Shear stability test and strength prediction of composite laminates
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摘要: 对无损伤及含冲击损伤的复合材料层合板进行了剪切稳定性试验，基于数字图像相关方法(Digital image correlation，DIC)对层合板屈曲后屈曲行为进行了实时测量。试验结果表明：引入冲击损伤后，复合材料层合板剪切屈曲波形、屈曲载荷无明显变化，失效模式转变，承载能力下降了9.69%。随后，基于断裂面失效理论，建立了考虑剪切非线性效应的复合材料渐进损伤失效模型，并对复合材料层合板剪切失效过程进行了模拟。模型采用软化夹杂法将冲击损伤等效简化，直接将损伤区的几何边界信息写入材料模型中，不需要对冲击损伤区进行切割，从而保证了整体网格质量。与试验结果对比发现：模型考虑剪切非线性对屈曲载荷预测无明显影响，对后屈曲承载能力的预测精度影响较大，不考虑剪切非线性效应时的误差可达20%以上；软化夹杂法可以有效地模拟冲击损伤，预测的含冲击损伤的复合材料层合板的屈曲载荷、破坏载荷误差分别为−3.17%、−1.27%。Abstract: The shear stability tests of composite laminates without damage and with impact damage were carried out. The post buckling behavior of composite laminates was measured in real time based on digital image correlation (DIC). The test results show that after the introduction of impact damage, the shear buckling waveform and buckling load of composite laminates do not change significantly, and the failure mode changes, the bearing capacity decreased by 9.69%. Then, based on the fracture surface failure theory, a progressive damage failure model of composite materials considering shear nonlinear effect was established, and the shear failure process of composite laminates was simulated. The softened inclusion method was used to simplify the impact damage, and the geometric boundary information of the damage area was directly written into the material model. There was no need to cut the impact damage area, so as to ensure the overall grid quality. Compared with the experimental results, it is found that the model considering shear nonlinearity has no obvious influence on the prediction of buckling load, and has a great influence on the prediction accuracy of post buckling capacity. The error without considering shear nonlinearity can reach more than 20%; The softened inclusion method can effectively simulate the impact damage. The predicted buckling load and failure load errors of composite laminates with impact damage are −3.17% and −1.27% respectively.
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图 2 T4试件冲击支持方式及分层尺寸
Figure 2. Impact support mode and delamination size of T4 specimen
图 3 无损伤试件(T1~T3)应变片分布及编号
Figure 3. Strain gauges distributions and numbers of undamaged specimens (T1-T3)
图 4 CCF300/BA3202复合材料层合板剪切试验方法
Figure 4. Shear test method for CCF300/BA3202 composite laminates
图 5 基体潜在断裂面上的应力分量[24]
Figure 5. Stress components on potential fracture surface of matrix[24]
$ {\sigma _1} $, $ {\sigma _2} $, $ {\sigma _3} $, $ {\tau _{12}} $, $ {\tau _{13}} $, $ {\tau _{23}} $, $ {\tau _{21}} $, $ {\tau _{31}} $, $ {\tau _{32}} $—Stress components in the material's principal axis coordinate system; $ {\theta _{{\text{fp}}}} $—Angle of the potential fracture surface of matrix; $ {\sigma _{\text{n}}} $, ${\tau _{{\text{nt}}}} $, ${\tau _{{\text{nl}}}} $—Stress components on potential fracture surface of matrix
图 7 CCF300/BA3202复合材料层板剪切试验有限元模型
Figure 7. Finite element model for shear test of CCF300/BA3202 composite laminates
MPC—Multi-point constraints
图 8 T4试件等效冲击损伤区域
Figure 8. Equivalent impact damage area of T4 specimen
F4—Impact damage field variable
图 10 无损伤的T1试件屈曲及失效时的面外位移云图
Figure 10. Out-of-plane displacement cloud diagram of undamaged T1 specimen during buckling and failure
W—Out of plane displacement
图 11 含冲击损伤的T4试件屈曲及失效时的面外位移云图
Figure 11. Out-of-plane displacement cloud diagram of T4 specimen with impact damage during buckling and failure
图 12 几何缺陷因子和剪切非线性对CCF300/BA3202复合材料层合板屈曲载荷、破坏载荷的影响
Figure 12. Effects of geometric defect factor and shear nonlinearity on buckling load and failure load of CCF300/BA3202 composite laminates
图 13 刚度折减系数对CCF300/BA3202复合材料层板破坏载荷的影响
Figure 13. Effects of stiffness reduction factor on failure load of CCF300/BA3202 composite laminates
FEM—Finite element modeling
图 14 T4试件仿真的屈曲模态
Figure 14. Simulated buckling mode of T4 specimen
U3—Out of plane displacement
图 15 T4试件仿真的失效模式
Figure 15. Simulated failure mode of T4 specimen
F1—Fiber damage field variable; F2—Matrix damage field variable
图 17 T4试件纤维间损伤扩展过程
Figure 17. Inter-fiber failure propagation process of T4 specimen
P—Load; U—Displacement
表 1 CCF300/BA3202碳纤维增强环氧树脂复合材料性能参数
Table 1. Material properties of CCF300/BA3202 carbon fiber reinforced epoxy composite
Parameter Value E1/GPa 118 E2/GPa 8.98 G12/GPa 4.21 ν12 0.306 XT/MPa 1835 XC/MPa 1296 YT/MPa 82.5 YC/MPa 240 SL/MPa 166 GIC/(N·mm−1) 0.744 GIIC/(N·mm−1) 1.90 Notes：$ {E_1} $—Longitudinal elastic modulus; $ {E_2} $—Ransverse elastic modulus; $ {G_{12}} $—Shear modulus; $ {\nu _{{\text{12}}}} $—Poisson's ratio; $ {X_{\text{T}}} $—Longitudinal tensile strength; $ {X_{\text{C}}} $—Longitudinal compressive strength; $ {Y_{\text{T}}} $—Transverse tensile strength; $ {Y_{\text{C}}} $—Transverse compressive strength; $ {S_{\text{L}}} $—Shear strength; GIC—Mode I fracture toughness ; GIIC—Mode II fracture toughness. 
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表 2 材料性能退化方案
Table 2. Material performance degradation scheme
Fail mode No damage zone Impact damage zone None — $ \begin{gathered} {E_1} \to \eta {E_1} \\ {E_2} \to \eta {E_2} \\ G_{12}^{{\text{eq}}} \to \eta G_{12}^{{\text{eq}}} \\ \end{gathered} $ Fiber failure $ \begin{gathered} {E_1} \to (1 - {d_{{\text{FF}}}}){E_1} \\ {E_2} \to (1 - {d_{{\text{FF}}}}){E_2} \\ G_{12}^{{\text{eq}}} \to (1 - {d_{{\text{FF}}}})G_{12}^{{\text{eq}}} \\ {\nu _{12}} \to (1 - {d_{{\text{FF}}}}){\nu _{12}} \\ \end{gathered} $ $ \begin{gathered} {E_1} \to (1 - {d_{{\text{FF}}}})\eta {E_1} \\ {E_2} \to (1 - {d_{{\text{FF}}}})\eta {E_2} \\ G_{12}^{{\text{eq}}} \to (1 - {d_{{\text{FF}}}})\eta G_{12}^{{\text{eq}}} \\ {\nu _{12}} \to (1 - {d_{{\text{FF}}}}){\nu _{12}} \\ \end{gathered} $ Inter-fiber failure $ \begin{gathered} {E_2} \to (1 - {d_{{\text{IFF}}}}){E_2} \\ G_{12}^{{\text{eq}}} \to (1 - {d_{{\text{IFF}}}})G_{12}^{{\text{eq}}} \\ {\nu _{12}} \to (1 - {d_{{\text{IFF}}}}){\nu _{12}} \\ \end{gathered} $ $ \begin{gathered} {E_2} \to (1 - {d_{{\text{IFF}}}})\eta {E_2} \\ G_{12}^{{\text{eq}}} \to (1 - {d_{{\text{IFF}}}})\eta G_{12}^{{\text{eq}}} \\ {\nu _{12}} \to (1 - {d_{{\text{IFF}}}}){\nu _{12}} \\ \end{gathered} $ Notes: $ G_{12}^{{\text{eq}}} $—Equivalent shear modulus; η—Stiffness reduction factor; $ {d_{{\text{FF}}}} $—Fiber damage state variable; $ {d_{{\text{IFF}}}} $—Matrix damage state variable.
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表 3 CCF300/BA3202复合材料层板剪切试验结果
Table 3. Shear test results of CCF300/BA3202 composite laminates
Number Buckling load/kN Fracture load/kN Test Average Test Average T1 64.6 64.2 153.5 156.8 T2 65.0 156.2 T3 63.1 160.7 T4 63.0 141.6
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