Wrinkles in fiber-reinforced resin composites: Heterogeneity and virtual test
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摘要: 在纤维增强树脂复合材料结构中，褶皱缺陷的物理形态及其空间分布通常具有分散性，如果仅追踪某个单一褶皱缺陷的行为演化，则不能有效控制复合材料批量构件性能的一致性。本论文提出了一种褶皱缺陷分散性模型，该模型包括褶皱形态的正态分布和空间位置的随机分布，以及将该模型植入自主开发的有限元程序的算法实现。由于计算程序中考虑了褶皱缺陷的概率分布，每进行一次力学响应计算就相当于进行一次复合材料结构虚拟测试，计算程序运行多次即可获得结构响应的上、下限，在设计阶段就可以预测褶皱缺陷分散性对结构宏观力学响应的影响，并在缺陷的统计指标和构件的力学性能之间建立量化关系。所建立的虚拟测试方法是复合材料创新设计方法的关键，能有效减少工程实践中复合材料结构对大批量试验的依赖。
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关键词:
- 纤维增强树脂复合材料 /
- 褶皱缺陷 /
- 分散性 /
- 概率分布 /
- 虚拟测试
Abstract: The physical morphology of wrinkles and their spatial distribution in fiber-reinforced resin composites show inhomogeneity. It’s no use to improve the performance consistency of composite structures if just tracking the evolution and effect of a specific wrinkle. This paper proposed a novel model which considered the normal distribution of wrinkle’s geometrical size and the spatial random distribution, and the implementation algorithm of the model implanted in a self-developed finite element procedure is achieved. The computation combining hetero-geneous wrinkles can be considered as a virtual test since it allows every computation to produce a different result, thus the upper and lower limits of structural response can be obtained by multiple computations. The influence of wrinkle heterogeneity on macro-mechanical response can be predicted in design stage, and a quantitative relationship between the statistical parameters of defects and mechanical properties can be established. The virtual test method is the key to the innovative design method of composites, which can effectively reduce the dependence of mass testing of composite material in engineering practice.-
Key words:
- fiber-reinforced resin composites /
- wrinkle defects /
- heterogeneity /
- random distribution /
- virtual test
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图 1 纤维偏转角随机正态分布[12]：(a)显微照相；(b)等值线图
Figure 1. Normal distribution of fiber orientations: (a) Micrograph section; (b) Contours of corresponding to fiber orientations
图 2 含褶皱缺陷的纤维增强树脂复合材料层合板代表性单元（RVE）
Figure 2. Represent volume elements (RVE) of wrinkled fiber-reinforced resin composite laminates
H—Thickness of each laminate; A—Amplitude of wrinkle；λ—Wavelength of wrinkle
图 4 褶皱模型植入有限元算法的流程图
Figure 4. Flow chart of implanting wrinkle model into finite element method
图 5 CF/EP复合材料层合板拉伸计算模型
Figure 5. Computation case for CF/EP composite laminates under tensile load
σ0—Axial tensile loading along horizontal direction
图 6 褶皱波纹比正态分布模型(波纹比均值ζ0=0，波纹比标准差S=0.08)
Figure 6. Normal distribution model of wavelength ratio of wrinkles (average value of wrinkle ratio ζ0=0, standard deviation S=0.08)
图 7 拉伸加载下无缺陷的CF/EP复合材料层合板归一化响应(ζ0=0, S=0)
Figure 7. Normalized displacement fields for pristine CF/EP composite laminates (ζ0=0, S=0) under tensile load
图 8 拉伸加载下含随机正态分布褶皱的CF/EP复合材料层合板归一化响应(ζ0=0, S=0.08)
Figure 8. Normalized displacement fields for CF/EP composite laminates with randomly distributed wrinkles (ζ0=0, S=0.08) under tensile load
图 9 CF/EP复合材料层合板横向低速冲击计算模型
Figure 9. Computation case for CF/EP composite laminates under transverse low-velocity impact load
p(t)—Periodic oscillation attenuation load; t—Time; f—Maximum load; w—Angular frequency; b—Attenuation coefficient
图 10 冲击载荷下无缺陷的CF/EP复合材料层合板归一化挠度响应(ζ0=0, S=0)
Figure 10. Normalized deflection response for pristine CF/EP composite laminates (ζ0=0, S=0) under impact load
图 11 冲击载荷下含随机正态分布褶皱的CF/EP复合材料层合板归一化挠度响应(ζ0=0, S=0.08)
Figure 11. Normalized deflection response for CF/EP composite laminates with randomly distributed wrinkles (ζ0=0, S=0.08) under impact load
图 12 含褶皱缺陷CF/EP复合材料层合板y方向位移时程曲线的振荡现象
Figure 12. Displacement oscillation in y direction for wrinkled CF/EP composite laminates
图 13 含缺陷CF/EP复合材料层合板离面位移的虚拟测试(ζ0=0, S=0.04)
Figure 13. Virtual testing of out-of-plane displacements for wrinkled CF/EP composite laminates (ζ0=0, S=0.04)
图 14 含缺陷CF/EP复合材料层合板离面位移的虚拟测试(ζ0=0, S=0.08)
Figure 14. Virtual testing of out-of-plane displacements for wrinkled CF/EP composite laminates (ζ0=0, S=0.08)
图 15 虚拟测试的含缺陷CF/EP复合材料层合板离面位移结果统计
Figure 15. Statistical results of virtual testing of out-of-plane displacements for wrinkled CF/EP composite laminates
图 16 基于虚拟测试的纤维增强树脂复合材料结构设计与无损检测策略
Figure 16. Strategy of structural design and non-destructive testing of fiber-reinforced resin composites based on virtual testing
表 1 用于数值模拟的碳纤维/环氧树脂（CF/EP）复合材料弹性参数
Table 1. Elastic parameters of carbon fiber/epoxy resin (CF/EP) composites used in numerical simulation
E11/GPa (E22/E33)/GPa G23/GPa G31/GPa G12/GPa ν21 ν32 ν31 133.3 9.09 3.16 7.24 7.23 0.261 0.436 0.261 Notes: E11, E22, E33—Elastic modulus (direction 11, 22, 33); G12, G23, G31—Shear modulus (direction 12, 23, 31); v21, v32, v31—Poisson’s ratio (direction 21, 32, 31). 
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