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摘要:
蜂窝或胞壁缺失是蜂窝夹层结构缺陷形式的一种，由于蜂窝（壁）的缺失，导致蜂窝芯子的连续性被破坏，并产生应力集中。本文从蜂窝细观尺度出发，通过数值解析与有限元模拟相结合的方式对缺陷周围胞壁正应力进行分析，首先，通过有限元模拟得到胞壁的拉应力结果，结果表明，应力集中带状区上的胞壁标准化拉应力沿横向符合近似卡方概率密度函数的分布形式；存在一个临界位置使蜂窝壁拉应力分布曲线出现反转。其次，对蜂窝缺陷最大拉应力处的壁内弯矩值与胞壁缺失个数的关系进行了推导。最后，给出了预估弯曲应力的公式，并分析了缺陷形状对预估公式参数的影响。
Abstract:A kind of defect with some of the cell walls missing in a honeycomb structure causes the loss of continuum of the honeycomb, and thus results in the stress concentration around the defect tip. Combined with the finite element and the analytic methods, this paper analyzed the normal stresses distribution on the cell wall at the defect tip in meso-scale. The finite element results of the tensile stress of the cell walls are obtained first. The results shows that the
x -directional stress distribution in the stress concentration strip area fits the probability distribution function of the quasi chi square distribution. There exists a band zone in which the normal stress is much higher than the rest of areas. The distribution of the normal stress of cell walls conform the in the band; there also exists a critical position at which the variation trend of distribution function inverses; secondly, the relation between moments of cell wall and the number of the missing walls is analytically researched. At last. a prediction equation of the bending stress is developed and the influence of defect shape on formula is analyzed.-
Key words:
- honeycomb structure /
- embed structure /
- defect /
- stress concentration /
- finite element method
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图 2 蜂窝壁单元缺失
σ2, maxP-缺陷蜂窝胞壁拉应力最大值；ycr-临界y值。
Figure 2. Honeycomb with missing cell wall elements
图 3 缺陷蜂窝芯子有限元模型及缺失单元
Figure 3. Finite element model of honeycomb core with defects and corresponding missing element
图 4 应力集中带状区胞壁标准化拉应力分布
Figure 4. Normalized tensile stress distribution of cell walls in stress concentration strip area
图 5 m=3, n=7缺陷附近竖向蜂窝壁内拉应力分布
Figure 5. Tensile stress distribution of y-direction honeycomb walls with defect of m=3, n=7
图 6 m=3, n=3缺陷附近竖向蜂窝壁内拉应力分布
Figure 6. Tensile stress distribution of y-direction honeycomb walls with defect of m=3, n=3
图 7 m=5, n=1缺陷附近竖向蜂窝壁内拉应力分布
Figure 7. Tensile stress distribution of y-directionhoneycomb walls with defect of m=5, n=1
图 8 最大拉应力所在胞壁应力分解
Figure 8. Stress decomposition on cell wall with maximum tensile stress
图 9 最大拉应力处蜂窝壁静力分析
-蜂窝壁A所受y向拉力。
Figure 9. Static analysis of honeycomb walls with maximum tensile stress
表 1 应力集中带状区的胞壁标准化拉应力有限元结果
Table 1. FEM results of normalized tensile stress of cell walls in stress concentration strip area
x/w σ2P/σ2∞ n=4 n=5 n=8 2(2.5) 1.265 7 (1.365 1) 3(3.5) 1.252 9 (1.325 9) 4(4.5) 1.195 1 (1.249 2) 1.628 5 5(5.5) 1.146 7 (1.188 0) 1.528 0 6(6.5) 1.112 3 (1.144 5) 1.403 9 7(7.5) 1.088 3 (1.114 1) 1.308 9 8(8.5) 1.071 5 (1.092 7) 1.241 4 9(9.5) 1.059 4 (1.077 1) 1.193 5 10(10.5) 1.050 5 (1.065 6) 1.158 9 11(11.5) 1.043 9 (1.056 9) 1.133 3 12(12.5) 1.038 9 (1.050 1) 1.114 0 13(13.5) 1.034 9 (1.044 8) 1.099 0 14 1.087 2 15 1.077 8 
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表 2 蜂窝壁横向拉应力值拟合残差
Table 2. Fitting error of x-directional tensile stress of cell walls
% 公式号 n=4 n=5 n=8 式(3) 0.04 0.07 0.19 式(6) 0.40 0.66 1.80 式(7) 1.98 16.10
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表 3 不同n值时的α/α0
Table 3. Variations of α/α0 with different n
n 4 5 6 7 8 α/α0 1.000 0 0.844 2 0.880 0 0.943 3 1.019 8
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