﻿ 二维编织C/SiC复合材料板疲劳损伤分析<sup>*</sup>
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Fatigue damage analysis of 2D braided C/SiC composite plate
CHEN Tianxiong, ZHANG Zheng, WANG Qizhi, LIN Huixing
School of Aeronautic Science and Engineering, Beihang University, Beijing 100083, China
Received: 2018-04-09; Accepted: 2018-05-04; Published online: 2018-05-19 19:48
Corresponding author. ZHANG Zheng, E-mail: jordanzzhang@buaa.edu.cn
Abstract: To explore the basic laws of composite damage, first, based on damage mechanics, combined with Tsai-Hill criterion of strength, a damage evolution equation that can characterize the damage anisotropy of 2D braided C/SiC composites was proposed.Second, a damage simulation program considered material stiffness reduction depend on the damage degree, as an add-on function, was developed and inserted in the commercial finite element software ANSYS environment. Third, the damage evolution of the 2D braided C/SiC composite plate model was simulated, and the result shows stress and damage degree have coupling effects on the element damage during the damage process. Finally, the form of damage evolution equation is discussed and improved, and the anisotropic characteristics of damage evolution under the material property and the action of damage driving force is revealed by analog computation, indicating that the material anisotropy damage is the inevitable result of its material properties and loaded form.
Keywords: composite     2D braided     damage     anisotropy     finite element

1 损伤演化方程

 (1)

 (2)

 (3)

 (4)

 (5)

 (6)

2 二次开发程序及损伤仿真计算结果分析

 图 1 计算程序流程图 Fig. 1 Flowchart of calculation program

2.1 均布循环载荷下正文各向异性薄板损伤分析

 参数 数值 弹性模量E1、E2/GPa 187.06 弹性模量E3/GPa 16.49 泊松比μ12 0.175 泊松比μ13、μ23 0.492 剪切模量G12/GPa 57.66 剪切模量G13、G23/GPa 27.51

 图 2 模型及约束条件 Fig. 2 Model and constraint condition

 图 3 应力分布云图 Fig. 3 Stress distribution contour

 (7)

 图 4 正交各向异性板正反表面损坏单元数 Fig. 4 Number of damaged units on front-side and back-side surface of orthotropic plate

 图 5 正交各向异性板正反表面损伤进程分离 Fig. 5 Front-side and back-side surface damage evolution separation of orthotropic plate

 图 6 板背面单元和板正面单元损伤度 Fig. 6 Damage degree of plate back-side units and plate front-side units

 图 7 板背面单元和板正面单元等效应力 Fig. 7 Equivalent stress of plate back-side units and plate front-side units

 图 8 板正面单元和背面单元的损伤度对比 Fig. 8 Comparison of damage degree between plate units of front-side and back-side
 图 9 板正面单元和背面单元的等效应力对比 Fig. 9 Comparison of equivalent stress between plate units of front-side and back-side
2.2 考虑基体沉积工艺情况的正交各向异性薄板损伤分析

 参数 中间层 表面层 弹性模量E1、E2/GPa 107.06 187.06 弹性模量E3/GPa 9.43 16.49 泊松比μ12 0.1 0.175 泊松比μ13、μ23 0.484 5 0.492 剪切模量G12/GPa 52.75 57.66 剪切模量G13、G23/GPa 15.75 27.51

 图 10 正交各向异性三层板损坏单元数 Fig. 10 Number of damaged units of orthotropic three-layer plate model

3 损伤演化方程建立及损伤演化仿真

 (8)

 (9)

 图 11 正方形板不同强度条件下损伤扩展云图 Fig. 11 Damage extension contour of square plate under different strength conditions

4 结论

1) 材料或结构的损伤，是由损伤驱动力主导的，同时受材料强度和应力状态影响。因此无论材料是各向同性还是各向异性，损伤一旦发生，损伤驱动力中的主要应力成分仍将对后继损伤演化产生决定性作用，所以损伤的发展必然是各向异性的。

2) 在复杂应力状态下，损伤演化的基本状况仍然如上所述。对于各向异性材料而言，材料的基本特征首先体现在材料模量的各向异性，同时，也反映在材料各方向强度的不同上。但就损伤演化而言，材料强度的不同对材料各向异性演化将起到更重要的作用。

3) 基于对正交各向异性复合材料的损伤分析的结果，提出了式(9)所定义的损伤驱动力，用以反映主要应力成分及材料强度对损伤演化的作用，从而揭示损伤演化在损伤驱动力的影响下所必然呈现的各向异性特征。

4) 受限于相关实验基础的欠缺，提出的如式(8)、式(9)和式(2)所构成的损伤演化描述体系尚有待通过实践进一步验证和改进。但本文基于损伤力学理论，根据材料标准试样疲劳S-N曲线确定损伤演化方程参数，进行了定性模拟分析，具有理论严谨性和一定的实验基础。通过本文损伤模拟的结果，说明损伤演化方程具有基本的理论合理性和与基本损伤演化认识的一致性。

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#### 文章信息

CHEN Tianxiong, ZHANG Zheng, WANG Qizhi, LIN Huixing

Fatigue damage analysis of 2D braided C/SiC composite plate

Journal of Beijing University of Aeronautics and Astronsutics, 2019, 45(1): 192-199
http://dx.doi.org/10.13700/j.bh.1001-5965.2018.0194