Stochastic fracture analysis of systems with moving material

Abstract

This paper considers the probability of fracture in a system in which a material travels supported by rollers. The moving material is subjected to longitudinal tension for which deterministic and stochastic models are studied. In the stochastic model, the tension is described by a multi-dimensional Ornstein-Uhlenbeck process. The material is assumed to have initial cracks perpendicular to the travelling direction, and a stochastic counting process describes the occurrence of cracks in the longitudinal direction of the material. The material is modelled as isotropic and elastic, and LEFM is applied. For a general counting process, when there is no fluctuation in tension, the reliability of the system can be simulated by applying conditional sampling. With the stochastic tension model, considering fracture of the material leads to a first passage time problem, the solution of which is estimated by simulation. As an example, the probability of fracture is computed for periodically occurring cracks with parameters typical to printing presses and paper material. The numerical results suggest that small cracks are not likely to affect the pressroom runnability. The results also show that tension variations may significantly increase the probability of fracture.