AEROSPACE SHANGHAI, Volume. 42, Issue 1, 68(2025)

Research Progresses in Constitutive Models for Carbon Fiber Reinforced Resin Matrix Composites

Yudi GAO*... Chengwen SUN, Jingshu ZHUO, Guoqiang GUO, Kun JIA and Xia JI |Show fewer author(s)
Author Affiliations
  • College of Mechanical Engineering,Donghua University,Shanghai201620,China
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    Figures & Tables(11)
    Constitutive models for unidirectional carbon fiber composites in all directions[42-45]
    Two-step homogenization[48]
    Ideal single cell for three-dimensional braided preforms
    Spiral model
    Multivariate single-cell models for three-dimensional braided composites[33,35,63-65]
    Spatial relationships of yarns in three-dimensional n-directional braided structures[71]
    Schematic diagram of a set of yarns as global and local coordinates[72]
    • Table 1. Characterization of the mixing and bridging principles<sup>[<a class="aTag" href="#Ref_49" target="_self" style="display: inline;">49</a>]</sup>

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      Table 1. Characterization of the mixing and bridging principles<sup>[<a class="aTag" href="#Ref_49" target="_self" style="display: inline;">49</a>]</sup>

      特性混合法则桥联法则
      复杂性简单,公式直观复杂,需要结合微观 力学模型
      适用范围单向纤维复合材料, 线弹性非线性分析、多轴 加载、失效行为
      物理机理基于体积分数的 加权平均考虑纤维-基体- 界面的应力传递
      计算精度精度有限,适用理想 条件精度高,能反映界面 效应和局部行为
    • Table 2. Mechanical equivalent models and single-cell geometric models for 3D braided structural components

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      Table 2. Mechanical equivalent models and single-cell geometric models for 3D braided structural components

      模型类型典型模式
      力学等效模型纤维倾斜模型
      螺旋模型
      单胞几何模型三单胞模型
      多单胞模型
    • Table 3. Progressive damage criteria for three-dimensional braided composites<sup>[<a class="aTag" href="#Ref_82" target="_self" style="display: inline;">82</a>-<a class="aTag" href="#Ref_83" target="_self" style="display: inline;">83</a>]</sup>

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      Table 3. Progressive damage criteria for three-dimensional braided composites<sup>[<a class="aTag" href="#Ref_82" target="_self" style="display: inline;">82</a>-<a class="aTag" href="#Ref_83" target="_self" style="display: inline;">83</a>]</sup>

      损伤模式损伤准则损伤因子
      渐进损伤准则一[83]ff2=σ1Xt2+1S122τ122+τ1321,σ1>0σ1Xc21,σ1<0df=1-1ffe-Xt2C11ff-1Lc/Gf
      fm2=1Yt2σ2+σ32+1S232τ232-σ2σ32+1S122τ122+τ1321,σ2>01YCYC2S232-1σ2+σ3+14S232σ2+σ32+1S232τ232-σ2σ3+       1S122τ122+τ1321,σ2<0dm=1-1fme-Yt2C22fm-1Lc/Gm
      渐进损伤准则二[82]ff=ε11f,tε11f,cε112+ε11f,t-ε11f,t2ε11f,cε11>ε11f,tdf=1-ε11f,tffe-C11ε11f1'tff-ε111f1tLc/Gf
      fm=ε22f,tε22f,cε222+ε22f,t-ε22f,t2ε22f,cε22+ε22f,tε12f2ε122>ε22f,tdm=1-ε22f,tfme-C22ε22f(fm-ε22fffLc/Gm
    • Table 4. Failure criteria of fibers and resins

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      Table 4. Failure criteria of fibers and resins

      标准公式附加条件
      纤维最大应力准则的失效条件σ1XT,σ1XC 
      纤维最大应变准则的失效条件ε1ε1T,ε1ε1c
      Hashin-3D纤维拉伸失效条件[84]σ1XT2+1S122τ122+τ1321
      Maimi纤维压缩失效条件[85]τ12m+η12σ22m/S121σ22mτ12m在2D屈曲坐标系中的应力, 角度为φc
      树脂最大应力准则的失效条件σ2YT,σ2YC 
      树脂最大应变准则的失效条件ε2ε2T,ε2ε2c
      Hashin-3D树脂拉伸失效条件[84]σ2+σ32YT2+τ232-σ2σ3S232+τ122-τ132S1221
      Cuntze树脂压缩失效条件[86]

      bτ-1I2/YC+bτI4+bτI3/YC21

      I2=σ2+σ3,I3=τ312+τ122,I4=σ2-σ32+4τ232

      bτ=1,bτ=0
      纤维-树脂基最大应力准则的失效条件τ12S12
      纤维-树脂基最大应变准则的失效条件γ12γ12uγ122极限剪切应变
      Hashin纤维-树脂基剪切失效条件[84]σ1/XT2+τ12/S1221
      Shahid-Chang纤维-树脂基剪切失效条件[87]σ¯1/XT2+τ¯12/S12(ϕ)21σ¯有效层应力ϕ基体裂纹密度
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    Yudi GAO, Chengwen SUN, Jingshu ZHUO, Guoqiang GUO, Kun JIA, Xia JI. Research Progresses in Constitutive Models for Carbon Fiber Reinforced Resin Matrix Composites[J]. AEROSPACE SHANGHAI, 2025, 42(1): 68

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    Paper Information

    Category: Integration of Material Structure and Function

    Received: Dec. 10, 2024

    Accepted: --

    Published Online: Apr. 2, 2025

    The Author Email:

    DOI:10.19328/j.cnki.2096-8655.2025.01.007

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