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A probabilistic analysis on variability of fatigue crack growth using the markov chain

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Abstract

Understanding the stochastic properties of variability in fatigue crack growth is important to maintaining the reliability and safety of structures. In this study, a stochastic model is proposed to describe crack growth behavior considering the variability of fatigue crack growth rates due to the heterogeneity of material. Fatigue life distribution is then predicted based on this model To construct this model, fatigue tests are conducted on a high strength aluminum alloy 7075 T6 under constant stress intensity factor range control. The variability of fatigue crack growth rates is expressed by random variablesZ and Γ based on the variability of material constantsC andm of the Paris-Erdogan equation. The distribution of fatigue life under constant stress intensity factor ranges is evaluated by the stochastic Markov chain model based on the Paris-Erdogan equation. The merit of the proposed model is that only a small number of tests are required to determine this function, and fatigue life required to reach certain crack length at a given stress intensity factor range can be easily predicted.

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Abbreviations

a :

Crack length

a o :

Initial crack length

a r :

Final crack length

b :

State number

B :

Thickness

C, m :

Material constants in Paris Erdogan equation

C o ,m o :

Expected values ofC andm

ΔK :

Stress intensity factor range

N :

Number of cycles

P :

Transition matrix

p :

Transition probability

P o :

Initial probability vector

P x :

Probability vector

s :

Number of specimen

U :

Random number

Z, Γ:

Random variables according to material constantsC andm

α, β:

Parameters of the 2 parameter Weibull distribution

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Authors and Affiliations

  1. School of Mechanical Eng., Hanyang University, 17, Sungdong Ku, 133-791, Seoul, Korea

    Jung-Kyu Kim

Authors
  1. Jung-Kyu Kim
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  2. Dong-Suk Shim
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Department of Mechanical Design and Production Eng.

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Kim, JK., Shim, DS. A probabilistic analysis on variability of fatigue crack growth using the markov chain. KSME International Journal 12, 1135–1142 (1998). https://doi.org/10.1007/BF02942587

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  • DOI: https://doi.org/10.1007/BF02942587

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