Micromechanical model of tensile properties of poplar fiber/polyethylene composite
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摘要: 制备了不同杨木纤维含量的杨木纤维/聚乙烯复合材料，利用Hirsch模型、Kelly-Tyson模型和Bowyer-Bader模型对杨木纤维/聚乙烯复合材料的微观力学进行建模，通过对杨木纤维/聚乙烯复合材料及塑料基体的拉伸应力-应变曲线和杨木纤维长度分布的研究，计算得到杨木纤维在聚乙烯基体中的取向系数、界面剪切强度和本征抗拉强度，解释了杨木纤维/聚乙烯复合材料拉伸性能的变化规律。此外，利用微观力学模型计算得到了亚临界纤维、超临界纤维、塑料基体对杨木纤维/聚乙烯复合材料拉伸强度的贡献比例。
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关键词:
- 微观力学 /
- 纤维含量 /
- 拉伸性能 /
- Kelly-Tyson模型 /
- Bowyer-Bader模型
Abstract: The poplar fiber/polyethylene composites with different contents of poplar fiber were prepared. The micromechanics of poplar fiber/polyethylene composites were modeled by Hirsch model, Kelly-Tyson model and Bowyer-Bader model. By studying the tensile stress-strain curves of the poplar fiber/polyethylene composite and plastic matrix and the length distribution of poplar fiber in the composite, the orientation coefficient, interfacial shear strength and intrinsic tensile strength of poplar fiber in polyethylene matrix were calculated, and the variation law of the tensile properties of poplar fiber/polyethylene composites was explained. In addition, the contribution ratio of subcritical fiber, supercritical fiber, plastic matrix to the tensile strength of poplar/polyethylene composites was obtained by using micromechanical model calculation.-
Key words:
- micromechanics /
- fiber content /
- tensile behavior /
- Kelly-Tyson model /
- Bowyer-Bader model
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图 1 纤维轴向与受力方向关系示意图
Figure 1. Schematic diagram of relationship between axial direction and load force of fiber
图 2 挤出方向和拉伸受力示意图
Figure 2. Schematic diagram of extrusion direction and tensile load direction
图 5 通过应力-应变曲线确定相关参数示意图
Figure 5. Schematic diagram of determining relevant parameters by stress-strain curves
图 7 纤维取向角度的SEM图像: (a)壳层; (b)芯层; 挤出方向为自左向右
Figure 7. SEM images of fiber orientation angle: (a) Shell; (b) Core; Extrusion direction from left to right
图 8 纤维取向角度统计
Figure 8. Statistical diagram of fiber orientation angle ((a) Shell; (b) Core)
图 9 杨木纤维/聚乙烯复合材料的拉伸模量和拉伸强度
Figure 9. Tensile modulus and tensile strength of poplar fiber/polyethylene composites
图 10 杨木纤维/聚乙烯复合材料拉伸性能理想趋势
Figure 10. Ideal trend of tensile properties of poplar fiber/polyethylene composites
图 11 纤维及塑料基体对杨木纤维/聚乙烯复合材料强度的贡献比例
Figure 11. Proportion of contribution of fiber and matrix to strength of poplar fiber/polyethylene composites
图 12 不同杨木纤维含量的杨木纤维/聚乙烯复合材料断面的SEM图像
Figure 12. SEM images of cross-section of poplar fiber/polyethylene composites with different poplar fiber contents ((a) 20wt%; (b) 30wt%; (c) 40wt%; (d) 50wt%; (e) 60wt%)
表 1 杨木纤维/聚乙烯复合材料的配方
Table 1. Formulation of poplar fiber/ polyethylene composites
Group Poplar fiber/
wt%HDPE/
wt%MAPE/
wt%Lubricant/
wt%PF/PE0 0 100 0 0 PF/PE20 20 75 3 2 PF/PE30 30 65 3 2 PF/PE40 40 55 3 2 PF/PE50 50 45 3 2 PF/PE60 60 35 3 2 Notes: PF—Poplar fiber; PE—Polyethylene; HDPE—High-density polyethylene; MAPE—Maleic anhydride grafted polyethylene. 
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表 2 杨木纤维的平均长度、直径和长径比
Table 2. Average length, diameter and aspect ratio of poplar fibers
Average length/μm Average diameter/μm Average aspect ratio 290.35 (314.89) 50.00 (10.24) 5.807 Note: Figures in parentheses represent standard deviations.
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表 3 杨木纤维/聚乙烯复合材料的杨木纤维体积分数(Vf)
Table 3. Volume fraction of poplar fiber in poplar fiber/polyethylene composites (Vf)
Group PF/PE0 PF/PE20 PF/PE30 PF/PE40 PF/PE50 PF/PE60 ${V_{\rm{f}}}$/vol% 0 15.4 23.8 32.8 42.2 52.3
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表 4 杨木纤维/聚乙烯复合材料在应变水平1和2(
${\varepsilon _1}$ 和${\varepsilon _2}$ )时的参数Table 4. Parameters of poplar fiber/polyethylene composites at strain level 1 and 2 (
${\varepsilon _1}$ and${\varepsilon _2}$ )Sample PF/PE20 PF/PE30 PF/PE40 PF/PE50 PF/PE60 ${\varepsilon _1}$/% 0.5 0.75 0.35 0.35 0.3 ${\sigma _{{{\rm{c}}_1}}}$/MPa 10.5 15.1 11.8 13.1 13.5 ${\sigma _{{{\rm{m}}_1}}}$/MPa 5.01 7.02 3.5 3.5 3.25 ${L_{{\varepsilon _1}}}$/μm 472.7 189.1 264.7 220.6 270.1 ${\varepsilon _2}$/% 1.0 1.5 0.7 0.7 0.6 ${\sigma _{{{\rm{c}}_2}}}$/MPa 15.4 20.2 18.2 20.75 20.75 ${\sigma _{{{\rm{m}}_2}}}$/MPa 8.7 10.89 6.47 6.47 5.68 ${L_{{\varepsilon _2}}}$/μm 945.4 378.2 529.4 441.2 540.2 Notes: $\varepsilon $—Strain; ${\sigma _{{{\rm{c}}_{}}}}$—Stress of poplar fiber/polyethylene composites; ${\sigma _{{{\rm{m}}_{}}}}$—Stress of polyethylene; ${L_\varepsilon }$—Critical fiber length; Subscripts 1, 2—Two strain levels.
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表 5 杨木纤维/聚乙烯复合材料参数的计算结果
Table 5. Calculation results of parameters of poplar fiber/polyethylene composites
Sample PF/PE20 PF/PE30 PF/PE40 PF/PE50 PF/PE60 $\tau $/MPa 4.13 5.07 5.19 6.11 4.56 $K$ 0.940 0.665 0.730 0.621 0.718 ${\sigma _{\rm{f}}}$/MPa 80 80 100 135 75 Notes: $\tau $—Interfacial shear strength of poplar fibers and plastics; $K$—Spatial orientation coefficient of poplar fibers; ${\sigma _{\rm{f}}}$—Intrinsic tensile strength of poplar fibers.
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