Inversion study on the correlation between the mesh size and the adhesive properties
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摘要: 在使用内聚力模型对复合材料胶层进行有限元失效分析时，为了保证计算结果的准确性和收敛性，胶层网格尺寸应小于1 mm。然而当使用内聚力模型对飞机上的大型复合材料结构进行有限元分析时，模型将会产生上百万的有限元单元，这将耗费大量的计算资源。本文在研究胶层参数对胶层失效分析影响的基础上，通过对不同网格尺寸下胶层参数进行反演，提出了一种修改胶层参数的方法以适用于不同网格尺寸下胶层失效分析。使用此方法对不同网格尺寸的混合型弯曲(MMB)有限元模型和复合材料圆壳模型进行了有限元仿真。结果表明：所提出的方法能够大幅降低模型的网格数量，减小计算规模，快速准确地计算出混合加载条件下胶层损伤演化和破坏情况。Abstract: In order to ensure the accuracy and convergence of the calculation results, the mesh size of the adhesive layer should be less than 1 mm for the failure analysis of composite adhesive layer using the cohesive zone model. However, when the cohesive zone model is used to analysis a large composite material structure in the aircraft, the model will generate millions of finite elements, which will consume numerous computing resources. Based on the research of the influence of the adhesive properties on the adhesive layer failure analysis, by inversion of the adhesive properties with different mesh sizes, the method that can accurately describe the failure behavior of the adhesive layer by changing the parameters of the adhesive layer to adapt to different mesh sizes was proposed. This method was used to simulate the mixed-mode-bending (MMB) model and composite cylindrical shell model with different mesh sizes. The results show that the method proposed can greatly reduce the number of meshes in the model and the calculation scale, and quickly and accurately calculate the damage evolution and failure of the adhesive layer under mixed loading conditions.
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Key words:
- cohesive zone model /
- adhesive properties /
- mesh size /
- cohesive zone length /
- parameter inversion
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图 2 双悬臂梁(DCB)、端部缺口弯曲(ENF)和混合型弯曲(MMB)有限元模型示意图
Figure 2. Schematic diagram of double cantilever beam (DCB), end-notched flexure (ENF) and mixed-mode-bending (MMB) models
图 3 不同界面强度下TC350-1/IM7-12K复合材料层合板载荷-位移曲线
Figure 3. Load-displacement curves of TC350-1/IM7-12K composite laminates under different interface strengths
${\sigma _{{\rm{nc}}}}$—Tensile strength; ${\sigma _{{\rm{tc}}}}$—Shear strength
图 4 不同界面强度下TC350-1/IM7-12K复合材料层合板胶层内聚区长度
Figure 4. Cohesive zone length of TC350-1/IM7-12K composite laminates under different interface strength values
图 5 不同断裂韧性下TC350-1/IM7-12K复合材料层合板载荷-位移曲线
Figure 5. Load-displacement curves of TC350-1/IM7-12K composite laminates under different fracture toughness
图 6 不同混合值
$ \eta $ 下TC350-1/IM7-12K复合材料层合板BK准则曲线Figure 6. BK rule curves of TC350-1/IM7-12K composite laminates under different values of
$ \eta $ 
图 7 不同
$\eta $ 值下TC350-1/IM7-12K复合材料层合板载荷-位移曲线Figure 7. Load-displacement curves of TC350-1/IM7-12K composite laminates under different values of
$\eta $ 
图 8 不同界面刚度下TC350-1/IM7-12K复合材料层合板载荷-位移曲线
Figure 8. Load-displacement curves of TC350-1/IM7-12K composite laminates under different penalty stiffness K
图 10 TC350-1/IM7-12K复合材料层合板载荷-位移曲线中对比目标点分布
Figure 10. Target point distribution in the load-displacement curve of TC350-1/IM7-12K composite laminate
图 11 DCB有限元模型反演前后TC350-1/IM7-12K复合材料层合板载荷-位移曲线
Figure 11. Load-displacement curves of TC350-1/IM7-12K composite laminates in DCB model before and after inversion
图 12 ENF有限元模型不同网格尺寸下TC350-1/IM7-12K复合材料层合板载荷-位移曲线
Figure 12. Load-displacement curves of TC350-1/IM7-12K composite laminates with different mesh sizes in ENF model
图 13 ENF有限元模型TC350-1/IM7-12K复合材料层合板胶层内聚区长度
Figure 13. Cohesive zone length of TC350-1/IM7-12K composite laminates in ENF model
图 14 混合比0.2时TC350-1/IM7-12K复合材料层合板MMB模型反演后不同网格尺寸下裂纹扩展情况
Figure 14. Crack propagation of MMB model of TC350-1/IM7-12K composite laminates with different mesh sizes after inversion at mixed-mode ratio of 0.2
图 15 不同混合比下TC350-1/IM7-12K复合材料层合板MMB模型载荷-位移曲线
Figure 15. Load-displacement curves of TC350-1/IM7-12K composite laminates in the MMB model with different mixed-mode ratios
图 17 复合材料圆壳模型反演后不同网格尺寸下裂纹扩展情况
Figure 17. Crack propagation of composite circular shell model with different mesh sizes after inversion
图 18 复合材料圆壳模型反演前后不同网格尺寸下载荷-位移曲线
Figure 18. Load-displacement curves of composite circular shell model with different mesh sizes before and after inversion
表 1 碳纤维增强环氧树脂复合材料层合板TC350-1/IM7-12K材料参数[29]
Table 1. Material parameters of TC350-1/TM7-12K carbon fiber reinforced epoxy composite laminates [29]
E1/MPa E2/MPa E3/MPa ${\mu _{12}}$ ${\mu _{13}}$ ${\mu _{23}}$ G12/MPa G13/MPa G23/MPa 158600 9700 9700 0.32 0.32 0.461 5000 5000 3319 Notes: Ei (i=1,2,3)—Elastic modulus in material principle directions; Gij (1≤i<j≤3)—Shear elastic modulus in material principle directions; ${\mu _{ij}}$(1≤i<j≤3)—Poison’s ratio in material principal directions. 
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${\sigma _{{\rm{nc}}}}$/MPa ${\sigma _{{\rm{tc}}}}$/MPa GIC/(kJ·m−2) GIIC/(kJ·m−2) $\eta $ K/(N·mm−3) 36 37 0.741 3.8 1.5 106 Notes: ${\sigma _{{\rm{nc}}}}$—Tensile strength; ${\sigma _{{\rm{tc}}}}$—Shear strength; GIC—Type I fracture toughness; GIIC—Type II fracture toughness; $\eta $—B-K criterion parameter; K—Interface stiffness.
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表 3 TC350-1/IM7-12K复合材料层合板DCB有限元模型J-271胶层参数反演结果
Table 3. Inversion results of J-271 adhesive properties in DCB model of TC350-1/IM7-12K composite laminates
Mesh size/mm ${\sigma _{{\rm{nc}}}}$/MPa GIC/(kJ·m−2) Computation time/s 0.5 36.00 0.741 15 795 1 36.00 0.741 2 160 1.5 35.96 0.741 904 2 29.34 0.741 590 2.5 23.21 0.741 415 3 18.64 0.741 258
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表 4 TC350-1/IM7-12K复合材料层合板不同网格尺寸下的J-271胶层参数
Table 4. Mechanical properties of J-271 adhesive layer of TC350-1/IM7-12K composite laminates with different mesh sizes
Mesh size/mm ${\sigma _{{\rm{nc}}}}$/MPa ${\sigma _{{\rm{tc}}}}$/MPa GIC/(kJ·m−2) GIIC/(kJ·m−2) $\eta $ 0.5 36.00 37 0.741 3.8 1.5 1 36.00 37 0.741 3.8 1.5 1.5 35.96 37 0.741 3.8 1.5 2 29.34 37 0.741 3.8 1.5 2.5 23.21 37 0.741 3.8 1.5 3 18.64 37 0.741 3.8 1.5
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表 5 反演后圆壳模型不同尺寸网格下计算时间
Table 5. Calculation time of circular shell model with different mesh sizes after inversion
Mesh size/mm 0.5 1 1.5 2 2.5 3 Computation time/s 7730 1010 395 238 172 127
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