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正交各向异性材料应力体积-偏量拉压分解的断裂相场模型

张志超 董洪承 王方鑫

张志超, 董洪承, 王方鑫. 正交各向异性材料应力体积-偏量拉压分解的断裂相场模型[J]. 复合材料学报, 2024, 42(0): 1-10.
引用本文: 张志超, 董洪承, 王方鑫. 正交各向异性材料应力体积-偏量拉压分解的断裂相场模型[J]. 复合材料学报, 2024, 42(0): 1-10.
ZHANG Zhichao, DONG Hongcheng, WANG Fangxin. Phase-field fracture model of anisotropic materials based on strain energy volumetric-deviatoric split[J]. Acta Materiae Compositae Sinica.
Citation: ZHANG Zhichao, DONG Hongcheng, WANG Fangxin. Phase-field fracture model of anisotropic materials based on strain energy volumetric-deviatoric split[J]. Acta Materiae Compositae Sinica.

正交各向异性材料应力体积-偏量拉压分解的断裂相场模型

基金项目: 国家自然科学基金(12102380);中国博士后科学基金资助项目(2023 M732986)
详细信息
    通讯作者:

    张志超,博士,讲师,研究方向为复合材料力学 E-mail:zhangzhch@yzu.edu.cn

  • 中图分类号: TM247; O344

Phase-field fracture model of anisotropic materials based on strain energy volumetric-deviatoric split

Funds: National Natural Science Foundation of China (12102380); China Postdoctoral Science Foundation (2023 M732986)
  • 摘要: 断裂相场法被广泛应用于各向同性和复合材料的断裂分析之中。目前,针对各向异性材料和复合材料的断裂问题仍然是断裂相场法的研究重点。本文基于应力拉压的球偏分解方式对弹性应变能进行分解,排除了压缩体积应变能造成的裂纹扩展,并考虑材料拉、压本构关系的非对称情况,建立了一个针对正交各向异性材料断裂问题的相场分析模型。为了验证模型的可靠性,分别对各向同性材料、正交各向异性材料的单边开口板的拉伸和剪切问题进行了分析。对单向纤维夹杂的复合材料板,应用Hashin准则对损伤裂纹驱动力进行了修正,并对不同碳纤维铺设方向复合材料板的拉伸问题进行了模拟。本文建立的模型能够模拟各向异性材料和单向纤维夹杂复合材料的裂纹扩展问题。对于各向同性材料和正交各向异性材料,模拟得到的裂纹扩展路径与现有模型一致,复合材料中裂纹扩展方向和纤维铺设方向平行,预测结果和实验结果吻合良好。

     

  • 图  1  二维平面应变几何结构和边界条件:(a)受拉;(b)受剪

    Figure  1.  Geometry and boundary condition of the single-edge-notched squareplate subjected: (a) Tension; (b) Shear

    图  2  二维平面应变单边开口板的剪切开裂(平面应变板的厚度h=1,长度参数l0=1.0×10−2 mm)

    Figure  2.  Shear cracking of 2 D single-edge-notched square(Thickness of the plane strain plate h=1, Length parameter l0=1.0×10−2 mm)

    图  3  二维平面应变单边开口板的拉伸开裂(平面应变板的厚度h=1,长度参数l0=1.0×10−2 mm)

    Figure  3.  Tensile cracking of 2 D single-edge-notched square(Thickness of the plane strain plate h=1, Length parameter l0=1.0×10−2 mm)

    图  4  单边开口板的平均应力-位移曲线:(a)剪切;(b)拉伸

    Figure  4.  Average stress-displacement curve of 2 D single-edge-notched square: (a) Shear; (b) Tensile

    图  5  各向异性材料不同剪切位移和拉伸位移时的裂纹

    Figure  5.  Cracks in anisotropic materials under different shear displacement and tensile displacement

    图  6  单边开口板平均应力应变关系:(a)y方向平均正应力;(b)平均切应力

    Figure  6.  Average stress-strain relationship of 2 D single-edge-notched square: (a) Normal stress in y direction; (b) Average shear stress

    图  7  受拉的纤维复合材料单边开口板(α0为纤维和x轴夹角,α为裂纹和x轴夹角)

    Figure  7.  2 D single-edge-notched plate of fiber composite material under tension (α0 is the Angle between fiber and x-axis, and α is the angle between crack and x-axis)

    图  8  受拉伸位移单边开口板裂纹扩展的有限元分析结果和试验结果[29]对比(l0=1.0×10−2 mm, β=15)

    Figure  8.  Comparison of FEM and experimental results [29] on crack growth of 2 D single-edge-notched plate subjected to tensile displacement (l0=1.0×10−2 mm, β=15)

    图  9  单边开口板拉伸位移时的平均应力-位移曲线

    Figure  9.  Average stress-displacement curve of 2 D single-edge-notched plate subjected to tensile displacement

    图  10  不同长度参数下单边开口板的裂纹偏转角度

    Figure  10.  Crack deflection angles of the single-edge-notched plate under different length parameters

    图  11  中心开口板纤维不同分布角度下的裂纹偏转

    Figure  11.  Crack deflection under different distribution angles of fiber in the central opening plate

    表  1  各向同性材料参数

    Table  1.   Material properties of an isotropic material

    E/GPa ν Gc/(GPa∙mm) k
    210 0.3 2700 1.0×10−6
    Notes: E is the elastic modulus; ν is the Poisson's ratio; Gc is the critical fracture energy density; k is a model parameter that prevents the positive part of the elastic energy density.
    下载: 导出CSV

    表  2  各向异性材料参数[16]

    Table  2.   Material properties of anisotropic HCP material[16]

    PropertyValue
    C11/GPa115.8
    C12/GPa39.8
    C13/GPa40.6
    C33/GPa51.4
    C44/GPa20.4
    Gc/(GPa∙mm)1.0×10−3
    Notes: C11-C44 is the elastic constants in stiffness matrix; Gc is the critical fracture energy density.
    下载: 导出CSV

    表  3  正交各向异性复合材料板材料参数

    Table  3.   Material properties of the composite lamina

    PropertyValue
    E11/GPa114.8
    E22, E33/GPa11.7
    G12/GPa9.66
    ν120.21
    Gf/( kJ·m−2)106.3
    Gm/( kJ·m−2)0.2774
    Notes: E11 is the longitudinal stiffness of composites; E22 and E33 is the transverse stiffness along the 2- and 3-axis; G12 is the shear stiffness; ν12 is the major poisson’s ratio; Gf is the longitudinal critical energy release rate; Gm is the transverse normal critical energy release rate.
    下载: 导出CSV

    表  4  正交各向异性复合材料板材料参数[11]

    Table  4.   Material properties of the composite lamina[11]

    PropertyValue
    E11/GPa26.5
    E22, E33/GPa2.6
    G12/GPa1.3
    ν120.35
    Gm/( kJ·m−2)0.622
    Notes: E11 is the longitudinal stiffness of composites; E22 and E33 is the transverse stiffness along the 2- and 3-axis; G12 is the shear stiffness; ν12 is the major poisson’s ratio; Gm is the transverse normal critical energy release rate.
    下载: 导出CSV
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出版历程
  • 收稿日期:  2023-11-06
  • 修回日期:  2024-01-02
  • 录用日期:  2024-01-09
  • 网络出版日期:  2024-02-01

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