疲劳短裂纹扩展中的混沌现象

The Chaotic Behaviors in the Development of Fatigue Short Crack

在低周疲劳的短裂纹扩展中 ,利用非线性动力学理论 ,分析 Hobson的短裂纹扩展公式 [1 ] ,发现在一定条件下会出现分岔、混沌现象。计算机模拟试验显示 ,在混沌区域内 ,即使初始裂纹尺寸相差很小 ,在经过若干次的应力循环后 ,两者之间会相差很大。如果假设裂纹是以单裂纹穿晶形式扩展 ,发现参数在许多取值区间会发生分岔、混沌现象。由此可知 ,短裂纹扩展的分岔和混沌 ,是导致疲劳试验结果分散性大的原因之一。

According to the equation of a crack growth for short cracks ,with the nonlinear dynamics,the bifurcation and chaotic phenomena can be occurred in the low cycle fatigue short crack growth.When a computer simulates an experiment,it is showed that the last results are much different from each other even if the error between initial crack sizes is very small.Furthermore,if supposed a crack is to cross grain boundary,there are many areas of bifurcation and chaotic phenomena to be found.As a consequence,the bifurcation and chaotic phenomena in fatigue short crack growth is one of reasons of high dispersion in the experiment of fatigue short cracks.