Response Surface Optimization of Matched-Die Consolidation for BMI-Based CFRP Prepreg Laminates Toward Stiffened-Shell Manufacturing
Abstract
1. Introduction
2. Materials and Methods
2.1. Materials
2.2. The Theoretical Basis of the Forming Process
2.2.1. Chemorheological Behavior of BMI Resin and Viscosity Window Control
2.2.2. Theory of Preform Compression Displacement
2.2.3. Thermal Residual Stress and Cooling-Rate Theory
2.3. Forming Process of BMI–CFRP Unidirectional Laminates
2.4. Preliminary Experiments and Single-Factor Experiments
2.5. Response Surface Experiments
2.6. Mechanical Performance Characterization
3. Results
3.1. Microstructure Analysis and Process Discussion
3.2. Results of Single-Factor Experiment
3.3. Response Surface Model Establishment and Significance Analysis
3.4. The Application of the Optimal Process in Aircraft Shell Manufacturing
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
| BBD | Box–Behnken design |
| BDM | 4,4′-Bismaleimidodiphenylmethane |
| BMI | Bismaleimide |
| CCD | Central composite design |
| CF | Carbon fiber |
| CFRP | Carbon fiber-reinforced polymer |
| CNC | Computer numerical control |
| CTE | Coefficient of thermal expansion |
| DABPA | 2,2′-Diallylbisphenol A |
| DMA | Dynamic mechanical analysis |
| DSC | Differential scanning calorimetry |
| FRP | Fiber-reinforced polymer |
| RH | Relative humidity |
| RSM | Response surface methodology |
| SEM | Scanning electron microscopy |
| Tg | Glass transition temperature |
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| Procedure | Value |
|---|---|
| Coating temperature (°C) | 110 |
| Coating speed (m/min) | 6 |
| Coating pressure (N) | 20 |
| Infiltration temperature (°C) | 120 |
| Infiltration speed (m/min) | 3 |
| Infiltration pressure (N) | 30 |
| Serial Number | Test Conditions | Observations |
|---|---|---|
| 1 | Heating sealing temperature: 120 °C Heating rate: 1.5 °C/min Cooling rate: 10 °C/min | Amount of compression (mm): 0.05; 0.1; 0.15; 0.2; 0.25 |
| 2 | Amount of compression: 0.15 mm Heating rate: 1.5 °C/min Cooling rate: 10 °C/min | Heating sealing temperature (°C): 80; 100; 120; 140; 160 |
| 3 | Amount of compression: 0.15 mm Heating sealing temperature: 120 °C Cooling rate: 10 °C/min | Heating rate 0.5 (°C/min): 1; 1.5; 2; 2.5 |
| 4 | Amount of compression: 0.15 mm Heating sealing temperature: 120 °C Heating rate: 1.5 °C/min | Cooling rate (°C/min): 2; 6; 10; 14; 18 |
| Levels | Factors | |||
|---|---|---|---|---|
| A Amount of Compression (mm) | Heating Sealing Temperature (°C) | Heating Rate 0.5 (°C/min) | Cooling Rate (°C/min) | |
| −1 | 0.05 | 80 | 0.5 | 2 |
| 0 | 0.10 | 100 | 1.0 | 6 |
| 1 | 0.15 | 120 | 1.5 | 10 |
| No. | Amount of Compression (mm) | Heating Sealing Temperature (°C) | Heating Rate (°C/min) | Cooling Rate (°C/min) | Tensile Strength (Mpa) |
|---|---|---|---|---|---|
| 1 | 0.05 | 80 | 1 | 6 | 507.99 |
| 2 | 0.15 | 80 | 1 | 6 | 1198.62 |
| 3 | 0.05 | 120 | 1 | 6 | 2247.24 |
| 4 | 0.15 | 120 | 1 | 6 | 2095.06 |
| 5 | 0.1 | 100 | 0.5 | 2 | 1766.22 |
| 6 | 0.1 | 100 | 1.5 | 2 | 1887.23 |
| 7 | 0.1 | 100 | 0.5 | 10 | 1322.69 |
| 8 | 0.1 | 100 | 1.5 | 10 | 1136.78 |
| 9 | 0.05 | 100 | 1 | 2 | 1906.63 |
| 10 | 0.15 | 100 | 1 | 2 | 1600.11 |
| 11 | 0.05 | 100 | 1 | 10 | 796.3 |
| 12 | 0.15 | 100 | 1 | 10 | 1356.35 |
| 13 | 0.1 | 80 | 0.5 | 6 | 600.23 |
| 14 | 0.1 | 120 | 0.5 | 6 | 2001.87 |
| 15 | 0.1 | 80 | 1.5 | 6 | 808.23 |
| 16 | 0.1 | 120 | 1.5 | 6 | 1916.75 |
| 17 | 0.05 | 100 | 0.5 | 6 | 1587.83 |
| 18 | 0.15 | 100 | 0.5 | 6 | 2000.54 |
| 19 | 0.05 | 100 | 1.5 | 6 | 1597.25 |
| 20 | 0.15 | 100 | 1.5 | 6 | 1765.2 |
| 21 | 0.1 | 80 | 1 | 2 | 606.77 |
| 22 | 0.1 | 120 | 1 | 2 | 2174.89 |
| 23 | 0.1 | 80 | 1 | 10 | 507.52 |
| 24 | 0.1 | 120 | 1 | 10 | 1502.44 |
| 25 | 0.1 | 100 | 1 | 6 | 1877.57 |
| 26 | 0.1 | 100 | 1 | 6 | 2026.68 |
| 27 | 0.1 | 100 | 1 | 6 | 2117.62 |
| 28 | 0.1 | 100 | 1 | 6 | 2209.55 |
| 29 | 0.1 | 100 | 1 | 6 | 2076.15 |
| Source | Sum of Squares | Degrees of Freedom | Mean Square | F-Value | p-Value |
|---|---|---|---|---|---|
| Model | 8,662,866.94 | 14 | 618,776.21 | 38.10 | 0.0000 |
| Amount of compression | 157,011.71 | 1 | 157,011.71 | 9.67 | 0.0077 |
| Heating sealing temperature | 4,952,248.75 | 1 | 4,952,248.75 | 304.96 | 0.0000 |
| Heating rate | 2350.32 | W1 | 2350.32 | 0.14 | 0.7093 |
| Cooling rate | 918,406.07 | 1 | 918,406.07 | 56.56 | 0.0000 |
| AB | 177,582.17 | 1 | 177,582.17 | 10.94 | 0.0052 |
| AC | 14,976.86 | 1 | 14,976.86 | 0.92 | 0.3532 |
| AD | 187,735.89 | 1 | 187,735.89 | 11.56 | 0.0043 |
| BC | 21,479.83 | 1 | 21,479.83 | 1.32 | 0.2694 |
| BD | 82,139.56 | 1 | 82,139.56 | 5.06 | 0.0411 |
| CD | 23,549.97 | 1 | 23,549.97 | 1.45 | 0.2485 |
| A2 | 150,155.44 | 1 | 150,155.44 | 9.25 | 0.0088 |
| B2 | 1,394,027.16 | 1 | 1,394,027.16 | 85.85 | 0.0000 |
| C2 | 223,647.85 | 1 | 223,647.85 | 13.77 | 0.0023 |
| D2 | 1,112,008.04 | 1 | 1,112,008.04 | 68.48 | 0.0000 |
| Residual error | 227,343.56 | 14 | 16,238.83 | ||
| Missing item | 167,018.00 | 10 | 16,701.80 | 1.11 | 0.5021 |
| Error | 60,325.56 | 4 | 15,081.39 | ||
| Total | 8,890,210.49 | 28 |
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© 2026 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
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Yu, B.; Dan, Y.; Sun, H.; Kang, Y.; Zhang, B.; Chen, Y.; Wang, Z.; Liu, J. Response Surface Optimization of Matched-Die Consolidation for BMI-Based CFRP Prepreg Laminates Toward Stiffened-Shell Manufacturing. Polymers 2026, 18, 483. https://doi.org/10.3390/polym18040483
Yu B, Dan Y, Sun H, Kang Y, Zhang B, Chen Y, Wang Z, Liu J. Response Surface Optimization of Matched-Die Consolidation for BMI-Based CFRP Prepreg Laminates Toward Stiffened-Shell Manufacturing. Polymers. 2026; 18(4):483. https://doi.org/10.3390/polym18040483
Chicago/Turabian StyleYu, Bo, Yinghao Dan, Haiyang Sun, Yu Kang, Bowen Zhang, Yuning Chen, Ziqiao Wang, and Jiuqing Liu. 2026. "Response Surface Optimization of Matched-Die Consolidation for BMI-Based CFRP Prepreg Laminates Toward Stiffened-Shell Manufacturing" Polymers 18, no. 4: 483. https://doi.org/10.3390/polym18040483
APA StyleYu, B., Dan, Y., Sun, H., Kang, Y., Zhang, B., Chen, Y., Wang, Z., & Liu, J. (2026). Response Surface Optimization of Matched-Die Consolidation for BMI-Based CFRP Prepreg Laminates Toward Stiffened-Shell Manufacturing. Polymers, 18(4), 483. https://doi.org/10.3390/polym18040483
