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Abstract

This work is a novel attempt to identify the optimum process parameters in cold upsetting of Al–TiC metal matrix composites with multiple responses using grey Taguchi approach. The formation of barrel and workability are the important attributes that greatly influence the process of upsetting. Three independently controllable process variables, namely, aspect ratio, friction factor and load, each at four levels are considered to find their optimum levels which yields maximum barrel radius and workability simultaneously. Grey Taguchi analysis has been performed to optimize the levels of input parameters. Both the quality characteristics are improved significantly at the optimal process condition as verified by the confirmation test. The effect of individual process variables on the responses is determined using analysis of variance.

Keywords

Upsetting metal matrix composites grey Taguchi method analysis of variance

Introduction

Aluminium metal matrix composites (AMMCs) are widely used in the automotive, aerospace and electronics industries due to their lightweight, high strength and ease of fabrication.¹ In past, many researchers have carried out the investigations into upset forging due to their vast use in the metal forming process. Narayanasamy et al.² studied barrelling in magnesium alloy solid cylinders during cold upset forming and found empirical relationships between the measured radius of curvature of the barrel and other variables such as the hydrostatic stress and the stress ratio parameter. Malayappan and Narayanasamy³ studied the phenomenon of barrelling of aluminium solid cylinders during cold upsetting using different lubricants. Manisekar et al.⁴ studied the effect of friction on barrelling in square billets of aluminium during cold upset forging and established the relationship between the experimentally derived values of friction factors for different lubricants from standard compression tests and bulge parameters such as new hoop strain, geometrical shape factor, stress ratio parameter and hydrostatic stress. Baskaran and Narayanasamy⁵ studied some aspects of barrelling in elliptical shaped billets of aluminium during cold upset forging with lubricant. Experiments were carried out to generate data on cold upset forging of commercially pure aluminium solid of irregular shaped billets with white grease as a lubricant applied on both sides in order to evaluate the bulging characteristics. Baskaran and Narayanasamy⁶ investigated experimentally the work hardening behaviour of elliptical shaped billets of aluminium during cold upsetting. The parameters, namely, instantaneous strain hardening exponent and instantaneous strength coefficient, were evaluated during the cold upsetting of commercially pure aluminium under various stress conditions. Narayanasamy et al.⁷ investigated the effect of geometric work hardening and matrix work hardening on workability and densification of aluminium–3.5% alumina composite during cold upsetting. Narayanasamy et al.⁸ compared the workability strain and stress parameters of powder metallurgy steels AISI 9840 and AISI 9845 during cold upsetting. Narayanasamy et al.⁹ studied the effect of carbon content on workability of powder metallurgy steels. Workability behaviour of steel powder metallurgy preforms containing 0%, 0.4% and 0.8% of carbon were completely investigated experimentally. Narayanasamy et al.¹⁰ investigated the effect of the addition of molybdenum on the workability of the powdered metallurgy steels during cold upsetting. Ferrous powder metallurgy preforms containing 0%, 0.5%, 1.0% and 1.5% of molybdenum were completely investigated experimentally to study workability behaviour. Sivasankaran et al.¹¹ analysed the workability behaviour of Al–SiC P/M composites using back propagation neural network model and statistical technique. An artificial neural network (ANN) model for predicting and analysing the workability behaviour during cold upsetting of sintered Al–SiC powder metallurgy (P/M) metal matrix composites (MMCs) was proposed. Most of the previous published articles deal with the experimental investigations on the workability and barrelling of the billets during upsetting.^2–10 Except few investigations,^1,12,13 there is a lack of studies investigating the optimization of process parameters in forming aluminium-based MMCs.

Researchers have successfully employed robust parameter design (RPD) methodology virtually in every field of engineering to optimize the process parameters for better results.^12–18 Taguchi optimization method has been widely used by the researchers as it is a powerful tool for the design of experiments and is very effective to optimize the process with single-performance characteristics influenced by several variables.^16–18 But the method fails to deal with the multiple response optimization problems. The process of upsetting is a typical multiple response optimization problem which is more complicated than the single-objective optimization of a process. Grey relational analysis (GRA), introduced by Deng,¹⁹ can effectively deal with the poor, incomplete and uncertain information. Grey relational grade (GRG) is obtained with GRA as the multiple performance index which converts the multiple-objective optimization problem into a single-objective optimization. Considering all the above, this work attempts to identify the optimum process parameters in cold upsetting of Al–TiC MMCs with multiple responses using grey Taguchi approach.

Experimental studies

The cold upsetting experiments were performed on cylindrical specimens of Al–TiC MMCs with initial diameter (D₀) of 24 mm and four different initial heights (h₀) of 12, 18, 24 and 30 mm to give an aspect ratio of 0.50, 0.75, 1.0 and 1.25, respectively. The upsetting of the specimen was carried out between two flat, mirror finished open dies on a universal resting machine with different load conditions and with different lubricants, namely, molybdenum disulphide (MoS₂), zinc sulphide (ZnS), graphite (Gr) and dry condition (D) using a universal testing machine as per L16 orthogonal arrays. The levels of the input parameters are selected based on earlier research^6–11 and are given in Table 1. The schematic representation of the upsetting process and the experimental set-up are shown in Figures 1 and 2, respectively. After compression, the dimensional changes in the specimen such as height after deformation (h_f), top contact diameter (D_TC), bottom contact diameter (D_BC) and bulge diameter (D_B) were measured by means of digital vernier caliper and are listed in Table 2. Each experimental trial was repeated thrice. The measurements were recorded at three different locations and their averages are used for the determination of barrel radius and workability.

Table 1.

Factors and level considered for upsetting.

Control factor		Level 1	Level 2	Level 3	Level 4
A	Aspect ratio	0.50	0.75	1.00	1.25
B	Friction factor	0.47 (MoS₂)	0.61 (ZnS)	0.55 (Gr)	0.76 (D)
C	Load (kN)	100	200	300	400

MoS₂: molybdenum disulphide; ZnS: zinc sulphide; Gr: graphite; D: dry condition.

Figure 1.

Shape of the billet⁸ (a) before deformation and (b) after deformation.

Figure 2.

Experimental set-up in universal testing machine.

Table 2.

Experimental values obtained based on L₁₆ design.

Experiment number	Aspect ratio	Friction factor	Load (kN)	h₀ (mm)	D₀ (mm)	h_f (mm)	D_B (mm)	D_TC (mm)	D_BC (mm)
1	0.50	0.47	100	12	24	11.18	26.11	25.480	25.962
2	0.50	0.61	200	12	24	7.51	32.51	32.060	32.044
3	0.50	0.55	300	12	24	5.76	37.25	36.968	36.184
4	0.50	0.76	400	12	24	5.32	38.57	37.100	37.476
5	0.75	0.47	200	18	24	12.67	31.12	29.850	30.172
6	0.75	0.61	100	18	24	17.91	25.85	25.738	25.714
7	0.75	0.55	400	18	24	7.38	40.51	39.244	39.254
8	0.75	0.76	300	18	24	9.36	36.29	34.806	34.510
9	1.00	0.47	300	24	24	10.72	38.81	36.860	36.640
10	1.00	0.61	400	24	24	8.79	43.06	42.012	41.502
11	1.00	0.55	100	24	24	23.29	26.20	26.018	26.038
12	1.00	0.76	200	24	24	15.22	32.58	30.800	30.956
13	1.25	0.47	400	30	24	11.29	42.88	39.918	40.364
14	1.25	0.61	300	30	24	13.45	38.40	37.576	37.136
15	1.25	0.55	200	30	24	19.34	32.27	31.182	31.674
16	1.25	0.76	100	30	24	29.42	26.08	25.494	25.764

h₀: initial height; D₀: initial diameter; h_f: height after deformation; D_B: bulge diameter; D_TC: top contact diameter; D_BC: bottom contact diameter.

Analysis and discussion

Theoretical calculations

The method for calculating the responses (barrel radius and workability) is discussed under this section.

Barrel radius

The expression proposed by Malayappan and Narayanasamy³ is used to calculate the barrel radius as below

R_{b} = \frac{h_{f}^{2}}{4 (D_{B} - D_{C})}

(1)

where D_B is the bulge diameter, D_C is the average of top and bottom contact diameters and h_f is the height after deformation.

Stress formability parameter

Vujovic and Shabaik²⁰ proposed a parameter called formability stress index, which is given as

β = \frac{3 σ_{m}}{σ_{eff}}

(2)

where $σ_{m}$ is the hydrostatic stress and $σ_{eff}$ is the effective stress.

According to Narayanasamy and Pandey,²¹ $σ_{m}$ is given as

σ_{m} = \frac{σ_{z} + 2 σ_{θ}}{3}

(3)

where $σ_{z}$ is the axial stress and $σ_{θ}$ is the hoop stress, which can be determined using equations (4) and (5)

σ_{θ} = (\frac{2 α + 1}{1 + 2 α}) σ_{z}

(4)

According to Narayanasamy and Pandey,²¹ the state of stress under the triaxial stress state condition is as follows

α = \frac{ε_{θ}}{2 ε_{z}}

(5)

From equation (4), for the known values of Poisson’s ratio $(α)$ and axial stress $(σ_{z})$ , the hoop stress component $(σ_{θ})$ can be determined.

The expression for calculating the axial true strain $(ε_{z})$ is given as

ε_{z} = \ln (\frac{h_{0}}{h_{f}})

(6)

The hoop strain $(ε_{θ})$ can be determined by the following expression²

ε_{θ} = \ln (\frac{2 D_{B}^{2} + D_{C}^{2}}{3 D_{0}^{2}})

(7)

The effective stress can be determined from the following expression in terms of cylindrical coordinates²

σ_{eff} = {[σ_{z}^{2} + 2 σ_{θ}^{2} - (σ_{θ}^{2} + 2 σ_{z} σ_{θ})]}^{0.5}

(8)

The results obtained from the above theoretical calculations are given in Table 3.

Table 3.

Upsetting parameters calculated.

Experiment number	$ε_{z}$	$ε_{θ}$	$α$	Area (mm²)	$σ_{z}$	$σ_{θ}$	$σ_{m}$	$σ_{eff}$	Responses
									$β$	$R_{b}$
1	0.071	0.159	1.1205	519.60	1888	196.1	67.79	384.9	0.528	80.329
2	0.469	0.598	0.6376	806.86	243.2	209.8	58.78	452.9	0.389	30.786
3	0.734	0.867	0.5907	1050.70	280.1	235.9	63.87	515.9	0.371	12.306
4	0.813	0.927	0.5697	1092.00	359.3	299.2	79.66	658.5	0.363	5.519
5	0.351	0.496	0.7063	707.38	277.4	247.3	72.38	524.6	0.414	36.188
6	0.005	0.145	14.4960	519.80	188.7	343.1	165.80	531.9	0.935	646.710
7	0.892	1.026	0.5756	1209.90	324.3	270.9	72.48	595.2	0.365	10.798
8	0.654	0.797	0.6096	943.40	312.0	265.3	72.87	577.2	0.379	13.421
9	0.806	0.926	0.5746	1060.70	277.5	231.6	61.92	509.1	0.365	13.946
10	1.004	1.149	0.5720	1369.50	286.5	238.9	63.72	525.4	0.364	14.824
11	0.030	0.171	2.8478	532.07	184.4	254.7	108.30	439.0	0.740	788.410
12	0.455	0.577	0.6332	748.84	262.0	225.5	63.00	487.5	0.388	34.026
13	0.977	1.119	0.5723	1265.50	310.1	258.5	68.99	568.6	0.364	11.634
14	0.802	0.922	0.5746	1096.00	268.5	224.2	59.93	492.7	0.365	43.320
15	0.439	0.575	0.6547	775.75	252.9	220.0	62.37	472.9	0.396	111.060
16	0.020	0.155	3.9630	515.89	190.2	284.7	126.40	474.8	0.799	479.790

$ε_{z}$ : axial true strain; $ε_{θ}$ : hoop strain; $α$ : Poisson’s ratio; $σ_{z}$ : axial stress (MPa); $σ_{θ}$ : hoop stress (MPa); $σ_{m}$ : hydrostatic stress (MPa); $σ_{eff}$ : effective stress (MPa); $β$ : formability stress index; $R_{b}$ : barrel radius (mm).

Taguchi methodology

The Taguchi methodology proposed by Genichi Taguchi is an effective technique for determining the optimum settings of the design parameters for a process. Taguchi employs special orthogonal arrays for the experimental design to study the parameters’ space with minimum number of experiments.²² It uses the signal-to-noise ratio as a quality indicator which indicates the scattering around a target value. Higher values of signal-to-noise ratio represent better performance. Three categories of signal-to-noise ratio are proposed by Taguchi: (a) higher the better, (b) lower the better and (c) nominal the best. In upsetting process, the main aim is to obtain maximum barrel radius and workability. Hence, higher the better signal-to-noise ratio (equation (9)) of Taguchi is used for this study

η = - 10 \log_{10} (\frac{1}{n} \sum_{i = 1}^{n} \frac{1}{y_{ij}^{2}})

(9)

GRA

In GRA, the obtained signal-to-noise ratios are first normalized ranging from 0 to 1 using higher the better characteristics (equation (10)) for simultaneous maximization of barrel radius and workability. This process is known as grey relational generation

x_{i} (k) = \frac{y_{i} (k) - min y_{i} (k)}{max y_{i} (k) - min y_{i} (k)}

(10)

where x_i (k) = value after grey relational generation, miny_i(k) = smallest value of y_i(k) for the kth response and maxy_i(k) = largest value of y_i(k) for the kth response. In the next step, the grey relational coefficient (GRC) $ξ_{i} (k)$ is calculated using equation (11) from the normalized values of the signal-to-noise ratio to represent the correlation between the desired and actual experimental data

ξ_{i} (k) = \frac{Δ_{min} + ψ Δ_{max}}{Δ_{0 i} (k) + ψ Δ_{max}}

(11)

where $Δ_{0 i} = ‖ x_{0} (k) - x_{i} (k) ‖$ is the deviation of sequence between the reference sequence and the comparability sequence, that is, difference of absolute value $x_{0} (k)$ and $x_{i} (k)$ ; $Δ_{min} = \forall j^{min} \in i \forall k^{min} ‖ x_{0} (k) - xj (k) ‖$ is the smallest value of $Δ_{0 i}$ ; $Δ_{max} = \forall j^{max} \in i \forall k^{max} ‖ x_{0} (k) - xj (k) ‖$ is the largest value of $Δ_{0 i}$ and $ψ$ is the distinguishing coefficient. The value of $ψ$ is set to be 0.5, the quantity used in most situations.^23–27

The signal-to-noise ratio, normalized signal-to-noise ratio and the deviation sequences are shown in Table 4. Then, the overall GRG is determined by equation (12), that is, averaging the GRC corresponding to selected responses

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

(12)

Table 4.

S/N ratio values, normalized S/N ratio values and deviation sequences.

Experiment number	S/N ratios		Normalized S/N ratio		Deviation sequences ( $Δ_{0 i}$ )
	Workability	Barrel radius	Workability	Barrel radius	Workability	Barrel radius
1	−5.54732	38.09748029	0.396022195	0.539705834	0.603977805	0.460294166
2	−8.20101	29.76708809	0.073114223	0.346414087	0.926885777	0.653585913
3	−8.61252	21.80250158	0.023040605	0.161610202	0.976959395	0.838389798
4	−8.80187	14.83750496	0	0	1	1
5	−7.65999	31.17123385	0.138946959	0.378994760	0.861053041	0.62100524
6	−0.58377	56.21418990	1	0.960071451	0	0.039928549
7	−8.75414	20.66675291	0.005807912	0.135257200	0.994192088	0.864742800
8	−8.42722	22.55543103	0.045588396	0.179080574	0.954411604	0.820919426
9	−8.75414	22.88924718	0.005807912	0.186826176	0.994192088	0.813173824
10	−8.77797	23.41946686	0.002908215	0.199128969	0.997091785	0.800871031
11	−2.61537	57.93501078	0.752789574	1	0.247210426	0
12	−8.22337	30.63619516	0.070393400	0.366580151	0.929606600	0.633419849
13	−8.77797	21.31471721	0.002908215	0.150292044	0.997091785	0.849707956
14	−8.75414	32.73368157	0.005807912	0.415248546	0.994192088	0.584751454
15	−8.04610	40.91081713	0.091964079	0.604984249	0.908035921	0.395015751
16	−1.94906	53.62097607	0.833867926	0.899900595	0.166132074	0.100099405

S/N: signal to noise.

where $n$ is the number of process response. The overall performance of the process depends on the calculated GRG. The parametric combination with highest GRG implies that the corresponding experimental run is closest to the optimal value of the desired multiple response.^23–25 The values of GRC for each response obtained in every experimental trial along with the GRG are shown in Table 5. It was observed from Table 5 that the experiment number 6 exhibits the highest GRG. Analysis of the means is performed for the obtained GRG and is given in Table 6. The rank of the parameter affecting the GRG is also listed in Table 6 based on the difference between the highest and the lowest average of GRG (Δ value).

Table 5.

GRC and GRG.

Experiment number	GRC		GRG
	Workability	Barrel radius
1	0.452907656	0.520673787	0.486790722
2	0.350413473	0.433431090	0.391922281
3	0.338533342	0.373583242	0.356058292
4	0.333333333	0.333333333	0.333333333
5	0.367362612	0.446028245	0.406695428
6	1	0.926048458	0.963024229
7	0.334628997	0.366369399	0.350499198
8	0.343781636	0.378524223	0.361152930
9	0.334628997	0.380756904	0.357692951
10	0.333980859	0.384357856	0.359169357
11	0.669155545	1	0.834577773
12	0.349746567	0.441142795	0.395444681
13	0.333980859	0.370450510	0.352215684
14	0.334628997	0.460935081	0.397782039
15	0.355104577	0.558649386	0.456876981
16	0.750601899	0.833195293	0.791898596

GRC: grey relational coefficient; GRG: grey relational grade.

Table 6.

Response table for grey relational grade.

Process parameters	Level 1	Level 2	Level 3	Level 4	Δ (max − min)	Rank
A	0.392	0.5203	0.487	0.499	0.128	2
B	0.401	0.5280	0.499	0.471	0.127	3
C	0.769	0.4130	0.368	0.349	0.420	1

Total mean value of the grey relational grade is 0.474692.

The average values of GRG at each level are plotted as a response graph shown in Figure 3. From the analysis of the response table and response graph, the optimal process parameters’ combination for upsetting of Al–TiC MMCs is the second level of the aspect ratio, second level of the friction factor and the first level of the load applied during upsetting, that is, A2B2C1. The values of (Δ) max–min average of GRG indicate the most influential factor affecting the multi-performance characteristics. The maximum value of Δ in Table 6 is 0.420 for the control factor load and has the strongest effect on multi-performance characteristics for the upsetting process. The order of importance of the control factors on the GRG is listed in Table 6 as factor C (applied load) > A (aspect ratio) > B (friction factor).

Figure 3.

Response graph for each level of upsetting parameters.

The significance of each process parameter on multiple performance characteristics was tested by analysis of variance (ANOVA). Using GRG obtained for workability and barrel radius, ANOVA was performed to find out the significant factors. The results obtained from ANOVA analysis are shown in Table 7. It can be concluded from Table 7 that the significant factor affecting the GRG is load (78.837%) followed by aspect ratio (6.4891%) and friction factor (5.9786%).

Table 7.

ANOVA results for grey relational grade.

Parameter	DOF	SS	V	F ratio	P
A	3	0.0388	0.0129	1.4926	6.4891
B	3	0.0357	0.0119	1.3751	5.9786
C	3	0.4707	0.1569	18.133	78.8373
Error	6	0.0519	0.0086		8.6950
Total	15	0.5971			100.0000

DOF: degree of freedom; SS: sum of squares; V: variance; P: percentage contribution.

Confirmation test

The confirmation test is conducted to validate the accuracy of the optimal level parameters established for the upsetting of Al–TiC MMCs. The predicted GRG for the optimal setting of the parameters, that is, A2B2C1 can be obtained from equation (13) as below

\overset{⌢}{Y} = Y_{m} + \sum_{i = 1}^{k} ({\bar{Y}}_{i} - Y_{m})

(13)

where $\overset{⌢}{Y}$ is the predicted GRG, $Y_{m}$ is the total mean GRG, ${\bar{Y}}_{i}$ is the mean value of the GRG at the optimal level and $k$ is the number of upsetting process parameter.

The predicted value of GRG obtained by using equation (13) is 0.86792. At the optimal setting, the GRG value obtained from the confirmation experiment is 0.9630. The results of the confirmation tests are shown in Table 8. A gain in the experimental GRG signifies that the method adopted can be effectively utilized for the multi-response optimization of upsetting process.

Table 8.

Confirmation experiment result.

	Optimal process parameters
	Predicted	Experimental
Level	A2B2C1	A2B2C1
GRG	0.86792	0.9630

GRG: grey relational grade.

Conclusion

In this investigation, Taguchi’s L16 orthogonal array with GRA is used for the multiple performance optimization characteristics such as workability and barrel radius in cold upsetting of Al–TiC MMCs. The difference (max − min) between the average values of the GRG is calculated for every factor at each level, and the values clearly show that the load had the strongest effect on upsetting process among the other process parameters. The order of their importance is given as load, aspect ratio and friction factor. The results obtained from ANOVA also confirmed that load had maximum contribution to the multi-performance characteristics. The values of the optimum process parameters are load = 100 kN, aspect ratio = 0.75 and friction factor = 0.61. The confirmation test performed shows that the determined optimal combination of the process parameters satisfies the requirement of maximizing the workability and barrel radius during cold upsetting of Al–TiC MMC.

Footnotes

Declaration of conflicting interests

The authors declare that there is no conflict of interest.

Funding

This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors.

References

Dharmalingam

Subramanian

Somasundara Vinoth

. Optimization of tribological properties in aluminum hybrid metal matrix composites using Gray-Taguchi method. J Mater Eng Perform 2011; 20(8): 1457–1466.

Narayanasamy

Sathiyanarayanan

Ponalagusamy

. A study on barrelling in magnesium alloy solid cylinders during cold upset forming. J Mater Process Tech 2000; 101: 64–69.

Malayappan

Narayanasamy

. Observations on barreling of aluminium solid cylinders during cold upsetting using different lubricants. Mater Sci Tech Ser 2003; 19: 1705–1708.

Manisekar

Narayanasamy

Malayappan

. Effect of friction on barrelling in square billets of aluminium during cold upset forging. Mater Design 2006; 27: 147–155.

Baskaran

Narayanasamy

. Some aspects of barrelling in elliptical shaped billets of aluminium during cold upset forging with lubricant. Mater Design 2008; 29: 638–661.

Baskaran

Narayanasamy

. An experimental investigation on work hardening behaviour of elliptical shaped billets of aluminium during cold upsetting. Mater Design 2008; 29: 1240–1265.

Narayanasamy

Anandakrishnan

Pandey

. Effect of geometric work-hardening and matrix work-hardening on workability and densification of aluminium–3.5% alumina composite during cold upsetting. Mater Design 2008; 29: 1582–1599.

Narayanasamy

Anandakrishnan

Pandey

. Comparison of workability strain and stress parameters of powder metallurgy steels AISI 9840 and AISI 9845 during cold upsetting. Mater Design 2008; 29: 1919–1925.

Narayanasamy

Anandakrishnan

Pandey

. Effect of carbon content on workability of powder metallurgy steels. Mat Sci Eng A: Struct 2008; 494: 337–342.

10.

Narayanasamy

Anandakrishnan

Pandey

. Effect of molybdenum addition on workability of powder metallurgy steels during cold upsetting. Mat Sci Eng A: Struct 2009; 517: 30–36.

11.

Sivasankaran

Narayanasamy

Ramesh

. Analysis of workability behavior of Al–SiC P/M composites using backpropagation neural network model and statistical technique. Comp Mater Sci 2009; 47: 46–59.

12.

Singh

Raghukandan

Pai

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

13.

Siriyala

Alluru

Penmetsa

RMR

. Application of Grey-Taguchi method for optimization of dry sliding wear properties of aluminum MMCs. Front Mech Eng 2012; 7(3): 279–287.

14.

Tsao

. Grey–Taguchi method to optimize the milling parameters of aluminum alloy. Int J Adv Manuf Tech 2009; 40: 41–48.

15.

Lin

. Use of the Taguchi method and Grey relational analysis to optimize turning operations with multiple performance characteristics. Mater Manuf Process 2007; 19(2): 209–220.

16.

Tsao

. Taguchi analysis of drilling quality associated with core drill in drilling of composite material. Int J Adv Manuf Tech 2007; 32: 877–884.

17.

Pandey

Panda

. Optimization of orthopaedic drilling: a Taguchi approach. Int J Theor Appl Res Mech Eng 2012; 1(1): 9–12.

18.

Mehat

Kamaruddin

. Investigating the effects of injection molding parameters on the mechanical properties of recycled plastic parts using the Taguchi method. Mater Manuf Process 2011; 26(2): 202–209.

19.

Deng

. Introduction to grey system. J Grey Syst 1989; 1(1): 1–24.

20.

Vujovic

Shabaik

. A new workability criterion for ductile metals. J Eng Mater Technol 1986; 108(3): 245–249.

21.

Narayanasamy

Pandey

. Phenomenon of barrelling in Al solid cylinders during cold upset-forging. J Mater Process Tech 1997; 70: 17–27.

22.

Philip

. Taguchi technique for quality engineering. New York: McGraw-Hill, 1988.

23.

Palanikumar

Latha

Senthilkumar

. Analysis on drilling of Glass Fiber–Reinforced Polymer (GFRP) composites using grey relational analysis. Mater Manuf Process 2012; 27(3): 297–305.

24.

Şefika

. 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(1–4): 795–804.

25.

Singh

. Optimization of machining characteristics in electric discharge machining of 6061Al/Al₂O₃P/20P composites by grey relational analysis. Int J Adv Manuf Tech 2012; 63(9–12): 1191–1202.

26.

Meena

Azad

. Grey relational analysis of micro-EDM machining of Ti-6Al-4V alloy. Mater Manuf Process 2012; 27(9): 973–977.

27.

Kasman

. Optimisation of dissimilar friction stir welding parameters with grey relational analysis. Proc IMechE, Part B: J Engineering Manufacture 2013; 227(9): 1317–1324.

Multi-objective optimization of upsetting parameters of Al–TiC metal matrix composites: A grey Taguchi approach

Abstract

Keywords

Introduction

Experimental studies

Analysis and discussion

Theoretical calculations

Barrel radius

Stress formability parameter

Taguchi methodology

GRA

Confirmation test

Conclusion

Footnotes

Declaration of conflicting interests

Funding

References