Time-dependent statistical failure of fiber networks

Abstract

Numerical simulations of time-dependent stochastic failure of fiber network have been performed by using a central-force, triangular lattice model. This two-dimensional (2D) network can be seen as the next level of structural hierarchy to fiber bundles, which have been investigated for many years both theoretically and numerically. Unlike fiber bundle models, the load sharing of the fiber network is determined by the network mechanics rather than a preassigned rule, and its failure is defined as the point of avalanche rather than the total fiber failure. We have assumed that the fiber in the network follows Coleman's probabilistic failure law [B. D. Coleman, J. Appl. Phys. 29, 968 (1958)] with the Weibull shape parameter β = 1 (memory less fiber). Our interests are how the fiber-level probabilistic failure law is transformed into the one for the network and how the failure characteristics and disorders on the fiber level influence the network failure response. The simulation results showed that, with increasing the size of the network (N ), weakest-link scaling (WLS) appeared and each lifetime distribution at a given size approximately followed Weibull distribution. However, the scaling behavior of the mean and the Weibull shape parameter clearly deviate from what we can predict from the WLS of Weibull distribution. We have found that a characteristic distribution function has, in fact, a double exponential form, not Weibull form. Accordingly, for the 2D network system, Coleman's probabilistic failure law holds but only approximately. Comparing the fiber and network failure properties, we found that the network structure induces an increase of the load sensitivity factor ρ (more brittle than fiber) and Weibull shape parameter β (less uncertainty of lifetime). Superimposed disorders on the fiber level reduce all these properties for the network.

Characterisation of time-dependent, statistical failure of cellulose fibre networks

“…Figure 4b shows the cumulative distribution function of lifetime, Fðt B Þ plotted in a Weibull format. The creep lifetime data approximately follow Weibull distribution, as was observed earlier (Mattsson and Uesaka 2013) and also predicted by the current model.…”

“…We have used a long-span compression tester (LCT) with finger supports, which was built at Rise Bioeconomy (formerly Swedish Forest Products Research Laboratories, STFI). Testing procedures were detailed in Mattsson and Uesaka (2013). Applied loads have been varied on 3-4 levels, and at each load level 50-100 samples have been tested.…”

Predicting sample lifetimes in creep fracture of heterogeneous materials

“…A linear behavior cannot be established (a Weibull exponent fit shows a very small exponent value of about 0.8, which should not be meaningful), and the statistics obtained from the model simulations are even less Weibull-like. Thus, the lifetime distributions do not follow weakest link scenarios of brittle time-dependent failure, in which the system failure takes place when the weakest subsystem reaches its lifetime [37][38][39]. This is not a surprise in the SFBM because it exhibits a more complex rheology than models of brittle fracture do.…”

Predicting creep lifetime performance in edgewise compression of containerboards and for stacked corrugated board boxes

“…In a series of publications, they investigated the applicability of a lifetime distribution model presented by Coleman to the time dependence of mechanical breakdown of fibres 14 . Mattsson and Uesaka studied the model both numerically and experimentally and found it applicable to fibre network systems and, to a good approximation, Weibull distributed for large enough networks 13,15,16 . They also identified and promoted three parameters, originating from the Coleman model, to study time‐dependent statistical failure for characterization of a material 17 .…”