A Markov chain model for interface fracture during fiber pull‐out under sustained loading

Abstract Fiber pull‐out from concrete involves fracture of the fiber‐matrix interface. For cases of sustained loading, the fracture process may induce large variations in the time to complete pull‐out of the fiber. Such observations complicate the development and use of deterministic modeling approaches. In this research, fracture of the fiber‐matrix interface, and the associated debonding process, are modeled as stochastically evolving phenomena over time. For an individual fiber, debonding extension length is determined using a fracture mechanics approach, based on comparisons between energy release rate and the corresponding fracture resistance. In accordance with these quantities, the transition probability to the debonded state is quantified and introduced to a discrete‐time Markov chain model. The Markov model accommodates the progression of debonding over time until complete pull‐out, producing the probability distribution of pull‐out time as well. The results indicate heavy‐tailed distributions of the pull‐out time. The statistical variations agree reasonably well with those obtained from test data. The proposed model is a requisite step toward simulating the behavior of fiber bundle systems under sustained loading.