A Markov Chain Model for Fatigue Crack Growth, Inspection and Repair: The Relationship Between Probability of Detection, Reliability and the Number of Repairs in Fleets of Railroad Tank Cars

2005 ◽  
Author(s):  
William T. Riddell ◽  
James Lynch
Keyword(s):  
Markov Chain ◽  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Markov Chain Model ◽  
Probability Of Detection ◽  
Chain Model ◽  
Car Industry ◽  
Inspection Techniques ◽  
Non Destructive

A Markov chain model to simulate the process of fatigue crack growth, non-destructive inspection and repair in a fleet of railroad tank cars is developed and presented. Crack growth is modeled to reproduce crack shapes that were observed during destructive tear-down tests at the end of life for several tank cars. The Markov chain model is further extended to include non-destructive inspections using POD curves that were established during baseline tests of several methods used in the railroad tank car industry. Next, the model is used to predict the effect of various non-destructive inspection techniques on fatigue-related reliability of the fleet, as well as the number of repairs that are required as a result of the inspections.

scholarly journals Initial Probability Distribution in Markov Chain Model for Fatigue Crack Growth Problem

2018 ◽  
Vol 7 (3.20) ◽  
pp. 136
Author(s):  
Siti Sarah Januri ◽  
Zulkifli Mohd Nopiah ◽  
Ahmad Kamal Ariffin Mohd Ihsan ◽  
Nurulkamal Masseran ◽  
Shahrum Abdullah
Keyword(s):  
Markov Chain ◽  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Probability Distribution ◽  
Crack Growth ◽  
Markov Chain Model ◽  
Initial Crack ◽  
Chain Model ◽  
Initial Probability Distribution ◽  
Growth Problem

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. 

Impact of Prognosis on Asset Life Extension and Readiness

2003 ◽  
Author(s):  
Yevgeny Macheret ◽  
Leo Christodoulou
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Crack Detection ◽  
Crack Size ◽  
Probability Of Detection ◽  
Life Extension ◽  
Growth Data ◽  
Damage State ◽  
The Impact

Fatigue response of structural components is determined by environmental conditions, material microstructure, and loading history. Variation of these factors results in significant scatter in fatigue-crack growth rates and component life. In this paper, the impact of prognosis capability on asset life extension and readiness is evaluated. Fatigue-crack growth data on aluminum samples under controlled spectrum loading are used to describe the statistics of the crack-size distribution. Several sensors with different probability of detection (POD) characteristics are considered for detecting cracks of critical size, and the effect of the POD on the component life extension is evaluated. Although the crack-detection capability leads to the asset life extension, it is not sufficient to maintain required mission readiness. On the other hand, the prognosis capability, which is based on the knowledge of the component’s current damage state, damage evolution laws, and upcoming mission loading, allows required mission readiness to be maintained.

Non-destructive observation of internal fatigue crack growth in Ti–6Al–4V by using synchrotron radiation μCT imaging

2016 ◽  
Vol 93 ◽  
pp. 397-405 ◽  
Author(s):  
Fumiyoshi Yoshinaka ◽  
Takashi Nakamura ◽  
Shinya Nakayama ◽  
Daiki Shiozawa ◽  
Yoshikazu Nakai ◽  
...  
Keyword(s):  
Fatigue Crack ◽  
Synchrotron Radiation ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Non Destructive

Scaling of Static Fracture of Quasi-Brittle Structures: Strength, Lifetime, and Fracture Kinetics

2012 ◽  
Vol 79 (3) ◽  
Author(s):  
Jia-Liang Le ◽  
Zdeněk P. Bažant
Keyword(s):  
Growth Rate ◽  
Fatigue Crack ◽  
Crack Growth Rate ◽  
Fatigue Crack Growth ◽  
Size Effect ◽  
Crack Growth ◽  
Failure Probability ◽  
Structural Strength ◽  
Chain Model ◽  
Weakest Link

The paper reviews a recently developed finite chain model for the weakest-link statistics of strength, lifetime, and size effect of quasi-brittle structures, which are the structures in which the fracture process zone size is not negligible compared to the cross section size. The theory is based on the recognition that the failure probability is simple and clear only on the nanoscale since the probability and frequency of interatomic bond failures must be equal. The paper outlines how a small set of relatively plausible hypotheses about the failure probability tail at nanoscale and its transition from nano- to macroscale makes it possible to derive the distribution of structural strength, the static crack growth rate, and the lifetime distribution, including the size and geometry effects [while an extension to fatigue crack growth rate and lifetime, published elsewhere (Le and Bažant, 2011, “Unified Nano-Mechanics Based Probabilistic Theory of Quasibrittle and Brittle Structures: II. Fatigue Crack Growth, Lifetime and Scaling,” J. Mech. Phys. Solids, 1322–1337), is left aside]. A salient practical aspect of the theory is that for quasi-brittle structures the chain model underlying the weakest-link statistics must be considered to have a finite number of links, which implies a major deviation from the Weibull distribution. Several new extensions of the theory are presented: (1) A derivation of the dependence of static crack growth rate on the structure size and geometry, (2) an approximate closed-form solution of the structural strength distribution, and (3) an effective method to determine the cumulative distribution functions (cdf’s) of structural strength and lifetime based on the mean size effect curve. Finally, as an example, a probabilistic reassessment of the 1959 Malpasset Dam failure is demonstrated.

Transition probabilities matrix of Markov Chain in the fatigue crack growth model

2016 ◽  
Author(s):  
Zulkifli Mohd Nopiah ◽  
Siti Sarah Januri ◽  
Ahmad Kamal Ariffin ◽  
Nurulkamal Masseran ◽  
Shahrum Abdullah
Keyword(s):  
Markov Chain ◽  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Growth Model ◽  
Transition Probabilities ◽  
Crack Growth Model
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