The Analysis of Fatigue Lifetime using Markov Chain Model based on Randomization Paris Law Equation
Siti Sarah Januri1, Zulkifli Mohd Nopiah2, Ahmad Kamal Ariffin Mohd Ihsan3, Nurulkamal Masseran4, Shahrum Abdullah5
1Siti Sarah Januri, Department of Statistics and Decision Sciences Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Cawangan Negeri Sembilan, Seremban, Malaysia.
2Zulkifli Mohd Nopiah, Department of Statistics and Decision Sciences Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Cawangan Negeri Sembilan, Seremban, Malaysia.
3Ahmad Kamal Ariffin Mohd Ihsan, Department of Statistics and Decision Sciences Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Cawangan Negeri Sembilan, Seremban, Malaysia.
4Nurulkamal Masseran, Department of Statistics and Decision Sciences Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Cawangan Negeri Sembilan, Seremban, Malaysia.
5Shahrum Abdullah, Department of Statistics and Decision Sciences Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Cawangan Negeri Sembilan, Seremban, Malaysia.
Manuscript received on 03 February 2019 | Revised Manuscript received on 10 February 2019 | Manuscript Published on 22 March 2019 | PP: 282-286 | Volume-8 Issue-5S April 2019 | Retrieval Number: ES3429018319/19©BEIESP
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: The experimental data of fatigue crack growth scatter even under identical experimental conditions, including constant amplitude loading. Thus, it is important to take into account the data scatter of crack growth rates by using statistical approach analysis. In this study, the distribution of the fatigue crack growth life was estimated using Markov chain approach based on the modified Paris law equation to consider the variability in the growth of the fatigue crack. In this regard, in the Markov Chain model, the Paris law equation was integrated with the probability distribution of the initial crack length to calculate the probability transition matrix. The result shows that the initial probability distribution was represented by lognormal distribution and it can be said that the initial crack will happen only in state 1 and state 2. The consideration of probability distribution into Paris law equation to represent the physical meaning of fatigue crack growth process. The fatigue life estimation using the Markov chain model are found to be agreed well with experimental results and the value of R2 showed the model is good. The results provide a reliable prediction and show excellent agreement between proposed model and experimental result. This indicates that the model can be an effective tool for safety analysis of structure.
Keywords: Fatigue Crack Growth, Markov Chain Model, Probability Distribution, Randomization Paris law Equation.
Scope of the Article: Cryptography and Applied Mathematics