Time-dependent breakdown of fiber networks: Uncertainty of lifetime

Abstract

Materials often fail when subjected to stresses over a prolonged period. The time to failure, also called the lifetime, is known to exhibit large variability of many materials, particularly brittle and quasibrittle materials. For example, a coefficient of variation reaches 100% or even more. Its distribution shape is highly skewed toward zero lifetime, implying a large number of premature failures. This behavior contrasts with that of normal strength, which shows a variation of only 4%-10% and a nearly bell-shaped distribution. The fundamental cause of this large and unique variability of lifetime is not well understood because of the complex interplay between stochastic processes taking place on the molecular level and the hierarchical and disordered structure of the material. We have constructed fiber network models, both regular and random, as a paradigm for general material structures. With such networks, we have performed Monte Carlo simulations of creep failure to establish explicit relationships among fiber characteristics, network structures, system size, and lifetime distribution. We found that fiber characteristics have large, sometimes dominating, influences on the lifetime variability of a network. Among the factors investigated, geometrical disorders of the network were found to be essential to explain the large variability and highly skewed shape of the lifetime distribution. With increasing network size, the distribution asymptotically approaches a double-exponential form. The implication of this result is that, so-called "infant mortality," which is often predicted by the Weibull approximation of the lifetime distribution, may not exist for a large system.

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

“…This parameter is affected by both fibre and network disorders Uesaka 2015, 2017). The parameter b of the network is directly proportional to the one for the constituent fibres (Mattsson and Uesaka 2017). Therefore, any non-uniformity of fibre will affect the b parameter of network.…”

A Stochastic Model Based on Fiber Breakage and Matrix Creep for the Stress-Rupture Failure of Unidirectional Continuous Fiber Composites 2. Non-linear Matrix Creep Effects

“…The failure of heterogeneous materials typically involves timedependence of some form, and in accommodating such features, fiber bundle models become more complex, but also richer in features, as can be seen in . Time dependence can enter into the bundle failure process in various ways: First, the fiber breakdown process may be thermally activated as for instance in [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], or may involve time-dependent kinetics of flaw growth in the fiber as in [30,31]. On the other hand, the matrix may creep, or the fiber/matrix interface may slip over time, thus causing relaxation in broken fibers and overloading of others , thus altering the length scale of fiber-to-fiber load transfer.…”

“…This integral then becomes the argument of a second function controlling the shape of the lifetime distribution, and when of power form and the fiber is under a constant stress, Weibull fiber lifetime results. Several works specifically focus on such time-dependent fiber bundles as well as more elaborate network and lattice extensions, a sampling of which are discussed in [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. In papers involving varying ranges of lateral load transfer somewhere between the ELS and LLS extremes, crossovers from mean-field to short range behavior are seen where break clusters form and instability is seen.…”

“…To span ELS to LLS, the degree of localization also depends on the magnitude of the power-law breakdown exponent. Even in LLS bundles, one may see ELS-like diffuse fiber failure when the power-paw exponent approaches two and especially below 1 as shown in [24][25][26][27].…”

“…The works [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], which span the last 25 years of research, reveal surprising consistency in the overall behavior observed, in terms of size effects, localization in cluster growth and the types of lifetime distributions obtained, especially in the lower tails. Numerical Monte Carlo methods have become more efficient and computational power has increased, for a bundle with a given geometric and load-sharing complexity, by two to three orders of magnitude in size, which has been critical to providing insight into ultimate convergent (or divergent) behavior as the size scale increases.…”