基于细观力学模型的单向纤维复合材料的力学行为

裴柯磊; 李志强; 何航宇; 郑少秋; 苏亚男

doi:10.11883/bzycj-2025-0222

基于细观力学模型的单向纤维复合材料的力学行为

doi: 10.11883/bzycj-2025-0222

裴柯磊^1,,
李志强^{1, 2, 3, 4, ,},
何航宇¹,
郑少秋¹,
苏亚男¹

1.
太原理工大学航空航天学院，山西太原 030024
2.
太原理工大学材料强度与结构冲击山西省重点实验室，山西太原 030024
3.
太原理工大学山西省力学基础学科研究中心，山西太原 030024
4.
太原理工大学力学国家级实验教学示范中心，山西太原 030024

基金项目: 山西省科技重大专项计划项目（202301120401010）

详细信息

作者简介:
裴柯磊（2000－　），男，博士研究生，2024310006@link.tyut.edu.cn

通讯作者:
李志强（1973－　），男，博士，教授，lizhiqiang@tyut.edu.cn

中图分类号: 0341
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- HTML全文浏览量: 43
- PDF下载量: 60
- 被引次数: 0
出版历程
- 收稿日期: 2025-07-17
- 修回日期: 2025-10-20
- 网络出版日期: 2025-10-21

Mechanical behavior of unidirectional fiber reinforced polymer based on micromechanical model

PEI Kelei^1
,,
LI Zhiqiang^{1, 2, 3, 4
, ,},
HE Hangyu¹,
ZHENG Shaoqiu¹,
SU Yanan¹

1.
College of Aeronautics and Astronautics, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China
2.
Shanxi Key Laboratory of Material Strength & Structural Impact, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China
3.
Shanxi Research Center of Basic Discipline of Mechanics, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China
4.
National Demonstration Center for Experimental Mechanics Education, Taiyuan university of Technology, Taiyuan 030024, Shanxi, China

摘要

摘要: 基于Hashin等复合材料经典失效准则的宏观有限元模拟虽然能够考虑纤维断裂、基体损伤以及分层等宏观损伤机制，但无法反映碳纤维增强复合材料（Carbon fiber reinforced polymer，CFRP）内部的微观损伤行为，例如纤维和基体之间的界面脱粘。为了解决这个问题，建立了一个同时考虑纤维、基体和界面的多相细观力学模型，综合考虑纤维断裂、基体失效和界面脱粘等多种损伤机制，系统分析了横向拉伸/压缩、纵向拉伸/压缩以及面内/外剪切等典型载荷路径下单向碳纤维增强复合材料（Unidirectional carbon fiber reinforced polymer，UD CFRP）的损伤演化过程。结果表明：实验与仿真得到的峰值应力和失效应变的相对误差小于5%，同时模型预测的裂纹扩展路径与扫描电镜的观测结果一致，验证了考虑微观结构的微观力学模型的准确性。在此基础上，模型准确捕捉到了不同载荷条件下UD CFRP的损伤演化规律，这对于构建CFRP损伤容限设计准则和结构完整性评估体系具有重要工程价值。
- 碳纤维增强复合材料 /
- 细观力学模型 /
- 损伤演化 /
- 裂纹扩展
Abstract: Although macroscopic finite-element simulations based on classical composite failure criteria such as Hashin’s can account for macroscopic damage mechanisms such as fiber fracture, matrix damage, and delamination, these approaches are unable to represent microscopic damage mechanisms within carbon-fiber-reinforced polymer (CFRP), particularly interfacial debonding between fibers and the matrix. To overcome this limitation, a multiphase micromechanical model was developed that explicitly incorporates distinct constituent phases-fiber, matrix, and interface. This model integrates multiple damage mechanisms such as fiber fracture, matrix failure, and interfacial debonding, enabling a more granular analysis of damage initiation and progression. Periodic boundary conditions were applied to the model to ensure kinematic consistency and mechanical representativeness. A mesh-convergence study was subsequently carried out on the basis of the predicted elastic moduli of CFRP in various material directions, leading to an optimized discretization strategy that balances accuracy and computational cost. Comprehensive validation was performed by comparing the model-predicted stress-strain responses with experimental data obtained from unidirectional CFRP (UD CFRP) under a range of loading conditions, including transverse tension and compression, longitudinal tension and compression, and in-plane and out-of-plane shear. The damage-evolution processes under these representative loading paths were systematically analyzed. The results indicate that the relative errors in peak stress and failure strain between simulations and experiments are less than 5 %. Moreover, the crack-propagation paths predicted by the model show strong agreement with observations from scanning electron microscopy, thereby confirming the accuracy of the proposed microstructure-aware micromechanical modeling framework. Furthermore, the model successfully captures the detailed damage evolution of UD CFRP under various loading scenarios. Under transverse tensile loading, damage is initiated by interfacial debonding, followed by plastic deformation and eventual failure of the matrix near debonded regions. In contrast, under transverse compression, interfacial debonding and matrix plastic deformation are observed to occur simultaneously. Under longitudinal loading, the dominant damage mechanism is identified as fiber fracture, whereas the damage patterns under in-plane and out-of-plane shear are found to be consistent with those under transverse compression and transverse tension, respectively. These insights offer significant engineering value for the development of damage-tolerant design criteria and structural-integrity evaluation frameworks for CFRP components and assemblies.
- UD CFRP /
- micromechanical model /
- damage evolution /
- crack propagation

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图 1 RVE三相几何模型

Figure 1. Geometric model of RVE with three phases

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图 2 Drucker-Prager结合延性损伤模型和双线性牵引分离模型

Figure 2. Drucker-Prager combined with ductile damage and model Bilinear traction separation model

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图 3 网格收敛性分析

Figure 3. Mesh convergence analysis

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图 4 实验与数值模拟的横向应力应变曲线

Figure 4. Transverse stress-strain curves of experiment and numerical simulation

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图 5 横向拉伸条件下UD CFRP损伤演化过程

Figure 5. Damage evolution process of UD CFRP under transverse tensile loading

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图 6 RVE模型预测最终裂纹与SEM电镜表征结果^[35]对比

Figure 6. Comparison of the final crack predicted by the RVE model and the characterization results of SEM electron microscopy^[35]

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图 7 横向压缩条件下UD CFRP损伤演化过程

Figure 7. Damage evolution process of UD CFRP under transverse compression loading

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图 8 RVE模型预测裂纹角度与SEM电镜表征结果^[35]对比

Figure 8. Comparison of the crack Angle predicted by the RVE model and the characterization results of SEM electron microscopy^[35]

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图 9 实验与数值模拟的纵向应力应变曲线

Figure 9. longitudinal stress-strain curves of experiment and numerical simulation

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图 10 纵向拉伸条件下UD CFRP的初始损伤和最终损伤时刻应力分布

Figure 10. The initial damage and final damage stress distribution of UD CFRP under longitudinal tensile conditions

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图 11 偏光显微镜下UD CFRP的纤维断裂^[37]

Figure 11. Fiber fracture of UD CFRP under polarizing microscope^[37]

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图 12 纵向压缩条件下UD CFRP的初始损伤和最终损伤时刻的应力分布

Figure 12. The initial damage and final damage stress distribution of UD CFRP under longitudinal compression conditions

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图 13 光学显微镜下UD CFRP的“扭结带”和纤维断裂^[38]

Figure 13. The "kink-band" and fiber fracture of UD CFRP under the optical microscope^[38]

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图 14 实验与数值模拟的剪切应力应变曲线

Figure 14. Shear stress-strain curves of experiment and numerical simulation

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图 15 面外剪切条件下UD CFRP损伤演化过程

Figure 15. Damage evolution process of UDCFRP under out-of-plane shear loading.

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图 16 面内剪切条件下UD CFRP损伤演化过程

Figure 16. Damage evolution process of UDCFRP under in-plane shear loading.

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图 17 RVE模型预测最终裂纹与SEM电镜表征结果^[35]对比

Figure 17. Comparison of the final crack predicted by the RVE model and the characterization results of SEM electron microscopy^[35]

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表 1 IM7碳纤维属性^[27]

Table 1. IM7 Carbon fiber properties^[27]

E₁₁/GPa	E₂₂/GPa	E₃₃/GPa	ν₁₂	ν₁₃	ν₂₃
276	19	19	0.2	0.2	0.357

G₁₂/GPa	G₁₃/GPa	G₂₃/GPa	S_11T/GPa	S_11C/GPa	S₁₂/GPa
27	27	7	5.18	3.2	3.5

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表 2 基体模型参数^[20]

Table 2. Matrix model parameter^[20]

E	ν	β	k	θ	σ_y	G_f
4.08 GPa	0.38	0°	0.89	30°	130MPa	1J/m²

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表 3 界面模型参数^[35]

Table 3. Interface model parameter^[35]

K₁/(MPa·mm⁻¹)	K₂ /(MPa·mm⁻¹)	K₃ /(MPa·mm⁻¹)	$t^0_n $/MPa	$t^0_s t_s $/MPa
10⁸	10⁸	10⁸	57	96

$t^0_t $/MPa	G_n/(J·m⁻²)	G_s/(J·m⁻²)	G_t/(J·m⁻²)	η
96	2	104	104	1.45

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表 4 不同载荷条件下RVE模型预测峰值应力与失效应变和实验结果^[27]对比

Table 4. Comparison of peak stress and failure strain predicted by the RVE model under different load conditions and experimental results^[27]

载荷工况	实验结果^[27]		预测结果		误差
载荷工况	峰值应力/MPa	失效应变/%	峰值应力/MPa	失效应变/%	应力误差/%	应变误差/%
横向拉伸	63	0.69	64	0.65	1.56	2.52
横向压缩	185	3.20	184	3.21	0.54	0.31
纵向拉伸	2560	1.51	2580	1.52	0.78	0.66
纵向压缩	1590	1.10	1610	1.13	1.20	3.63
面外剪切	56	2.09	54	2.13	3.57	1.91
面内剪切	90	4.99	88	4.83	2.22	3.2

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