含内聚裂纹弹性体的能量释放率与断裂能
On Energy Release Rates and Fracture Energy of Elastic Bodies With Cohesive Cracks
安蕊梅 1侯永康 2李云峰 3段树金4
作者信息
- 1. 石家庄铁道大学 土木工程学院,石家庄 050043;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
- 2. 河北地质大学 城市地质与工程学院,石家庄 050031
- 3. 山东科技大学 土木工程与建筑学院,山东 青岛 266590
- 4. 石家庄铁道大学 土木工程学院,石家庄 050043;山东华宇工学院 能源与建筑工程学院,山东 德州 253034
- 折叠
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Gb,J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GF,Gbc 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.
Abstract
According to the cohesive crack model,there is a cohesive region near the crack tip of a cracked e-lastomer,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 re-placed 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 cal-culating methods for energy release rate Ga of physical crack tip propagation and energy release rate Gb of cohe-sive crack tip propagation,were proposed.The relationships between Gb,the J integral and fracture energy GF were discussed.The results show that,critical energy release rate Gbc equals fracture energy GF,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.
关键词
内聚区/虚拟裂纹/能量释放率/J积分/断裂能Key words
cohesive zone/fictitious crack/energy release rate/J-integral/fracture energy引用本文复制引用
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)
出版年
2024
国家科技期刊平台
NSTL
万方数据