Reliability Theory of Stochastic Fracture Processes in Sustained Loading: Part I

Abstract

It is shown that the physical mechanism of thermally activated subcritical crack growth is always a stochastic process and leads, therefore, to probabilistic crack propagation. This process is the result of the random breaking of atomic bonds and has to be clearly distinguished from the well known Weibull distribution. A Markov chain analysis leads to the normal distribution of crack sizes. The results demonstrate that conventional deterministic finite life-time designs are unsatisfactory and can lead to early failure of machine or structure elements as the consequence of the probabilistic process of crack propagation. The conclusions lead to the reliability analysis of Part II.

The conceptual physical framework of stochastic fracture kinetics

“…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.…”