基于自适应双相场模型的纤维增强复合材料单层板断裂性能

郭雯; 马玉娥; Sundar Natarajan; 陈鹏程; 彭帆

doi:10.13801/j.cnki.fhclxb.20230816.003

基于自适应双相场模型的纤维增强复合材料单层板断裂性能

doi: 10.13801/j.cnki.fhclxb.20230816.003

1.
西北工业大学航空学院，西安 710072
2.
Indian Institute of Technology Madras, School of Mechanical Engineering, Chennai 600036
3.
长安大学理学院，西安 710064

基金项目: 国家自然科学基金国际(地区)合作与交流项目(52061135101)

详细信息

通讯作者:
马玉娥，博士，教授，博士生导师，研究方向为复合材料结构力学　E-mail: ma.yu.e@nwpu.edu.cn

中图分类号: TB332
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- 被引次数: 0
出版历程
- 收稿日期: 2023-06-21
- 修回日期: 2023-07-26
- 录用日期: 2023-08-06
- 网络出版日期: 2023-08-21
- 刊出日期: 2024-03-01

Study on fracture of fiber-reinforced composite single layer laminate based on adaptive double phase-field model

1.
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China
2.
School of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India
3.
College of Science, Chang'an University, Xi'an 710064, China

Funds: Projects of International Cooperation and Exchanges NSFC (52061135101)

摘要

摘要: 相场法可以自动捕捉裂纹的萌生和演化，因此在模拟复合材料的复杂失效行为时具有明显优势。为区分纤维增强复合材料(Fiber-reinforced composites，FRC)中存在的不同断裂模式，采用双相场断裂模型来分别表征基体和纤维的损伤演化。同时采用相场变量作为误差指标，在各向异性的双相场模型中引入了基于四叉树分解的网格自适应细化策略。设计并开发了相应的Matlab程序，研究了单向及变刚度纤维增强复合材料单层板在拉伸位移载荷下的断裂行为。计算结果表明：采用基于自适应算法的各向异性双相场模型所得到的数值计算结果与试验结果吻合良好；自适应双相场模型能在保证较高计算精度的同时，配合序参量的演化准确地在裂纹路径上进行网格自动加密，简化网格前处理过程，减少网格数量，降低计算成本，提高计算效率。
- 纤维增强复合材料 /
- 双相场 /
- 各向异性 /
- 自适应 /
- 有限元
Abstract: The phase-field method can automatically capture crack initiation and propagation, which has obvious advantages in simulating complex fracture behaviors in composites. To distinguish different fracture modes in fiber-reinforced composites (FRC), two phase-field variables were introduced to represent the damage evolution of fiber and matrix, respectively. An adaptive mesh refinement scheme based on the quadtree decomposition was incorporated into the anisotropic double phase-field formulations using the phase-field variables as the error indicators. The corresponding Matlab programs were designed and developed to study the fracture behaviors of the unidirectional and variable stiffness fiber-reinforced composite single layer laminate under tensile load. The results show that: The numerical results are in good agreement with the experimental results; and the adaptive double phase-field method can not only guarantee high computational accuracy but also refine the mesh along the crack paths with the evolution of phase-field parameters automatically and accurately. Moreover, this method can simplify the mesh pre-processing process, greatly reduce the number of unnecessary elements and the calculation cost, improve the calculation efficiency.
- fiber-reinforced composites /
- double phase-field /
- anisotropic /
- adaptive /
- finite element method

HTML全文

图 1 (a) 尖锐裂纹模型；(b) 双相场模型

Figure 1. (a) Sharp crack model; (b) Double phase-field model

${{\bar t}}$—Surface traction; ${{\bar u}}$—Surface displacement; $\partial {\varOmega _{\rm{t}}}$—Neuman boundary; $\partial {\varOmega _{\rm{u}}}$—Dirichlet boundary; ${\varGamma _{\text{m}}}$—Crack surface of matrix; ${\varGamma _{\text{f}}}$—Crack surface of fiber; ${d_{\text{m}}},{d_{\text{f}}}$—Phase field of matrix and fiber

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图 2 四叉树网格及带悬点单元的形函数构造

Figure 2. Quadtree mesh and the construction of shape function of elements with hanging nodes

${v_i}$—Node; ${\alpha _i}$—Internal angle; P—Pole

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图 3 单边裂纹纤维增强复合材料(FRC)试样：几何尺寸及边界条件

Figure 3. Single edge notched fiber-reinforced composites (FRC) specimen: Geometric size and boundary conditions

${e_1},{e_2}$—Orthogonal basis of local coordinate system; u—Displacement; θ—Angle between fiber and x-axis

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图 4 不同相场阈值下单边裂纹FRC试样的位移-载荷曲线

d_c—Phase field threshold

Figure 4. Displacement-load curves of single edge notched FRC specimen with different phase-field thresholds

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图 5 单边裂纹FRC试样沿不同纤维方向下的裂纹扩展：(a)计算结果；(b)试验结果^[35]；(c)自适应网格

Figure 5. Crack propagation paths of single edge notched FRC specimen with different fiber orientation: (a) Simulation results; (b) Experimental results^[35]; (c) Adaptive elements

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图 6 不同纤维方向的单边裂纹FRC试样位移-载荷曲线

Figure 6. Displacement-load curves of single edge notched FRC specimen with different fiber directions

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图 7 中心含孔FRC试样：(a)几何尺寸及边界条件；(b)部分计算结果

R—Radius; d_m—Phase field of matrix

Figure 7. Open hole FRC specimen: (a) Geometric size and boundary conditions; (b) Some calculation results

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图 8 不同纤维角度对应下中心含孔FRC试样的结构等效强度

σ_f—Effective strength

Figure 8. Effective strengths of the central circle FRC specimen with different fiber orientations

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图 9 中心含孔FRC试样的自适应和非自适应的网格数量对比

Figure 9. Comparison of the number of elements between adaptive and unadaptive schemes for central circle FRC specimen

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图 10 变刚度FRC试样的几何尺寸及边界条件

Figure 10. Geometric size and boundary conditions of variable stiffness FRC specimen

${T_0}$—Initial angle of fiber; $a$—Characteristic length of one period; T₁—Termination angle of fiber; φ—Rotation angle of fiber path

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图 11 变刚度FRC试件部分模拟结果：((a)~(c)), ((e)~(g))裂纹扩展路径；((d), (h))自适应网格

Figure 11. Some simulation results of variable stiffness FRC specimen：((a)-(c)), ((e)-(g)) Crack propagation paths; ((d),(h)) Adaptive elements

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图 12 变刚度FRC试样等效强度对比：不同旋转角度和不同特征尺寸

Figure 12. Comparison of the effective strength of variable stiffness FRC specimen: Different rotation angles and different reference length

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表 1 单边裂纹纤维增强复合材料试样材料参数^[35]

Table 1. Material parameters of single edge notched fiber reinforced composite specimen^[35]

Material parameter	Value
E₁₁/GPa	114.8
E₂₂/GPa	11.7
G₁₂/GPa	9.66
${v_{{\text{12}}}}$	0.21
G_f/(kJ·m⁻²)	106.3
G_mI/(kJ·m⁻²)	0.2774
G_mII/(kJ·m⁻²)	0.7879
Notes: E₁₁, E₂₂ and G₁₂—Longitudinal modulus, transverse modulus and in-plane shear modulus; ${v_{{\text{12}}}}$—Poisson's ratio; G_f—Longitudinal critical energy release rate; G_mI and G_mII—Transverse normal and shear critical energy release rate.

下载: 导出CSV

表 2 不同相场阈值对应的网格数

Table 2. Number of elements with different phase-field thresholds

d_c	Number of elements
0.1	15966
0.3	9469
0.5	7794
0.7	8313
0.9	7479

下载: 导出CSV

表 3 计算时间和网格数量对比

Table 3. Comparison of computation time and number of elements

Fiber orientation	CPU time/s			Number of elements
Fiber orientation	Unadaptive	Adaptive	Percent reduction/%	Unadaptive	Adaptive	Percent reduction/%
30°	14537.263827	5910.201207	59.34	80000	7794	90.25
45°	21364.296175	7913.423786	62.96	80000	8057	89.37
60°	21604.274280	11615.330524	46.23	80000	8964	88.80

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表 4 中心含孔FRC试样材料参数^[36]

Table 4. Material parameters of open hole FRC specimen^[36]

Material parameter	Value
E₁₁/GPa	26.5
E₂₂/GPa	2.6
G₁₂/GPa	1.3
${v_{12}}$	0.35
G_f/(kJ·m^–²)	31.1
G_mI/(kJ·m^–²)	0.622
G_mII/(kJ·m^–²)	0.472

下载: 导出CSV

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