裂纹面分布加载裂尖SIFs分析的广义参数Williams单元

徐华; 曹政; 邹云鹏; 杨绿峰

doi:10.21656/1000-0887.420317

裂纹面分布加载裂尖SIFs分析的广义参数Williams单元

doi: 10.21656/1000-0887.420317

徐华^{1, 2,},
曹政^{1, 2},
邹云鹏³,
杨绿峰^{1, 2}

1.
广西大学土木建筑工程学院工程防灾与结构安全教育部重点实验室，南宁 530004
2.
广西大学土木建筑工程学院广西防灾减灾与工程安全重点实验室，南宁 530004
3.
广西桂能工程咨询集团有限公司，南宁 530015

基金项目: 国家自然科学基金(重点项目)(51738004)；广西自然科学基金(2019GXNSFAA245012)

详细信息

作者简介:
徐华(1979—)，男，副教授，博士，硕士生导师(通讯作者. E-mail: xuhua@gxu.edu.cn）

中图分类号: O346.1
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出版历程
- 收稿日期: 2021-10-25
- 修回日期: 2021-12-20
- 刊出日期: 2022-07-15

Williams Elements With Generalized Degrees of Freedom for Crack Tip SIFs Analysis Under Crack Surface Distributed Loading

XU Hua^{1, 2
,},
CAO Zheng^{1, 2},
ZOU Yunpeng³,
YANG Lüfeng^{1, 2}

1.
Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education, School of Civil Engineering and Architecture, Guangxi University, Nanning 530004, P.R.China
2.
Guangxi Key Laboratory of Disaster Prevention and Engineering Safety, School of Civil Engineering and Architecture, Guangxi University, Nanning 530004, P.R.China
3.
Guangxi G-Energy Engineering Consulting Group Co. Ltd. , Nanning 530015, P.R.China

摘要

摘要:
带裂缝服役是工程结构的常态，由于流体侵入到裂缝内部，裂纹面直接受荷，使得裂缝进一步扩展，甚者影响结构的安全性。广义参数Williams单元（简记W单元）在分析断裂问题中，利用Williams级数建立裂尖奇异区的位移场，通过求解广义刚度方程可直接获得应力强度因子（stress intensity factors，SIFs），具有高精高效性；但W单元需满足奇异区内裂纹面自由的边界条件，故在分析裂纹面加载的问题中受限。该文基于SIFs互等，在等效奇异区范围中，将裂纹面的荷载等效为奇异区外围边界裂纹面上的集中力，避免奇异区内裂纹面受荷，故采用W单元即可简便计算。算例分析表明：等效奇异区尺寸取裂纹长度的1/20，等效荷载系数P建议取2.0，W单元计算精度均满足1%的误差限，证明该文在奇异区裂纹面受荷等效处理方法上具有合理性、通用性，克服了W单元在分析裂纹面加载问题的局限性。
- 裂纹面加载 /
- 荷载等效 /
- 应力强度因子 /
- Williams单元 /
- 广义参数
Abstract:
Service with cracks is the normal state of engineering structures. Due to the fluid invading into the crack, the crack surface is loaded directly, which makes the crack further expand, and even affects the safety of the structure. In the analysis of fracture problems, according to the Williams element with generalized degrees of freedom (W element), the Williams series was used to establish the displacement field of the singular zone around the crack tip, and the stress intensity factors (SIFs) can be directly obtained by solving the generalized stiffness equation with high precision and high efficiency. However, the W element needs to satisfy the free boundary condition of the crack surface in the singular zone, so it is limited in the analysis of crack surface loading. Based on the SIFs reciprocity, the loading on the crack surface is equivalent to the concentrated force on the crack surface at the periphery of the equivalent singular zone, so the loading on the crack surface in the singular zone can be avoided, and the W element can be easily used for calculation. The numerical examples show that, the size of the equivalent singular zone is 1/20 of the crack length, the suggested equivalent load coefficient P is 2.0, and the calculation accuracy of the W element meets the error limit of 1%. The equivalent treatment method for the analysis of crack surface loading in the singular zone is reasonable and universal, and overcomes the limitation on the W element in analysis of the loading problem on crack surface.
- loading on the crack /
- load equivalence /
- stress intensity factor /
- Williams element /
- generalized degrees of freedom

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图 1 裂尖局部面荷载等效

注　为了解释图中的颜色，读者可以参考本文的电子网页版本，后同。

Figure 1. Crack tip local surface load equivalence

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图 2 裂尖奇异区网格划分及分布荷载等效

Figure 2. Discretization and distributed load equivalence in the crack tip singular region

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图 3 常规区网格离散

Figure 3. Discretization in the regular region

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图 4 边界裂纹面受均布压力计算结果

Figure 4. Calculation results for uniformly distributed pressure on the crack surface

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图 5 中心裂纹面受均布荷载

Figure 5. The uniformly distributed load on the central crack surface

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图 6 常规区网格离散

Figure 6. Discretization in the regular region

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图 7 中心裂纹面受均布压力计算结果

Figure 7. Calculation results for uniformly distributed pressure on the central crack surface

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图 8 裂纹面受线性压力计算结果

Figure 8. Calculation results for linear pressure on the crack surface

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图 9 无量纲SIFs随尺寸变化的计算结果

Figure 9. Calculation results for dimensionless SIFs varying with sizes

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表 1 模型参数（λ=0）

Table 1. Model parameters (λ=0)

a/W	$\displaystyle \int_{a - c}^a {\sigma \left( X \right){\text{d} }X}$	P	Q
0.05	0.5	1.96	0.982
0.10	0.5	1.98	0.991
0.20	0.5	1.99	0.997
0.30	0.5	1.98	0.988
0.40	0.5	1.93	0.963
0.50	0.5	1.85	0.924
0.60	0.5	1.74	0.869
0.70	0.5	1.60	0.800

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