Moving line crack accompanied with damage zone subject to remote tensile loading  

作　　者：Minwei CHEN Min LI Xuesong TANG 

机构地区：[1]School of Aeronautic Science and Engineering,Beihang University [2]Department of Mechanics,School of Civil Engineering and Architecture,Changsha University of Science & Technology

出　　处：《Applied Mathematics and Mechanics(English Edition)》2015年第9期1213-1222,共10页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(No.51175404)

摘　　要：In the 1920s, a closed-form solution of the moving Criffith crack was first obtained by Yoffe. Based on Yoffe＇s solution, the Dugdale model for the moving crack case gives a good result. However, the Dugddle model fails when the crack speed is closed to the Rayleigh wave speed because of the discontinuity occurred in the crack opening displacement （COD）. The problem is solved in this paper by introducing a restraining stress zone ahead of the crack tip and two velocity functions. The restraining stresses are linearly distributed and related to the velocity of the moving crack. An analytical solution of the problem is obtained by use of the superposition principle and a complex function method. The final result of the COD is continuous while the crack moves at a Rayleigh wave speed. The characteristics of the strain energy density （SED） and numerical results are discussed, and conclusions are given.In the 1920s, a closed-form solution of the moving Criffith crack was first obtained by Yoffe. Based on Yoffe＇s solution, the Dugdale model for the moving crack case gives a good result. However, the Dugddle model fails when the crack speed is closed to the Rayleigh wave speed because of the discontinuity occurred in the crack opening displacement （COD）. The problem is solved in this paper by introducing a restraining stress zone ahead of the crack tip and two velocity functions. The restraining stresses are linearly distributed and related to the velocity of the moving crack. An analytical solution of the problem is obtained by use of the superposition principle and a complex function method. The final result of the COD is continuous while the crack moves at a Rayleigh wave speed. The characteristics of the strain energy density （SED） and numerical results are discussed, and conclusions are given.

关 键 词：moving crack restraining stress zone complex function method crackopening displacement （COD） strain energy density （SED） 

分 类 号：O346.1[理学—固体力学] TE921.2[理学—力学]