Numerical study on the effect of void content on hygrothermal performances of carbon fiber reinforced polyamide 6 composites
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摘要: 孔隙在复合材料制造过程中广泛存在，在湿热环境下孔隙的存在会改变应力场和水分场，进而影响复合材料的吸湿性能与力学老化性能。对碳纤维/尼龙6(Carbon fiber reinforced polyamide 6，CF/PA6)复合材料在不同温度浸水环境下吸湿老化后的力学性能测试，研究了温度与吸湿量对其力学性能的影响及强度与模量等力学参数的演化规律，建立吸湿参数与力学参数的关联函数。基于随机顺序吸附法算法(Random sequential adsorption，RSA)，建立了纤维、界面和孔隙随机分布的代表性体积单元(Representative volume element，RVE)模型。在本构模型中引入依赖于吸湿量的退化因子，研究了孔隙含量对复合材料横向拉伸、压缩、剪切强度和模量的影响，揭示了湿热老化前后不同的失效机制。结果表明：在热湿老化前，由于应力集中，孔隙会导致复合材料力学性能下降，孔隙率含量每增加1%，横向拉伸强度降低6.4%；湿热老化后，基体吸湿塑化效应是复合材料力学性能降低主要因素，对应降低率为3.86%。Abstract: Voids are comment defects generated during the manufacturing process and highly sensitive to moisture in the hygrothermal environment. The presence of voids will change the stress field and moisture field, which has deleterious effects on the mechanical performances. The mechanical properties of carbon fiber reinforced polyamide 6 (CF/PA6) composites after hygrothermal aging under different temperature immersion environment were tested to study the effects of temperature and water absorbed content on the mechanical properties. The correlation function between water content and mechanical parameters was established. Based on the random sequential adsorption algorithm (RSA), the representative volume element (RVE) model with random distribution of fibers, interfaces and voids was established. The quantitative effects of voids content on strength and modulus under the loading of transverse tension, compression and shear were investigated, by introducing a degradation factor dependent on water content into the constitutive model, and the failure mechanisms before and after hygrothermal aging were revealed. Conclusively, before hygrothermal aging, voids induce the decrease of mechanical properties due to stress concentration, and every 1% increase in the voids content results in a 6.4% decrease of transverse tensile strength. However, matrix degradation due to the absorbed water content after hygrothermal aging is the dominant factor, and the corresponding rate is 3.86%.
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Key words:
- voids content /
- hygrothermal aging /
- RVE /
- failure mechanism /
- numerical simulation
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图 1 吸湿量与老化温度对尼龙6(PA6)基体拉伸力学性能影响
Figure 1. Effect of absorbed water content and temperature on the tensile properties of polyamide 6 (PA6)
图 2 吸湿量与老化温度对碳纤维(CF)/PA6横向拉伸力学性能的影响
Figure 2. Effect of absorbed water content and temperature on the transverse tensile properties of carbon fiber (CF)/PA6
图 3 吸湿量对PA6基体和CF/PA6复合材料拉伸强度与弹性模量的影响
Figure 3. Effect of water content on the tensile strength and elastic modulus of PA6 resin and CF/PA6 composites
图 4 不同孔隙含量的CF/PA6复合材料代表性体积单元(RVE)模型
Figure 4. Representative volume element (RVE) models with different contents of voids for CF/PA6 composites
图 5 CF/PA6复合材料RVE模型在横向拉伸 (a)、横向压缩 (b) 和横向剪切 (c) 荷载作用下的渐进失效
FEM—Finite element analysis; EXP—Experimental
Figure 5. Failure progression in RVE model of CF/PA6 composites under the loading of tension (a), compression (b) and shearing (c)
图 6 CF/PA6复合材料预测模型与数值模拟计算结果对比
Figure 6. Comparison of prediction models and numerical simulation results of CF/PA6 composites
图 7 CF/PA6复合材料孔隙含量对吸湿性能的影响
Figure 7. Effect of voids content on the water absorption performance of CF/PA6 composites
图 8 孔隙含量对CF/PA6未老化试样力学性能的影响：(a) 强度；(b) 弹性模量
σt, σc, σs—Tensile strength, compressive strength and shear strength of CF/PA6 composites before hygrothermal aging; Et, Ec, Es—Tensile modulus, compressive modulus and shear modulus of CF/PA6 composites before hygrothermal aging
Figure 8. Effect of voids content on the mechanical performance for unaged CF/PA6 samples: (a) Strength; (b) Elastic modulus
图 9 孔隙含量对CF/PA6复合材料湿热老化模型力学性能的影响：(a)强度；(b)弹性模量
σt', σc', σs'—Tensile strength, compressive strength and shear strength of CF/PA6 composites after hygrothermal aging; Et', Ec', Es'—Tensile modulus, compressive modulus and shear modulus of CF/PA6 composites after hygrothermal aging
Figure 9. Effect of voids content on the mechanical performance for hygroscopic saturated CF/PA6 composite: (a) Strength; (b) Elastic modulus
图 10 CF/PA6复合材料未老化模型在横向拉伸(a)、横向压缩(b)及横向剪切(c)模式下的失效模式
Figure 10. Failure patterns of unaged CF/PA6 composite in the tension (a), compression (b) and shear simulation (c)
图 11 CF/PA6复合材料湿热老化模型在横向拉伸(a)、横向压缩(b)及横向剪切(c)模式下的失效模式
Figure 11. Failure patterns of hygroscopic saturated CF/PA6 composite in the tension (a), compression (b) and shear simulation (c)
表 1 CF/PA6复合材料各组分材料在50℃浸水环境的吸湿参数
Table 1. Water absorption parameters for component materials in the CF/PA6 composites immersed at 50℃ water bath
Parameter Diffusivity/(106 mm2·s−1) Water content/% PA6 4.64 9.40 CF 0.00 0.00 Voids 46.40 23.50 CF/PA6 2.16 5.26 
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表 2 CF/PA6复合材料力学性能
Table 2. Mechanical properties for CF/PA6 composites
Fiber $E_2^{\rm f}/{\text{GPa}}$ $\mu _{23}^{\rm f}$ $\alpha^{\mathrm{f}} /\left(10^{-6} {\text{℃}}^{-1}\right)$ $ {\beta ^{\rm f}} $ ${\rho ^{\rm f}}/({\text{kg} } \cdot { {\text{m} }^{ {\text{-3} } } })$ 16.54 0.25 −0.83 0 1810 Matrix $ {E^{\rm m}}/{\text{GPa}} $ ${\mu ^{\rm m}}$ ${\sigma _{y{\rm t}}}/{\text{MPa}}$ $ {\sigma _{y{\rm c}}}/{\text{MPa}} $ $\alpha^{\mathrm{m}} /\left(10^{-6} {\text{℃}} ^{-1}\right)$ 2.19 0.34 25 50 4 $ {\beta ^{\rm m}} $ ${\rho ^{\rm m}}/({\text{kg}} \cdot {{\text{m}}^{{{ - 3}}}})$ 0.1 1080 Interface $ K_{\rm n}^0/({\text{N}} \cdot {\text{m}}{{\text{m}}^{{{ - 3}}}}) $ $K_{\rm s}^0/({\text{N}} \cdot {\text{m}}{{\text{m}}^{{{ - 3}}}})$ $K_{\rm t}^0/({\text{N}} \cdot {\text{m}}{{\text{m}}^{{{ - 3}}}})$ $t_{\rm n}^0/{\text{MPa}}$ $t_{\rm s}^0/{\text{MPa}}$ $3.13 \times {10^4}$ $5.0 \times {10^4}$ $5.0 \times {10^4}$ 17.11 40.67 $t_{\rm t}^0/{\text{MPa}}$ $G_{\rm n}^{\rm c}{\text{/(N}} \cdot {\text{m}}{{\text{m}}^{ - 1}}{\text{)}}$ $G_{\rm s}^{\rm c}{\text{/(N}} \cdot {\text{m}}{{\text{m}}^{ - 1}}{\text{)}}$ $G_{\rm t}^{\rm c}{\text{/(N}} \cdot {\text{m}}{{\text{m}}^{ - 1}}{\text{)}}$ 40.67 0.22 0.23 0.23 Notes: $E_2^{\rm f}$ and $ {E^{\rm m}} $—Tensile modulus of the carbon fiber and the PA6 matrix; $\mu _{23}^{\rm f}$ and ${\mu ^{\rm m}}$—Poisson's ratio of the carbon fiber and the PA6 matrix; $ {\alpha ^{\rm f}} $ and $ {\alpha ^{\rm m}} $—Coefficient of thermal expansion for the carbon fiber and the PA6 matrix; $ {\beta ^{\rm f}} $ and $ {\beta ^{\rm m}} $—Coefficient of moisture expansion for the carbon fiber and the PA6 matrix; ${\rho ^{\rm f}}$ and ${\rho ^{\rm m}}$—Density of the carbon fiber and the PA6 matrix; ${\sigma _{y{\rm t}}}$ and $ {\sigma _{y{\rm c}}} $—Tensile and compressive yield strength of the PA6 matrix; $ K_{\rm n}^0 $, $K_{\rm s}^0$ and $K_{\rm t}^0$—Interfacial stiffness; $t_{\text{n}}^{\text{0}}$, $t_{\text{s}}^{\text{0}}$ and $t_{\text{t}}^{\text{0}}$—Interfacial strength; $G_{\text{n}}^{\text{c}}$, $G_{\text{s}}^{\text{c}}$ and $G_{\text{t}}^{\text{c}}$—Fracture toughness.
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表 3 含孔隙缺陷复合材料的相对扩散系数的预测模型[17]
Table 3. Several theoretical models for calculating effective diffusion coefficient of composites containing voids[17]
Model Expression Porous-Matrix model $ \dfrac{{{D_{{\rm{eff}}}}}}{{{D_{\rm{m}}}}} = \left[ {1 + 2{\alpha _{{\rm{mv}}}}{V_{\rm{v}}}\dfrac{{\left( {{{{D_{\rm{v}}}}/ {{D_{\rm{m}}}}}} \right) - 1}}{{\left( {{{{D_{\rm{v}}}} / {{D_{\rm{m}}}}}} \right) + 1}}} \right]\dfrac{{1 - {V_{\rm{f}}}}}{{1 + {V_{\rm{f}}}}} $，
${\alpha _{ {\rm{mv} } } } = \dfrac{ { {\rho _{ {\rm{water} } } } } }{ { {M_{\rm{m} } }{\rho _{\rm{m}}}(1 - {v_{ {\rm{void} } } })} }$Four-Phase
model$ \dfrac{{{D_{{\rm{eff}}}}}}{{{D_{\rm{m}}}}} = \dfrac{{(1 - k{V_{\rm{f}}})(1 + k) + \varPhi (1 + k{V_{\rm{f}}})(k - 1)}}{{(1 + k{V_{\rm{f}}})(1 + k) + \varPhi (1 - k{V_{\rm{f}}})(k - 1)}} $，
$ k = {{({V_{\rm{v}}} + {V_{\rm{f}}})} / {{V_{\rm{f}}}}} $, $ \varPhi = {\alpha _{{\rm{mv}}}}({{{D_{\rm{v}}}} / {{D_{\rm{m}}}}}) $Self-consistent model $ \dfrac{{{D_{{\rm{eff}}}}}}{{{D_{\rm{m}}}}} = \dfrac{1}{{2(1 + k)}}\left( {\lambda + \sqrt {4\dfrac{{{D_{\rm{v}}}}}{{{D_{\rm{m}}}}}({k^2} - 1) + {\lambda ^2}} } \right) $，
$ \lambda = \dfrac{{{D_{\rm{v}}}}}{{{D_{\rm{m}}}}}\left( {1 + k\left( {2{V_{\rm{v}}} - 1} \right)} \right) + \left( {1 + k\left( {1 - 2{V_{\rm{v}}}} \right)} \right) $Notes: $ {D_{\rm{v}}} $, $ {D_{\rm{m}}} $ and $ {D_{{\rm{eff}}}} $—Diffusivity of voids, matrix and composites; $ {V_{\rm{f}}} $ and Vv—Volume fraction of carbon fiber and voids in CF/PA6 composites; $ {\alpha _{{\rm{mv}}}} $, $ k $, $ \varPhi $ and $ \lambda $—Intermediate variable; Vvoid—Void content in the matrix; ρm and ρwater—Density of matrix and water; Mm—Absorbed water content in the matrix.
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表 4 CF/PA6复合材料不同孔隙率RVE模型的湿热老化前后的裂纹数量对比
Table 4. Comparison of the number of cracks in RVE models of CF/PA6 composites with different porosities before and after hygrothermal aging
Porosity/% Unaged Aged Tension Compression Shear Tension Compression Shear 1 4 2 3 9 10 5 2 5 2 2 10 9 3 3 1 3 3 9 15 6 4 1 2 2 7 14 6 5 2 2 2 10 14 5
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