Simulation of curing process of epoxy resin with embedded FBGs considering interfacial strain transfer mechanism
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摘要: 采用实验与数值分析相结合的手段对光纤布拉格光栅传感器(Fiber Bragg grating sensor，FBGs)与基体间应变传递机制这一固化监测的基础问题进行了探索。首先，对树脂的固化动力学、热膨胀、化学收缩和玻璃化转变等物化变化进行了表征，然后，借助热电偶和FBGs开展了环氧树脂固化过程的温度和应变监测实验，最后，基于固化过程热-化-力多场耦合数值分析方法开展了固化过程模拟。通过对比纯树脂模型、界面采用绑定约束的含FBGs模型和界面采用内聚力行为的含FBSs模型分析结果，对界面传递机制进行了探讨。结果表明：固化前期界面处存在的剪滞效应和界面滑移行为导致FBGs监测应变相较树脂本体应变明显偏小，其中剪滞效应占主导作用。采用内聚力行为可以较好地描述固化过程界面应变传递机制，数值预测结果与实验值误差较小。
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关键词:
- 固化监测 /
- 界面 /
- 应变传递 /
- 光纤布拉格光栅传感器(FBGs) /
- 数值分析
Abstract: The strain transfer mechanism between fiber Bragg grating sensor (FBGs) and matrix, which is the basic problem of cure monitoring, was explored by combining of experimental and numerical analysis. Firstly, curing kinetics, thermal expansion, chemical shrinkage and glass transition behavior of the resin were characterized. Then, the developments of temperature and strain were monitored by thermocouple and FBGs during the curing process of epoxy resin. Finally, the thermal-chemical-mechanical multi-field coupling numerical analysis was used to simulate the curing process. The interface transfer mechanism was discussed by comparing the results of pure resin model, FBGs model with binding constraint and FBSs model with cohesive behavior. The results indicate that the strain monitored by FBGs is significantly smaller than that of the resin due to the shear lag effect and interface slip behavior at the early curing stage, and the shear lag effect plays a dominant role. The interfacial strain transfer mechanism during curing process can be described properly by cohesive behavior, and the error between numerical prediction and experimental value is small.-
Key words:
- cure monitoring /
- interface /
- strain transfer /
- fiber Bragg grating sensor (FBGs) /
- numerical analysis
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图 1 2511-1 A/BS树脂的动态升温DSC的热流曲线
Figure 1. Heat flow curves of dynamic DSC of 2511-1 A/BS resin
图 2 2511-1 A/BS环氧树脂玻璃化转变温度与固化度的关系
Figure 2. Relationship between glass transition temperature and curing degree of 2511-1 A/BS epoxy resin
图 3 2511-1 A/BS环氧树脂DMA测试的力学性能变化
Figure 3. Mechanical properties of 2511-1 A/BS epoxy resin by DMA testing
图 4 2511-1 A/BS环氧树脂TMA测试热膨胀系数的结果
Figure 4. TMA test results of thermal expansion coefficient of 2511-1 A/BS epoxy resin
△L—Change of length; L0—Initial length
图 5 2511-1 A/BS环氧树脂的化学收缩率随固化度变化曲线
Figure 5. Chemical shrinkage curve of 2511-1 A/BS epoxy resin with curing degree
αgel—Curing degree of gel point; ΔV—Chang of volume; V0—Initial volume of resin
图 6 光纤布拉格光栅传感器(FBGs)和热电偶的位置
Figure 6. Position of fiber Bragg grating sensor (FBGs) and thermocouple
TC—Thermocouple
图 7 树脂固化过程热-化-力多场耦合数值分析的流程
Figure 7. Process of thermo-chemical-mechanical coupling numerical analysis of resin curing process
图 9 热电偶位置的实验与模拟的内埋FBGs环氧树脂温度对比及固化度历程
Figure 9. Experimental and simulated temperature comparison and curing degree history of thermocouple position of epoxy resin with embedded FBGs
FEM—Finite element model
图 10 温度峰值时模拟的内埋FBGs环氧树脂温度和固化度分布
Figure 10. Simulated temperature and curing degree distributions at peak temperatures of epoxy resin with embedded FBGs
图 11 纯树脂模型模拟的热电偶位置的内埋FBGs环氧树脂温度和应变历程曲线
Figure 11. Temperature and strain history curves of thermocouple positions of epoxy resin with embedded FBGs simulated by pure resin model
图 12 纯树脂模型和Tie模型模拟的内埋FBGs环氧树脂应变历程与实验测试的对比
Figure 12. Comparison of strain history of epoxy resin with embedded FBGs simulated by pure resin model and Tie model with experimental tests
图 13 Tie模型和Cohesive模型模拟的内埋FBGs环氧树脂应变历程与实验测试的对比
Figure 13. Comparison of strain history simulated by Tie model and cohesive model with experimental tests of epoxy resin with embedded FBGs
图 14 3种模型固化结束时内埋FBGs环氧树脂位移云图
Figure 14. Displacement contour of epoxy resin with embedded FBGs at the end of curing for the three models
表 1 2511-1 A/BS环氧树脂在80℃恒温固化不同时间后的玻璃化转变温度和固化度
Table 1. Glass transition temperature and curing degree of 2511-1 A/BS epoxy resin after curing at 80℃ for different time
t/min Tg/℃ α 60 25 0.734 120 33 0.864 180 59.7 0.925 300 75 0.985 − −67.7 0 − 81.6 1 Notes：t—Resin curing time; Tg—Glass transition temperature; α—Curing degree of resin. 
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表 2 2511-1 A/BS环氧树脂热膨胀系数的参数值
Table 2. Parameter values of thermal expansion coefficients of 2511-1 A/BS epoxy resin
Parameter Value T1/K 2 T2/K 12 αEXP1/℃−1 89.5×10−6 αEXP2/℃−1 194.5×10−6 Notes: T1 and T2—Fitting values; αEXP1 and αEXP2—Fitting values of elastic modulus.
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表 3 热分析中树脂的热特性
Table 3. Thermal properties of resins in thermal analysis
Parameter Value ρr/(kg·m−3) 1088 Cpr/(J·(kg·K)−1) 1800-1500 kr/(W·(m·K)−1) 0.16 Notes: ρr—Density of resin; Cpr—Specific heat capacity of resin; kr—Thermal conductivity coefficient of resin.
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表 4 FBGs的计算参数
Table 4. Calculation parameters of FBGs
Parameter Value ρFBGs/(kg·m−3) 2500 CpFBGs/(J·(kg·K)−1) 966 kFBGs/(W·(m·K)−1) 1.1 EFBGs/MPa 72000 νFBGs 0.22 αFBGs 0 Notes: ρFBGs—Density of FBGs; CpFBGs—Specific heat capacity of FBGs; kFBGs—Thermal conductivity coefficient of FBGs; EFBGs—Elastic modulus of FBGs; νFBGs—Poisson's ratio of FBGs; αFBGs—Coefficient of thermal expansion of FBGs.
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表 5 实验和仿真的内埋FBGs环氧树脂温度峰值对比
Table 5. Comparison of experimental and simulated temperature peaks of epoxy resin with embedded FBGs
Location Test FEM ∆/% Tp/℃ tm/min Tp/℃ tm/min TC1 165 46.5 164 46.5 0.6 TC2 153 46.7 159 47.0 3.9 TC3 131 47.0 134 47.7 2.3 Notes: Tp—Peak temperature; tm—Time corresponding to peak temperature; ∆—Peak temperature error between simulation and experiment.
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表 6 实验和3种模型计算的内埋FBGs环氧树脂固化应变对比
Table 6. Comparison of curing strain of epoxy resin with embedded FBGs calculated by experiment and 3 models
Parameters Test Without FBGs Tie Cohesive Strain/10−6 −3826.4 −26356.7 −5870.9 −4053.2 ∆/% — 589.0 53.4 5.9 Note: ∆—Strain error of simulation relative to experiment.
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