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一种灌封结构用环氧树脂的固化行为表征和模拟

丁安心 俞星辰 杨鹏 康峻铭 倪爱清 王继辉 李小阳

丁安心, 俞星辰, 杨鹏, 等. 一种灌封结构用环氧树脂的固化行为表征和模拟[J]. 复合材料学报, 2022, 39(4): 1824-1833. doi: 10.13801/j.cnki.fhclxb.20210726.004
引用本文: 丁安心, 俞星辰, 杨鹏, 等. 一种灌封结构用环氧树脂的固化行为表征和模拟[J]. 复合材料学报, 2022, 39(4): 1824-1833. doi: 10.13801/j.cnki.fhclxb.20210726.004
DING Anxin, YU Xingchen, YANG Peng, et al. Characterization and simulation on the cure behavior of epoxy resin for encapsulation structure[J]. Acta Materiae Compositae Sinica, 2022, 39(4): 1824-1833. doi: 10.13801/j.cnki.fhclxb.20210726.004
Citation: DING Anxin, YU Xingchen, YANG Peng, et al. Characterization and simulation on the cure behavior of epoxy resin for encapsulation structure[J]. Acta Materiae Compositae Sinica, 2022, 39(4): 1824-1833. doi: 10.13801/j.cnki.fhclxb.20210726.004

一种灌封结构用环氧树脂的固化行为表征和模拟

doi: 10.13801/j.cnki.fhclxb.20210726.004
基金项目: 国家自然科学基金(11902231);中央高校基本科研业务费专项资金(203201006;203101002)
详细信息
    通讯作者:

    李小阳,博士,助理研究员,研究方向为高分子功能化与高性能化  E-mail:lixiaoyang20181314@163.com

  • 中图分类号: TB334

Characterization and simulation on the cure behavior of epoxy resin for encapsulation structure

  • 摘要: 以中高温固化的E39D环氧树脂为研究对象,基于顺序耦合热传导-固化和应力位移模块的数值仿真方法,选择合适的实验方法测试环氧树脂的固化性能,引入相关假设,推导与热传导-固化和应力位移模块相关的树脂固化性能参数和模型;然后,建立典型E39D树脂灌封结构的数值模型,模拟结构内部观测点在固化过程中的温度和应力演变,并基于FBG监测技术,与实验测试所得的观察点温度和应变进行对比;结果显示两者温度误差最大值为8.2%,应变的最大误差为17.3%,验证了固化性能参数测试方法和引入假设的合理性。

     

  • 图  1  E39D树脂在不同固化温度下的差示扫描量热(DSC)热流曲线

    Figure  1.  Heat flow curves of E39D resin at different cure temperatures using differential scanning calorimetry (DSC)

    图  2  E39D树脂储能剪切模量变化

    Figure  2.  Development of storage shear modulus for E39D resin

    图  3  不同固化度下E39D树脂玻璃化转变温度

    Figure  3.  Glass transition temperature for E39D resin with different degrees of cure

    图  4  E39D树脂化学收缩应变随固化度的变化

    Figure  4.  Development of chemical shrinkage strain with degree of cure for E39D resin

    图  5  降温阶段E39D树脂热膨胀应变随温度的变化

    Figure  5.  Development of thermal expansion strain with temperature for E39D resin under cool-down stage

    图  6  灌封结构用E39D树脂结构尺寸和有限元模型

    Figure  6.  Dimension and finite element model of encapsulation structure composed of E39D resin

    图  7  E39D树脂的固化工艺曲线

    Figure  7.  Cure cycle for E39D resin

    图  8  光纤布拉格光栅(FBG)工作原理图

    Figure  8.  Schematic of working principle for Fiber Bragg Grating (FBG)

    λB—Central wavelength; LS—Gate distance; λincident—Incident spectrum; λref—Reflectance spectrum; neff—Effective refractive index of the grating; Λ—Grating period

    图  9  固化结束后E39D树脂温度(a)和Z方向的应变云图(b)

    Figure  9.  Contour of temperature (a) and strain in Z-direction (b) for E39D resin after curing

    图  10  E39D树脂灌封结构数值仿真的B点温度、固化度和Z方向应变历程曲线

    Figure  10.  Curves of numerically simulated strain in Z-direction and temperature as well as degree of cure for B point of E39D resin encapsulated structure

    图  11  E39D树脂灌封结构B点在原始工艺下温度和Z方向的应变曲线

    Figure  11.  Curves of strain in Z-direction and temperature for B point of E39D resin encapsulated structure

    图  12  E39D树脂灌封结构B点在预设固化工艺下的实验和模拟温度曲线对比

    Figure  12.  Comparison of experimental and simulated temperature curves for B point of E39D resin encapsulated structure in prescribed cure cycle

    图  13  E39D树脂灌封结构B点在预设固化工艺下的实验和模拟应变曲线对比

    Figure  13.  Comparison of experimental and simulated strain curves for B point of E39D resin encapsulated structure in prescribed cure cycle

    符号定义符号定义
    A前因子Tg玻璃化转变温度
    C比热容t时间
    dα/dt固化速率α固化度
    E活化能αgel凝胶点
    G剪切模量Δε应变变化
    HR单位质量树脂的
    固化反应总热量
    Δεthe热膨胀导致的
    应变变化
    K固化反应速率常数Δεche化学收缩产生的
    应变变化
    k导热系数ν泊松比
    l常数ρ密度
    $\dot Q$材料内部产生的热量x,y,z坐标轴
    R气体常数下标u树脂未固化
    T温度下标c树脂固化结束
    TcTgT的差值下标1, 2, 3表示某个参数
    或性能特定值
    下载: 导出CSV

    表  1  常用树脂固化动力学模型

    Table  1.   Commonly used cure kinetics model of resin

    Cure kinetics modeldα/dtParameter
    n order model[17] $K{(1 - \alpha )^n}$ $A,E,n,K$
    Prount-Tompkins model[18] $K{\alpha ^m}{(1 - \alpha )^n}$ $A,E,m,n,K$
    Kamal model[19] $\dfrac{{{\rm{d}}\alpha }}{{{\rm{d}}t}} = \dfrac{{({K_1} + {K_2}{\alpha ^m}){{\left( {1 - \alpha } \right)}^n}}}{{1 + {{\rm{e}}^{D\left( {\alpha - {\alpha _{\rm{c}}}} \right)}}}}$ $A,E,m,n,{K_1},{K_2},D,{\alpha _c}$
    Gonzalez—Romeroand Casillas model[20] $\dfrac{{{\rm{d}}\alpha }}{{{\rm{d}}t}} = K{({\alpha _{\max }} - \alpha )^n}{{\rm{e}}^{m\alpha }}$ $A,E,m,K$
    Notes: dα/dt and α—Cure rate of resin and degree of cure; K, K1, K2—Reaction rate constants; A—Pre-exponential coefficient; E—Activation energy; αc—Temperature-dependent critical degree of cure; m and n—First and second exponential constants; D—Diffusion constant.
    下载: 导出CSV

    表  2  E39D树脂固化动力学模型参数值

    Table  2.   Parametric values of cure kinetics for E39D resin

    ParameterValue
    A/(106S−1) 1.38
    E/(104J·mol−1) 6.87
    m 0.3
    n 1.7
    D 30
    αc0 4.6
    αcT −0.01
    Note: αc0, αcT—Two fitting coefficients.
    下载: 导出CSV

    表  3  E39D树脂固化剪切模量模型的参数值

    Table  3.   Parameter values of curing shear modulus model for E39D resin

    ParameterValue
    α 0.48
    T1/K −5
    T2/K 5
    G1/MPa 3.5
    G2/GPa 1.0
    Notes: α—Degree of cure; T1 and T2—Temperature values at different critical points; G1 and G2—Shear moduli values at different states.
    下载: 导出CSV

    表  4  E39D树脂固化实验和模拟结果的对比

    Table  4.   Comparison of experimental and simulated results of E39D resin curing

    ItemMagnitude of
    temperature
    (100℃ stage)/℃
    Strain value
    (25℃)/10−6
    Experimental value 120.1 −13436.8
    Simulated result 110.3 −11107.5
    Error/% 8.2 17.3
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-04-08
  • 修回日期:  2021-07-08
  • 录用日期:  2021-07-13
  • 网络出版日期:  2021-07-27
  • 刊出日期:  2022-04-01

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