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
- 文章访问数: 78
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- PDF下载量: 33
- 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

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