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

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

安蕊梅^{1, 2,},
侯永康³,
李云峰⁴,
段树金^{1, 5, ,}

1.
石家庄铁道大学土木工程学院，石家庄 050043
2.
石家庄铁道大学道路与铁道工程安全保障省部共建教育部重点实验室，石家庄 050043
3.
河北地质大学城市地质与工程学院，石家庄 050031
4.
山东科技大学土木工程与建筑学院，山东青岛 266590
5.
山东华宇工学院能源与建筑工程学院，山东德州 253034

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
计量
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- 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

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

AN Ruimei^{1, 2
,},
HOU Yongkang³,
LI Yunfeng⁴,
DUAN Shujin^{1, 5
, ,}

1.
School of Civil Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, P.R.China
2.
Key Laboratory of Roads and Railway Engineering Safety Control, Ministry of Education, Shijiazhuang Tiedao University, Shijiazhuang 050043, P.R.China
3.
School of Urban Geology and Engineering, Hebei GEO University, Shijiazhuang 050031, P.R.China
4.
College of Civil Engineering and Architecture, Shandong University of Science and Technology, Qingdao, Shandong 266590, P.R.China
5.
School of Energy and Construction Engineering, Shandong Huayu University of Technology, Dezhou, Shandong 253034, P.R.China

摘要

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G_a、内聚裂纹尖端扩展的能量释放率G_b的计算公式；讨论了G_b，J积分和断裂能G_F之间的关系；从理论上证明了临界能量释放率G_bc就是断裂能G_F，G_bc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.
- 内聚区 /
- 虚拟裂纹 /
- 能量释放率 /
- J积分 /
- 断裂能
Abstract: According to the cohesive crack model, there is a cohesive region near the crack tip of a cracked elastomer, and the expressions of fracture parameters in the cohesive region make the core research content. Under the assumption of a cohesive zone existing at the tip of a linear crack in an elastic plate, the zone was replaced by a fictitious linear crack, and a definite nonlinear functional relationship between the fictitious crack opening displacement and the cohesion was given. An elastic plate with a mode-Ⅰ edge crack was taken as an example, and the analytical solution satisfying the fictitious crack condition was derived. On this basis, the calculating methods for energy release rate G_a of physical crack tip propagation and energy release rate G_b of cohesive crack tip propagation, were proposed. The relationships between G_b, the J integral and fracture energy G_F were discussed. The results show that, critical energy release rate G_bc equals fracture energy G_F, which can be used as a fracture parameter for crack instability propagation of materials with cohesive regions. The proposed method is applicable to all elastic bodies with mode-Ⅰ, Ⅱ and Ⅲ cohesive cracks.
- cohesive zone /
- fictitious crack /
- energy release rate /
- J-integral /
- fracture energy

HTML全文

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

图 3 J积分线路Γ

Figure 3. The J integral path Γ

下载: 全尺寸图片幻灯片

参考文献(26)

[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