Effect of resin-rich zone on fracture behavior of mode-I delamination of multi-directional laminates
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摘要: 双悬臂梁(Double Cantilever Beam，DCB)试验是测定复合材料层合板I型层间断裂能最主要方法。针对DCB试样因铺贴聚四氟乙烯薄膜预制分层产生树脂富集区对I型断裂能计算不准确的问题，本文设计三种铺层角度(0//0，0//45，0//90)的DCB试验，采用扫描电镜表征DCB裂纹断面的微观形貌，量化树脂富集影响区域，研究三种工况树脂富集对载荷-位移曲线的非线性行为的影响规律。建立含树脂富集区和纤维桥接扩展区的DCB数值模型，开展量化分析解释和揭示树脂富集区对断裂能R曲线的影响规律。试验结果表明：三种铺层角度对应的树脂富集区的长度明显不同，0//0试样最长，0//90试样最短。树脂富集区和纤维桥接扩展区的耦合作用，导致载荷-位移曲线呈现不同的非线性行为。构建的数值分析模型可以准确预测与试验一致的载荷-位移曲线，验证了树脂富集区对I型分层初始断裂韧性的影响规律。Abstract: The Double Cantilever Beam (DCB) test is the most primary method for determining the interlaminar fracture energy of composite laminate mode-I. In order to address the issue of inaccurate calculation of the mode-I fracture energy due to the resin-rich zone generated by prefabricated delamination from laying polytetrafluoroethylene film for DCB specimens, DCB tests with three laying angles (0//0,0//45,0//90) were designed and scanning electron microscopy was used to characterize the microstructure of DCB crack surfaces. the influence mechanism of resin-rich zone was quantified, and the nonlinear behavior of load-displacement curves under three working conditions of resin enrichment was studied. A numerical model of the DCB containing resin-rich zone and fiber bridging propagation zone was established to conduct quantitative analysis, interpretation, and reveal the mechanisms of the resin-rich zone on the fracture energy R curve. Experimental results show that the lengths of resin-rich zone corresponding to the three laying angles are significantly different, with the 0//0 specimen being the longest and the 0//90 specimen being the shortest. The coupling effect between the resin-rich zone and fiber bridging propagation zone results in different nonlinear behaviors in the load-displacement curves. The constructed numerical analysis model can accurately predict load-displacement curves consistent with experiments, verifying the influence of resin-rich zone on the initial fracture toughness of mode-I layer.
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图 3 (a)试验设备图；(b) DCB试样侧面图
Figure 3. (a) Diagram of test equipment; (b) Side view of the DCB specimen
图 4 不同层间铺层角度DCB试样的载荷-位移曲线：(a) 0//0；(b) 0//45；(c) 0//90
Figure 4. Load-displacement curves of DCB specimens with different interlayer ply angles: (a) 0//0; (b) 0//45; (c) 0//90
图 5 不同层间铺层角度DCB试样的$ {G_{{{{\rm I}C}}}} $曲线：(a) 0//0；(b) 0//45；(c) 0//90
Figure 5. $ {G_{{{{\rm I}C}}}} $curves of DCB specimens with different ply angles: (a) 0//0; (b) 0//45; (c) 0//90
图 6 DCB试样宏观断面图和微观形貌图：(a) 0//0；(b) 0//45；(c) 0//90
Figure 6. Macroscopic cross-sectional view and microscopic morphology of DCB specimens: (a) 0//0; (b) 0//45; (c) 0//90
图 8 网格敏感性分析：(a)裂纹尖端扩展区；(b)非裂纹尖端扩展区
Figure 8. Mesh sensitivity analysis in crack tip propagation zone (a) and non-crack tip propagation zone (b)
图 9 不同铺层角度的DCB试样的试验与数值模拟载荷-位移曲线对比：(a)0//0；(b)0//45；(c)0//90
Figure 9. Comparison of experiment and simulation load-displacement curves of DCB specimens with different ply angles: (a)0//0; (b)0//45; (c)0//90
表 1 复合材料层合板材料力学性能参数
Table 1. Mechanical property parameters of composite laminate materials
Module Value E11/GPa 117 E22/GPa 7.47 E33/GPa 7.47 G12/GPa 4.07 G13/GPa 4.07 G23/GPa 2.31 ν12 0.33 ν13 0.33 ν23 0.3 Notes: E−Elastic modulus; G−Shear modulus; ν−Poisson ratio; 1−Direction of fiber; 2−Direction of matrix; 3−Thickness direction of layer. 
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表 2 DCB试样的层间断裂韧性值
Table 2. Interlaminar fracture toughness of DCB specimens
Ply angles Specimen label ${G_{{\text{I - MC}}}}$ $ {G_{{\text{INI}}}} $ Ave. value/(J·m−2) CV/% /(J·m−2) /(J·m−2) ${G_{{\text{I - MC}}}}$ $ {G_{{\text{INI}}}} $ ${G_{{\text{I - MC}}}}$ $ {G_{{\text{INI}}}} $ 0//0 DCB-0-1
DCB-0-2
DCB-0-3343.4
326.6
352.1230.7
241.1
236.1340.7 235.9 3.80 2.21 0//45 DCB-45-1
DCB-45-2
DCB-45-3303.4
310.8
318.2247.6
242.1
251.5310.8 247.1 2.38 1.91 0//90 DCB-90-1
DCB-90-2
DCB-90-3246.6
261.3
301.1234.2
246.2
286.6270.7 255.7 10.43 10.74 Notes: ${G_{{\text{I - MC}}}}$-SERR for matrix cracking damage; $ {G_{{\text{INI}}}} $-SERR for initiation value; CV−Sample coefficient of variation.
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Resin-rich zone CZM SERR for matrix cracking damage $ {G_{{\text{{\rm I} - MC}}}} $ Interfacial strength $ {\sigma _0} = {\sigma _{\text{b}}} = 78.3 $MPa Initial interfacial stiffness $ {K_0} = {10^{15}} $N/m3[27] Damage initiation displacement $ \delta ' = {\sigma _0}/{K_0} = 7.83 \times {10^{ - 5}}{\text{mm}} $ Damage failure displacement $ {\delta _0} = 2{G_{{\text{{\rm I} - MC}}}}/{\sigma _0} $ MB-CZM Element E1 SERR for matrix cracking damage $ G{'_{{\text{{\rm I} - MC}}}} $=$ {G_{{\text{INI}}}} - {G_{{\text{I - FB}}}} - {G_{{\text{I - FD}}}} $ SERR for matrix/fiber interfacial
separation damage$ {G_{{\text{I - FD}}}} = {G_{{\text{INI}}}} - {G_{{\text{br}}}}(\delta ) - G{'_{{\text{{\rm I} - MC}}}} $ Initial interfacial stiffness $ {K_{{\text{E1}}}} $= 107 N/m3[26] Maximum interface strength $ \sigma _{\max }^c = 0.6{\sigma _{\text{b}}} = 47 $MPa[28] Element E2 Initial interfacial stiffness $ {K_{{\text{E2}}}} = \sigma _{{\text{br}}}^{\max }/{\delta _2} = 4.7 \times {10^{12}} $N/m3 Maximum fiber bridging interface strength $ \sigma _{{\text{br}}}^{\max } = ({G_a}/{\delta _a}) + ({G_b}/{\delta _b}) $ Maximum bridging opening
displacement$ \delta _{{\text{br}}}^{\max } $ Damage failure displacement $ {\delta _2} = 2{G_{{\text{IC}}}}/\sigma _{\max }^{\text{c}} $ Notes: $ {\sigma _{\text{b}}} $-Tensile strength of the matrix; $ {G_{{\text{I - FB}}}} $- SERR associated fiber bridging ahead of the crack tip;$ {G_{{\text{br}}}}(\delta ) $- Strain energy release rate $ {G_{{\text{br}}}}(\delta ) $ as a function of the initial crack tip opening displacement δ ;$ {G_{{\text{IC}}}} $-Interlayer strain energy release rate.
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表 4 不同层间铺层角度下DCB试样的拟合参数
Table 4. Fitting parameters of DCB specimens at different interlaminar ply angles
Ply angles ${G_a}$/(J·m−2) ${G_b}$/(J·m−2) ${\delta _a}$/mm $ {\delta _b} $/mm $ \sigma _{{\text{br}}}^{\max } $/MPa 0//0 28.49 254.3 1.504 0.05178 4.93 0//45 348.5 340.5 1.8 0.1 3.59 0//90 134.3 466.9 1.6 0.1 4.75 Notes: ${G_a}$,${G_b}$,${\delta _a}$,$ {\delta _b} $ are the fitting constant coefficients.
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表 5 MB-CZM中与分层起始相关的材料参数
Table 5. Material parameters associated with delamination initiation in the MB-CZM
Ply angles $ {\delta _0} $/mm $ G{'_{{\text{{\rm I} - MC}}}} $/(J·m−2) $ {G_{{\text{I - FD}}}} $/(J·m−2) $ {\delta _2} $/mm $ \delta _{{\text{br}}}^{\max } $/mm 0//0 0.00870 235 0.9 0.0100 5.9 0//45 0.00794 246.75 0.35 0.0105 5.3 0//90 0.00691 255.68 0.02 0.01088 3.4
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