Multiscale Simulation Method for Anti-Penetration of Fiber-Reinforced Composite Laminates
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摘要: 针对纤维增强复合材料层合板结构设计和抗侵彻数值仿真需要大量材料参数和动态试验数据的问题，以碳纤维增强复合材料层合板为研究对象，采用多尺度模拟方法，实现了纤维丝-纤维束-层合板的微观-介观-宏观力学性能和抗侵彻能力的全流程数值仿真预测。首先，建立微观代表性体积单元（representative volume elements，RVE），基于最大应力准则，预测出纤维束的力学性能；然后，根据编织结构的空间特征建立介观RVE模型，采用Hashin和Hou的失效准则，预测出宏观等效力学性能；最后，根据已发表的试验数据，建立了宏观弹道侵彻数值模型，提出了一种考虑材料应变率效应的改进Hashin失效准则，进而研究了弹道侵彻作用下纤维增强复合材料层合板的剩余速度和损伤特征。结果表明：试验与仿真得到的剩余速度的相对误差在5%以内，宏观数值模型准确捕捉到了纤维断裂、层间分层等损伤模式，验证了多尺度模拟方法的合理性和准确性；拟合得到了弹道极限速度随板厚变化的关系式，两者呈线性关系，且相关系数达0.97以上。研究结果有助于实现纤维增强复合材料层合板抗侵彻的低成本、短周期结构设计，对纤维增强复合材料层合板的正向性能预测和逆向结构设计均具有重要的科学和工程应用价值。Abstract: Aiming at the problem that a large number of material parameters and required for the structural design and numerical simulation of penetration resistance of fiber reinforced composite laminates, this article takes carbon fiber reinforced composite laminates as the research object, and adopts multi-scale simulation method to realize the whole process numerical simulation prediction of micro-, meso-, and macro-scale mechanical properties and penetration resistance of fiber-bundle-laminates. Firstly, microscopic representative volume elements (RVE) were established to predict the mechanical properties of fiber bundles based on the maximum stress criterion. Then, based on Hashin and Hou’s failure criteria, the macroscopic equivalent mechanical properties were predicted by the mesoscopic RVE models established according to the spatial characteristics of braided structures. Finally, an improved Hashin failure criterion considering the strain rate effect was proposed, and the numerical model of ballistic penetration was established based on the literature tests to study the residual velocities and damage characteristics. The results show that the errors of residual velocity results are less than 5%, and the macroscopic numerical models can accurately simulate the damage modes such as fiber fracture as well as interlayer delamination, which verifies the rationality and accuracy of multi-scale simulation method in this article. The relationship between the ballistic limit velocity and the thickness of the plate is linear and the correlation coefficient is above 0.97. The findings of this paper can help to realize the design of low-cost and short-period fiber reinforced composite laminates, which has important scientific and engineering application values for property prediction and inverse structural design of fiber reinforced composite laminates.
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Ef1/GPa Ef2/GPa Ef3/GPa Gf12/GPa μf12 μf13 μf23 Xft/MPa Xfc/MPa 221 13.81 13.81 9 0.27 0.27 0.30 3530 2470 
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Em/GPa μm Smt/MPa Smc/MPa Sms/MPa 3.55 0.33 80 241 60
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表 3 介观RVE模型参数
Table 3. Parameters of mesoscopic RVE model
L/mm W/mm ht/mm a0/mm a1/mm 4.00 1.75 0.10 0.25 1.50
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表 4 纤维束刚度参数计算结果
Table 4. Results of fiber bundle stiffness parameters
Method Elastic modulus/GPa Shear modulus/GPa Poisson’s ratio E1 E2 E3 G12 G13 G23 $ {\mu }_{12} $ $ {\mu }_{13} $ $ {\mu }_{23} $ Simulation 177.69 10.14 10.14 5.36 5.36 3.51 0.280 0.280 0.350 Equation 177.51 10.58 10.58 5.60 5.60 3.77 0.282 0.282 0.369 Error/% 0.10 −4.17 −4.17 −4.33 −4.33 −6.83 −0.71 −0.71 −5.06
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表 5 纤维束强度参数计算结果
Table 5. Results of fiber bundle strength parameters
Method Tension strength/MPa Compressive strength/MPa Shear strength/MPa Xt Yt Zt Xc Yc Zc S12 S13 S23 Simulation 2865.11 72.72 72.72 1938.67 208.44 208.44 64.50 64.50 52.26 Equation 2835.34 74.39 74.39 1983.94 224.09 224.09 Error/% 1.05 −2.24 −2.24 −2.28 −6.99 −6.99
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表 6 宏观等效力学参数对比
Table 6. Comparison of macroscopic equivalent mechanical parameters
Method E1/GPa E2/GPa E3/GPa G12/GPa G13/GPa G23/GPa Xt/MPa Simulation 56.50 56.50 7.90 3.59 2.51 2.51 740.37 Test[15] 57.94 57.94 3.59 726 Error/% −2.49 −2.49 0 1.98 Method Yt/MPa Xc/MPa Yc/MPa S12/MPa S13 /MPa S23/MPa Simulation 740.37 630.34 630.34 64.95 62.88 62.88 Test[15] 726 113.29 65.82 65.82 Error/% 1.98 −42.67 −4.47 −4.47
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$ {t}_{\mathrm{n}}^{0} $/MPa $ {t}_{\mathrm{s}}^{0} $/MPa $ {t}_{\mathrm{t}}^{0} $/MPa $ {G}_{\mathrm{c}}^{{Ⅰ}} $/(kJ·m−2) $ {G}_{\mathrm{c}}^{{Ⅱ}} $/(kJ·m−2) $ {G}_{\mathrm{c}}^{{Ⅲ}} $/(kJ·m−2) 50 90 90 0.52 0.92 0.92
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表 8 仿真与试验得到的剩余速度和单位面密度吸能的对比
Table 8. Comparison of residual velocity and energy absorption per unit surface density between simulation and test
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表 9 不同板厚下的拟合参数
Table 9. Fitting parameters under different plate thicknesses
h/mm a p 4.4 0.897 2.089 5.7 0.884 2.051 6.6 0.856 2.104 7.7 0.837 2.030 8.8 0.800 2.164 9.9 0.805 2.032
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