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.
Highlights
Metal are widely used as primary load-carrying components in engineering structure [1]
Fatigue reliability design becomes more significant in engineering structure design. p-S-N curve is the most straightforward way, which can predict fatigue life for given reliability under constant amplitude loading
P-S-N curve is fitted by linear regression and maximum likelihood method based on groups of fatigue test data [10], which is time-consuming
Summary
Metal are widely used as primary load-carrying components in engineering structure [1]. Non-intrusive polynomial chaos method is used to calculate statistical characteristics of C. K =0 where Npc is number of terms in polynomial chaos expansion, which is the minimum number of samples required to determine coefficient Ck. Eq (1) indicates that random function φ can be decomposed into deterministic and stochastic components. The weight function of polynomial basis contains probabilistic properties of random variables, which is reason that NIPC can calculate statistics based on small sample of random variables. In the view of statistics, numerous samples of fatigue test life are needed to obtain probabilistic properties of lgC with enough accuracy. We will use non-intrusive polynomial chaos to establish stochastic analysis framework on the basis of small sample of fatigue test life. Substituting samples of lgC into S-N model Eq (11), we can get samples of fatigue life, and fatigue life under different reliabilities can be calculated for fitting p-S-N curve
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