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

1998 ◽  
Vol 12 (6) ◽  
Author(s):  
Jung-Kyu Kim ◽  
Dong-Suk Shim
Keyword(s):  
Markov Chain ◽  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Probabilistic Analysis

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. 

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

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 Probabilistic Fatigue Damage Assessment for Small Crack Growth

2000 ◽  
Author(s):  
Zhengwei Jack Zhao ◽  
Irewole Wally Orisamolu
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Fracture Mechanics ◽  
Crack Growth ◽  
Fatigue Damage ◽  
Probabilistic Analysis ◽  
Damage Assessment ◽  
Small Crack ◽  
Assessment Methodology ◽  
Crack Growth Model

Abstract Fatigue and fracture are typical random phenomena due to various uncertainty sources, including material property, initial flaw and crack shape, structural configuration and geometry around crack tip, load fluctuation, and other environmental factors. As contrast to the most commonly used probabilistic fatigue growth models, which are built based on simplified fatigue crack growth law, a framework of probabilistic fracture mechanics based fatigue damage assessment methodology for small crack propagation is presented here. The proposed modeling is developed based on a comprehensive fatigue crack growth model, which accounts the effect of crack aspect ratio, stress ratio, and crack closure and retardation. Due to the complicated nature of the fatigue damage modeling adopted, a high non-linear limit state function with discontinuity resulted from physical domain jumping and overlapping are encountered. The advanced fast probability integration techniques in conjunction with response surface methodology and Monte Carlo simulation are used and the accuracy of the analysis is verified. The interface between probabilistic analysis package and the deterministic fracture mechanics analysis program is developed for the purpose of uncertainty propagation. The probability of failure of fatigue damage is computed first. The statistical characteristics of estimated fatigue life and critical crack size are obtained and presented through CDF/PDF curves. The sensitivity analysis is also performed, which provides an indication of the order of importance for the random variables considered. The results of the study have shown robustness and efficiency of the probabilistic analysis to deal with the real world challenge of uncertainty modelling, propagation, and quantification. Currently, possibility to combine the subject probabilistic damage assessment methodology with reliability updating techniques is under the investigation. The successfulness of the presented research activity will address an important issue of quantitative risk analysis for aging structures subjected to accumulative material damage.

A discrete dislocation analysis of fatigue crack growth

2001 ◽  
Vol 11 (PR5) ◽  
pp. Pr5-69-Pr5-75
Author(s):  
V. S. Deshpande ◽  
H. H.M. Cleveringa ◽  
E. Van der Giessen ◽  
A. Needleman
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Discrete Dislocation

Fatigue Investigation of Elastomeric Structures

2010 ◽  
Vol 38 (3) ◽  
pp. 194-212 ◽  
Author(s):  
Bastian Näser ◽  
Michael Kaliske ◽  
Will V. Mars
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Material Behavior ◽  
Period Effect ◽  
Numerical Representation ◽  
Material Force ◽  
Strain Behavior ◽  
Dissipative Effects ◽  
Elastomeric Materials

Abstract Fatigue crack growth can occur in elastomeric structures whenever cyclic loading is applied. In order to design robust products, sensitivity to fatigue crack growth must be investigated and minimized. The task has two basic components: (1) to define the material behavior through measurements showing how the crack growth rate depends on conditions that drive the crack, and (2) to compute the conditions experienced by the crack. Important features relevant to the analysis of structures include time-dependent aspects of rubber’s stress-strain behavior (as recently demonstrated via the dwell period effect observed by Harbour et al.), and strain induced crystallization. For the numerical representation, classical fracture mechanical concepts are reviewed and the novel material force approach is introduced. With the material force approach at hand, even dissipative effects of elastomeric materials can be investigated. These complex properties of fatigue crack behavior are illustrated in the context of tire durability simulations as an important field of application.

Expert system model of small fatigue crack growth

1998 ◽  
Author(s):  
D. Steadman ◽  
R. Carlson ◽  
G. Kardomateas
Keyword(s):  
Fatigue Crack ◽  
Expert System ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
System Model ◽  
Small Fatigue Crack
Sign in / Sign up

Export Citation Format

Share Document