Stochastic fracture mechanics using polynomial chaos |
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Affiliation: | 1. Center for Biomedical Technology, Technical University of Madrid, Campus Montegancedo, Pozuelo de Alarcón, Madrid 28223, Spain;2. Center for Technologies in Robotics and Mechatronics Components, Innopolis University, Universitetskaya Str., 1, Innopolis 420500, Republic of Tatarstan, Russia;3. Campus Universitario Lagos, Universidad de Guadalajara, Enrique Díaz de León, 1144, Paseo de la Montaña, Lagos de Moreno 47460, Jalisco, Mexico;4. Smart Human Capital, Edificio Musaat, Calle del Jazmín, 66, Madrid 28033, Spain;1. Northeastern University, Shenyang 110819, PR China;2. Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of Education, Shenyang 110819, PR China |
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Abstract: | Crack propagation in metals has long been recognized as a stochastic process. As a consequence, crack propagation rates have been modeled as random variables or as random processes of the continuous. On the other hand, polynomial chaos is a known powerful tool to represent general second order random variables or processes. Hence, it is natural to use polynomial chaos to represent random crack propagation data: nevertheless, no such application has been found in the published literature. In the present article, the large replicate experimental results of Virkler et al. and Ghonem and Dore are used to illustrate how polynomial chaos can be used to obtain accurate representations of random crack propagation data. Hermite polynomials indexed in stationary Gaussian stochastic processes are used to represent the logarithm of crack propagation rates as a function of the logarithm of stress intensity factor ranges. As a result, crack propagation rates become log-normally distributed, as observed from experimental data. The Karhunen–Loève expansion is used to represent the Gaussian process in the polynomial chaos basis. The analytical polynomial chaos representations derived herein are shown to be very accurate, and can be employed in predicting the reliability of structural components subject to fatigue. |
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Keywords: | Random crack propagation Random fatigue Stochastic processes Wiener chaos Chaos polynomials Karhunen–Loève expansion |
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