Research on impact behavior of CFRP aluminum alloy adhesive plate based on multiscale damage mechanism
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摘要: 碳纤维增强聚合物(CFRP)铝合金粘接板作为一种轻质高强的材料，被广泛用在飞机、汽车、高速列车等轻量化结构上。研究首先基于纤维/基体微观尺度建立代表性体积单元(RVE)单胞模型，预测单向CFRP的基本弹性力学参数，并通过RVE模型施加宏观单位载荷计算宏-微观应力放大系数。其次考虑纤维基体微观失效准则与演化规律，开发复合材料宏-微观渐进损伤演化程序，再结合金属与复合材料粘接面的损伤模型，建立多尺度损伤机制的CFRP铝合金粘接板冲击仿真模型，并通过实验验证了数值模型的准确性与可靠性。最后通过数值模拟对CFRP铝合金粘接板在不同纤维铺层角度与不同纤维体积分数下的抗冲击行为进行参数化研究，结果表明纤维铺层方向对粘接板的抗冲击力学性能影响不大，而纤维体积分数对结构的冲击行为影响较大。
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关键词:
- CFRP铝合金粘接板 /
- 复合材料 /
- 低速冲击 /
- 微观失效 /
- 多尺度模拟
Abstract: Carbon fiber reinforced polymer (CFRP) aluminum alloy adhesive plate is a lightweight and high-strength material, which has been widely applied in lightweight structures, such as airplanes, cars, and high-speed trains. This research first established an representative volume element (RVE) single cell model based on the microscale from fiber/matrix, predicted the elastic mechanical parameters of unidirectional CFRP, and calculated the macro-micro stress amplification coefficient by applying a macroscopic unit load to the RVE model. Secondly, considering the micro-failure criteria and evolution rules of fiber and matrix, the macro-micro progressive damage evolution program of CFRP unidirectional plates was developed. Then combining with the damage model of metal and adhesive interface, a multiscale damage mechanism impacted model of CFRP aluminum alloy adhesive plate was established, then the accuracy and reliability of the numerical model were verified through the experimental tests. Finally, based on the numerical simulation, the influences of fiber angle and fiber volume fraction on the impact behavior of CFRP aluminum alloy adhesive plate were studied in detail. The results show that the fiber layup direction has little effect on the impact mechanical performance of the adhesive plate, while the fiber volume fraction has a greater effect on the impact behavior of the structure. -
图 1 碳纤维增强聚合物(CFRP)铝合金粘接板的低速冲击实验
Figure 1. Low-velocity impact test for carbon fiber reinforced polymers (CFRP) aluminum alloy adhesive plate
图 2 代表性体积单元(RVE)模型的单元节点分布规律
Figure 2. Distribution rule of nodes in representative volume element (RVE) model
图 4 不同CFRP RVE模型弹性常数的数值与实验误差
Figure 4. Numerical and experimental error of elastic constantsfor different CFRP RVE models
图 5 CFRP RVE模型的选点分布(a)及宏观单位载荷加载工况(b)
Figure 5. Distribution of key points (a) and macro unit loadings (b) in RVE model of CFRP
${\bar \sigma _1} $, ${\bar \sigma _2} $, ${\bar \sigma _3} $—Normal stress; ${\bar \tau _{12}} $, ${\bar \tau _{23}} $, ${\bar \tau _{13}} $—Shear stress
图 6 考虑纤维/基体微观损伤的复合材料渐进损伤演化程序
Figure 6. Progressive damage progress of composite laminates based on the fiber/matrix micro-damage
FEM—Finite element method; f—Fiber; m—Matrix; SAFs—Stress amplification factors; D—Stiffness matrix; d—Damage parameter
图 7 CFRP铝合金粘接板的有限元模型
Figure 7. Finite element model of CFRP aluminum alloy adhesive plate
图 8 CFRP铝合金粘接板的数值与实验冲击载荷-位移响应对比
Figure 8. Comparison of impact load-displacement curves of experimental and numerical results of CFRP aluminum alloy adhesive plate
图 9 冲击载荷后CFRP铝合金粘接板的失效形貌对比
Figure 9. Comparison of damage morphologies of CFRP aluminum alloy adhesive plate after impact
图 10 不同铺层方向下CFRP铝合金粘接板的冲击响应
Figure 10. Impact response of CFRP aluminum alloy adhesive plate under different layer angles
图 11 不同铺层角度下CFRP铝合金粘接板的冲击损伤形貌
Figure 11. Damage morphologies of CFRP aluminum alloy adhesive plate under different layer angles
图 12 不同铺层角度复合材料层失效模式
Figure 12. Failure models of CFRP under different layer angles
S—Stress (Pa)
图 13 不同纤维体积分数Vf的CFRP铝合金粘接板的冲击响应
Figure 13. Impact response of CFRP aluminum alloy adhesive plate under different fiber volume fractions Vf
图 14 不同纤维体积分数的CFRP铝合金粘接板的失效形貌
Figure 14. Damage morphologies of CFRP aluminum alloy adhesive plate under different fiber volume fractions
图 15 不同纤维体积分数下复合材料层失效模式
Figure 15. Failure models of CFRP under different fiber volume fractions
表 1 T300碳纤维与基体的力学性能参数
Table 1. Material properties of T300 carbon fiber and matrix
Material Name Value Carbon fiber Ef11/GPa 185 Ef22/GPa 13 Ef33/GPa 15 Gf12/GPa 15 Gf13/GPa 15 Gf23/GPa 9 μf12 0.28 μf13 0.35 μf23 0.35 Matrix Em/GPa 2.6 μm 0.33 Notes: Ef11, Ef22, Ef33, Gf12, Gf23, Gf13—Elastic moduli of T300 carbon fiber in the 1, 2, 3, 12, 23, 13 directions, respectively; μf12, μf13, μf23—Poisson's ratios in the 12, 13, 23 directions, respectively; Em and μm—Micro elastic modulus and Poisson's ratio of the matrix, respectively. 
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表 2 CFRP RVE模型力学性能参数与实验对比
Table 2. Comparison of RVE models of CFRP and experimental tests
E11/GPa E22/GPa E33/GPa μ12 μ13 μ23 G12/MPa G13/MPa G23/MPa Experiments 108 8 8 0.320 0.320 0.300 3500 3500 3000 Square 111.9 6.8 6.8 0.297 0.297 0.364 3297 3297 2257 Rectangle 111.9 6.2 6.2 0.298 0.298 0.361 3157 3156 2672 Uniform distribution 111.1 6.7 6.7 0.298 0.298 0.363 3252 3251 2228 Random distribution 1 937.0 5.5 5.4 0.292 0.294 0.409 2739 2604 2174 Random distribution 2 108.9 6.4 6.4 0.302 0.303 0.423 3570 3596 2849 Notes: E11, E22, E33, G12, G23, G13—Elastic moduli of carbon fiber prepreg in the 1, 2, 3, 12, 23, 13 directions, respectively; μ12, μ13, μ23—Poisson's ratios in the 12, 13, 23 directions, respectively.
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表 3 CFRP多尺度模型的需求参数
Table 3. Parameters of CFRP multiscale model
E11/GPa E33/GPa μ13 G12/GPa G23/GPa $X_{\text{f}}^{0,{\text{T}}}/{\rm{MPa}}$ $X_{\text{f}}^{0,{\text{C}}}/{\rm{MPa}}$ $\gamma $ E22/GPa μ12 μ23 G13/GPa $Y_{\text{m}}^{0,{\text{T}}}/{\rm{MPa}}$ $Y_{\text{m}}^{0,{\text{C}}}/{\rm{MPa}}$ 108 8 0.32 3.5 3 2100 800 1.5 8 0.32 0.3 3.5 25 120 Notes: $X_{\text{f}}^{0,{\text{T}}}$, $X_{\text{f}}^{0,{\text{C}}}$—Longitudinal tensile strength and compres-sive strength, respectively; $Y_{\text{m}}^{0,{\text{T}}}$, $Y_{\text{m}}^{0,{\text{C}}}$—Transverse tensile strength and compressive strength, respectively; $\gamma $—Damage shape parameter of matrix.
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表 4 2024-T3铝合金板的材料属性
Table 4. Material properties of 2024-T3 aluminum
Density/(kg·m−3) 2700 Young's modulus/GPa 70 Poisson's ratio 0.3 Yield strength/MPa 292 Fracture strain 0.15 Fracture energy/(J·m−2) 10200
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表 5 内聚力单元参数
Table 5. Material properties of cohesive elements
E/GPa ${t}_{}^{\text{0}}/{\rm{MPa}}$ $ {G^{\text{c} }}/({\rm{N} }\cdot{\rm{mm} }^{-1})$ Density/(kg·m−3) ${E_{{\text{nn}}}}$ ${E_{{\text{ss}}}}$ ${E_{{\text{tt}}}}$ ${t}_{\text{n}}^{\text{0}}$ ${t}_{\text{s}}^{\text{0}}$ ${t}_{\text{t} }^{\text{0} }$ $ G_{\text{n}}^{\text{c}} $ $ G_{\text{s}}^{\text{c}} $ $ G_{\text{t}}^{\text{c}} $ $\rho $ 20500 7200 7200 140 300 300 2000 3000 3000 0.092 Notes: $ {E}_{\text{nn}}, {E}_{\text{ss}}, {E}_{\text{tt}} $—Stiffness coefficient in the normal and shear directions; ${t}_{\text{n} }^{\text{0} }, {t}_{\text{s} }^{\text{0} }, {t}_{\text{t} }^{\text{0} }$—Nominal stress in the normal and shear directions; $ G_{\text{n}}^{\text{c}} , G_{\text{s}}^{\text{c}} , G_{\text{t}}^{\text{c}} $—Critical fracture energies in the normal and shear directions.
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表 6 CFRP铝合金粘接板RVE模型力学性能参数与实验对比
Table 6. Comparison of mechanical parameters of RVE model of CFRP aluminum alloy adhesive plate and experimental tests
Fiber volume fraction (Vf) E11/GPa E22/GPa E33/GPa μ12 μ13 μ23 G12/MPa G13/MPa G23/MPa 0.4 75.4 4.6 4.6 0.308 0.308 0.440 2031 2031 1780 0.5 93.6 5.3 5.3 0.302 0.302 0.427 2503 2503 2154 0.6 111.9 6.2 6.2 0.298 0.298 0.361 3157 3156 2672 0.7 130.1 7.3 7.3 0.293 0.293 0.394 4136 4133 3404 0.8 148.3 8.7 8.7 0.288 0.288 0.380 5824 5824 4470
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