Mechanical properties and damage mechanisms of novel variable stiffness laminates
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摘要: 广泛应用于航空航天、交通运输等领域的复合材料层合板在实际应用中存在着承载能力和稳定性方面的挑战，为解决上述问题，采用自动铺丝可变刚度层合板，并对其力学特性及失效机制进行研究。首先，在线性变角度函数的基础上，提出一种新型周期线性延拓函数算法，以优化复合材料纤维铺放路径，实现更为详细和精确的纤维轨迹变化。其次，通过Python/Abaqus联合构建新型变刚度层合板有限元模型。最后，分析了定/变刚度层合板三点弯曲下的损伤机制，揭示了不同纤维铺放角对层合板力学特性、应力分布和损伤情况的影响。研究结果表明：三点工况下中心纤维取向角对弯曲性能产生显著影响，0°有利于性能提升，90°则导致性能下降；在中心纤维取向角为5°的基础上，采用变角度设计可以有效抑制弯曲损伤进一步扩展，均匀层合板面内应力分布，同时进一步提高弯曲极限应力，最大提升幅度为28.31%。本研究为后续复合材料层合板的抗弯曲设计和优化提供了重要的研究思路和流程，具有一定参考意义。Abstract: Laminated composite panels, widely employed in aerospace, aviation and transportation, face challenges in terms of load-bearing capacity and stability in practical applications. To address these issues, this study adopts an automated variable stiffness layup approach and investigates the mechanical properties and failure mechanisms of the resulting laminated composite panels. Firstly, a novel periodic linear extrapolation algorithm was proposed based on a linear variable angle function to optimize the fiber placement paths, achieving more detailed and precise variations in fiber trajectories. Subsequently, a finite element model for the new variable stiffness laminated panel was constructed using Python/Abaqus. Finally, the damage mechanisms under three-point bending for both constant and variable stiffness laminated panels were analyzed, revealing the impact of different fiber orientation angles on the mechanical properties, stress distribution and damage scenarios. The research findings indicate that the orientation angle of the central fiber significantly influences bending performance under three-point conditions, with 0° favoring performance enhancement and 90° leading to a decline in performance. Compared to the baseline with a central fiber orientation angle of 5°, employing a variable angle design effectively suppresses further extension of bending damage, ensures a uniform stress distribution within the laminated panel, and further enhances the ultimate bending stress, with a maximum improvement of 28.31%. This study provides crucial insights and a systematic approach for the subsequent design and optimization of laminated composite panels, contributing to advancements in bending resistance design for composite materials.
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Key words:
- composite laminate /
- variable stiffness /
- curve laying /
- mechanical properties /
- damage mechanism
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图 1 复合材料纤维铺放：(a)纤维自动铺放技术；(b)纤维铺放参考路径
Figure 1. Composite fiber placement: (a) Automatic fiber placement technology; (b) Fiber placement reference path
a—Length of laminate; T0—Starting angle of curved fiber; T1—Termination angle of curved fiber; θ—The angle between the tangent line at a certain point on the fiber and the x-axis; φ—Deflection angle of the reference coordinate system
图 2 周期线性延拓纤维铺放参考路径示意图
Figure 2. Schematic diagram of periodic linear extension fiber laying reference path
b—Width of laminate
图 3 周期n=1~4时周期线性延拓纤维铺放参考路径对比图
Figure 3. Comparison chart of reference paths for periodic linear extension fiber laying when periods n=1-4
图 5 1±0<15 |60>4曲线纤维轨迹离散化过程
Figure 5. Curved fiber trajectory discretization process of 1±0<15 |60>4
图 6 新型变刚度层合板二次开发建模流程
Figure 6. Secondary development modeling process of new variable stiffness laminates
图 7 复合材料层合板三点弯曲示意图
Figure 7. Schematic diagram of three-point bending of composite laminates
R—Radius of support column
图 8 复合材料层合板示意图：(a)层合板微观模型；(b)层合板铺层宏观示意图
Figure 8. Schematic diagram of composite laminates: (a) Composite laminate micro model; (b) Macroscopic diagram of composite laminate layup
图 9 复合材料层合板三点弯曲仿真模型
Figure 9. Three-point bending simulation model of composite laminates
图 10 不同始末角纤维轨迹对比
Figure 10. Comparison of fiber trajectories at different starting and ending angles
图 11 两种定刚度层合板三点弯曲工况下载荷-时间曲线：(a) [0°]8铺层；(b) [0°|90°]4铺层
Figure 11. Force-time curves of two types of constant-stiffness laminates under three-point bending conditions: (a) The layer is [0°]8; (b) The layer is [0°|90°]4
图 12 不同始末角角纤维铺层变刚度层合板三点弯曲工况下载荷-位移曲线
Figure 12. Force-displacement curves of variable stiffness laminates with different starting and ending angles under three-point bending conditions
图 13 1±0<5°|50°>4变刚度层合板三点弯曲工况下载荷-时间曲线
Figure 13. Force-time curve of 1±0<5°|50°>4 variable stiffness laminate under three-point bending condition
图 14 复合材料层合板三点弯曲工况下位移云图
Figure 14. Displacement cloud diagram of composite laminates under three-point bending conditions
U—Displacement (mm)
图 15 复合材料层合板三点弯曲失效分析步时间及底层Cohesive应力对比
Figure 15. Comparison of three-point bending failure analysis step time and underlying Cohesive stress of composite laminates
图 16 应力峰值时刻层合板底层Cohesive应力分布对比
Figure 16. Comparison of Cohesive stress distribution in the bottom layer of laminates at the moment of stress peak
表 2 层合板材料属性
Table 2. Composite laminate material parameters
Lamina constants Constitutive damage model parameters of lamina E11/MPa 463 Longitudinal tensile strength/MPa XT 2080 E22/MPa 700 Longitudinal compressive strength/MPa XC 1250 E33/MPa 700 Transverse tensile strength/MPa YT 60 G12/MPa 4800 Transverse compressive strength/MPa YC 140 G13/MPa 4800 Longitudinal shear strength/MPa SL 60 G23/MPa 3800 Transverse shear strength/MPa ST 140 ν12 0.33 Longitudinal tensile fracture energy/(mJ·mm−2) GXT 133 ν13 0.33 Longitudinal compressive fracture energy/(mJ·mm−2) GXC 40 ν23 0.3 Transverse tensile fracture energy/(mJ·mm−2) GYT 0.6 Transverse compressive fracture energy/(mJ·mm−2) GYC 2.1 Notes: E11, E22, E33—Stiffness; G12, G13, G23—Shear modulus; ν12, ν13, ν23—Poisson's ratio. 
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表 3 层合板铺层方案
Table 3. Composite laminate laying methods
Type of laminate Layer representation method The constant stiffness [0°]8 [0°/90°]4 [90°]8 The variable stiffness T1 remains unchanged 1±0<10°|5°>4 1±0<20°|5°>4 1±0<30°|5°>4 1±0<40°|5°>4 1±0<50°|5°>4 1±0<60°|5°>4 1±0<70°|5°>4 1±0<80°|5°>4 T0 remains unchanged 1±0<5°|10°>4 1±0<5°|20°>4 1±0<5°|30°>4 1±0<5°|40°>4 1±0<5°|50°>4 1±0<5°|60°>4 1±0<5°|70°>4 1±0<5°|80°>4
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表 4 三点弯曲工况下层合板极限应力对比
Table 4. Comparison of ultimate stress of laminates under three-point bending conditions
Layer Ultimate stress/MPa Compare Layer Ultimate stress/MPa Compare [0°]8 1618 – [0°/90°]4 1361 ↓ 15.884 1±0<10°|5°>4 2035 ↑ 25.773 1±0<5°|10°>4 2072 ↑ 28.059 1±0<20°|5°>4 2076 ↑ 28.307 1±0<5°|20°>4 2073 ↑ 28.121 1±0<30°|5°>4 2052 ↑ 26.823 1±0<5°|30°>4 2076 ↑ 28.307 1±0<40°|5°>4 861.5 ↓ 46.755 1±0<5°|40°>4 2076 ↑ 28.307 1±0<50°|5°>4 1149 ↓ 28.986 1±0<5°|50°>4 2072 ↑ 28.059 1±0<60°|5°>4 687.9 ↓ 57.485 1±0<5°|60°>4 2055 ↑ 27.009 1±0<70°|5°>4 493.4 ↓ 69.506 1±0<5°|70°>4 1656 ↑ 2.295 1±0<80°|5°>4 238.7 ↓ 85.247 1±0<5°|80°>4 2011 ↑ 24.289 [90°]8 58.48 ↓ 94.174
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