Table 1
Process factors and their levels used in the experiments
| Parameter destination | Input parameters | Parameter range | Level 1 | Level 2 | Level 3 |
|---|---|---|---|---|---|
| A | Molten metal temperature (°C) | 720–780 | 720 | 750 | 780 |
| B | Al-3.5FeNb-1.5C (wt%) | 0.0–0.1–1.0 | 0.0 | 0.1 | 1.0 |
| C | Al-6Ni (wt%) | 0.0–0.5–5.0 | 0.0 | 0.5 | 5.0 |
| D | Die temperature (°C) | 230–290 | 230 | 260 | 290 |
| E | Injection pressure (MPa) | 12–24 | 12 | 18 | 24 |
Table 2
Composition of Al-Si9.8-Cu3.4 alloy (wt.%) considered for this study
| Al% | Si% | Cu% | Fe% | Ti% | Mg% | Ni% | Zn% | Pb% | Sn% | Mn% |
|---|---|---|---|---|---|---|---|---|---|---|
| 86.18 | 9.839 | 3.474 | 0.189 | 0.184 | 0.041 | 0.008 | 0.008 | 0.043 | 0.013 | 0.007 |

Fig. 1
Sample specimen of HPDC casting (A) Final castings with their dimensions (B) Tensile specimens with their dimensions used for the experimentations. HPDC, High pressure die casting
Table 3
Input parameters and experimental values of output characteristics along with average porosity values for L27 orthogonal array
| Expt. runs | Input factors | Output responses | Average porosity values | ||||||
|---|---|---|---|---|---|---|---|---|---|
| A (°C) | B (wt.%) | C (wt.%) | D (°C) | E (MPa) | Tensile strength | Brinell hardness | Microhardness | ||
| 1 | 720 | 0 | 0 | 230 | 12 | 218.39 | 85 | 113 | 0.88 |
| 2 | 720 | 0 | 0.5 | 260 | 18 | 223.76 | 85 | 116 | 0.53 |
| 3 | 720 | 0 | 5 | 290 | 24 | 245.50 | 88 | 119 | 0.36 |
| 4 | 720 | 0.1 | 0 | 260 | 18 | 239.88 | 90 | 136 | 0.26 |
| 5 | 720 | 0.1 | 0.5 | 290 | 24 | 249.09 | 91 | 135 | 0.25 |
| 6 | 720 | 0.1 | 5 | 230 | 12 | 237.31 | 85 | 136 | 0.47 |
| 7 | 720 | 1 | 0 | 290 | 24 | 220.53 | 83 | 112 | 0.85 |
| 8 | 720 | 1 | 0.5 | 230 | 12 | 214.67 | 83 | 114 | 0.71 |
| 9 | 720 | 1 | 5 | 260 | 18 | 208.63 | 86 | 118 | 0.75 |
| 10 | 750 | 0 | 0 | 260 | 24 | 217.87 | 85 | 114 | 0.95 |
| 11 | 750 | 0 | 0.5 | 290 | 12 | 210.73 | 85 | 116 | 0.77 |
| 12 | 750 | 0 | 5 | 230 | 18 | 230.46 | 89 | 116 | 0.49 |
| 13 | 750 | 0.1 | 0 | 290 | 12 | 230.19 | 86 | 118 | 0.63 |
| 14 | 750 | 0.1 | 0.5 | 230 | 18 | 237.29 | 88 | 130 | 0.44 |
| 15 | 750 | 0.1 | 5 | 260 | 24 | 212.70 | 85 | 120 | 0.62 |
| 16 | 750 | 1 | 0 | 230 | 18 | 208.26 | 80 | 106 | 1.01 |
| 17 | 750 | 1 | 0.5 | 260 | 24 | 218.83 | 85 | 113 | 0.88 |
| 18 | 750 | 1 | 5 | 290 | 12 | 201.05 | 80 | 108 | 0.97 |
| 19 | 780 | 0 | 0 | 290 | 18 | 219.96 | 85 | 115 | 0.89 |
| 20 | 780 | 0 | 0.5 | 230 | 24 | 224.58 | 88 | 125 | 0.33 |
| 21 | 780 | 0 | 5 | 260 | 12 | 240.50 | 87 | 118 | 0.49 |
| 22 | 780 | 0.1 | 0 | 230 | 24 | 238.37 | 88 | 127 | 0.46 |
| 23 | 780 | 0.1 | 0.5 | 260 | 12 | 240.04 | 90 | 132 | 0.48 |
| 24 | 780 | 0.1 | 5 | 290 | 18 | 232.57 | 85 | 114 | 0.46 |
| 25 | 780 | 1 | 0 | 260 | 12 | 200.27 | 80 | 107 | 0.99 |
| 26 | 780 | 1 | 0.5 | 290 | 18 | 199.68 | 85 | 119 | 0.49 |
| 27 | 780 | 1 | 5 | 230 | 24 | 224.74 | 84 | 114 | 0.53 |

Fig. 2
(A) XRD results of the Al-3.5FeNb-1.5C master alloy; (B) SEM microstructure of dispersed intermetallic particles extracted from Al-3.5FeNb-1.5C master alloy. XRD, X-ray diffraction

Fig. 3
Optical microscopic images of experimental castings at 720°C, 750°C, and 780°C: (A–C) without grain refiner, (D–F) 0.1 wt% of Al-3.5FeNb-1.5C, (G–I) 1.0 wt% of Al-3.5FeNb-1.5C

Fig. 4
(A) Tensile strength values (B) Brinell hardness and microhardness values obtained from experimental runs. (C) and (D) show the optical microscope images of (C) R5 and (D) R25 experimental castings, which have the highest and lowest mechanical properties, respectively. (E) and (F) show the SEM and EDS images of R5, respectively
Table 4
Normalized data and deviation sequence values of the following characteristics
| Run | Deviation Tensile strength | Sequences Brinell hardness | (Δ0i) Microhardness | GRC Tensile strength | Brinell hardness | Microhardness | GRG | Rank |
|---|---|---|---|---|---|---|---|---|
| 1 | 0.62 | 0.55 | 0.77 | 0.45 | 0.48 | 0.39 | 0.44 | 20 |
| 2 | 0.47 | 0.55 | 0.67 | 0.49 | 0.48 | 0.43 | 0.47 | 13 |
| 3 | 0.07 | 0.27 | 0.57 | 0.87 | 0.65 | 0.47 | 0.66 | 6 |
| 4 | 0.19 | 0.09 | 0.00 | 0.73 | 0.85 | 1.00 | 0.86 | 2 |
| 5 | 0.00 | 0.00 | 0.03 | 1.00 | 1.00 | 0.94 | 0.98 | 1 |
| 6 | 0.24 | 0.55 | 0.00 | 0.68 | 0.48 | 1.00 | 0.72 | 4 |
| 7 | 0.58 | 0.73 | 0.80 | 0.46 | 0.41 | 0.38 | 0.42 | 23 |
| 8 | 0.69 | 0.73 | 0.73 | 0.42 | 0.41 | 0.41 | 0.41 | 24 |
| 9 | 0.82 | 0.45 | 0.60 | 0.38 | 0.52 | 0.45 | 0.45 | 15 |
| 10 | 0.63 | 0.55 | 0.73 | 0.44 | 0.48 | 0.41 | 0.44 | 18 |
| 11 | 0.51 | 0.55 | 0.67 | 0.39 | 0.48 | 0.43 | 0.43 | 21 |
| 12 | 0.38 | 0.18 | 0.67 | 0.57 | 0.73 | 0.43 | 0.58 | 9 |
| 13 | 0.38 | 0.45 | 0.60 | 0.57 | 0.52 | 0.45 | 0.52 | 11 |
| 14 | 0.24 | 0.27 | 0.20 | 0.68 | 0.65 | 0.71 | 0.68 | 5 |
| 15 | 0.74 | 0.55 | 0.53 | 0.40 | 0.48 | 0.48 | 0.46 | 14 |
| 16 | 0.83 | 1.00 | 1.00 | 0.38 | 0.33 | 0.33 | 0.35 | 25 |
| 17 | 0.61 | 0.55 | 0.77 | 0.45 | 0.48 | 0.39 | 0.44 | 19 |
| 18 | 0.97 | 1.00 | 0.93 | 0.34 | 0.33 | 0.35 | 0.34 | 26 |
| 19 | 0.59 | 0.55 | 0.70 | 0.46 | 0.48 | 0.42 | 0.45 | 16 |
| 20 | 0.49 | 0.27 | 0.37 | 0.50 | 0.65 | 0.58 | 0.58 | 10 |
| 21 | 0.17 | 0.36 | 0.60 | 0.74 | 0.58 | 0.45 | 0.59 | 8 |
| 22 | 0.22 | 0.27 | 0.30 | 0.70 | 0.65 | 0.63 | 0.66 | 7 |
| 23 | 0.18 | 0.09 | 0.13 | 0.73 | 0.85 | 0.79 | 0.79 | 3 |
| 24 | 0.33 | 0.55 | 0.73 | 0.60 | 0.48 | 0.41 | 0.49 | 12 |
| 25 | 0.99 | 1.00 | 0.97 | 0.34 | 0.33 | 0.34 | 0.34 | 27 |
| 26 | 1.00 | 0.55 | 0.57 | 0.33 | 0.48 | 0.47 | 0.43 | 22 |
| 27 | 0.49 | 0.64 | 0.73 | 0.50 | 0.44 | 0.41 | 0.45 | 17 |
[i] GRC, Grey relational coefficient; GRG, Grey relational grade.

Fig. 5
Effect of process parameters on GRG. GRA, grey relational analysis
Table 5
Mean values of GRG at different levels and their main effects
| Parameter destination | Input parameters | Level 1 | Level 2 | Level 3 | Max/min |
|---|---|---|---|---|---|
| A | Molten metal temperature (°C) | 0.601 | 0.470 | 0.530 | 0.131 |
| B | Al-3.5FeNb-1.5C (wt%) | 0.516 | 0.683 | 0.403 | 0.280 |
| C | Al-6Ni (wt%) | 0.496 | 0.578 | 0.527 | 0.082 |
| D | Die temperature (°C) | 0.539 | 0.537 | 0.525 | 0.015 |
| E | Injection pressure (MPa) | 0.508 | 0.528 | 0.565 | 0.056 |
[i] GRG, grey relational grade.
Table 6
TOPSIS results
| Expt. runs | Normalization | Weighted normalization | Separation | CC | |||||
|---|---|---|---|---|---|---|---|---|---|
| Tensile strength | Brinell hardness | Vickers hardness | Tensile | Brinell | Vickers | S− | S+ | ||
| 1 | 0.187 | 0.191 | 0.183 | 0.062 | 0.064 | 0.061 | 0.016 | 0.008 | 0.324 |
| 2 | 0.192 | 0.191 | 0.188 | 0.064 | 0.064 | 0.063 | 0.014 | 0.010 | 0.416 |
| 3 | 0.211 | 0.198 | 0.192 | 0.070 | 0.066 | 0.064 | 0.010 | 0.016 | 0.628 |
| 4 | 0.206 | 0.202 | 0.220 | 0.069 | 0.067 | 0.073 | 0.003 | 0.021 | 0.886 |
| 5 | 0.214 | 0.204 | 0.218 | 0.071 | 0.068 | 0.073 | 0.001 | 0.023 | 0.972 |
| 6 | 0.204 | 0.191 | 0.220 | 0.068 | 0.064 | 0.073 | 0.005 | 0.020 | 0.786 |
| 7 | 0.189 | 0.187 | 0.181 | 0.063 | 0.062 | 0.060 | 0.016 | 0.007 | 0.306 |
| 8 | 0.184 | 0.187 | 0.184 | 0.061 | 0.062 | 0.061 | 0.017 | 0.007 | 0.283 |
| 9 | 0.179 | 0.193 | 0.191 | 0.060 | 0.064 | 0.064 | 0.016 | 0.008 | 0.350 |
| 10 | 0.187 | 0.191 | 0.184 | 0.062 | 0.064 | 0.061 | 0.016 | 0.008 | 0.333 |
| 11 | 0.181 | 0.191 | 0.188 | 0.060 | 0.064 | 0.063 | 0.016 | 0.008 | 0.321 |
| 12 | 0.198 | 0.200 | 0.188 | 0.066 | 0.067 | 0.063 | 0.012 | 0.013 | 0.511 |
| 13 | 0.197 | 0.193 | 0.191 | 0.066 | 0.064 | 0.064 | 0.012 | 0.012 | 0.500 |
| 14 | 0.204 | 0.198 | 0.210 | 0.068 | 0.066 | 0.070 | 0.005 | 0.018 | 0.779 |
| 15 | 0.182 | 0.191 | 0.194 | 0.061 | 0.064 | 0.065 | 0.014 | 0.009 | 0.391 |
| 16 | 0.179 | 0.180 | 0.171 | 0.060 | 0.060 | 0.057 | 0.022 | 0.003 | 0.110 |
| 17 | 0.188 | 0.191 | 0.183 | 0.063 | 0.064 | 0.061 | 0.016 | 0.008 | 0.334 |
| 18 | 0.172 | 0.180 | 0.175 | 0.057 | 0.060 | 0.058 | 0.022 | 0.001 | 0.059 |
| 19 | 0.189 | 0.191 | 0.186 | 0.063 | 0.064 | 0.062 | 0.015 | 0.009 | 0.370 |
| 20 | 0.193 | 0.198 | 0.202 | 0.064 | 0.066 | 0.067 | 0.009 | 0.014 | 0.598 |
| 21 | 0.206 | 0.196 | 0.191 | 0.069 | 0.065 | 0.064 | 0.010 | 0.014 | 0.582 |
| 22 | 0.204 | 0.198 | 0.205 | 0.068 | 0.066 | 0.068 | 0.006 | 0.017 | 0.727 |
| 23 | 0.206 | 0.202 | 0.213 | 0.069 | 0.067 | 0.071 | 0.004 | 0.020 | 0.845 |
| 24 | 0.200 | 0.191 | 0.184 | 0.067 | 0.064 | 0.061 | 0.014 | 0.011 | 0.452 |
| 25 | 0.172 | 0.180 | 0.173 | 0.057 | 0.060 | 0.058 | 0.022 | 0.001 | 0.032 |
| 26 | 0.171 | 0.191 | 0.192 | 0.057 | 0.064 | 0.064 | 0.018 | 0.008 | 0.309 |
| 27 | 0.193 | 0.189 | 0.184 | 0.064 | 0.063 | 0.061 | 0.015 | 0.009 | 0.380 |
[i] CC, closeness coefficient.

Fig. 6
Effect of process parameters on CC. CC, closeness coefficient
Table 7
Response table of average values of CC for TOPSIS
| Parameter destination | Input parameters | Level 1 | Level 2 | Level 3 | Max/min |
|---|---|---|---|---|---|
| A | Molten metal temperature (°C) | 0.550 | 0.371 | 0.478 | 0.179 |
| B | Al-3.5FeNb-1.5C (wt%) | 0.454 | 0.704 | 0.240 | 0.464 |
| C | Al-6Ni (wt%) | 0.399 | 0.540 | 0.460 | 0.141 |
| D | Die temperature (°C) | 0.499 | 0.463 | 0.435 | 0.036 |
| E | Injection pressure (MPa) | 0.4147 | 0.465 | 0.519 | 0.104 |
[i] CC, Closeness coefficient.

Fig. 7
GRG and CC value of each experimental run. CC, closeness coefficient; GRG, Grey relational grade
Table 8
Results’ comparison at initial and optimal levels by GRA and TOPSIS methods
| S. No | Parameter | Initial value | Predicted value | Experimental value |
|---|---|---|---|---|
| A2, B1, C1, D2, E3 | A1, B2, C2, D1, E3 | A1, B2, C2, D1, E3 | ||
| 1 | Tensile strength | 218.388 | – | 249.085 |
| 2 | Brinell hardness | 85 | – | 91 |
| 3 | Vickers microhardness | 113 | – | 135 |
| 4 | Grey relational grade | 0.4396 | 0.8087 | 0.9792 |
| 5 | Closeness coefficient | 0.3242 | 0.9481 | 0.9715 |
| 6 | Improvement of GRG | – | 0.5396 | – |
| 7 | Improvement of CC | - | 0.6473 | – |
[i] CC, closeness coefficient; GRA, grey relational analysis; GRG, grey relational grade.

Fig. 8
SEM images of Al-Si9.8-Cu3.4 alloy: Experimental runs of (A) R5 at 0.1 wt.% of Al3.5FeNb-1.5C and 0.5 wt.% of Al-6Ni with base alloy and (B) R25 at 1.0 wt.% of Al3.5FeNb-1.5C with base alloy; EDX pattern of (C) Experimental run R5 and (D) Experimental run R25

Fig. 9
SEM images of fracture pattern of experimental runs of (A) R5 at 0.1 wt.% of Al3.5FeNb-1.5C and 0.5 wt.% of Al-6Ni with base alloy and (B) R25 at 1.0 wt.% of Al3.5FeNb-1.5C with base alloy