A Markov Chain Fracture Model for Intergranular Crack Propagation in Polycrystalline Materials

2010 ◽  
Vol 89-91 ◽  
pp. 29-34
Author(s):  
Muhammad A. Arafin ◽  
Jerzy A. Szpunar
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Crack Propagation ◽  
Intergranular Crack ◽  
Crack Nucleation ◽  
External Stress ◽  
Polycrystalline Materials ◽  
Multiple Crack ◽  
Stress Direction ◽  
Nucleation Sites

A model for intergranular damage propagation in polycrystalline materials is proposed, based on Markov Chain theory, Monte Carlo simulation and percolation concept. The model takes into account crack branching and coalescence, multiple crack nucleation sites, crack-turning etc., as well as the effect of grain boundary plane orientations with respect to the external stress direction. Both honeycomb and voronoi microstructures were utilized as the input microstructures. The effect of multiple crack nucleation sites has been found to have great influence on the crack propagation length. It has been observed that percolation threshold reported in the literature based on hexagonal microstructure is not applicable when the effect of external stress direction on the susceptibilities of grain boundaries is considered. The successful integration of voronoi algorithm with the Markov Chain and Monte Carlo simulations has opened up the possibilities of evaluating the intergranular crack propagation behaviour in a realistic manner.

A Multi-Scale Modeling Approach to Simulate Intergranular Crack Propagation in Textured Polycrystalline Materials

2011 ◽  
Vol 702-703 ◽  
pp. 932-938
Author(s):  
Muhammad A. Arafin ◽  
Jian Lu ◽  
Jerzy Szpunar
Keyword(s):  
Crack Propagation ◽  
Intergranular Crack ◽  
Md Simulations ◽  
Polycrystalline Materials ◽  
Embedded Atom Method ◽  
Multi Scale ◽  
Modeling Approach ◽  
Embedded Atom ◽  
Scale Modeling ◽  
Different Types

In this paper, a multiscale modeling approach has been developed to simulate the intergranular crack propagation in textured polycrystalline materials. Embedded Atom Method (EAM) and Molecular Dynamics (MD) simulations were carried out to determine the energy and fracture strength of different types of grain boundaries in Ni3Al. Subsequently, the atomistic model has been integrated with the microstructure based model of crack propagation using the Voronoi-Markov Chain-Monte Carlo approach. The model has been utilized to evaluate the crack length for various scenarios and reasonable results are obtained.

Monte-Carlo simulation of crack propagation in polycrystalline materials

2004 ◽  
Vol 387-389 ◽  
pp. 372-376 ◽  
Author(s):  
Maria G. Ganchenkova ◽  
Vladimir A. Borodin
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Crack Propagation ◽  
Polycrystalline Materials

Bayesian Applications in Auditory Research

2019 ◽  
Vol 62 (3) ◽  
pp. 577-586 ◽  
Author(s):  
Garnett P. McMillan ◽  
John B. Cannon
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Bayesian Methods ◽  
Prior Distribution ◽  
Interim Analysis ◽  
Iterative Process ◽  
Bayes Theorem ◽  
Sound Therapy ◽  
The Many ◽  
Auditory Research

Purpose This article presents a basic exploration of Bayesian inference to inform researchers unfamiliar to this type of analysis of the many advantages this readily available approach provides. Method First, we demonstrate the development of Bayes' theorem, the cornerstone of Bayesian statistics, into an iterative process of updating priors. Working with a few assumptions, including normalcy and conjugacy of prior distribution, we express how one would calculate the posterior distribution using the prior distribution and the likelihood of the parameter. Next, we move to an example in auditory research by considering the effect of sound therapy for reducing the perceived loudness of tinnitus. In this case, as well as most real-world settings, we turn to Markov chain simulations because the assumptions allowing for easy calculations no longer hold. Using Markov chain Monte Carlo methods, we can illustrate several analysis solutions given by a straightforward Bayesian approach. Conclusion Bayesian methods are widely applicable and can help scientists overcome analysis problems, including how to include existing information, run interim analysis, achieve consensus through measurement, and, most importantly, interpret results correctly. Supplemental Material https://doi.org/10.23641/asha.7822592

AN ADAPTIVE MONTE CARLO MARKOV CHAIN METHOD APPLIED TO THE FLOW INVOLVING SELF-SIMILAR PROCESSES IN POROUS MEDIA

2014 ◽  
Vol 17 (3) ◽  
pp. 225-237
Author(s):  
Juarez S. Azevedo ◽  
Gildeberto S. Cardoso ◽  
Leizer Schnitman
Keyword(s):  
Porous Media ◽  
Monte Carlo ◽  
Markov Chain ◽  
Monte Carlo Markov Chain ◽  
Adaptive Monte Carlo ◽  
Markov Chain Method ◽  
Self Similar

Markov Chain Monte Carlo Methods for Reserves Estimation

2005 ◽  
Author(s):  
Andrew W. Wadsley
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Methods

Model Volatilitas Stokastik dengan Metode Markov Chain Monte Carlo

2018 ◽  
Vol 2 (1) ◽  
pp. 1
Author(s):  
Alfian Alfian
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo

On Markov Chain Monte Carlo Acceleration

1994 ◽  
Author(s):  
Alan E. Gelfand ◽  
Sujit K. Sahu
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo
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