考虑T-stress的非正态随机参数疲劳裂纹扩展寿命的可靠性分析

基于断裂力学的疲劳裂纹扩展寿命问题的研究常常将裂纹尖端应力展开项的高次项忽略,引起了裂纹扩展模拟的误差,本文考虑高次项T-stress对裂纹扩展角的影响,对裂纹扩展过程做了数值模拟,结果显示相同裂纹扩展长度下,考虑T-stress会延长裂纹扩展寿命。文章首先采用修正的Paris-Erdogan 公式计算了两端承受均布拉伸载荷的边缘斜裂纹板的疲劳裂纹扩展寿命,裂纹扩展方向采用两参数修正的最大拉应力准则。由于结构尺寸,材料特性和载荷等因素具有不确定性,导致疲劳裂纹扩展过程带有一定的随机性,本文以材料属性和载荷为随机变量,在随机有限元法的基础上,结合计算可靠度的四阶矩法,Edgeworth级数展开方法,提出随机参数服从任意分布时的结构疲劳裂纹扩展寿命可靠度的计算方法。分析了参数为非正态分布时的平板裂纹扩展寿命可靠度随裂纹扩展的变化过程。本文方法可预测工程中板裂纹的扩展行为,以及预测裂纹板的可靠度。

The reliability analysis of fatigue propagation life with non-normal \=random parameters taking T-stress into account

The study of fatigue crack propagation life based on fracture mechanics often ignore the higher order term of the crack tip stress expansion. This will cause the crack growth simulation error. This paper simulates the fatigue crack propagation considering the T-stress which influences the crack propagation angle. From the results, T-stress delays the propagation life of the plate. Based on the modified Paris-Endogan formula fatigue crack propagation life of a plate with a slope crack along the left edge and subjected to constant distributed stress at up&down edges of the plate is analyzed. The direction of the crack propagation follows the two-parameter modified maximum tensile stress criterion. Because of the geometrical dimension, material property, mechanical loads are often random variables, crack growth behavior is random process. Based on the former research, considering material properties and loads as non-normal random parameters, the variable reliability of fatigue crack propagation life to the targeted life is calculated using Stochastic Finite Element Method, Fourth Moment Method and Edgeworth series. This method can predict the behavior of the crack growth of plates and the reliability of it.