Biaxial loading verification for an in-plane failure criterion of laminates with barely visible impact damages (BVID)
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摘要: 在复合材料飞机结构设计中，由于应力的铺层相关性，工程上通常采用应变进行结构强度预测。另外，复合材料飞机需考虑损伤容限设计，必须对含损伤，尤其是目视几乎不可见损伤(Barely visible impact damages，BVID)结构的适航符合性进行评估。因此，民用飞机结构设计上更需要基于应变的并考虑含损伤的复合材料失效准则来预测结构强度。本文介绍了一种复合应变失效判据，为验证该失效判据的保守性，设计了面内双轴加载试验，对含BVID损伤的准各向同性铺层T800级碳纤增强环氧树脂基复合材料层压板进行了各种工况的面内失效测试。通过设计双轴加载载荷比，实现了不同的拉伸、压缩、剪切复合加载工况。理论分析与试验结果对比显示，理论方法的失效载荷约为试验失效载荷的80%。此方法的保守性和准确度既满足了结构安全性需求又不会引入不必要的结构质量，适合于实际工程应用。
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关键词:
- 复合材料层压板 /
- 面内失效 /
- 双轴加载 /
- 目视几乎不可见损伤(BVID) /
- 有限元分析(FEA)
Abstract: In engineering practice, strains are used for stress analysis of composite aircraft structures, instead of stresses due to their stacking sequence dependence. Besides, for composite airplane, damage tolerant design is necessary, the compliance of airworthiness for composite structures with damages, especially barely visible impact damages (BVID) should be assessed. Thus for civil aircraft structural design, a credible strain based failure criterion for composites that containing damage is in demand for stress prediction. In this paper, a combined strain failure criterion for laminates was introduced. In order to verify the conservation of this failure criterion, biaxial loading tests were designed. Quasi-isotropic T800 carbon fiber reinforced epoxy resin matrix composite laminates with BVID were used for in-plane failure tests under various load conditions. Various load conditions with different combination of tension, compression and shearing loads were obtained through diversified design of load ratios. It is shown from the comparison of theoretical results and test results that all the theoretical failure loads are lower than experimental ones with a ratio of about 80%. The criterion is conserved to assure the safety of structures, but not too conserved to bring unnecessary weight to structures, thus it is suitable for engineering exercise. -
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图 1 复合应变失效分析方法验证过程
Figure 1. Verification procedure for combined strain failure analyze method
MS—Margin of safety; CAI—Compression after impact; TAI—Tenion after impact; IPSAI—In−plane shear after impact
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图 2 准各向同性铺层[45/−45/0/90]2s的T800级碳纤维增强环氧树脂基复合材料层压板试件构型
Figure 2. Test specimen configuration of quasi-isotropic T800 carbon fiber reinforced epoxy resin composite laminates with stacking sequence of [45/−45/0/90]2s
Fx—Load in x direction; Fy—Load in y direction
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图 3 不同观察窗口开口尺寸层压板试件的失稳系数对比
Figure 3. Buckling eigenvalues for laminate with different investigating windows
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图 6 试件应变片位置及编号示意图
Figure 6. Locations and numbers of the data collection channels of strain rosettes
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图 7 双轴试验后层压板损伤状态，其中白线标识了原BVID损伤边界(a)；双轴试验后C扫描图像(b)
Figure 7. Damage of laminates after biaxial loading test, white lines indicate the damage area after the drop-weight impact test (a); C scan image of the damage after biaxial loading test (b)
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图 8 各种载荷比工况层压板的整体失效状态
Figure 8. Failure patterns of laminates under load cases with different Fx to Fy ratios
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图 9 典型的层压板试件双轴加载下x (a)、y (b)方向正应力、xy方向(c)剪应力云图
Figure 9. Typical contours of stress-x (a), stress-y (b) and stress-xy (c) under biaxial loading
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图 10 平板表面的应力分量及倾角θ斜面的应力分量示意图
Figure 10. Components of stress on the faces of a plate and on an inclined plane with inclination angle θ
σθ—Principle stress in θ direction; σθ+90—Principle stress in (θ+90) direction; τθ—Shear stress in (θ, θ+90) direction; σx—Principle stress in x direction; σy—Principle stress in y direction; τxy—Shear stress in xy direction
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图 11 计算的T800 CF/EP-1试件的应变随方向角的关系曲线
Figure 11. Calculated curves of strains vs. inclination angle for T800 CF/EP-1 specimen
表 1 不同
{\boldsymbol{F}}_{\boldsymbol{x}} ∶{\boldsymbol{F}}_{\boldsymbol{y}} 载荷工况下分析获得的层压板面内失效载荷与失稳载荷对比Table 1 Comparison of loads for buckling and in-plane failure of composite laminate under different
{\boldsymbol{F}}_{\boldsymbol{x}} ∶{\boldsymbol{F}}_{\boldsymbol{y}} ratiosFx∶Fy Fx_buckling/
(kN·m−1)Fx_failure/
(kN·m−1)Fx_buckling/
Fx_failure−4∶3 463.29 450.08 102.93% −3∶4 400.70 325.95 122.93% −2∶3 359.75 314.20 114.50% −3∶2 469.86 497.10 94.52% −5∶3 475.48 488.27 97.38% −3∶5 326.24 276.16 118.13% −2∶1 483.61 589.23 82.08% −1∶2 274.97 267.63 102.74% −1∶1 443.63 430.63 103.02% −5∶−1 534.88 858.04 62.34% −4∶−1 526.59 892.81 58.98% −4∶−2 473.00 996.66 47.46% −5∶−3 450.70 1028.39 43.83% 
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表 2 试验矩阵
Table 2 Test matrix
Specimen code Ply Fx∶Fy ratio T800 CF/EP-1 [45/−45/0/90]2s −3∶4 T800 CF/EP-2 [45/−45/0/90]2s −3∶5 T800 CF/EP-3 [45/−45/0/90]2s −1∶1 T800 CF/EP-4 [45/−45/0/90]2s −1∶2 T800 CF/EP-5 [45/−45/0/90]2s −4∶3 T800 CF/EP-6 [45/−45/0/90]2s −2∶3 T800 CF/EP-7 [45/−45/0/90]2s −5∶3 T800 CF/EP-8 [45/−45/0/90]2s −2∶1 Notes: CF—Carbon fiber; EP—Epoxy resin.
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表 3 不同载荷比下层压板试件
{\boldsymbol{x}} 和{\boldsymbol{y}} 方向的失效载荷Table 3 Failure loads in
{\boldsymbol{x}} and{\boldsymbol{y}} directions of laminates under different load ratiosSpecimen code Fx/(kN·m−1) Fy/(kN·m−1) T800 CF/EP-1 −255.86 340.28 T800 CF/EP-2 −217.31 361.67 T800 CF/EP-3 −278.33 278.06 T800 CF/EP-4 −193.53 385.28 T800 CF/EP-5 −307.22 230.28 T800 CF/EP-6 −232.00 346.11 T800 CF/EP-7 −330.28 197.61 T800 CF/EP-8 −331.94 165.42
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表 4 层压板理论失效载荷与试验失效载荷的比较
Table 4 Comparison of experimented and theoretical failure loads of laminates
Specimen code F_theory/F_failure T800 CF/EP-1 77.27% T800 CF/EP-2 80.66% T800 CF/EP-3 81.26% T800 CF/EP-4 81.57% T800 CF/EP-5 82.45% T800 CF/EP-6 80.26% T800 CF/EP-7 82.76% T800 CF/EP-8 86.79%
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