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Engineering Fracture Mechanics 74 (2007) 2952–2963 www.elsevier.com/locate/engfracmech

Statistical aspects of some fatigue crack growth data
W.F. Wu
a b

a,*

, C.C. Ni

b

Department of Mechanical Engineering, National Taiwan University, Taipei 10617, Taiwan Department of Mechanical Engineering, China Institute of Technology, Taipei 11522, Taiwan Received 7 October 2005; received inrevised form 24 May 2006; accepted 4 August 2006 Available online 19 October 2006

Abstract In this study, fatigue crack growth tests were performed for a considerable amount of specimens made of 2024T-351 aluminum alloy. In total, there are three data sets obtained, two of them are tested under constant-amplitude loading and the other under random loading. The results are reported in thepresent paper with special emphasis on the scatter and statistical aspect of these fatigue crack growth data. They are also compared with those of other available data sets. It is confirmed that the inhomogeneity of material does cause the scatter of fatigue crack growth. Whether the randomness of the applied load increases or decreases the scatter, however, needs to be investigated further since thereis no unique result for all data sets compared. Crack exceedance probabilities of random crack size and cumulative distributions of random loading cycle obtained by solving probabilistic models of fatigue crack growth curves are also presented, and conclusions are drawn. Comments on chi-square goodness-of-fit test and equivalent loading investigation are made as well. Ó 2006 Elsevier Ltd. Allrights reserved.
Keywords: Fatigue crack growth; Statistical analysis; Probabilistic model; Chi-square test; Equivalent load

1. Introduction It is known that fatigue crack growth of engineering materials exhibits a wide range of scatter, even under the same loading condition in a strictly controlled environment with specimens cut from the same sheet. To take into account the scatter, it isimportant to analyze fatigue crack growth data from a statistical viewpoint. In fact, many researchers have carried out studies in this aspect [1–9], and many stochastic fatigue crack growth models have been proposed to depict the scattering of the crack growth process [10–20]. To proceed with the investigation, experimental data are always needed. However, it is rather time-consuming to carry outexperiments in order to obtain sets of statistically meaningful fatigue crack growth data. Up to now, there are only a few data sets available in the literature. Among them, the most famous data set and frequently quoted by researchers [21,22] is perhaps the one obtained by Virkler et al. [1]. Some more frequently mentioned data sets include one reported by Ghonem and Dore [23] and the others released byYang and his coworkers [24–28]. As a result, many stochastic fatigue crack growth models are either lacking experimental verification
*

Corresponding author. Tel.: +886 2 2365 2164; fax: +886 2 2363 1755. E-mail address: wfwu@ntu.edu.tw (W.F. Wu).

0013-7944/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfracmech.2006.08.019

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or verified by only one data set. It is obvious that more experimental data sets are needed to provide for researchers with tools to verify the applicability of their models. Therefore, in the present paper, three newly obtained and statistically meaningful fatigue crack growth data sets are presented, two of them under constant-amplitude loadingtest and the other under random loading test. Statistical analyses are performed on these data and their results are compared with those obtained from other published data sets. These newly obtained data are also used to verify several stochastic fatigue crack growth models proposed either by the writers or other researchers. Comments on results of the analyses are made at the end of the paper....