Response prediction based on meso-mechanical model of graded wrinkle defects and shearography measurement
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摘要: 针对碳纤维增强树脂基复合材料(Carbon Fiber-reinforced Polymer, CFRP)中褶皱缺陷的力学响应，提出了一种基于激光剪切散斑干涉的检测方法。首先构建了表征梯度型褶皱缺陷的细观力学模型，采用两步均匀化方法推导了含褶皱缺陷的代表性体积单元等效刚度矩阵，分析褶皱缺陷对层合板试样等效刚度系数影响，通过有限元预测了不同褶皱缺陷参数(铺层顺序、波长λ、振幅A)在不同拉伸载荷条件下的力学响应。其次，基于激光剪切散斑干涉技术开展了褶皱缺陷位移响应实验研究。实验结果表明，在拉伸载荷作用下，褶皱缺陷区域因离面位移梯度变化而产生干涉条纹，通过干涉条纹图处理，得到褶皱缺陷引起的位移场。实验获取的离面位移值与有限元预测结果吻合良好，证实了梯度型褶皱缺陷的细观力学模型在CFRP褶皱缺陷响应分析方面的可靠性。
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关键词:
- 碳纤维增强树脂基复合材料 /
- 褶皱缺陷 /
- 细观力学模型 /
- 激光剪切散斑干涉 /
- 位移响应
Abstract: This study proposed a detection method based on shearography for the mechanical response of wrinkle defects in carbon fiber-reinforced resin polymer (CFRP). Firstly, a meso-mechanical model characterizing graded wrinkle defects was constructed. The equivalent stiffness matrix of the representative volume element containing wrinkle defects was derived using a two-step homogenization method, and the effect of graded wrinkles defects on the equivalent stiffness coefficients of laminates was analyzed. Finite element analysis was then employed to predict the mechanical response under different tensile loading conditions for various wrinkle defect parameters (such as ply sequence, wavelength λ, and amplitude A). Secondly, experimental research on wrinkle defects displacement response was conducted using shearography. Experimental results show that under tensile loading, the interference fringes are generated in the wrinkle defects region due to the gradient change in out-of-plane displacement. By processing the interference fringe images, the displacement field caused by wrinkle defects is obtained. The out-of-plane displacement values obtained from experiments match well with the finite element prediction, confirming the reliability of shearography in measuring the response of wrinkle defects in CFRP. -
图 2 梯度型褶皱的细观力学模型
Figure 2. Meso-mechanical modeling of graded wrinkle
RVE−Representative Volume Element; C'ij−Equivalent stiffness matrix of single prepreg layer; n−Number of layers in RVE; θn−Fiber orientation angle of the n-th layer; m−Number of horizontal divisions in RVE; $\phi _{k}^{l} $−Misalignment angle of fiber in the k-th segment of the l-th layer; kC*−Equivalent stiffness matrix of the k-th segment; [C**]−Equivalent stiffness matrix of the homogenized
图 3 梯度型褶皱缺陷试样：(a)试样几何参数示意图； (b)褶皱缺陷形貌特征
Figure 3. Graded wrinkled specimen: (a) Geometric sketch of specimen; (b) Morphology of the wrinkle
图 5 含褶皱缺陷试样与无缺陷试样的离面位移有限元结果对比
Figure 5. Comparison of finite element results on out-of-plane displacement between wrinkled specimen and non-wrinkle specimen
图 7 剪切散斑变形量与相位的关系[23]
Figure 7. Relationship between shear and phase[23]
P1, P2−Two adjacent points on the surface of specimen before surface deformation; P'1, P'2−New positions of P1 and P2 on the surface of specimen after surface deformation; S−Position of coherent light source; O−Position of image plane
图 8 含褶皱缺陷试样随拉伸载荷变化得到的干涉条纹图：(a) 试样I；(b) 试样II；(c) 试样III
Figure 8. Fringe patterns of specimen during tension test: (a) Specimen Ⅰ; (b) Specimen Ⅱ; (c) Specimen Ⅲ
图 10 沿评估线方向实验结果与有限元结果的离面位移对比
Figure 10. Comparison of shearography measurement and FEA along evaluation line
表 1 复合材料褶皱缺陷中最大纤维偏转角范围和波纹比
Table 1. Range of maximum misalignment angles and wrinkle ratio in wrinkle defects
A/λ 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 ${{\phi }_{\max }} $/(°) 32.14 43.30 51.49 57.52 62.05 65.55 68.30 70.52 72.34 
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表 2 CF/EP复合材料弹性参数
Table 2. Elastic parameters of CF/EP composites
E11/GPa E22/GPa E33/GPa v12 v23 v31 G12/GPa G23/GPa G31/GPa 133.3 9.09 9.09 0.261 0.436 0.261 7.24 3.16 7.24
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表 3 试样缺陷参数
Table 3. Defect parameters of specimen
Specimen Layup sequences Wrinkle parameter Wavelength /mm Amplitude /mm Wrinkle ratio Ⅰ [0/90]2s 6.6 1.2 0.1818 Ⅱ [0]30 8.3 1.0 0.1204 Ⅲ [0/90/±45/0]3s 5.8 0.7 0.1206
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表 4 铺层顺序和褶皱缺陷对等效刚度系数的影响
Table 4. Effect of layup sequence and wrinkle defects on effective stiffness coefficients
Effective stiffness/GPa Layup sequence [0/90]2 s [0]30 [0/90/±45/0]3 s Wrinkle ratio= 0.1818 Wrinkle ratio= 0.1204 Wrinkle ratio= 0.1206 Without wrinkle With wrinkle Difference/% Without wrinkle With wrinkle Difference/% Without wrinkle With wrinkle Difference/% C11 73.43 19.92 −72.87 135.53 37.14 −72.59 64.26 25.54 −60.26 C12 4.29 4.59 7.0 4.28 4.88 14.02 15.60 7.87 −49.55 C13 4.65 6.23 33.98 4.28 3.82 −10.75 4.64 5.94 28.2 C22 73.43 73.40 −0.04 11.36 11.35 −0.09 59.98 58.46 −2.53 C23 4.65 4.63 −0.43 5.02 5.01 −0.20 4.67 5.15 10.28 C33 11.36 13.85 21.92 11.36 13.24 16.55 11.36 12.40 9.15 C44 4.40 5.11 16.14 3.15 3.15 0 4.34 5.17 19.12 C55 4.40 7.35 67.05 7.24 9.06 25.14 4.46 6.08 36.32 C66 7.23 6.23 −13.83 3.16 3.16 0 18.54 15.58 −15.97
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