平板表面裂纹应力强度因子和应力分布规律的确定

Determination of stress intensity factors and stress distribution for surface crack in plates

基于有限元法(FEM)和节点位移方法,研究了在中间裂纹与侧裂纹处裂纹尖端的应力强度因子和应力场.使用8节点四边形等参元和1/4节点退化单元,对网格密度和裂纹长度对计算精度的影响进行了研究.改善裂纹尖端周围子区域的节点密度,在保证结果精度的同时,可以节省计算时间.为了计算和分析裂纹尖端的应力强度因子、应力场与位移场,利用Matlab/Simulink编写了关于平板Ⅰ型和Ⅱ型应力强度因子的代码,并比较了有限元方法与精确方法的计算结果.结果表明,所提出的方法有助于提高计算精度与收敛速度,且算法合理,可以提高仿真精度并指导工程设计.

The stress intensity factor （ SIF） and stress fields at the crack tips of a center crack and an edge crack are investigated by the finite element method （ FEM） and the nodal displacement method. With the use of the 8 node isoparametric quadrilateral element and the quarter singular element, the influence of meshing density and crack length on the calculation accuracy is studied.The nodal den-sity in sub-region around the crack tips is improved, which can ensure the calculation accuracy and save computing time.The code for calculating and analyzing stress intensity factor, stress fields and displacement fields at the crack tips for modeⅠand modeⅡSIFs of plate is written in Matlab/Sim-ulink.The results of the FEM-code are compared with those of the exact methods.The results show that this proposed method can improve the calculation accuracy and the converging speed.The algo-rithm is reasonable and the results can be used to improve the precision of simulation results and guide engineering design.