Multi-Scale Prediction of Thermal and Mechanical Properties of C/SiC Braided Composites
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摘要: C/SiC复合材料以其优异的力学和热学性能，在航空航天、国防和化学工业等领域都得到了广泛的应用. 精准获得C/SiC复合材料的热/力学性能，对该类材料在相关领域的高效应用至关重要. 基于代表性体积单元(RVE)和周期性边界条件，考虑纤维束的体积分数、交织方式、编织维度等非均匀、多尺度特征，建立了C/SiC复合材料的微/细观单胞模型. 使用有限元软件ABAQUS在微观尺度预测了纤维束的热/力学性能，将纤维束性能引入细观模型中，分析获得了该复合材料的宏观热/力学性能. 基于此多尺度关联分析方法，在27~1 227 ℃的工作温度范围内，进一步研究了纤维束和C/SiC复合材料的热导率和热膨胀系数随温度的变化规律. 该研究对C/SiC复合材料在工程上的应用具有一定的指导意义.Abstract: C/SiC composites have been widely used in aerospace, national defense, and chemical industries due to their excellent mechanical and thermal properties. Accurate knowledge about the mechanical/thermal properties of C/SiC composites is very important for their efficient application in related fields. Based on the representative volume element (RVE) and periodic boundary conditions, a micro/meso single-cell model for C/SiC composites was established in view of the non-uniform and multi-scale characteristics of fiber bundles, such as the volume fraction, the interweaving mode, and the weaving dimension. The finite element software ABAQUS was used to predict the micro-scale thermal and mechanical properties of the fiber bundle, and the fiber bundle properties were introduced into the mesoscopic model to analyze and obtain the macroscopic thermal and mechanical properties of the composite. Based on this multi-scale correlation analysis method, the thermal conductivity and thermal expansion coefficient of fiber bundles and C/SiC composites were further studied at the operating temperatures ranging from 27~1 227 ℃. The study has certain guiding significance for the application of C/SiC composites in engineering.
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Key words:
- C/SiC composite /
- multi-scale modeling /
- finite element analysis /
- periodic boundary condition /
- thermal/mechanical property
1) (我刊编委刘少宝推荐) -
图 1 三维C/SiC复合材料的多尺度有限元模型
Figure 1. The multi-scale finite element model for 3D C/SiC composites
图 4 计算径向热导率时的边界条件
Figure 4. Boundary conditions for calculating radial thermal conductivity
图 5 计算轴向热导率时的边界条件
Figure 5. Boundary conditions for calculating axial thermal conductivity
图 6 3D正交互锁编织型复合材料(单位: mm)
Figure 6. The 3D positive interlocking braided composite(unit: mm)
图 7 3D正交互锁编织型复合材料单胞的网格模型
Figure 7. The mesh model for 3D positive interlocking braided composite cells
图 8 弹性模量E11和Poisson比μ12的数值和实验结果的比较
Figure 8. Comparison of the values of Young's modulus E11 and Poisson's ratio μ12 with the experimental results
图 10 2D 1×1编织结构热/力学系数随纤维束体积分数的变化
Figure 10. Variations of thermal/mechanical coefficients of 2D 1×1 braided structure with the fiber bundle volume fraction
表 1 单位应变边界条件
Table 1. Unit strain boundary conditions
condition εx εy εz γxy γxz γyz 1 1 0 0 0 0 0 2 0 1 0 0 0 0 3 0 0 1 0 0 0 4 0 0 0 1 0 0 5 0 0 0 0 1 0 6 0 0 0 0 0 1 
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表 2 碳纤维和环氧树脂的属性
Table 2. Properties of the carbon fiber and the epoxy resin
property EP828 T-900 E1/GPa 3.40 294 E2/GPa 3.40 6.50 G12/GPa 1.26 18.2 G23/GPa 1.26 6.50 μ12 0.35 0.32 μ23 0.35 0.41 α11/℃-1 6.45×10-5 -5.6×10-7 α22/℃-1 6.45×10-5 5.6×10-6 α33/℃-1 6.45×10-5 5.6×10-6
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表 3 纱线热/力学性能的预测结果
Table 3. Predicted results of thermal/mechanical properties of yarns
property value (Vf=50%) our method AEH method[21] E1/GPa 4.96 4.96 E2/GPa 4.96 4.96 E3/GPa 148.63 148.70 G12/GPa 2.44 2.45 G13/GPa 3.20 3.21 G23/GPa 3.20 3.21 μ12 0.475 0.476 μ13 0.336 0.335 μ23 0.011 0.011 α11/℃-1 4.5×10-5 4.5×10-5 α22/℃-1 4.5×10-5 4.5×10-5 α33/℃-1 2.0×10-7 2.0×10-7
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表 4 三维正交编织复合材料热/力学性能的预测结果
Table 4. Prediction results of thermal/mechanical properties of 3D orthogonal braided composite
property our method FEM method[16] E1/GPa 34.10 32.97 E2/GPa 52.01 51.21 E3/GPa 11.85 11.13 G12/GPa 2.94 2.88 G13/GPa 2.51 2.43 G23/GPa 2.53 2.45 μ12 0.062 0 0.061 7 μ13 0.486 0 0.497 0 μ23 0.441 0 0.456 0 α11/℃-1 1.310×10-5 12.920×10-5 α22/℃-1 6.930×10-6 6.890×10-6 α33/℃-1 8.110×10-6 7.940×10-6
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表 5 纤维束的弹性常数
Table 5. Elastic constants of fiber bundles
E1/GPa E2/GPa E3/GPa G12/GPa G13/GPa G23/GPa μ12 μ13 μ23 308.24 76.59 76.59 43.02 43.02 25.44 0.28 0.28 0.41
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表 6 纤维束的热膨胀系数和热导率
Table 6. Thermal expansion coefficients and thermal conductivities of the fiber bundle
T/℃ α11/℃-1 (α22=α33)/℃-1 k11/(W·m-1·℃-1) (k22=k33)/(W·m-1·℃-1) 27 3.80×10-5 4.48×10-6 147.17 83.84 227 1.00×10-6 4.90×10-6 142.91 79.66 427 1.72×10-6 5.65×10-6 138.32 72.07 627 2.06×10-6 5.92×10-6 133.77 64.85 827 2.36×10-6 6.18×10-6 131.13 60.21 1 027 2.64×10-6 6.42×10-6 125.42 54.52 1 227 2.90×10-6 6.69×10-6 118.61 45.06
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表 7 5种编织结构的弹性常数
Table 7. Elastic constants of 5 braided structures
braided structure E1/GPa E2/GPa E3/GPa G12/GPa G13/GPa G23/GPa 1×1 2D 299.22 299.22 161.23 92.50 56.40 56.40 2×1 2D 299.94 299.94 161.80 92.71 56.49 56.49 2×2 2D 298.23 298.23 160.18 91.77 56.15 56.15 2.5D coss-linking 280.73 300.09 169.10 91.70 57.37 63.16 3D orthogonal 289.49 322.89 175.19 96.76 56.60 66.04
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