Table 1
Design input parameters (MT, MS, BPMR, and CC) and experimental results (RD, crystallite size, and lattice strain) obtained in the present study
| Exp. no. | Alloy code | MT, h | BPMR, n | MS, rev/min | CC, wt% | RD, % | Crystallite size (from Fe peak), nm | Lattice strain (from Fe peak), % |
|---|---|---|---|---|---|---|---|---|
| 1 | BD0-1 | 5.5 | 10 | 100 | 0 | 71.65 | 37.0 | 0.3120 |
| 2 | BD0-2 | 5.5 | 10 | 300 | 0 | 65.94 | 28.0 | 0.3340 |
| 3 | BD0-3 | 1.0 | 10 | 200 | 0 | 66.63 | 32.0 | 0.3030 |
| 4 | BD0-4 | 10.0 | 10 | 200 | 0 | 67.76 | 25.0 | 0.3730 |
| 5 | BD0-5 | 5.5 | 5 | 200 | 0 | 67.99 | 44.0 | 0.2850 |
| 6 | BD0-6 | 5.5 | 15 | 200 | 0 | 68.53 | 25.0 | 0.3760 |
| 7 | BD5-1 | 1.0 | 5 | 200 | 5 | 75.04 | 58.0 | 0.1650 |
| 8 | BD5-2 | 10.0 | 5 | 200 | 5 | 72.66 | 18.0 | 0.5070 |
| 9 | BD5-3 | 1.0 | 15 | 200 | 5 | 73.49 | 38.0 | 0.2480 |
| 10 | BD5-4 | 10.0 | 15 | 200 | 5 | 66.04 | 22.0 | 0.4180 |
| 11 | BD5-5 | 5.5 | 5 | 100 | 5 | 75.46 | 58.0 | 0.1650 |
| 12 | BD5-6 | 5.5 | 15 | 100 | 5 | 72.08 | 28.0 | 0.3340 |
| 13 | BD5-7 | 5.5 | 5 | 300 | 5 | 71.20 | 41.0 | 0.2740 |
| 14 | BD5-8 | 5.5 | 15 | 300 | 5 | 64.30 | 26.0 | 0.3550 |
| 15 | BD5-9 | 1.0 | 10 | 100 | 5 | 75.19 | 58.0 | 0.1670 |
| 16 | BD5-10 | 10.0 | 10 | 100 | 5 | 71.79 | 17.0 | 0.5560 |
| 17 | BD5-11 | 1.0 | 10 | 300 | 5 | 70.98 | 21.0 | 0.4610 |
| 18 | BD5-12 | 10.0 | 10 | 300 | 5 | 66.16 | 18.0 | 0.5050 |
| 19 | BD5-13 | 5.5 | 10 | 200 | 5 | 69.66 | 22.0 | 0.4180 |
| 20 | BD10-1 | 5.5 | 10 | 100 | 10 | 75.23 | 25.0 | 0.3740 |
| 21 | BD10-2 | 5.5 | 10 | 300 | 10 | 67.80 | 23.0 | 0.4080 |
| 22 | BD10-3 | 1.0 | 10 | 200 | 10 | 75.08 | 33.0 | 0.3360 |
| 23 | BD10-4 | 10.0 | 10 | 200 | 10 | 67.32 | 28.0 | 0.3340 |
| 24 | BD10-5 | 5.5 | 5 | 200 | 10 | 75.38 | 23.0 | 0.4080 |
| 25 | BD10-6 | 5.5 | 15 | 200 | 10 | 72.19 | 24.0 | 0.4580 |
| 26 | BD5-13R | 5.5 | 10 | 200 | 5 | 68.99 | 22.0 | 0.4180 |
| 27 | BD5-13R | 5.5 | 10 | 200 | 5 | 69.12 | 22.0 | 0.4180 |
[i] BPMR, ball-to-powder mass ratio; CC, Cu content; Exp. No., Experiment Number; MT, milling time; MS, milling speed; RD, relative density.
Fig. 1
SEIs of the as-received (A) Fe, (B) Mn, and (C) Cu powders used in the present study. SEI, secondary electron image
Fig. 2
SEIs of the size and shape of the selected processed alloy powders: (A) BD5-1; (B) BD5-3; and (C) BD5-4 alloys. SEI, secondary electron image
Fig. 3
Results of EDS analysis of the alloys in powder form: (A–C) BD5-1; (D–F) BD5-3; (G–I) BD5-4. EDS, energy dispersive spectroscopy
Fig. 4
The distribution of particle size for BD5-1, BD5-2, BD5-4, BD5-9, BD5-10, and BD5-11 alloys. d, diameter
Table 2
The results of particle size analysis for selected alloys
| Alloy code | Average particle size, nm | Standard deviation, nm | % intensity (main peak) | PDI |
|---|---|---|---|---|
| BD5-1 | 1,477.00 | 480.50 | 96.50 | 0.33 |
| BD5-2 | 655.40 | 220.30 | 91.20 | 0.49 |
| BD5-4 | 327.10 | 53.28 | 100.00 | 0.52 |
| BD5-9 | 1,274.00 | 315.90 | 96.20 | 0.42 |
| BD5-10 | 638.70 | 214.10 | 91.10 | 0.41 |
| BD5-11 | 499.50 | 129.40 | 99.10 | 0.35 |
[i] PDI, polydispersity index.
Fig. 5
XRD patterns of all powder samples: (A) BD0-1 to BD0-6; (B) BD5-7 to BD5-12; (C) BD5-13 to BD5-19; (D) BD10-20 to BD10-25. CPS, counts/s; XRD, X-ray diffraction
Fig. 6
The experimental results of RD versus CP for [(Fe–35 wt%Mn)95–Cu5] green samples. CP, compaction pressure; RD, relative density
Fig. 7
EDS analysis results of the compacted samples: (A–C) BD5-1; (D–F) BD5-3; and (G–I) BD5-4. EDS, energy dispersive spectroscopy
Fig. 8
EDS analysis results of the green samples: (A–C) BD5-9; (D–F) BD5-10; and (G–I) BD5-11. EDS, energy dispersive spectroscopy
Table 3
The results of the ANOVA test performed for the crystallite size
| Source | Sum of squares | DF | Mean square | F-value | p-value |
|---|---|---|---|---|---|
| Model | 2.696 × 105 | 10 | 26,963.56 | 3.89 | 0.0079 |
| MT | 1.025 × 105 | 1 | 1.025 × 105 | 14.78 | 0.0014 |
| BPMR | 56,033.33 | 1 | 56,033.33 | 8.08 | 0.0118 |
| MS | 33,920.33 | 1 | 33,920.33 | 4.89 | 0.0419 |
| CC | 12,610.08 | 1 | 12,610.08 | 1.82 | 0.1963 |
| (MT) × (BPMR) | 14,520.25 | 1 | 14,520.25 | 2.09 | 0.1672 |
| (MT) × (MS) | 36,100.00 | 1 | 36,100.00 | 5.20 | 0.0366 |
| (MT) × (CC) | 144.00 | 1 | 144.00 | 0.0208 | 0.8872 |
| (BPMR) × (MS) | 5,402.25 | 1 | 5,402.25 | 0.7789 | 0.3906 |
| (BPMR) × (CC) | 7,225.00 | 1 | 7,225.00 | 1.04 | 0.3226 |
| (MS) × (CC) | 1,190.25 | 1 | 1,190.25 | 0.1716 | 0.6842 |
| Residual | 1.110E × 105 | 16 | 6,936.07 | ||
| Lack of Fit | 1.109E × 105 | 14 | 7,923.37 | 316.93 | 0.0031 |
| Pure Error | 50.00 | 2 | 25.00 | ||
| Total | 3.806 × 105 | 26 |
[i] ANOVA, analysis of variance; BPMR, ball-to-powder mass ratio; CC, Cu content; DF, degree of freedom; MS, milling speed; MT, milling time.
Table 4
The results of the ANOVA test performed for the lattice strain
| Source | Sum of squares | DF | Mean square | F-value | p-value |
|---|---|---|---|---|---|
| Model | 0.1630 | 10 | 0.0163 | 2.49 | 0.0499 |
| MT | 0.0855 | 1 | 0.0855 | 13.08 | 0.0023 |
| BPMR | 0.0128 | 1 | 0.0128 | 1.96 | 0.1807 |
| MS | 0.0147 | 1 | 0.0147 | 2.25 | 0.1532 |
| CC | 0.0092 | 1 | 0.0092 | 1.41 | 0.2518 |
| (MT) × (BPMR) | 0.0074 | 1 | 0.0074 | 1.13 | 0.3032 |
| (MT) × (MS) | 0.0298 | 1 | 0.0298 | 4.55 | 0.0487 |
| (MT) × (CC) | 0.0013 | 1 | 0.0013 | 0.1983 | 0.6621 |
| (BPMR) × (MS) | 0.0019 | 1 | 0.0019 | 0.2962 | 0.5938 |
| (BPMR) × (CC) | 0.0003 | 1 | 0.0003 | 0.0442 | 0.8361 |
| (MS) × (CC) | 0.0001 | 1 | 0.0001 | 0.0169 | 0.8983 |
| Residual | 0.1046 | 16 | 0.0065 | ||
| Lack of fit | 0.1045 | 14 | 0.0075 | 355.54 | 0.0028 |
| Pure error | 0.0000 | 2 | 0.0000 | ||
| Total | 0.2676 | 26 |
[i] ANOVA, analysis of variance; BPMR, ball-to-powder mass ratio; CC, Cu content; DF, degree of freedom; MS, milling speed; MT, milling time.
Table 5
The results of ANOVA test performed for the RD
| Source | Sum of squares | DF | Mean square | F-value | p-value |
|---|---|---|---|---|---|
| Model | 274.0800 | 10 | 27.4100 | 12.2300 | <0.0001 |
| MT | 50.7600 | 1 | 50.7600 | 22.6400 | 0.0002 |
| BPMR | 37.1000 | 1 | 37.1000 | 16.5500 | 0.0009 |
| MS | 102.2000 | 1 | 102.2000 | 45.5900 | <0.0001 |
| CC | 50.0200 | 1 | 50.0200 | 22.3100 | 0.0002 |
| (MT) × (BPMR) | 6.4300 | 1 | 6.4300 | 2.8700 | 0.1098 |
| (MT) × (MS) | 0.5041 | 1 | 0.5041 | 0.2249 | 0.6418 |
| (MT) × (CC) | 19.7600 | 1 | 19.7600 | 8.8100 | 0.0090 |
| (BPMR) × (MS) | 3.1000 | 1 | 3.1000 | 1.3800 | 0.2570 |
| (BPMR) × (CC) | 3.4800 | 1 | 3.4800 | 1.5500 | 0.2308 |
| (MS) × (CC) | 0.7396 | 1 | 0.7396 | 0.3299 | 0.5737 |
| Residual | 35.8700 | 16 | 2.2400 | ||
| Lack of fit | 35.6100 | 14 | 2.5400 | 20.1700 | 0.0482 |
| Pure error | 0.2522 | 2 | 0.1261 | ||
| Total | 309.9500 | 26 |
[i] ANOVA, analysis of variance; BPMR, ball-to-powder mass ratio; CC, Cu content; DF, degree of freedom; MS, milling speed; MT, milling time; RD, relative density.
Fig. 9
ANOVA results of RD: (A) The experimental and the predicted values of RD; and (B) normal probability of residuals of RD of the developed compacted samples. RD, relative density
Fig. 10
The impact of the input variables on the RD of the developed green samples: (A, C, E, G, I, K) 3D surface plots; (B, D, F, H, J, L) 2D contour plots. RD, relative density