Uncertain theory for fatigue crack extension

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.