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

Based on small sample of fatigue test data, a new method to obtain <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> curve for fatigue reliability analysis using non-intrusive polynomial chaos (NIPC) is proposed to lower test cost. Parameter <inline-formula> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> in Basquin <inline-formula> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> model is regarded as random variable. Samples of <inline-formula> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> are calculated through inverse analysis based on small sample of fatigue test life. Then non-intrusive polynomial chaos expansions of <inline-formula> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> with respect to fatigue life are constituted under different stress levels. Statistics of <inline-formula> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> can be calculated directly by polynomial coefficients. A fast large-sample of <inline-formula> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> can be obtained based on NIPC and probability distribution type can be determined through EDF test. Then samples of <inline-formula> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> under the stress levels can be obtained and substituted into <inline-formula> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> model to calculate corresponding fatigue life samples. The fatigue life under different reliabilities are calculated for fitting <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> curve. Fatigue test of Al 2024-T3 plate with hole is performed. <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> curve effectively.

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