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预测纳米纤维复合材料有效弹性性能的界面模型和界面相模型

崔春丽 徐耀玲

崔春丽,徐耀玲. 预测纳米纤维复合材料有效弹性性能的界面模型和界面相模型 [J]. 应用数学和力学,2022,43(8):877-887 doi: 10.21656/1000-0887.420231
引用本文: 崔春丽,徐耀玲. 预测纳米纤维复合材料有效弹性性能的界面模型和界面相模型 [J]. 应用数学和力学,2022,43(8):877-887 doi: 10.21656/1000-0887.420231
CUI Chunli, XU Yaoling. The Interface Model and the Interphase Model for Predicting the Effective Elastic Properties of Nano-Fiber Composites[J]. Applied Mathematics and Mechanics, 2022, 43(8): 877-887. doi: 10.21656/1000-0887.420231
Citation: CUI Chunli, XU Yaoling. The Interface Model and the Interphase Model for Predicting the Effective Elastic Properties of Nano-Fiber Composites[J]. Applied Mathematics and Mechanics, 2022, 43(8): 877-887. doi: 10.21656/1000-0887.420231

预测纳米纤维复合材料有效弹性性能的界面模型和界面相模型

doi: 10.21656/1000-0887.420231
详细信息
    作者简介:

    崔春丽(1995—),女,硕士生(E-mail:cuichunli@stumail.ysu.edu.cn

    徐耀玲(1968—),男,教授(通讯作者. E-mail:xylysu@163.com

  • 中图分类号: O31

The Interface Model and the Interphase Model for Predicting the Effective Elastic Properties of Nano-Fiber Composites

  • 摘要:

    基于广义自洽法,同时采用Gurtin-Murdoch界面模型和界面相模型研究了纳米纤维复合材料的有效弹性性能,获得了两种模型下有效体积模量的封闭解析解和计算有效面内剪切模量数值解的全部公式。基于界面模型的解答,讨论了有效体积模量和有效面内剪切模量的界面效应。证明了界面模型的解答可由界面相模型的解答退化得到,其中有效体积模量可以实现解析退化,有效面内剪切模量则可以数值退化。以含纳米孔洞的金属铝为例,比较了两种模型计算结果的差异。结果表明,当纳米孔洞半径较小时,两个模型的结果存在很大差异,而当半径较大时两个模型的结果差别不大。

  • 图  1  预测纳米纤维复合材料有效性质的两种模型:(a) 界面模型; (b) 界面相模型

    Figure  1.  Two models for predicting the effective elastic properties of nano-fiber composites: (a) the interface model; (b) the interphase model

    图  2  无量纲有效体积模量和有效面内剪切模量随纤维半径的变化

    Figure  2.  Variations of the dimensionless effective bulk modulus and the in-plane shear modulus with the fiber radius

    图  3  无量纲有效体积模量和有效面内剪切模量随纤维刚度的变化

    Figure  3.  Variations of the dimensionless effective bulk modulus and the in-plane shear modulus with the fiber rigidness

    图  4  界面模型和界面相模型的结果对比

    Figure  4.  Results comparisons between the interface model and the interphase model

    表  1  体积模量和剪切模量的退化

    Table  1.   Degradation of the bulk modulus and the shear modulus

    $ {E^{{S_{\text{f}}}}} $/(N/m)interphase model t/nminterface model
    10−110−210−310−410−510−6
    10$ {B_{{\text{em}}}}/{B_{\text{m}}} $
    $ {\mu _{{\text{em}}}}/{\mu _{\text{m}}} $
    0.886 870.906 100.906 770.906 820.906 830.906 830.906 83
    0.849 550.854 380.854 380.854 380.854 380.854 380.854 61
    −10$ {B_{{\text{em}}}}/{B_{\text{m}}} $
    $ {\mu _{{\text{em}}}}/{\mu _{\text{m}}} $
    0.900 760.892 140.892 580.892 640.892 650.892 650.892 65
    0.834 820.831 020.831 130.831 150.831 150.831 150.831 37
    下载: 导出CSV

    表  2  界面相力学性质[18]

    Table  2.   Properties of the interphase[18]

    A-{111} B-{100}
    t1t2t1t2
    bulk modulus B2/GPa80.9079.17 74.3775.21
    shear modulus $ {\mu _2} $/GPa26.7526.6121.1923.46
    下载: 导出CSV

    C1  界面模型和界面相模型中的对应符号

    C1.   Conespording symbols in the interface model and the interphase model

    interphase modelinterface model
    $ R{}_1 $,$R{}_3$$ {R_{\text{f}}} $,$ {R_{\text{m}}} $
    $ {c_1} $,$ {c_3} $$ {c_{\text{f}}} $,$ {c_{\text{m}}} $
    ${\varGamma _1}$,${\varGamma _3}$${\varGamma _{\text{f} } }$,${\varGamma _{\text{m} } }$
    ${\varOmega _1}$,${\varOmega _3}$,${\varOmega _4}$${\varOmega _{\text{f} } }$,${\varOmega _{\text{m} } }$,${\varOmega _{ {\text{em} } } }$
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-08-05
  • 修回日期:  2021-11-24
  • 网络出版日期:  2022-07-01
  • 刊出日期:  2022-08-01

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