The Inherently Probabilistic Character of Subcritical Fracture Processes

Krausz, A. S.; Krausz, K.

doi:10.1115/1.3256403

Cited by 8 publications

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“…The process can then be described wit the Markov-chain mathematics of the typically stochastic behavior, and with the Fokker-Planck equation of transport processes [8][9][10]. Both were applied to environmental crack growth in stress corrosion cracking and corrosion fatigue [11][12][13]. The random walk, and one of its mathematical formulations the Markov-chain, is not a common concept.…”

Section: The Stochastic Synthesis Model Of Crack Growthmentioning

confidence: 99%

The conceptual physical framework of stochastic fracture kinetics

Krausz

1989

Int J Fract

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Physically based, rational, constitutive laws are developed by analysis or synthesis: the second represents the maturity of deformation and fracture science. The basic processes are thermally activated discrete steps, each controlled by the elementary rate constant derived rigorously by rate theory considerations of statistical mechanics. The rate constants are combined by the laws of kinetics, leading to the constitutive relations which express the rate of the process as a function of the applied load, component geometry, temperature, and microstructure. The physical process is stochastic and the appropriate mathematics is expressed by the Markov chain or by the Fokker-Planck transport differential equation: both are the appropriate forms of the random walk process. The constitutive laws can lead to direct engineering applications and have critical significance at the threshold conditions.

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