北京航空航天大学学报 ›› 2014, Vol. 40 ›› Issue (11): 1637-1642.doi: 10.13700/j.bh.1001-5965.2013.0717

• 论文 • 上一篇    

夹持边界条件下表面裂纹应力强度因子求解

曹淑森, 贺小帆, 杨博霄, 刘文珽   

  1. 北京航空航天大学 航空科学与工程学院, 北京 100191
  • 收稿日期:2013-12-06 出版日期:2014-11-20 发布日期:2014-12-02
  • 通讯作者: 贺小帆 E-mail:xfhe@buaa.edu.cn
  • 作者简介:曹淑森(1991-),男,山东沂水人,硕士生,sy1305102@ase.buaa.edu.cn

Solution of stress intensity factor of surface cracked geometry with clamped ends

Cao Shusen, He Xiaofan, Yang Boxiao, Liu Wenting   

  1. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
  • Received:2013-12-06 Online:2014-11-20 Published:2014-12-02

摘要:

为了进行试验室条件下表面裂纹扩展行为研究,需要进行试验机夹持边界条件下的表面裂纹应力强度因子求解.通过对夹持特点的分析,将其等效为均匀拉伸和弯矩的共同作用,并使得试件端部转角为0°.以自由均匀拉伸和纯弯载荷作用下表面裂纹应力强度因子解的Newman-Raju公式为基础,计算得到了等效模型弹性位能表达式,应用卡氏第一定理求得了弯矩与拉伸载荷的关系,采用叠加原理得到了夹持边界条件下表面裂纹应力强度因子解.为了验证解的适用性,采用Abaqus软件计算得到夹持边界条件下若干典型表面裂纹的应力强度因子数值解,对比表明了提出的应力强度因子解法是足够精确的.随后探讨了裂纹形状、试件长厚比等对夹持边界条件下应力强度因子修正因子的影响规律.

关键词: 表面裂纹, 应力强度因子, 夹持边界条件, 叠加原理, 有限元法

Abstract:

Determination of the stress intensity factor (SIF) of surface cracked geometry with clamped ends is necessary for crack growth analysis in laboratory. Based on the feature of the clamped ends, the clamped condition was simplified as a combined uniform tension stress and bending moment act with the rotation angles of the specimen ends retained to be zero. The elastic potential energy of the equivalent model was derived based on Newman-Raju expression of SIF for surface crack under free uniform tension and bending moment, and then the function relationship between the uniform tension stress and the bending moment was deduced using Castigliano's first theorem. By superposition, the SIF expression of the equivalent model was given. To verify the validity of the expression, SIF solutions of some representative surface cracked geometry with clamped ends were obtained by Abaqus. Comparisons indicate that the expression is accurate enough. In addition, the relationship of crack shape and length-to-thickness ratio to the modifying factor for clamped ends was analyzed.

Key words: surface crack, stress intensity factor, clamped ends, superposition principle, finite element method

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