Small Sample-Based Fatigue Reliability Analysis Using Non-Intrusive Polynomial Chaos

Abstract

Based on small sample of fatigue test data, a new method to obtain p-S-N curve for fatigue reliability analysis using non-intrusive polynomial chaos (NIPC) is proposed to lower test cost. Parameter C in Basquin S-N model is regarded as random variable. Samples of C are calculated through inverse analysis based on small sample of fatigue test life. Then non-intrusive polynomial chaos expansions of C with respect to fatigue life are constituted under different stress levels. Statistics of C can be calculated directly by polynomial coefficients. A fast large-sample of C can be obtained based on NIPC and probability distribution type can be determined through EDF test. Then samples of C under the stress levels can be obtained and substituted into S-N model to calculate corresponding fatigue life samples. The fatigue life under different reliabilities are calculated for fitting p-S-N curve. Fatigue test of Al 2024-T3 plate with hole is performed. p-S-N curves are obtained by proposed method and compared with that obtained by linear regression based on least square method. Almost all relative errors are less than 5%, which show that the proposed method can predict p-S-N curve effectively. INDEX TERMS Fatigue reliability analysis, non-intrusive polynomial chaos, p-S-N curve, small sample, Basquin S-N model, aluminium alloy 2024-T3.

Determination of the Statistical Power of Fatigue Characteristics in Relation to the Number of Samples

“…Both methods require at least 15 samples. Another approach was presented by Liu and Sun in a paper [14], where non-invasive polynomial chaos was used to determine fatigue characteristics. This approach requires 16 samples.…”

A general method for determining probabilisticS-Ncurve based on static strength data of material

“…Equation (11) indicates that α N ðSÞ can be figured out when u and v are known. Suppose u ¼ 0:50 and v ¼ 0:632, then equation ( 11) can be rewritten as follows On the basis of the probabilistic mapping relationship mentioned above, if the static strength of a specimen is equal to S u 0:50 , then its corresponding fatigue life is equal to N 0:50 .…”

“…Bai et al 10 introduced the concept of equivalent fatigue life, and a new method for estimating probabilistic S-N curve was developed based on the mixed samples. To minimize the experimental cost, Liu and Sun 11 developed a novel approach to determine the probabilistic S-N curve of material based on the non-intrusive polynomial chaos. Paolino et al 12 considered the failure mechanisms and fatigue limit of material, and a unified statistical model for estimating the probabilistic S-N curve was proposed.…”