留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

含内聚裂纹弹性体的能量释放率与断裂能

安蕊梅 侯永康 李云峰 段树金

安蕊梅, 侯永康, 李云峰, 段树金. 含内聚裂纹弹性体的能量释放率与断裂能[J]. 应用数学和力学, 2024, 45(3): 295-302. doi: 10.21656/1000-0887.440289
引用本文: 安蕊梅, 侯永康, 李云峰, 段树金. 含内聚裂纹弹性体的能量释放率与断裂能[J]. 应用数学和力学, 2024, 45(3): 295-302. doi: 10.21656/1000-0887.440289
AN Ruimei, HOU Yongkang, LI Yunfeng, DUAN Shujin. On Energy Release Rates and Fracture Energy of Elastic Bodies With Cohesive Cracks[J]. Applied Mathematics and Mechanics, 2024, 45(3): 295-302. doi: 10.21656/1000-0887.440289
Citation: AN Ruimei, HOU Yongkang, LI Yunfeng, DUAN Shujin. On Energy Release Rates and Fracture Energy of Elastic Bodies With Cohesive Cracks[J]. Applied Mathematics and Mechanics, 2024, 45(3): 295-302. doi: 10.21656/1000-0887.440289

含内聚裂纹弹性体的能量释放率与断裂能

doi: 10.21656/1000-0887.440289
基金项目: 

河北省自然科学基金 A2015210029

河北省研究生创新项目 CXZZBS2017132

详细信息
    作者简介:

    安蕊梅(1974—),女,副教授,硕士(E-mail: arm@stdu.edu.cn)

    通讯作者:

    段树金(1955—),男,教授,博士(通讯作者. E-mail: duanshujin@stdu.edu.cn)

  • 中图分类号: O346.1

On Energy Release Rates and Fracture Energy of Elastic Bodies With Cohesive Cracks

  • 摘要: 根据内聚裂纹模型,含裂纹的弹性体在裂纹尖端附近存在一内聚区,内聚区断裂参数表达是其核心研究内容. 该文假定弹性平板直线裂纹尖端存在一带状内聚区,并由一条虚拟线裂纹代替,其张开位移与内聚力存在确定的非线性函数关系. 以Ⅰ型边裂纹为例,导出了满足虚拟裂纹条件的解析解;在此基础上给出了物理裂纹尖端扩展的能量释放率Ga、内聚裂纹尖端扩展的能量释放率Gb的计算公式;讨论了GbJ积分和断裂能GF之间的关系;从理论上证明了临界能量释放率Gbc就是断裂能GFGbc可以作为含内聚区材料裂纹失稳扩展的断裂参数. 提出的方法适用于所有含Ⅰ、Ⅱ、Ⅲ型内聚裂纹的弹性体.
  • 图  1  Ⅰ型边裂纹的椭圆张开位移和奇异应力

    Figure  1.  The elliptic opening displacement and singular stress of a mode-Ⅰ edge crack

    图  2  内聚区模型的尖劈形张开位移和非奇异应力分布

    Figure  2.  The wedge opening displacement and nonsingular stress distribution based on the cohesive zone model

    图  3  J积分线路Γ

    Figure  3.  The J integral path Γ

  • [1] ELICES M, GUINEA G V, GÓMEZ J, et al. The cohesive zone model: advantages, limitations and challenges[J]. Engineering Fracture Mechanics, 2002, 69(2): 137-163. doi: 10.1016/S0013-7944(01)00083-2
    [2] 嵇醒. 断裂力学判据的评述[J]. 力学学报, 2016, 48(4): 741-753. https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB201604001.htm

    JI Xing. A critical review on criteria of fracture mechanics[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(4): 741-753. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB201604001.htm
    [3] BARENBLATT G I. The formation of equilibrium crack during brittle fracture, general ideas and hypotheses, axially-symmetric cracks[J]. Journal of Applied Mathematics and Mechanics, 1959, 23(3): 622-636. doi: 10.1016/0021-8928(59)90157-1
    [4] DUGDALE D S. Yielding of steel sheets containing slits[J]. Journal of the Mechanics and Physics of Solids, 1960, 8(2): 100-104. doi: 10.1016/0022-5096(60)90013-2
    [5] VINCENTE P, XAI L, ANDY Z, et al. Integration of an adaptive cohesive zone and continuum ductile fracture model to simulate crack propagation in steel structures[J]. Engineering Fracture Mechanics, 2021, 258(6): 108041.
    [6] BARSOUM I, YURINDATAMA D T. Collapse analysis of a large plastic pipe using cohesive zone modelling technique[J]. International Journal of Pressure Vessels and Piping, 2020, 187(11): 104155.
    [7] 邓健, 肖鹏程, 王增贤, 等. 基于黏聚区模型的ENF试件层间裂纹扩展分析[J]. 应用数学和力学, 2022, 43(5): 515-523. doi: 10.21656/1000-0887.430082

    DENG Jian, XIAO Pengcheng, WANG Zengxian, et al. Interlaminar crack propagation analysis of ENF specimens based on the cohesive zone model[J]. Applied Mathematics and Mechanics, 2022, 43(5): 515-523. (in Chinese) doi: 10.21656/1000-0887.430082
    [8] HILLERBORG A, MODÉER M, PETERSSON P E. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements[J]. Cement and Concrete Research, 1976, 6(6): 773-781. doi: 10.1016/0008-8846(76)90007-7
    [9] NAIRN J A, AIMENE Y E. A re-evaluation of mixed-mode cohesive zone modeling based on strength concepts instead of traction laws[J]. Engineering Fracture Mechanics, 2021, 248: 107704. doi: 10.1016/j.engfracmech.2021.107704
    [10] YANG Z, ZHU Z, XIA Y, et al. Modified cohesive zone model for soft adhesive layer considering rate dependence of intrinsic fracture energy[J]. Engineering Fracture Mechanics, 2021, 258: 108089. doi: 10.1016/j.engfracmech.2021.108089
    [11] FARLE A S, KRISHNASAMY J, TURTELTAUB S, et al. Determination of fracture strength and fracture energy of (metallo-) ceramics by a wedge loading methodology and corresponding cohesive zone-based finite element analysis[J]. Engineering Fracture Mechanics, 2018, 196: 56-70. doi: 10.1016/j.engfracmech.2018.03.014
    [12] LI Y, REESE S, SIMON J W. Modeling the fiber bridging effect in cracked wood and paperboard using a cohesive zone model[J]. Engineering Fracture Mechanics, 2018, 196: 83-97. doi: 10.1016/j.engfracmech.2018.04.002
    [13] ESMAILI A, TAHERI-BEHROOZ F. Effect of cohesive zone length on the delamination growth of the composite laminates under cyclic loading[J]. Engineering Fracture Mechanics, 2020, 237: 107246 doi: 10.1016/j.engfracmech.2020.107246
    [14] PONNUSAMI S A, KRISHNASAMY J, TURTELTAUB S, et al. A cohesive-zone crack healing model for self-healing materials[J]. International Journal of Solids and Structures, 2018, 134: 249-263. doi: 10.1016/j.ijsolstr.2017.11.004
    [15] ETIENNE M, MOUAD J, FREDERIC J, et al. A cohesive zone model for the characterization of adhesion between cement paste and aggregates[J]. Construction and Building Materials, 2018, 193: 64-71. doi: 10.1016/j.conbuildmat.2018.10.188
    [16] DUAN S J, NAKAGAWA K. Stress functions with finite stress concentration at the crack tips for central cracked panel[J]. Engineering Fracture Mechanics, 1988, 29(5): 517-526. doi: 10.1016/0013-7944(88)90177-4
    [17] 段树金, 藤井康寿, 中川建治. 构成单材料裂纹和双材料界面裂纹有限应力集中的一般解析函数[J]. 应用数学和力学, 2018, 39(12): 1364-1376. doi: 10.21656/1000-0887.390030

    DUAN Shujin, FUJⅡ Koju, NAKAGAWA Kenji. Construction of general analytic functions with finite stress concentration for mono-material cracks and bi-material interface cracks[J]. Applied Mathematics and Mechanics, 2018, 39(12): 1364-1376. (in Chinese) doi: 10.21656/1000-0887.390030
    [18] RICE J R. A path independent integral and the approximate analysis of strain concentration by notches and cracks[J]. Journal of Applied Mechanics, 1968, 35(2): 379-386. doi: 10.1115/1.3601206
    [19] DUAN S J, FUJⅡ K, NAKAGAWA K. Finite stress concentrations and J-integrals from normal loads on a penny-shaped crack[J]. Engineering Fracture Mechanics, 1989, 32(2): 67-176.
    [20] AN R M, DUAN S J, GUO Q M. A new method to determine tensile strain softening curve of quasi-brittle materials[C]//Sustainable Solutions in Structural Engineering and Construction. Singapore: Research Publishing, 2014.
    [21] PETERSSON P E. Crack growth and formation of fracture zones in plain concrete and similar materials[R]. 1981.
    [22] 郭向勇, 方坤河, 冷发光. 混凝土断裂能的理论分析[J]. 哈尔滨工业大学学报, 2005, 37(9): 1219-1222. https://www.cnki.com.cn/Article/CJFDTOTAL-HEBX200509017.htm

    GUO Xiangyong, FANG Kunhe, LENG Faguang. Analysis of the theory fracture energy of concrete[J]. Journal of Harbin Institute of Technology, 2005, 37(9): 1219-1222. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HEBX200509017.htm
    [23] 卿龙邦, 李庆斌, 管俊峰. 混凝土断裂过程区长度计算方法研究[J]. 工程力学, 2012, 29(4): 197-201. https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201204032.htm

    QING Longbang, LI Qingbin, GUAN Junfeng. Calculation method of the length of fracture process zone of concrete[J]. Engineering Mechanics, 2012, 29(4): 197-201. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201204032.htm
    [24] 徐平, 郑满奎, 王超, 等. 考虑尺寸及纤维掺量影响的高强混凝土断裂能试验研究[J]. 硅酸盐通报, 2020, 39(11): 3488-3495. https://www.cnki.com.cn/Article/CJFDTOTAL-GSYT202011013.htm

    XU Ping, ZHENG Mankui, WANG Chao, et al. Experimental study on fracture energy of high strength concrete considering the influence of size and fiber content[J]. Bulletin of The Chinese Ceramic Society, 2020, 39(11): 3488-3495. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GSYT202011013.htm
    [25] 段树金, 解沅衡, 侯永康, 等. 含裂纹简支梁在均布荷载作用下的内聚区模型解析函数[J]. 应用力学学报, 2019, 36(2): 310-315. https://www.cnki.com.cn/Article/CJFDTOTAL-YYLX201902010.htm

    DUAN Shujin, XIE Yuanheng, HOU Yongkang, et al. Cohesive zone model analytic function to simply supported beam with an edge-crack under uniform distributed load[J]. Chinese Journal of Applied Mechanics, 2019, 36(2): 310-315. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YYLX201902010.htm
    [26] 侯永康, 段树金, 安蕊梅. 满足断裂过程区裂纹张开位移条件应力函数的半解析解法[J]. 应用数学和力学, 2018, 39(8): 979-988. doi: 10.21656/1000-0887.380296

    HOU Yongkang, DUAN Shujin, AN Ruimei. Cohesive zone model analytic function to simply supported beam with an edge-crack under uniform distributed load[J]. Applied Mathematics and Mechanics, 2018, 39(8): 979-988. (in Chinese) doi: 10.21656/1000-0887.380296
  • 加载中
图(3)
计量
  • 文章访问数:  149
  • HTML全文浏览量:  47
  • PDF下载量:  47
  • 被引次数: 0
出版历程
  • 收稿日期:  2023-09-21
  • 修回日期:  2023-11-15
  • 刊出日期:  2024-03-01

目录

    /

    返回文章
    返回