Multi-objective optimization of adhesively bonded single-lap joints of carbon fiber reinforced polymer laminates based on genetic algorithm
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摘要: 基于遗传算法对碳纤维增强树脂复合材料(CFRP)层合板单搭胶接结构进行了多目标优化，以提高其结构性能。首先，通过三维Hashin准则和三角形内聚力模型建立三维有限元模型来预测CFRP层内损伤过程、层间失效和胶层损伤过程，并通过试验验证其有效性。其次，利用拉丁超立方抽样(LHS)方法和二次多项式响应面法(RSM)，基于搭接长度、胶层厚度和被胶接件宽度等胶接参数建立以拉伸强度和剪切强度为目标函数的多目标优化代理模型。最后，基于遗传算法(GA)对拉伸强度和剪切强度代理模型进行优化，得出一组Pareto解集，并基于理想解排序方法(TOPSIS)对Pareto非劣解集进行折中处理，得到最好的胶接参数设计方案。结果表明：CFRP层合板单搭胶接结构的数值模拟结果与试验结果相比具有很高的吻合度，验证了有限元方法的可靠性；CFRP层合板单搭胶接结构的拉伸强度和剪切强度与搭接长度、胶层厚度和被胶接件宽度具有显著的关联性；二次响应面代理模型结果与数值模拟结果相比误差均小于2.3%；与常规的单搭胶接结构方案进行对比，搭接拉伸强度和剪切强度分别提高了2.65%和17.24%。Abstract: To improve its structural performance, the multi-objective optimization of adhesively bonded single-lap joints of carbon fiber reinforced polymer (CFRP) laminates was carried out based on genetic algorithm. Firstly, finite element (FE) models were constructed using 3D Hashin damage criteria and triangle cohesive zone model (CZM), those well capture the intra-laminar, inter-laminar and adhesive damages during the tensile loads, respectively. And its effectiveness was verified through experiments. Secondly, using the Latin hypercube sampling (LHS) method and polynomial response surface method (RSM), a multi-objective optimization agent model with tensile strength and shear strength as the objective function was established based on lap the length, the adhesive thickness and the width of the bonded parts. Finally, the tensile strength and shear strength agent model was optimized to obtain Pareto solution set based on genetic algorithm (GA), and the Pareto solution set was sequenced by technique for order preference by similarity to ideal solution (TOPSIS) method to obtain the optimized single-bonded joint structure design scheme. The result shows that the experimental measurements of tensile load tests concur with the numerical predictions and validate the FE models. The tensile strength and shear strength of the adhesively bonded single-lap joints of CFRP laminates have a significant correlation with the lap length, the thickness of the adhesive layer and the width of the bonded parts. Compared with the numerical simulation results, the error of the quadratic response surface proxy model results is less than 2.3%. Compared with the conventional single lap bonding structure, the tensile strength and shear strength are increased by 2.65% and 17.24%, respectively.
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Key words:
- composite material /
- single lap /
- surrogate model /
- genetic algorithm /
- multi-objective optimization
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图 1 碳纤维增强树脂复合材料(CFRP)层合板单搭胶接结构试件示意图与WDW-300型万能拉伸试验机
Figure 1. Adhesively bonded single-lap joint of carbon fiber reinforced polymer (CFRP) laminate specimen sketch and WDW-300 universal tensile test machine
图 2 Cohesive单元的双线性本构模型
Figure 2. Bilinear constitutive model of cohesive element
σ and σmax—Interface strength and maximum interface strength; δ0, δmax and δ—Initial separation displacement, maximum separation displacement and separation displacement.
图 3 CFRP层合板单搭接结构有限元模型
Figure 3. Finite element model of CFRP laminate single lap structure
图 4 不同搭接长度的CFRP层合板单搭胶接结构的极限失效载荷
Figure 4. Ultimate failure loads of adhesively bonded single-lap joints of CFRP laminates with different lap lengths
图 5 搭接长度为15 mm的CFRP层合板单搭胶接结构的载荷-位移曲线
Figure 5. Load-displacement curves of single lap bonded structures of CFRP laminates with lap length of 15 mm
图 6 搭接长度对CFRP层合板单搭胶接结构拉伸强度和剪切强度的影响
Figure 6. Effects of lap length on tensile strength and shear strength of adhesively bonded single-lap joints of CFRP laminates
图 7 不同搭接长度CFRP层合板单搭胶接结构的失效模式
Figure 7. Failure modes of adhesively bonded single-lap joints of CFRP laminates with different lap lengths
图 8 不同搭接长度CFRP层合板单搭胶接结构的胶层自身剪切失效 (a)及层合板层间分层失效 (b)
Figure 8. Adhesive shear failure (a) and delamination of laminates (b) of adhesively bonded single-lap joints of CFRP laminates with different lap lengths
图 9 不同搭接宽度的CFRP层合板单搭胶接结构的极限失效载荷变化曲线
Figure 9. Ultimate failure load curves of adhesively bonded single-lap joints of CFRP laminates with different lap widths
图 10 搭接宽度对CFRP层合板单搭胶接结构拉伸强度和剪切强度的影响
Figure 10. Effects of lap width on tensile strength and shear strength of adhesively bonded single-lap joints of CFRP laminates
图 11 不同搭接宽度CFRP层合板单搭胶接结构的失效模式
Figure 11. Failure modes of adhesively bonded single-lap joints of CFRP laminates with different lap widths
图 12 不同搭接宽度CFRP层合板单搭胶接结构的胶层自身剪切失效 (a)及层合板层间分层失效 (b)
Figure 12. Adhesive shear failure (a) and delamination of laminates (b) of adhesively bonded single-lap joints of CFRP laminates with different lap widths
图 13 不同情况下CFRP层合板单搭胶接结构失效载荷F的三维分布和等值线分布
Figure 13. Three-dimensional distribution and contour distribution of failure load F of adhesively bonded single-lap joints of CFRP laminates under different conditions
图 14 CFRP层合板单搭胶接结构Pareto前沿
Figure 14. Pareto front of adhesively bonded single-lap joints of CFRP laminates
表 1 T300/7901碳纤维/环氧树脂复合材料层合板力学参数[23-24]
Table 1. Mechanical properties of T300/7901 carbon fiber/epoxy resin composite laminate
Property Value Young’s modulus E11/MPa 125 000 Young’s modulus E22,E33/MPa 11 300 Shear modulus G12,G13/MPa 5 430 Shear modulus G23/MPa 3 980 Poisson’s ratio v12,v13 0.3 Poisson’s ratio v23 0.42 Longitudinal tensile strength Xt/MPa 2 000 Longitudinal compressive strength Xc/MPa 1 100 Transverse tensile strength Yt/MPa 80 Transverse compressive strength Yc/MPa 280 Shear strength S/MPa 120 Interface stiffness Knn, Kss, Ktt/(N·mm−3) 105 Maximum normal traction $t_{\rm{n}}^0$/MPa 50 Maximum shear traction $t_{\rm{s}}^0$, $t_{\rm{t}}^0$/MPa 90 Toughness in tension $G_{\rm{n}}^{\rm{C}}$/(kJ·m−2) 0.52 Toughness in shear $G_{\rm{s}}^{\rm{C}}$, $G_{\rm{t}}^{\rm{C}}$/(kJ·m−2) 0.92 
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表 2 LJM-170胶膜的力学参数[25]
Table 2. Mechanical properties of adhesive film LJM-170
Property Value Young’s modulus E/MPa 2 200 Shear modulus G/MPa 815 Tensile strength $t_{\rm{n}}^0$/MPa 31.9 Shear strength $\tau _{\rm{s}}^0$, $\tau _{\rm{t}}^0$/MPa 21.2 Toughness in tension $G_{\rm{n}}^{\rm{C}}$/(kJ·m-2) 0.48 Toughness in shear $G_{\rm{s}}^{\rm{C}}$, $G_{\rm{t}}^{\rm{C}}$/(kJ·m-2) 1.83
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表 3 CFRP层合板单搭胶接结构代理模型样本点与对应的模拟结果
Table 3. Samples and corresponding simulation results of agent model of adhesively bonded single-lap joints of CFRP laminates
Sample number L/mm T/mm W/mm F/N σ/MPa τ/MPa 1 16.82 0.081 27.97 10734 106.61 22.82 2 10.80 0.128 23.98 7876 91.230 30.41 3 18.99 0.134 29.71 11605 108.50 20.57 4 11.89 0.105 20.01 6868 95.340 28.87 5 18.16 0.123 25.71 9930 107.28 21.27 6 20.23 0.095 18.93 7523 110.39 19.64 7 14.24 0.143 28.76 10511 101.52 25.67 8 11.63 0.109 26.84 9181 95.010 29.41 9 15.43 0.158 19.00 7007 102.44 23.90 10 15.15 0.120 23.97 8911 103.26 24.54 11 17.55 0.151 21.83 8290 105.49 21.64 12 12.69 0.092 22.94 8125 98.390 27.91 Notes：L—Lap the length; T—Adhesive thickness; W—Width of the bonded parts; F—Ultimate failure load; σ—Tension strength; τ—Shear strength.
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表 4 CFRP层合板单搭胶接结构代理模型检验样本的τ和σ估计值与模拟值对比
Table 4. Comparison between the estimated by agent model and simulated values of τ and σ for the test samples of adhesively bonded single-lap joints of CFRP laminates
Sample number L/mm T/mm W/mm τ/MPa σ/MPa Estimated value Analog value Relative error/% Estimated value Analog value Relative error/% 1 10.91 0.112 25.33 30.43 30.33 0.33 92.360 91.920 0.477 2 18.92 0.146 21.62 20.44 20.45 0.049 107.28 107.47 0.177 3 17.26 0.113 29.04 22.33 22.23 0.45 107.22 106.58 0.600 4 14.60 0.090 24.95 25.38 25.37 0.039 102.82 102.93 0.166 5 13.30 0.130 18.62 26.77 27.38 2.23 98.900 101.15 2.220
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表 5 CFRP层合板单搭胶接结构多目标优化方案排序结果
Table 5. Ranking result of the multi-objective optimization schemes of adhesively bonded single-lap joints of CFRP laminates
Sample number Parameter value Target value Standardized indicators Euclide-an
distance
from positive
ideal solutionEuclide-an
distance
from negative
ideal solutionRelative
proximityResult L/
mmT/
mmW/
mmσ/
kNτ/
MPaσ τ 1 14.51 0.082 10.57 108.21 25.99 0.3099 0.3312 0.0160 0.0484 0.7516 3 2 15.48 0.08 12.74 108.91 24.69 0.3119 0.3146 0.0261 0.0320 0.5508 6 3 16.05 0.08 10 112.11 24.28 0.3211 0.3094 0.0281 0.0294 0.5113 7 4 14.14 0.083 10 107.72 26.47 0.3085 0.3373 0.0162 0.0545 0.7709 2 5 16.16 0.08 10 112.33 24.15 0.3217 0.3078 0.0297 0.0283 0.4879 9 6 15.84 0.084 11.73 110.14 24.34 0.3154 0.3102 0.0287 0.0283 0.4965 8 7 14.62 0.08 10 109.42 25.91 0.3134 0.3302 0.0133 0.0477 0.782 1 8 15.74 0.081 10 111.51 24.62 0.3193 0.3138 0.0241 0.0328 0.5764 5 9 17.91 0.08 12.02 113.37 22.19 0.3247 0.2828 0.0545 0.0162 0.2291 10 10 15.19 0.08 10 110.35 25.24 0.3160 0.3217 0.0179 0.0396 0.6887 4
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