Inner stress field in epoxy resin with moisture absorption
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摘要: 环氧树脂及其制品因其优良性能广泛应用在船舶制造中，长期在潮湿环境中服役时，基体吸收水分易引起膨胀翘曲等变形，进而引发失效隐患。本文采用重量分析试验、光纤布拉格光栅(FBG)传感器应变监测技术，确定了环氧树脂中的饱和吸湿量、水分扩散系数和湿膨胀系数等吸湿系数，在此基础上构建了能够预测环氧树脂中随时间变化的水分扩散及应力场分布的湿-力模型，用有限元方法实现了对随吸湿时间变化的树脂中应力场的数值模拟。并结合相移数字光弹试验方法，将数值模拟结果与试验结果进行了比较，显示了良好的一致性，发现环氧树脂吸湿过程中切应力随时间呈现出先升后降的趋势。Abstract: Epoxy and epoxy-based components have been extensively used in marine industry due to their excellent performance. When exposed to moist environment, the matrix of such materials absorbs significant amount of water and damages are caused including warpage, expansion and other deformations. In this study, weight analysis experiment were carried out and fibre Bragg grating (FBG) sensors were used to monitor the effects of moisture absorption. The maximum water absorption, water diffusion coefficient, and coefficients of moisture expansion were determined thereafter. Numerical simulation was then built accordingly by finite element method to predict the evolution of moisture absorption and the stress field developed in the epoxy resin. Finally, the simulation results were compared with the experimental ones by phase-shift digital photoelastic method and good agreement is achieved. The shearing stresses in the resin show the trend of initial increase and later decline during the course of water absorption.
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图 1 光纤布拉格光栅(FBG)埋置位置与试样尺寸
Figure 1. Embedding position of fibre Bragg grating (FBG) and dimension of test piece
Φ—Diameter
图 3 平面环氧树脂模型
Figure 3. Plate epoxy resin model
a—0.5 mm from the border; b—Central area
图 4 平面偏振光场元件及布置
Figure 4. Planar polarized light field set-up
$\alpha $—Angle between the transmission axis of the polarizer and the horizontal reference axis; $\beta $—Angle between the transmission axis of the analyser and the horizontal reference axis; P—Polarization direction of polarizer; A—Polarization direction of analyzer; ${\sigma _1}$,${\sigma _2}$—Principal stresses (${\sigma _1}$>${\sigma _2}$); CCD—Charge-coupled device; θ—Angle between the principal stress σ1 and the x axis direction
图 5 圆偏振光场元件及布置
Figure 5. Circularly polarized light field set-up
$\xi $—Angle between the horizontal reference axis and the fast axis of the input (P) quarterwave plate; $\eta $—Angle between the horizontal reference axis and the slow axis of the output (A) quarterwave plate; F—Fast axis of the output or the input quarter-wave plate; S—Slow axis of the output or the input quarter-wave plate
图 6 对径压缩试验
Figure 6. Diameter compression experiment
D—Round set diamter; P—Diametrically compressed load
图 7 DER330-DER732树脂的水分浓度与浸泡时间平方根的关系
Figure 7. Dependence of the moisture content in DER330-DER732 resin on the square root of immersion time
图 8 DER330-DER732树脂应变随平均水分浓度的变化
Figure 8. Dependence of the strains on average moisture absorption in DER330-DER732 resin
图 9 DER330-DER732树脂杨氏模量随水分浓度变化曲线
Figure 9. Experimental Young’s modulus of DER330-DER732 resin vs. water absorption
图 10 未吸湿DER330-DER732树脂与65天吸湿DER330-DER732树脂FTIR图谱
Figure 10. FTIR spectra of the dry (0 day) and soaked DER330-DER732 resin samples (65 days)
图 11 DER330-DER732树脂对径压缩试验图像
Figure 11. Images of diameter compression experiment of DER330-DER732 resin
图 12 DER330-DER732树脂圆偏振光场中吸湿过程中等差线条纹的变化
Figure 12. Evolution of the isochromatic fringes of DER330-DER732 resin during absorption obtained in a circular field polariscope
图 15 在吸湿15 h时DER330-DER732树脂应力光弹分析结果
Figure 15. Stresses distributions of DER330-DER732 resin at 15 h
txy—Shear stress xy; σx—Stress in the x direction; σy—Stress in the y direction
图 16 在15 h、39 h、63 h、159 h、255 h、351 h时DER330-DER732树脂切应力τxy光弹分析结果
Figure 16. Photoelastic results of shear stresses τxy of DER330-DER732 resin at 15 h, 39 h, 63 h, 159 h, 255 h, 351 h
图 17 沿路径a在15 h、39 h、63 h、159 h、255 h、351 h时DER330-DER732树脂切应力τxy的光弹分析结果
Figure 17. Photoelastic results of the shear stresses τxy of DER330-DER732 resin at 15 h, 39 h, 63 h, 159 h, 255 h, 351 h along path a
图 18 在15 h、39 h、63 h、159 h、255 h、351 h时DER330-DER732树脂切应力τxy的数值模拟结果
Figure 18. Numerical results of shear stresses τxy of DER330-DER732 resin at 15 h, 39 h, 63 h, 159 h, 255 h, 351 h
图 19 在15 h、39 h、63 h、159 h、255 h、351 h时沿路径a的DER330-DER732树脂切应力τxy的数值结果
Figure 19. Numerical results of the shear stresses τxy of DER330-DER732 resin at 15 h, 39 h, 63 h, 159 h, 255 h, 351 h along path a
图 20 在15 h、39 h、63 h、159 h、255 h、351 h时DER330-DER732树脂切应力τxy最大值与最小值曲线
Figure 20. Maximum and minimum of shear stresses τxy of DER330-DER732 resin at 15 h, 39 h, 63 h, 159 h, 255 h, 351 h
表 1 左右六步相移法的偏振光场设置与光强等式
Table 1. Polarized light field set-up and light intensities equations of six phase steps method
Α/(°) ξ/(°) η/(°) β/(°) Light intensities 90 135 45 90 I1 90 135 45 0 I2 90 135 0 0 I3 90 135 45 45 I4 90 45 0 0 I5 90 45 135 45 I6 
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表 2 四步相移法的偏振光场设置与光强等式
Table 2. Polarized light field set-up and light intensities equations of four phase steps method
α/(°) β/(°) Light intensities equation 90 0 I7 112.5 22.5 I8 135 45 I9 157.5 67.5 I10
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