Mid Sweden University

A fibre network is a ubiquitous structure widely seen in industrial materials (paper, nonwoven, composites), biological tissues (collagen and cytoskeleton), and basic polymers. These materials all exhibit time-dependent failures under general loading histories (e.g. creep, constant-rate loading, impacts).

One of the important features of the time-dependent failure is that time to failure, i.e. lifetime shows enormous variability, e.g. a coefficient of variation of 100% or even more. This contrasts with that of normal strength (short-term strength), which typically shows the variation of only 4%–10% (Christensen, 2005; Hristopulos and Uesaka, 2003). A basic question is what causes such large uncertainty of lifetime.

In this chapter, we discuss fundamental causes of the uncertainty of lifetimes, starting from the stochastic process taking place on the molecular level, and describing complex interplays between the molecular process and disordered network structures. A special focus is placed on non-traditional size scaling, asymptotic distributions, and the impacts of different types of disorders.