higher UTS and higher micro-hardness are TRS of 950 r/min, TS of 28 mm/min and TTA of 3°.

Two input parameters are dominating for FSW. The percent contributions of these parameters – TRS and TS in affecting the GRG value – are 55.18 and 36.64, respectively, as evidenced by ANOVA.

Taguchi with GRA provides a better optimization solution for FSW. The existence of the confirmation experiments’ values within the predicted range of the characteristics demonstrates it.

This investigation suggests that the complex optimization of multi-response problems can easily be simplified through Taguchi-based GRA and joint strength also enhanced at optimized settings.

Footnotes

Acknowledgements

The authors would like to acknowledge National Institute of Technology, Kurukshetra, India, for providing requisite facilities to accomplish this work.

Academic Editor: Alokesh Pramanik

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship and/or publication of this article.

References

Kevorkijan

Economic benefits of the substitution of traditional cast iron and steel by aluminium and magnesium based material in automotive segment. J Metall Mater Eng 2002; 8: 251–258.

Praveen

Yarlagadda

PKDV

. Meeting challenges in welding of aluminum alloys through pulse gas metal arc welding. J Mater Process Tech 2005; 164–165: 1106–1112.

Taban

Kaluc

Microstructural and mechanical properties of double-sided MIG, TIG and friction stir welded 5083-H321 aluminium alloy. Met Mater 2006; 44: 24.

Cavaliere

Friction stir welding of Al alloys: analysis of processing parameters affecting mechanical behavior. Proced CIRP 2013; 11: 139–144.

Khodaverdizadeh

Mahmoudi

Heidarzadeh

. Effect of friction stir welding (FSW) parameters on strain hardening behavior of pure copper joints. Mater Design 2012; 35: 330–334.

Hari Babu

Madhivanan

. Experimental analysis of process parameters on friction stir welding of aluminium 6061 alloy. Int J Adv Res Trends Eng Technol 2015; 2: 78–83.

Kundu

Singh

Friction stir welding of dissimilar Al alloys: effect of process parameters on mechanical properties. Eng Solid Mech 2016; 4: 125–132.

Bagheri Hariri

Gholami Shiri

Yaghoubinezhad

. The optimum combination of tool rotation rate and traveling speed for obtaining the preferable corrosion behavior and mechanical properties of friction stir welded AA5052 aluminum alloy. Mater Design 2013; 50: 620–634.

Aydin

Tutar

Durmuş

. Effect of welding parameters on tensile properties and fatigue behavior of friction stir welded 2014-T6 aluminum alloy. T Indian I Metals 2012; 65: 21–30.

10.

Kumar

Kailas

SV.

On the role of axial load and the effect of interface position on the tensile strength of a friction stir welded aluminium alloy. Mater Design 2008; 29: 791–797.

11.

Verma

Misra

. A critical review of friction stir welding process. In: Katalinic

(ed.) DAAAM international scientific book. Vienna: DAAAM International Vienna, 2015, pp.249–266, http://www.daaam.info/Downloads/Pdfs/science_books_pdfs/2015/Sc_Book_2015-022.pdf

12.

Singh

Kumar

Optimizing feed force for turned parts through the Taguchi technique. Sadhana 2006; 31: 671–681.

13.

Singh

Kumar

Optimizing multi-machining characteristics through Taguchi’s approach and utility concept. J Manuf Tech Manag 2006; 17: 255–274.

14.

Kesharwani

Panda

Pal

SK.

Multi objective optimization of friction stir welding parameters for joining of two dissimilar thin aluminum sheets. Proced Mater Sci 2014; 3: 178–187.

15.

Ghetiya

Patel

Kavar

AJ.

Multi-objective optimization of FSW process parameters of aluminium alloy using Taguchi-based grey relational analysis. T Indian I Metals 2016; 69: 917–923.

16.

Kasman

Multi-response optimization using the Taguchi-based grey relational analysis: a case study for dissimilar friction stir butt welding of AA6082-T6/AA5754-H111. Int J Adv Manuf Tech 2013; 68: 795–804.

17.

Park

J-U

Kim

H-J

. Development of fatigue life improvement technology of butt joints using friction stir processing. Adv Mech Eng 2014; 6: 943476.

18.

Senthilkumar

Tamizharasan

Anandakrishnan

An hybrid Taguchi-Grey relational technique and cuckoo search algorithm for multi-criteria optimization in hard turning of AISI D3 steel. J Adv Eng Res 2014; 1: 16–31.

19.

Ravichandran

Thirunavukkarasu

Sathish

. Optimization of welding parameters to attain maximum strength in friction stir welded AA7075 joints. Mater Test 2016; 58: 206–210.

20.

Kuram

Ozcelik

Multi-objective optimization using Taguchi based grey relational analysis for micro-milling of Al 7075 material with ball nose end mill. Measurement 2013; 46: 1849–1864.

21.

Gupta

Kumar

Multi-objective optimization of cutting parameters in turning using grey relational analysis. Int J Ind Eng Comput 2013; 4: 547–558.

22.

Singh

Raghukandan

Pai

BC.

Optimization by grey relational analysis of EDM parameters on machining Al–10%SiC_P composites. J Mater Process Tech 2004; 155–156: 1658–1661.

23.

Tosun

Determination of optimum parameters for multi-performance characteristics in drilling by using grey relational analysis. Int J Adv Manuf Tech 2005; 28: 450–455.

24.

Ju-Long

Control problems of grey systems. Syst Control Lett 1982; 1: 288–294.

25.

Kumar

Balaji

Prrithvi

PM.

Influence of residual stress on stress intensity factor estimation of multiple cracks in a dissimilar welded joint. Proced Eng 2014; 86: 234–241.

26.

Çaydaş

Hasçalık

Use of the grey relational analysis to determine optimum laser cutting parameters with multi-performance characteristics. Optic Laser Tech 2008; 40: 987–994.

Friction stir welding of AA5083 aluminium alloy: Multi-response optimization using Taguchi-based grey relational analysis

Abstract

Keywords

Introduction

Experimental set-up

Taguchi approach and GRA

Results and discussion

Calculation of signal-to-noise ratio

Data processing and calculation of deviation sequence

Estimation of GRCs and grades

Estimation of optimum levels of input process parameters

Implementation of ANOVA

Optimal GRG value prediction and calculation of confidence interval

Confirmation experiments and GRG linear mathematical model

Conclusion

Footnotes

Acknowledgements

Declaration of conflicting interests

Funding

References