Characterization and simulation on the cure behavior of epoxy resin for encapsulation structure
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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。Abstract: Based on simulation method which sequentially couples the heat transfer-cure and stress deformation modules for cure behavior, cure-related parameters were tested using adequate approaches for medium-high temperature curing resin E39D. In combination with reasonable hypotheses, curing resin property parameters or model which are related to heat transfer-cure and stress deformation modulus were derived. Then, finite element model of typical encapsulation structure containing E39D resin was built to simulate evolution of temperature and stress of the chosen point in the encapsulation structure, and the experimentally measured temperature and stress curves of the chose point were also given by means of Fiber Bragg Grating (FBG) monitoring technique. It can be observed that 8.2% maximum discrepancy in temperature and 17.3% maximum discrepancy in strain between experimental and numerical results exist, showing the validity of accepted assumptions and characterization methods.
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Key words:
- epoxy resin /
- cure simulation /
- encapsulation structure /
- residual/internal stress /
- Fiber Bragg Grating
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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 Tc Tg与T的差值 下标1, 2, 3 表示某个参数
或性能特定值表 1 常用树脂固化动力学模型
Table 1. Commonly used cure kinetics model of resin
Cure kinetics model dα/dt Parameter 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. 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
Parameter Value 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. 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
Parameter Value 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. 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
Item Magnitude of
temperature
(100℃ stage)/℃Strain value
(25℃)/10−6Experimental value 120.1 −13436.8 Simulated result 110.3 −11107.5 Error/% 8.2 17.3 -
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