无机材料学报 ›› 2017, Vol. 32 ›› Issue (11): 1147-1153.DOI: 10.15541/jim20170050
郑金煌1, 李贺军1, 崔红1,2, 王毅2, 邓海亮2, 殷忠义2, 姚冬梅2, 苏红2
收稿日期:
2017-01-22
修回日期:
2017-03-19
出版日期:
2017-11-20
网络出版日期:
2017-10-20
作者简介:
郑金煌(1973-), 男, 高级工程师. E-mail: zjh114@sohu.com
基金资助:
ZHENG Jin-Huang1, LI He-Jun1, CUI Hong1,2, WANG Yi2, DENG Hai-Liang2, YIN Zhong-Yi2, YAO Dong-Mei2, SU Hong2
Received:
2017-01-22
Revised:
2017-03-19
Published:
2017-11-20
Online:
2017-10-20
摘要:
采用Design-expert软件设计预制体不同针刺成型参数组合试验, 研究预制体针刺成型参数对针刺碳/碳(C/C)复合材料拉伸强度的影响, 并构建了响应曲面数学模型, 实现对针刺C/C复合材料拉伸强度的优化与预测, 其模型显著性P=0.0206, 各试验实测值与预测值相对误差≤10.82%, 模型具有较高的拟合度。响应曲面回归分析表明: 针刺深度对拉伸强度有极显著影响, 针刺密度对拉伸强度有显著影响, 在本研究的针刺成型参数取值范围内, 拉伸强度的预测区间为42.31~91.87 MPa。通过模型优化出的针刺成型参数组合为: 针刺密度11 pin/cm2、针刺深度 11 mm、网胎面密度50 g/m2, 相应拉伸强度预测值为88.62 MPa, 验证值为90.71 MPa, 相对误差2.36%。
中图分类号:
郑金煌, 李贺军, 崔红, 王毅, 邓海亮, 殷忠义, 姚冬梅, 苏红. C/C复合材料拉伸强度与针刺成型参数相关性研究[J]. 无机材料学报, 2017, 32(11): 1147-1153.
ZHENG Jin-Huang, LI He-Jun, CUI Hong, WANG Yi, DENG Hai-Liang, YIN Zhong-Yi, YAO Dong-Mei, SU Hong. Relations between Needling Processing Parameters and Tensile Strength of C/C Composites[J]. Journal of Inorganic Materials, 2017, 32(11): 1147-1153.
No. | X1 | X2 | X3 | Tensile strength /MPa |
---|---|---|---|---|
1 | 8 | 10 | 100 | 89.80 |
2 | 16 | 16 | 100 | 47.30 |
3 | 12 | 13 | 100 | 87.56 |
4 | 16 | 13 | 50 | 69.44 |
5 | 12 | 10 | 150 | 86.72 |
6 | 12 | 13 | 100 | 90.00 |
7 | 16 | 13 | 150 | 83.70 |
8 | 8 | 13 | 50 | 74.13 |
9 | 16 | 10 | 100 | 72.83 |
10 | 12 | 16 | 50 | 61.46 |
11 | 12 | 13 | 100 | 79.66 |
12 | 8 | 13 | 150 | 82.73 |
13 | 12 | 13 | 100 | 93.10 |
14 | 12 | 16 | 150 | 73.90 |
15 | 12 | 13 | 100 | 80.73 |
16 | 12 | 10 | 50 | 89.00 |
17 | 8 | 16 | 100 | 70.96 |
表1 预制体针刺参数及拉伸强度试验结果
Table 1 Needling parameters and tested tensile strengths of C/C composites
No. | X1 | X2 | X3 | Tensile strength /MPa |
---|---|---|---|---|
1 | 8 | 10 | 100 | 89.80 |
2 | 16 | 16 | 100 | 47.30 |
3 | 12 | 13 | 100 | 87.56 |
4 | 16 | 13 | 50 | 69.44 |
5 | 12 | 10 | 150 | 86.72 |
6 | 12 | 13 | 100 | 90.00 |
7 | 16 | 13 | 150 | 83.70 |
8 | 8 | 13 | 50 | 74.13 |
9 | 16 | 10 | 100 | 72.83 |
10 | 12 | 16 | 50 | 61.46 |
11 | 12 | 13 | 100 | 79.66 |
12 | 8 | 13 | 150 | 82.73 |
13 | 12 | 13 | 100 | 93.10 |
14 | 12 | 16 | 150 | 73.90 |
15 | 12 | 13 | 100 | 80.73 |
16 | 12 | 10 | 50 | 89.00 |
17 | 8 | 16 | 100 | 70.96 |
Source | Sum of squares | df | Mean square | F Value | P-value prob > F |
---|---|---|---|---|---|
Model | 1978.209000 | 9 | 219.800900 | 5.180009 | 0.0206 |
X1 | 245.865300 | 1 | 245.865300 | 5.794263 | 0.0470 |
X2 | 897.290700 | 1 | 897.290700 | 21.146290 | 0.0025 |
X3 | 136.248800 | 1 | 136.248800 | 3.210950 | 0.1163 |
X1X2 | 11.172310 | 1 | 11.172310 | 0.263296 | 0.6237 |
X1X3 | 8.023056 | 1 | 8.023056 | 0.189078 | 0.6768 |
X2X3 | 54.169600 | 1 | 54.169600 | 1.276605 | 0.2958 |
X12 | 299.220600 | 1 | 299.220600 | 7.051679 | 0.0327 |
X22 | 280.274500 | 1 | 280.274500 | 6.605179 | 0.0370 |
X32 | 3.269901 | 1 | 3.269901 | 0.077061 | 0.7893 |
Residual | 297.027800 | 7 | 42.432540 | - | - |
Lack of Fit | 192.536200 | 3 | 64.178730 | 2.456799 | 0.2027 |
Pure Error | 104.491600 | 4 | 26.122900 | - | - |
Cor Total | 2275.236000 | 16 | - | - | - |
R-Squared | 0.869500 | - | - | - | - |
Adj R-Squared | 0.701600 | - | - | - | - |
表2 针刺C/C拉伸强度响应曲面模型回归方程及相关系数显著性分析表
Table 2 Analysis of signification for response surface model and its correlation coefficient of tensile strength
Source | Sum of squares | df | Mean square | F Value | P-value prob > F |
---|---|---|---|---|---|
Model | 1978.209000 | 9 | 219.800900 | 5.180009 | 0.0206 |
X1 | 245.865300 | 1 | 245.865300 | 5.794263 | 0.0470 |
X2 | 897.290700 | 1 | 897.290700 | 21.146290 | 0.0025 |
X3 | 136.248800 | 1 | 136.248800 | 3.210950 | 0.1163 |
X1X2 | 11.172310 | 1 | 11.172310 | 0.263296 | 0.6237 |
X1X3 | 8.023056 | 1 | 8.023056 | 0.189078 | 0.6768 |
X2X3 | 54.169600 | 1 | 54.169600 | 1.276605 | 0.2958 |
X12 | 299.220600 | 1 | 299.220600 | 7.051679 | 0.0327 |
X22 | 280.274500 | 1 | 280.274500 | 6.605179 | 0.0370 |
X32 | 3.269901 | 1 | 3.269901 | 0.077061 | 0.7893 |
Residual | 297.027800 | 7 | 42.432540 | - | - |
Lack of Fit | 192.536200 | 3 | 64.178730 | 2.456799 | 0.2027 |
Pure Error | 104.491600 | 4 | 26.122900 | - | - |
Cor Total | 2275.236000 | 16 | - | - | - |
R-Squared | 0.869500 | - | - | - | - |
Adj R-Squared | 0.701600 | - | - | - | - |
图1 针刺密度、针刺深度交互作用拉伸强度响应曲面及等高线图(网胎面密度100 g/m2)
Fig. 1 Response surface and contour of tensile strength influenced by the interaction of needling density and needling depth (The density of non-woven is 100 g/m2)
图2 针刺密度、网胎面密度交互作用拉伸强度响应曲面及等高线图(针刺深度13 mm)
Fig. 2 Response surface and contour of tensile strength influenced by the interaction of needling density and density of non-woven (The needling depth is 13 mm)
图3 针刺深度、网胎面密度交互作用拉伸强度响应曲面及等高线图(针刺密度12 pin/cm2)
Fig. 3 Response surface and contour of tensile strength influenced by interaction of needling depth and density of non-woven (The needling density is 12 pin/cm2)
Actual value | Predicted value | Residual | Relative error |
---|---|---|---|
89.80 | 84.684375 | 5.115625 | 5.70% |
72.83 | 76.939375 | -4.114375 | 5.65% |
70.96 | 66.845625 | 4.114375 | 5.80% |
47.30 | 52.415625 | -5.115625 | 10.82% |
74.13 | 80.331875 | -6.201875 | 8.37% |
69.44 | 66.411875 | 3.028125 | 4.36% |
82.73 | 85.753125 | -3.028125 | 3.66% |
83.70 | 77.498125 | 6.201875 | 7.41% |
89.00 | 87.913750 | 1.086250 | 1.22% |
61.46 | 59.372500 | 2.087500 | 3.40% |
86.72 | 88.807500 | -2.087500 | 2.41% |
73.90 | 74.986250 | -1.086250 | 1.47% |
90.00 | 86.810000 | 3.190000 | 3.54% |
87.56 | 86.810000 | 0.750000 | 0.86% |
82.66 | 86.810000 | -4.150000 | 5.02% |
80.73 | 86.810000 | -6.080000 | 7.53% |
93.10 | 86.810000 | 6.290000 | 6.76% |
表3 针刺C/C复合材料拉伸强度响应面拟合值与实际值的对照表
Table 3 Comparison of the fitting values of the fitting equation of response surface with the actual values
Actual value | Predicted value | Residual | Relative error |
---|---|---|---|
89.80 | 84.684375 | 5.115625 | 5.70% |
72.83 | 76.939375 | -4.114375 | 5.65% |
70.96 | 66.845625 | 4.114375 | 5.80% |
47.30 | 52.415625 | -5.115625 | 10.82% |
74.13 | 80.331875 | -6.201875 | 8.37% |
69.44 | 66.411875 | 3.028125 | 4.36% |
82.73 | 85.753125 | -3.028125 | 3.66% |
83.70 | 77.498125 | 6.201875 | 7.41% |
89.00 | 87.913750 | 1.086250 | 1.22% |
61.46 | 59.372500 | 2.087500 | 3.40% |
86.72 | 88.807500 | -2.087500 | 2.41% |
73.90 | 74.986250 | -1.086250 | 1.47% |
90.00 | 86.810000 | 3.190000 | 3.54% |
87.56 | 86.810000 | 0.750000 | 0.86% |
82.66 | 86.810000 | -4.150000 | 5.02% |
80.73 | 86.810000 | -6.080000 | 7.53% |
93.10 | 86.810000 | 6.290000 | 6.76% |
Needling density /(pin·cm-2) | Needling depth/mm | Density of non-woven /(g·m-2) | Tensile strength /MPa | |
---|---|---|---|---|
Max | 11.17 | 11.79 | 150.00 | 91.87 |
Min | 16.00 | 16.00 | 50.00 | 42.31 |
表4 拉伸强度取值范围
Table 4 Scope of tensile strength
Needling density /(pin·cm-2) | Needling depth/mm | Density of non-woven /(g·m-2) | Tensile strength /MPa | |
---|---|---|---|---|
Max | 11.17 | 11.79 | 150.00 | 91.87 |
Min | 16.00 | 16.00 | 50.00 | 42.31 |
Needling density /(pin·cm-2) | Needling depth /mm | Density of non-woven /(g·m-2) | Tensile strength/ MPa | Relative error | |
---|---|---|---|---|---|
Predictive value | Actual value | ||||
11 | 12 | 50 | 86.72 | 83.53 | 3.68% |
11 | 11 | 50 | 88.62 | 90.71 | 2.36% |
12 | 11 | 50 | 87.69 | 85.23 | 2.28% |
12 | 12 | 50 | 85.65 | 88.64 | 3.49% |
表5 拉伸强度优化结果
Table 5 Optimization results of tensile strength
Needling density /(pin·cm-2) | Needling depth /mm | Density of non-woven /(g·m-2) | Tensile strength/ MPa | Relative error | |
---|---|---|---|---|---|
Predictive value | Actual value | ||||
11 | 12 | 50 | 86.72 | 83.53 | 3.68% |
11 | 11 | 50 | 88.62 | 90.71 | 2.36% |
12 | 11 | 50 | 87.69 | 85.23 | 2.28% |
12 | 12 | 50 | 85.65 | 88.64 | 3.49% |
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