A physical–statistical model of overload retardation for crack propagation and application in reliability estimation

ABSTRACT

Crack propagation subjected to fatigue loading has been widely studied under the assumption that loads are ideally cyclic with a constant amplitude. In the real world, loads are not exactly cyclic, due to either environmental randomness or artificial designs. Loads with amplitudes higher than a threshold limit are referred to as overloads. Researchers have revealed that for some materials, overloads decelerate rather than accelerate the crack propagation process. This effect is called overload retardation. Ignoring overload retardation in reliability analysis can result in a biased estimation of product life. In the literature, however, research on overload retardation mainly focuses on studying its mechanical properties without modeling the effect quantitatively and, therefore, it cannot be incorporated into the reliability analysis of fatigue failures. In this article, we propose a physical–statistical model to quantitatively describe overload retardation considering random errors. A maximum likelihood estimation approach is developed to estimate the model parameters. In addition, a likelihood ratio test is developed to determine whether the tested material has either an overload retardation effect or an overload acceleration effect. The proposed model is further applied to reliability estimation of crack failures when a material has the overload retardation effect. Specifically, two algorithms are developed to calculate the failure time cumulative distribution function and the corresponding pointwise confidence intervals. Finally, designed experiments are conducted to verify and illustrate the developed methods along with simulation studies.

KEYWORDS:

• Fatigue failure
• modified Paris law
• likelihood ratio test
• failure time distribution
• pointwise confidence interval
• bootstrap

Additional information

Notes on contributors

Wujun Si

Wujun Si is a Ph.D. candidate in the Department of Industrial & Systems Engineering at the Wayne State University. He received his B.Eng. degree in Mechanical Engineering from the University of Science and Technology of China in 2013. His research interests include statistical methods in reliability engineering as well as maintenance planning for complex systems.

Qingyu Yang

Qingyu Yang received B.S. and M.S. degrees in Automatic Control and Intelligent Systems from the University of Science and Technology of China in 2000 and 2003, respectively, an M.S. degree in Statistics, and Ph.D. in Industrial Engineering from the University of Iowa in 2007 and 2008, respectively. Currently, he is an Assistant Professor in the Department of Industrial and Systems Engineering at Wayne State University. His research interests include statistical data analysis, reliability and quality, and complex system modeling. He is a member of INFORMS and IIE.

Xin Wu

Xin Wu received his B.S. and M.S. degrees from the Xi'an Institute of Metallurgy and Construction Engineering and Beijing University of Science & Technology in 1975 and 1981, respectively, a M.S. degree and a Ph.D. from the University of Michigan in 1988 and 1991, respectively. Currently, he is an Associate Professor in the Department of Mechanical Engineering at the Wayne State University. His research interests include Material processing and manufacturing, metal forming, material behavior and plasticity.