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

doi:10.1007/s10483-015-1975-6

Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (9): 1213-1222.doi: https://doi.org/10.1007/s10483-015-1975-6

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

Minwei CHEN¹, Min LI¹, Xuesong TANG²

1. School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China;
2. Department of Mechanics, School of Civil Engineering and Architecture, Changsha University of Science & Technology, Changsha 410004, China

收稿日期:2014-09-08 修回日期:2015-01-26 出版日期:2015-09-01 发布日期:2015-09-01
通讯作者: Min LI E-mail:limin@buaa.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (No. 51175404)

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

Minwei CHEN¹, Min LI¹, Xuesong TANG²

1. School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China;
2. Department of Mechanics, School of Civil Engineering and Architecture, Changsha University of Science & Technology, Changsha 410004, China

Received:2014-09-08 Revised:2015-01-26 Online:2015-09-01 Published:2015-09-01
Contact: Min LI E-mail:limin@buaa.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (No. 51175404)

摘要/Abstract

摘要： In the 1920s, a closed-form solution of the moving Griffith 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 Dugdale 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, strain energy density (SED), complex function method, crack opening displacement (COD)

Abstract: In the 1920s, a closed-form solution of the moving Griffith 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 Dugdale 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.

Key words: moving crack, crack opening displacement (COD), strain energy density (SED), restraining stress zone, complex function method

中图分类号:

O346

Minwei CHEN, Min LI, Xuesong TANG. Moving line crack accompanied with damage zone subject to remote tensile loading[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(9): 1213-1222.

参考文献

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

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

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