2D-C/SiC复合材料热膨胀系数演化模型

郑茹悦; 杨成鹏; 贾斐

doi:10.13801/j.cnki.fhclxb.20230808.001

2D-C/SiC复合材料热膨胀系数演化模型

doi: 10.13801/j.cnki.fhclxb.20230808.001

1.
西北工业大学　力学与土木建筑学院，西安 710072
2.
西安电子科技大学　机电工程学院，西安 710071

基金项目: 国家自然科学基金(12072274)；陕西省自然科学基础研究计划(2021JM-123)

详细信息

通讯作者:
杨成鹏，博士，副教授，博士生导师，研究方向为复合材料力学　E-mail: yang@mail.nwpu.edu.cn

中图分类号: TB332
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出版历程
- 收稿日期: 2023-06-02
- 修回日期: 2023-06-29
- 录用日期: 2023-07-28
- 网络出版日期: 2023-08-08
- 刊出日期: 2024-04-01

Evolution model of thermal expansion coefficient for 2D-C/SiC composites

1.
School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an 710072, China
2.
School of Mechano-Electronic Engineering, Xidian University, Xi'an 710071, China

Funds: National Natural Science Foundation of China (12072274); Natural Science Basic Research Program of Shaanxi Province (2021JM-123)

摘要

摘要: 热膨胀系数是耐高温复合材料的重要热力学参数。针对复合材料在服役条件下存在基体开裂和界面脱粘而影响其热膨胀变形的现象，通过理论模拟和实验测试，研究了含损伤2D-C/SiC复合材料热膨胀系数随环境温度的演变行为。首先，基于Mini复合材料模型给出了组分材料的三维热失配应力计算模型；其次，引入基体开裂和界面脱粘损伤，并考虑组分材料热膨胀性能差异、纤维的横观各向同性以及泊松效应的影响，推导了Mini复合材料轴向和径向热膨胀系数的解析表达式；再次，基于[0/90]正交层压板模型和宏观应变的一致性假设，建立了2D-C/SiC复合材料含损伤表观热膨胀系数的分析预测模型；最后，将本模型与经典Schapery模型及实验值进行对比，分析了热膨胀系数的主要影响因素。参数分析表明：基体裂纹间距、界面脱粘率、孔隙率、组分材料的弹性模量及热膨胀系数等均会影响复合材料的表观热膨胀系数，其中基体膨胀系数的影响尤为显著；验证结果表明：本模型具有合理性与正确性，其预测值与经典模型及实验曲线均吻合良好。
- 热膨胀系数 /
- Mini复合材料模型 /
- 2D-C/SiC /
- 热失配应力 /
- Schapery 模型
Abstract: Thermal expansion coefficient (TEC) is an important thermodynamic parameter of high-temperature resistant composites. The evolution behavior of the TEC of damaged 2D-C/SiC composites with ambient temperature was studied by theoretical model and experimental tests for the phenomenon of matrix cracking and interface debonding, which affects the thermal expansion deformation of the material under service condition. Firstly, the three-dimensional thermal mismatch stress calculation model of constituents was given based on minicomposite model. Secondly, matrix cracking and interface debonding were introduced, and the analytical expressions for axial and radial TECs of minicomposite were derived by considering thermal expansion difference between the fibers and matrix, transverse isotropy of fibers and the Poisson's effect. Thirdly, based on the [0/90] cross-ply laminate model and the macro-strain consistency assumption, a predictive model was established towards the apparent TEC of damaged 2D-C/SiC composites. Finally, the present model was compared with the classical Schapery model and experimental data, and the main influencing factors of TEC were analyzed. Parameter analysis indicate that the apparent TEC of the material is affected by matrix crack spacing, interface debonding ratio, porosity, elastic modulus and TEC of the constituents, among which the influence of the matrix expansion coefficient is particularly significant. The verification results show that the proposed model is reasonable and correct, and the predicted results are in good agreement with the classical model and experimental curve.
- TEC /
- minicomposite model /
- 2D-C/SiC /
- thermal mismatch stress /
- Schapery model

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图 1 同心圆柱单胞模型

Figure 1. Concentric cylindrical unit cell model

r_f—Fiber radius; r_m—External radius

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图 2 Mini复合材料细观损伤模型

Figure 2. Microscopic damages model of minicomposite

$ \tau $—Interface sliding stress; $ {\sigma }_{\mathrm{m}} $—Matrix stress; $ {\sigma }_{\mathrm{f}} $—Fiber stress; $ {L}_{\mathrm{d}} $—Interface debonding length; L—Matrix crack spacing

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图 3 纤维和基体的应力分布

Figure 3. Stress distribution of fiber and matrix

$ {T}_{\mathrm{p}} $—Processing temperature; T—Arbitrary temperature; $ {T}_{0} $—Room temperature; σ—Stress

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图 4 纵向热膨胀变形图

Figure 4. Deformation diagram of longitudinal thermal expansion

$ {T}_{\mathrm{h}} $ —Crack-healing temperature; ${\varepsilon }_{1\mathrm{m}}$—Longitudinal strain of matrix; ε_1f—Longitudinal strain of fiber; $ {\varepsilon }_{1} $—Longitudinal strain

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图 5 基体相对纤维滑移示意图

Figure 5. Schematic of matrix sliding relative to fiber

$ {L}_{1} $—Counter-slip length

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图 6 径向热膨胀变形图

Figure 6. Deformation diagram of radial thermal expansion

ε_2m—Radial strain of matrix; ε_2f—Radial strain of fiber; $ {\alpha }_{2} $—Radial TEC; TEC—Thermal expansion coefficient; $ \mathrm{\Delta }T $—Temperature difference

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图 7 [0/90]层合板膨胀变形图

Figure 7. Expansion deformation diagram of [0/90] laminate

$ {\varepsilon }_{0} $—0° ply strain; $ {\varepsilon }_{90} $—90° ply strain; $ {\varepsilon }_{\mathrm{L}} $—Apparent strain; $ {\alpha }_{\mathrm{L}} $—Apparent TEC

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图 8 2D-C/SiC复合材料表观热膨胀系数(TEC)的试验曲线及预测值

Figure 8. Tested and predicted curves of apparent thermal expansion coefficient (TEC) of 2D-C/SiC composites

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图 9 Mini复合材料纵向(a)和径向(b)TEC预测曲线

Figure 9. Predicted curves of longitudinal (a) and radial (b) TEC of minicomposites

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图 10 纤维径向模量对Mini复合材料(a)及2D-C/SiC材料(b) TEC的影响

Figure 10. Effect of fiber radial modulus on TEC of minicomposites (a) and 2D-C/SiC (b) composites

α₁—Longitudinal TEC of minicomposites; α₂—Radial TEC of minicomposites

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图 11 基体模量对Mini复合材料(a)及2D-C/SiC材料(b) TEC的影响

Figure 11. Effect of matrix modulus on TEC of minicomposites (a) and 2D-C/SiC composites (b)

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图 12 考虑孔隙率V_p的2D-C/SiC表观TEC预测曲线

Figure 12. Predicted curve of apparent TEC of 2D-C/SiC considering porosity V_p

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图 13 界面滑移应力(a)和裂纹间距(b)对Mini复合材料纵向及径向TEC的影响

Figure 13. Effect of interface sliding stress (a) and crack spacing (b) on TEC of minicomposites

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图 14 界面滑移应力τ (a)和基体裂纹间距L (b)对2D-C/SiC表观热膨胀系数的影响

Figure 14. Effects of interface sliding stress τ (a) and matrix crack spacing L (b) on apparent TEC of 2D-C/SiC composites

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图 15 SiC基体(a)和2D-C/SiC (b)表观TEC随温度的演变规律

Figure 15. Evolution behavior of TEC of SiC matrix (a) and 2D-C/SiC (b) with temperature

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表 1 2D-C/SiC复合材料模型基本参数

Table 1. Basic parameters of 2D-C/SiC composites model

Parameter	Value
Longitudinal modulus of fiber $ {E}_{1\mathrm{f}} $/GPa	230
Transverse modulus of fiber $ {E}_{2\mathrm{f}} $/GPa	14
Matrix modulus $ {E}_{\mathrm{m}} $/GPa	350
Fiber volume fraction $ {V}_{\mathrm{f}} $/vol%	40
Matrix volume fraction $ {V}_{\mathrm{m}} $/vol%	60
Fiber volume fraction in bundle $ {V}_{\mathrm{f}\mathrm{b}} $/vol%	70
Matrix volume fraction in bundle $ {V}_{\mathrm{m}\mathrm{b}} $/vol%	30
Axial Poisson's ratio of fiber $ {\nu }_{1\mathrm{f}} $	0.2
Transverse Poisson's ratio of fiber $ {\nu }_{2\mathrm{f}} $	0.07
Matrix Poisson's ratio $ {\nu }_{\mathrm{m}} $	0.2
Interface sliding stress $ \tau $/MPa	10
Crack spacing L/μm	400

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