Volume 43 Issue 7
Jul.  2022
Turn off MathJax
Article Contents
XU Hua, CAO Zheng, ZOU Yunpeng, YANG Lüfeng. Williams Elements With Generalized Degrees of Freedom for Crack Tip SIFs Analysis Under Crack Surface Distributed Loading[J]. Applied Mathematics and Mechanics, 2022, 43(7): 752-760. doi: 10.21656/1000-0887.420317
Citation: XU Hua, CAO Zheng, ZOU Yunpeng, YANG Lüfeng. Williams Elements With Generalized Degrees of Freedom for Crack Tip SIFs Analysis Under Crack Surface Distributed Loading[J]. Applied Mathematics and Mechanics, 2022, 43(7): 752-760. doi: 10.21656/1000-0887.420317

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

doi: 10.21656/1000-0887.420317
  • Received Date: 2021-10-25
  • Rev Recd Date: 2021-12-20
  • Publish Date: 2022-07-15
  • 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
  • [1]
    刘钧玉, 林皋, 范书立, 等. 裂纹面受荷载作用的应力强度因子的计算[J]. 计算力学学报, 2008, 25(5): 621-626. (LIU Junyu, LIN Gao, FAN Shuli, et al. The calculation of stress intensity factor including the effects of surface tractions[J]. Chinese Journal of Computational Mechanics, 2008, 25(5): 621-626.(in Chinese)

    LIU Junyu, LIN Gao, FAN Shuli, et al. The calculation of stress intensity factor including the effects of surface tractions[J]. Chinese Journal of Computational Mechanics, 2008, 25(5): 621-626. (in Chinese))
    [2]
    LIU J Y, LIN G, LI X C, et al. Evaluation of stress intensity factors for multiple cracked circular disks under crack surface tractions with SBFEM[J]. China Ocean Engineering, 2013, 27(3): 417-426. doi: 10.1007/s13344-013-0036-6
    [3]
    ZHONG H, LI C L, LI H J, et al. Stress intensity factors of interfacial crack with arbitrary crack tractions[J]. IOP Conference Series: Earth and Environmental Science, 2019, 304(5): 052111. doi: 10.1088/1755-1315/304/5/052111
    [4]
    陈白斌, 李建波, 林皋. 无需裂尖增强函数的扩展比例边界有限元法[J]. 水利学报, 2015, 46(4): 489-496, 504. (CHEN Baibin, LI Jianbo, LIN Gao. An extended scaled boundary finite element method without asymptotic enrichment of the crack tip[J]. Journal of Hydraulic Engineering, 2015, 46(4): 489-496, 504.(in Chinese)

    CHEN Baibin, LI Jianbo, LIN Gao. An extended scaled boundary finite element method without asymptotic enrichment of the crack tip[J]. Journal of Hydraulic Engineering, 2015, 46(4): 489-496, 504. (in Chinese))
    [5]
    李亚, 易志坚, 王敏, 等. 裂纹面局部均布荷载下Ⅰ型裂纹有限宽板应力强度因子[J]. 应用数学和力学, 2020, 41(10): 1083-1091. (LI Ya, YI Zhijian, WANG Min, et al. The stress intensity factor of a finite-width plate with a mode-Ⅰcenter crack subjected to uniform stress on the crack surface near the crack tip[J]. Applied Mathematics and Mechanics, 2020, 41(10): 1083-1091.(in Chinese)

    LI Ya, YI Zhijian, WANG Min, et al. The stress intensity factor of a finite-width plate with a mode-Ⅰcenter crack subjected to uniform stress on the crack surface near the crack tip[J]. Applied Mathematics and Mechanics, 2020, 41(10): 1083-1091. (in Chinese))
    [6]
    FETT T, RIZZI G. Weight functions for stress intensity factors and T-stress for oblique cracks in a half-space[J]. International Journal of Fracture, 2005, 132(1): L9-L16. doi: 10.1007/s10704-005-0024-9
    [7]
    LI J, WANG X, TAN C L. Weight functions for the determination of stress intensity factor and T-stress for edge-cracked plates with built-in ends[J]. International Journal of Pressure Vessels and Piping, 2004, 81(3): 285-296. doi: 10.1016/j.ijpvp.2003.12.013
    [8]
    WALTERS M C, PAULINO G H, DODDS JR R H. Interaction integral procedures for 3-D curved cracks including surface tractions[J]. Engineering Fracture Mechanics, 2005, 72(11): 1635-1663. doi: 10.1016/j.engfracmech.2005.01.002
    [9]
    MUTHU N, MAITI S K, FALZON B G, et al. A comparison of stress intensity factors obtained through crack closure integral and other approaches using extended element-free Galerkin method[J]. Computational Mechanics, 2013, 52(3): 587-605. doi: 10.1007/s00466-013-0834-y
    [10]
    贾金生, 汪洋, 冯炜, 等. 重力坝高压水劈裂模拟方法与特高重力坝设计准则初步探讨[J]. 水利学报, 2013, 44(2): 127-133. (JIA Jinsheng, WANG Yang, FENG Wei, et al. Simulation method of hydraulic fracturing and discussions on design criteria for super high gravity dams[J]. Journal of Hydraulic Engineering, 2013, 44(2): 127-133.(in Chinese) doi: 10.3969/j.issn.0559-9350.2013.02.003

    JIA Jinsheng, WANG Yang, FENG Wei, et al. Simulation method of hydraulic fracturing and discussions on design criteria for super high gravity dams[J]. Journal of Hydraulic Engineering, 2013, 44(2): 127-133. (in Chinese)) doi: 10.3969/j.issn.0559-9350.2013.02.003
    [11]
    唐世斌, 刘向君, 罗江, 等. 水压诱发裂缝拉伸与剪切破裂的理论模型研究[J]. 岩石力学与工程学报, 2017, 36(9): 2124-2135. (TANG Shibin, LIU Xiangjun, LUO Jiang, et al. Theoretical model for tensile and shear crack initiation at the crack tip in rock subjected to hydraulic pressure[J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(9): 2124-2135.(in Chinese)

    TANG Shibin, LIU Xiangjun, LUO Jiang, et al. Theoretical model for tensile and shear crack initiation at the crack tip in rock subjected to hydraulic pressure[J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(9): 2124-2135. (in Chinese))
    [12]
    杨绿峰, 徐华, 李冉, 等. 广义参数有限元法计算应力强度因子[J]. 工程力学, 2009, 26(3): 48-54. (YANG Lüfeng, XU Hua, LI Ran, et al. The finite element with generalized coefficients for stress intensity factor[J]. Engineering Mechanics, 2009, 26(3): 48-54.(in Chinese)

    YANG Lufeng, XU Hua, LI Ran, et al. The finite element with generalized coefficients for stress intensity factor[J]. Journal of Engineering Mechanics, 2009, 26(3): 48-54. (in Chinese))
    [13]
    徐华, 邓鹏, 蓝淞耀, 等. 曲线裂纹裂尖SIFs等效分析的广义参数Williams单元确定方法[J]. 工程力学, 2020, 37(6): 34-41. (XU Hua, DENG Peng, LAN Songyao, et al. The determination method of Williams element with generalized degrees of freedom for equivalent analysis of SIFs at the curved crack tip[J]. Engineering Mechanics, 2020, 37(6): 34-41.(in Chinese)

    XU Hua, DENG Peng, LAN Songyao, et al. The determination method of Williams element with generalized degrees of freedom for equivalent analysis of SIFs at the curved crack tip[J]. Engineering Mechanics, 2020, 37(6): 34-41. (in Chinese))
    [14]
    中国航空研究院. 应力强度因子手册[M]. 增订版. 北京: 科学出版社, 1993.

    Chinese Aeronautical Establishment. Handbook of Stress Intensity Factors[M]. Revised ed. Beijing: Science Press, 1993. (in Chinese)
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(9)  / Tables(1)

    Article Metrics

    Article views (608) PDF downloads(32) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return