Optimisation of Heat Treatment Process for Damping Properties of Mg-13Gd-4Y-2Zn-0.5Zr Magnesium Alloy Using Box–Behnken Design Method
Abstract
:1. Introduction
2. Experimental
2.1. Damping Experiment
2.2. Heat Treatment
2.3. Microstructure Observation and Mechanical Properties Test
3. Optimisation Analysis of Solid Solution Parameters
4. Optimisation Analysis of Ageing Parameters
5. Mathematical Models
5.1. Design of Experiments
5.2. Regression Analysis of Tensile Strength
5.78889 × 10−3AC + 4.22222 × 10−3AD + 0.078917BC − 0.44542BD − 0.13733CD +
0.060104A2 + 0.66115B2 − 0.12332C2 + 0.79231D2
5.3. Regression Analysis of Damping Coefficient
6.55556 × 10−5AC + 4.72222 × 10−4AD + 1.91667 × 10−4BC − 2.41667 × 10−3BD + 6.33333
× 10−4CD + 1.17222 × 10−4A2 − 7.50000 × 10−4B2 + 1.05556 × 10−4C2 − 1.51389 × 10−3D2
5.4. Parameter Optimisation
6. Verification Experiment
7. Conclusions
Author Contributions
Funding
Acknowledgements
Conflicts of Interest
References
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Mg | Gd | Y | Zn | Zr |
---|---|---|---|---|
Bal | 13.77 | 4.64 | 2.39 | 0.29 |
Sample | Detection Position | Element Content (at. %) | The Possible Phase | ||||
---|---|---|---|---|---|---|---|
Mg | Gd | Y | Zn | Zr | |||
190 °C × 20 h | Spot 1 | 56.01 | 20.70 | 21.02 | 0.65 | 1.63 | RE-rich phase |
Spot 2 | 93.17 | 4.42 | 1.64 | 0.49 | 0.29 | Mg5Gd | |
Spot 3 | 89.92 | 3.62 | 2.21 | 3.99 | 0.26 | Mg12YZn | |
Spot 4 | 91.80 | 5.40 | 1.85 | 0.66 | 0.29 | Mg5Gd | |
210 °C × 20 h | Spot 1 | 96.09 | 1.77 | 0.95 | 0.96 | 0.22 | LPSO |
Spot 2 | 94.20 | 3.18 | 1.48 | 0.86 | 0.29 | Mg5Gd | |
Spot 3 | 93.63 | 2.28 | 1.47 | 2.34 | 0.28 | Mg5Gd | |
230 °C × 20 h | Spot 1 | 94.25 | 3.54 | 1.42 | 0.52 | 0.28 | Mg5Gd |
Spot 2 | 90.65 | 3.23 | 1.90 | 3.94 | 0.28 | Mg12YZn | |
Spot 3 | 93.70 | 2.49 | 1.30 | 2.23 | 0.27 | LPSO | |
250 °C × 20 h | Spot 1 | 94.46 | 3.41 | 1.46 | 0.40 | 0.27 | Mg5Gd |
Spot 2 | 88.76 | 3.84 | 2.46 | 4.64 | 0.30 | Mg12YZn | |
Spot 3 | 96.89 | 1.63 | 0.76 | 0.51 | 0.21 | LPSO |
Ageing Treatment | 190 °C × 20 h | 210 °C × 20 h | 230 °C × 20 h | 250 °C × 20 h |
---|---|---|---|---|
Volume (Second phases)% | 29.652 | 33.394 | 28.219 | 29.233 |
Input | Notation | Level | ||
---|---|---|---|---|
−1 | 0 | 1 | ||
Solution temperature (°C) | A | 495 | 510 | 525 |
Solution time (h) | B | 10 | 12 | 14 |
Ageing temperature (°C) | C | 215 | 230 | 245 |
Ageing time (h) | D | 17 | 20 | 23 |
Experiment Number | Experimental Conditions | Yield Strength (MPa) | Calculated Parameters | ||||
---|---|---|---|---|---|---|---|
Solution | Ageing | ||||||
A (°C) | B (h) | C (°C) | D (h) | Y1 (MPa) | Y2 | ||
1 | 510 | 12 | 215 | 17 | 208.89 | 282.28 | 0.287 |
2 | 495 | 12 | 215 | 20 | 227.26 | 307.11 | 0.294 |
3 | 510 | 10 | 215 | 20 | 225.09 | 304.18 | 0.235 |
4 | 510 | 14 | 215 | 20 | 201.18 | 271.86 | 0.197 |
5 | 525 | 12 | 215 | 20 | 231.36 | 312.65 | 0.254 |
6 | 510 | 12 | 215 | 23 | 228.56 | 308.87 | 0.211 |
7 | 495 | 12 | 230 | 17 | 244.81 | 349.73 | 0.279 |
8 | 510 | 10 | 230 | 17 | 229.37 | 327.67 | 0.254 |
9 | 510 | 14 | 230 | 17 | 233.39 | 333.42 | 0.229 |
10 | 525 | 12 | 230 | 17 | 250.19 | 357.41 | 0.244 |
11 | 495 | 10 | 230 | 20 | 237.89 | 339.84 | 0.257 |
12 | 495 | 14 | 230 | 20 | 247.72 | 353.88 | 0.249 |
13 | 510 | 12 | 230 | 20 | 226.04 | 322.91 | 0.243 |
14 | 510 | 12 | 230 | 20 | 230.7 | 329.57 | 0.241 |
15 | 510 | 12 | 230 | 20 | 228.57 | 326.53 | 0.224 |
16 | 525 | 10 | 230 | 20 | 239.58 | 342.26 | 0.236 |
17 | 525 | 14 | 230 | 20 | 235 | 335.72 | 0.289 |
18 | 495 | 12 | 230 | 23 | 232.02 | 331.45 | 0.195 |
19 | 510 | 10 | 230 | 23 | 243.64 | 348.05 | 0.258 |
20 | 510 | 14 | 230 | 23 | 240.18 | 343.11 | 0.175 |
21 | 525 | 12 | 230 | 23 | 237.92 | 339.89 | 0.245 |
22 | 510 | 12 | 245 | 17 | 221.04 | 315.77 | 0.221 |
23 | 495 | 12 | 245 | 20 | 231.52 | 312.87 | 0.308 |
24 | 510 | 10 | 245 | 20 | 237.64 | 321.13 | 0.289 |
25 | 510 | 14 | 245 | 20 | 220.73 | 298.28 | 0.274 |
26 | 525 | 12 | 245 | 20 | 232.08 | 313.62 | 0.327 |
27 | 510 | 12 | 245 | 23 | 222.35 | 317.64 | 0.259 |
Variables | Sum of Squares of Deviations | Degree of Freedom | Mean Square | F-Value | p-Value | Significant |
---|---|---|---|---|---|---|
Model | 9167.77 | 14 | 654.84 | 4.18 | 0.0088 | Extremely Significant |
A | 0.92 | 1 | 0.92 | 5.90 × 10−3 | 0.9401 | - |
B | 182.99 | 1 | 182.99 | 1.17 | 0.3011 | - |
C | 565.26 | 1 | 565.26 | 3.61 | 0.0818 | - |
D | 43.06 | 1 | 43.05 | 0.27 | 0.6097 | - |
AB | 105.88 | 1 | 105.88 | 0.68 | 0.4271 | - |
dAC | 6.79 | 1 | 6.79 | 0.043 | 0.8387 | - |
AD | 0.14 | 1 | 0.14 | 9.21 × 10−4 | 0.9763 | - |
BC | 22.42 | 1 | 22.42 | 0.14 | 0.7119 | - |
BD | 28.57 | 1 | 28.57 | 0.18 | 0.677 | - |
CD | 152.77 | 1 | 152.77 | 0.97 | 0.343 | - |
A2 | 975.36 | 1 | 975.36 | 6.22 | 0.0282 | - |
B2 | 37.3 | 1 | 37.3 | 0.24 | 0.6344 | - |
C2 | 4106.38 | 1 | 4106.38 | 26.2 | 0.0003 | - |
D2 | 271.19 | 1 | 271.19 | 1.73 | 0.2129 | - |
Residuals | 1880.66 | 12 | 156.72 | - | - | - |
Lack of fit | 1858.43 | 10 | 185.84 | 16.72 | 0.0577 | Not Significant |
Pure Error | 22.23 | 2 | 11.12 | - | - | - |
Total | 11,048.43 | 26 | - | - | - | - |
Variables | Sum of Squares of Deviations | Degree of Freedom | Mean Square | F-Value | p-Value | Significant |
---|---|---|---|---|---|---|
Model | 0.025 | 14 | 1.78 × 10−3 | 2.69 | 0.0470 | Significant |
A | 1.41 × 10−5 | 1 | 1.41 × 10−5 | 0.021 | 0.8864 | - |
B | 1.12 × 10−3 | 1 | 1.12 × 10−3 | 1.69 | 0.2174 | - |
C | 3.33 × 10−3 | 1 | 3.33 × 10−3 | 5.04 | 0.0444 | - |
D | 2.44 × 10−3 | 1 | 2.44 × 10−3 | 3.68 | 0.0791 | - |
AB | 9.30 × 10−4 | 1 | 9.30 × 10−4 | 1.41 | 0.2587 | - |
AC | 8.70 × 10−4 | 1 | 8.70 × 10−4 | 1.32 | 0.2738 | - |
AD | 1.81 × 10−3 | 1 | 1.81 × 10−3 | 2.73 | 0.1244 | - |
BC | 1.32 × 10−4 | 1 | 1.32 × 10−4 | 0.2 | 0.6628 | - |
BD | 8.41 × 10−4 | 1 | 8.41 × 10−4 | 1.27 | 0.2816 | - |
CD | 3.25 × 10−3 | 1 | 3.25 × 10−3 | 4.91 | 0.0468 | - |
A2 | 3.71 × 10−3 | 1 | 3.71 × 10−3 | 5.61 | 0.0355 | - |
B2 | 4.80 × 10−5 | 1 | 4.80 × 10−5 | 0.073 | 0.7922 | - |
C2 | 3.01 × 10−3 | 1 | 3.01 × 10−3 | 4.55 | 0.0543 | - |
D2 | 9.90 × 10−4 | 1 | 9.90 × 10−4 | 1.5 | 0.2447 | - |
Residuals | 7.94 × 10−3 | 12 | 6.62 × 10−4 | - | - | - |
Lack of fit | 7.72 × 10−3 | 10 | 7.72 × 10−4 | 7.08 | 0.1299 | Not Significant |
Pure Error | 2.18 × 10−4 | 2 | 1.09 × 10−4 | - | - | - |
Total | 0.033 | 26 | - | - | - | - |
Sample | Heat Treatment | Tensile Strength (MPa) | Damping Coefficient |
---|---|---|---|
1 | 520 °C × 10 h + 239 °C × 22 h | 346.78 | 0.296 |
2 | 520 °C × 10 h + 205 °C × 22 h | 340.21 | 0.257 |
3 | 520 °C × 9 h + 230 °C × 20 h | 298.53 | 0.247 |
4 | 520 °C × 11 h + 249 °C × 24 h | 330.94 | 0.288 |
5 | 510 °C × 9 h + 230 °C × 20 h | 317.33 | 0.252 |
Sample | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|
Volume (Second phases )% | 17.104 | 20.973 | 22.31 | 16.322 | 17.463 |
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Zhang, J.; Kou, Z.; Yang, Y.; Li, B.; Li, X.; Yi, M.; Han, Z. Optimisation of Heat Treatment Process for Damping Properties of Mg-13Gd-4Y-2Zn-0.5Zr Magnesium Alloy Using Box–Behnken Design Method. Metals 2019, 9, 157. https://doi.org/10.3390/met9020157
Zhang J, Kou Z, Yang Y, Li B, Li X, Yi M, Han Z. Optimisation of Heat Treatment Process for Damping Properties of Mg-13Gd-4Y-2Zn-0.5Zr Magnesium Alloy Using Box–Behnken Design Method. Metals. 2019; 9(2):157. https://doi.org/10.3390/met9020157
Chicago/Turabian StyleZhang, Jun, Ziming Kou, Yaqin Yang, Baocheng Li, Xiaowen Li, Ming Yi, and Zhongjian Han. 2019. "Optimisation of Heat Treatment Process for Damping Properties of Mg-13Gd-4Y-2Zn-0.5Zr Magnesium Alloy Using Box–Behnken Design Method" Metals 9, no. 2: 157. https://doi.org/10.3390/met9020157