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Interval prediction of the fatigue crack cycle using evidence theory and the Kriging meta-model

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Abstract

The fatigue crack cycle is calculated via a specimen experiment under specific stress conditions; however, the experimental results are scattered due to various causes (e.g., experimental conditions, material specifications). Therefore, the fatigue crack cycle is evaluated by fitting it to a specific probability model after carrying out a sufficient amount of testing. If the number of tests is insufficient, a specific probability model is unobtainable. The uncertainty due to an insufficient number of tests is referred to as the epistemic uncertainty. In this paper, evidence theory is employed to deal with epistemic uncertainty. Through the use of evidence theory, belief and plausibility functions are obtained. Belief and plausibility may be implied as the lower and upper bounds for the limited state function. Here, the belief and plausibility functions are approximated to the Kriging meta-model using sample data generated by the Cartesian product. These approximated functions can then be used to calculate the optimal solution using a genetic algorithm. Finally, the fatigue crack cycle is predicted in terms of the interval (belief and plausibility).

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Abbreviations

C :

material constant

n :

material constant

ΔK :

stress intensity factor range

a i :

initial crack length

a f :

critical crack length

N f :

the number of cycles to reach material fracture

Bel :

upper bound

Pl :

lower bound

K c :

fracture toughness

f i :

constant value representing crack geometry

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Authors and Affiliations

  1. Department of Mechanical Engineering, Yonsei University, 50, Yonsei-ro, Seodaemun-gu, Seoul, 03722, South Korea

    Dong Soo Kim & Jongsoo Lee

Authors
  1. Dong Soo Kim
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  2. Jongsoo Lee
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Correspondence to Jongsoo Lee.

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Kim, D.S., Lee, J. Interval prediction of the fatigue crack cycle using evidence theory and the Kriging meta-model. Int. J. Precis. Eng. Manuf. 16, 2315–2320 (2015). https://doi.org/10.1007/s12541-015-0297-5

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  • DOI: https://doi.org/10.1007/s12541-015-0297-5

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