疲劳裂纹扩展的不确定理论

Uncertain theory for fatigue crack extension

在原有处理不确定问题的两种非概率方法的基础上,提出二阶区间分析方法和二阶凸模型方法,将不确定参数用区间或者凸集来描述;再利用Taylor级数展开法对含有不确定参数的裂纹扩展速率及寿命进行估计.同时给出传统的概率方法和两种不确定性方法的相互包含关系,对算例结果进行验证.通过对00Cr17Ni14Mo2材料裂纹扩展速率及寿命的计算,将区间分析方法、凸模型理论和传统的概率方法进行比较.结果表明,该理论在处理不确定问题时是有效的,且具有对统计信息依赖小,计算方法简便、实用和精度高的特点.

Based on the foremost two non-probabilistic methods, second-order interval analysis method and second-order convex model method were advanced. The uncertain theories described all the uncertainties as interval or convex set. Then through the Taylor series expansion, the interval range of fatigue crack growth rate and its life with uncertainty parameters can be estimated. The inclusion relation of traditional probabilistic method and two uncertain theories was presented. This inclusion relation can verify the results of examples. The fatigue crack growth rate and its life of 00Cr17Ni14Mo2 were computed to illustrate that uncertain theories are effective by comparing with the interval analysis method, convex model method and the traditional probabilistic method. Their advantages are that they only need less statistical data and the method is simple, practical and with high precision.