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

作　　者：安蕊梅 侯永康[3] 李云峰 段树金 AN Ruimei;HOU Yongkang;LI Yunfeng;DUAN Shujin(School of Civil Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,P.R.China;Key Laboratory of Roads and Railway Engineering Safety Control,Ministry of Education,Shijiazhuang Tiedao University,Shijiazhuang 050043,P.R.China;School of Urban Geology and Engineering,Hebei GEO University,Shijiazhuang 050031,P.R.China;College of Civil Engineering and Architecture,Shandong University of Science and Technology,Qingdao,Shandong 266590,P.R.China;School of Energy and Construction Engineering,Shandong Huayu University of Technology,Dezhou,Shandong 253034,P.R.China)

机构地区：[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

出　　处：《应用数学和力学》2024年第3期295-302,共8页Applied Mathematics and Mechanics

基　　金：河北省自然科学基金(A2015210029);河北省研究生创新项目(CXZZBS2017132)。

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.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-Ⅰedge 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,ⅡandⅢcohesive cracks.

关 键 词：内聚区 虚拟裂纹 能量释放率 J积分 断裂能 

分 类 号：O346.1[理学—固体力学]