### Abstract

Stochastic processes in fatigue crack growth problem usually due to the uncertainties factors such as material properties, environmental conditions and geometry of the component. These random factors give an appropriate framework for modelling and predicting a lifetime of the structure. In this paper, an approach of calculating the initial probability distribution is introduced based on the statistical distribution of initial crack length. The fatigue crack growth is modelled and the probability distribution of the damage state is predicted by a Markov Chain model associated with a classical deterministic crack Paris law. It has been used in calculating the transition probabilities matrix to represent the physical meaning of fatigue crack growth problem. The initial distribution has been determined as lognormal distribution which 66% that the initial crack length will happen in the first state. The data from the experimental work under constant amplitude loading has been analyzed using the Markov Chain model. The results show that transition probability matrix affect the result of the probability distribution and the main advantage of the Markov Chain is once all the parameters are determined, the probability distribution can be generated at any time, x.

Original language | English |
---|---|

Pages (from-to) | 136-139 |

Number of pages | 4 |

Journal | International Journal of Engineering and Technology(UAE) |

Volume | 7 |

Issue number | 3.20 Special Issue 20 |

Publication status | Published - 1 Jan 2018 |

### Fingerprint

### Keywords

- Fatigue crack growth
- Initial distribution
- Markov Chain model
- Paris law equation

### ASJC Scopus subject areas

- Biotechnology
- Computer Science (miscellaneous)
- Environmental Engineering
- Chemical Engineering(all)
- Engineering(all)
- Hardware and Architecture

### Cite this

*International Journal of Engineering and Technology(UAE)*,

*7*(3.20 Special Issue 20), 136-139.

**Initial probability distribution in Markov Chain model for fatigue crack growth problem.** / SarahJanuri, Siti; Mohd Nopiah, Zulkifli; Mohd Ihsan, Ahmad Kamal Ariffin; Masseran, Nurulkamal; Abdullah, Shahrum.

Research output: Contribution to journal › Article

*International Journal of Engineering and Technology(UAE)*, vol. 7, no. 3.20 Special Issue 20, pp. 136-139.

}

TY - JOUR

T1 - Initial probability distribution in Markov Chain model for fatigue crack growth problem

AU - SarahJanuri, Siti

AU - Mohd Nopiah, Zulkifli

AU - Mohd Ihsan, Ahmad Kamal Ariffin

AU - Masseran, Nurulkamal

AU - Abdullah, Shahrum

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Stochastic processes in fatigue crack growth problem usually due to the uncertainties factors such as material properties, environmental conditions and geometry of the component. These random factors give an appropriate framework for modelling and predicting a lifetime of the structure. In this paper, an approach of calculating the initial probability distribution is introduced based on the statistical distribution of initial crack length. The fatigue crack growth is modelled and the probability distribution of the damage state is predicted by a Markov Chain model associated with a classical deterministic crack Paris law. It has been used in calculating the transition probabilities matrix to represent the physical meaning of fatigue crack growth problem. The initial distribution has been determined as lognormal distribution which 66% that the initial crack length will happen in the first state. The data from the experimental work under constant amplitude loading has been analyzed using the Markov Chain model. The results show that transition probability matrix affect the result of the probability distribution and the main advantage of the Markov Chain is once all the parameters are determined, the probability distribution can be generated at any time, x.

AB - Stochastic processes in fatigue crack growth problem usually due to the uncertainties factors such as material properties, environmental conditions and geometry of the component. These random factors give an appropriate framework for modelling and predicting a lifetime of the structure. In this paper, an approach of calculating the initial probability distribution is introduced based on the statistical distribution of initial crack length. The fatigue crack growth is modelled and the probability distribution of the damage state is predicted by a Markov Chain model associated with a classical deterministic crack Paris law. It has been used in calculating the transition probabilities matrix to represent the physical meaning of fatigue crack growth problem. The initial distribution has been determined as lognormal distribution which 66% that the initial crack length will happen in the first state. The data from the experimental work under constant amplitude loading has been analyzed using the Markov Chain model. The results show that transition probability matrix affect the result of the probability distribution and the main advantage of the Markov Chain is once all the parameters are determined, the probability distribution can be generated at any time, x.

KW - Fatigue crack growth

KW - Initial distribution

KW - Markov Chain model

KW - Paris law equation

UR - http://www.scopus.com/inward/record.url?scp=85063184413&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063184413&partnerID=8YFLogxK

M3 - Article

VL - 7

SP - 136

EP - 139

JO - International Journal of Engineering and Technology(UAE)

JF - International Journal of Engineering and Technology(UAE)

SN - 2227-524X

IS - 3.20 Special Issue 20

ER -