基于多裂纹扩展随机模型估算疲劳寿命的方法研究

A New Method for Computing Fatigue Life Based on Stochastic Modeling of Multi-Crack Propagation

随机变量多裂纹随机模型可以很好地体现多裂纹结构件的破坏寿命及破坏模式,具有很大的分散性,但是该随机模型难以直接用数值方法求解。文中给出了一种处理整个裂纹扩展过程的递推求解区间内裂纹扩展长度的方法,同时提出了更为合理的变间隔分段处理方法来解决计算精度和计算量间的矛盾。基于该方法,文中对共线孔有限宽薄板受远场均匀载荷作用的试样进行了计算分析。由结果可以看出,所提方法能很好地解决随机变量多裂纹随机模型在估算结构件疲劳寿命时所带来的困难,对求解长寿命、大规模多裂纹结构件疲劳寿命问题有很大的帮助。

Aim. The otherwise excellent stochastic modeling of multi-crack propagation brings unfortunately great difficulty in computation. We now present a new method that we believe can overcome this computational difficulty to a certain extent. In the full paper, we use Sections 1 and 2 to explain our method in some detail. Essentially in Sections 1 and 2, we do three things： （1） using the recursion relations we derive, we solve the approximate eq. （3）, which is the new approximate stochastic model of multi-crack propagation, to compute the lengths of cracks under cyclic loading; （2） we propose the variable interval method to simplify the computation while retaining acceptable precision of fatigue life; （3） we define the two types of factor of influence and obtain the recursion relations as expressed by eq. （5）. To verify the rationality of our method, we give as numerical example the panel with finite breadth and collinear holes under evenly distributed loading. The computed results, given in Table 1 in the full paper, show preliminarily that the fatigue life of the multi-crack panel decreases with each increasing stochastic variable provided that the other two stochastic variables are kept unchanged.