Predicting sample lifetimes in creep fracture of heterogeneous materials

Abstract

Materials flow-under creep or constant loads-and, finally, fail. The prediction of sample lifetimes is an important and highly challenging problem because of the inherently heterogeneous nature of most materials that results in large sample-to-sample lifetime fluctuations, even under the same conditions. We study creep deformation of paper sheets as one heterogeneous material and thus show how to predict lifetimes of individual samples by exploiting the "universal" features in the sample-inherent creep curves, particularly the passage to an accelerating creep rate. Using simulations of a viscoelastic fiber bundle model, we illustrate how deformation localization controls the shape of the creep curve and thus the degree of lifetime predictability.

Time-dependent fracture under unloading in a fiber bundle model

“…Careful experiments revealed a universality of the multiplication factor t c ≈ 3/2t m significantly larger than our one [33,34]. Recently, a similar relation was suggested to describe the lifetime of loaded paper sheets where the creep process proved to be more anisotropic with t c ≈ 1.2t m [32].…”

Avalanche Behavior in Creep Failure of Disordered Materials

“…A wide range of disordered materials exhibit a common rheological response when loaded under creep conditions at constant stress levels below their short-time strength [1][2][3][4]: after a decelerating and a constant strain rate regime, deformation enters an accelerating regime where macroscopic failure is approached as a finite time singularity of the creep rate. Deformation proceeds in avalanches which reveal the discrete nature of plastic flow at the microscopic scale and the internal collective dynamics in the run-up to failure.…”

Catastrophic Failure and Critical Scaling Laws of Fiber Bundle Material

“…Many catastrophic events, such as the collapse of engineering structures, natural catastrophes and abrupt weather changes, all share similar critical scaling laws [1,2,15,16]. In many current models for precursory acceleration, the rate of an observable quantity Ω is usually described by an empirical relationship [1,2,3,4,11,12,13,14,15,16,20,21,22,23,24,25,26]:$\dot{\Omega }=C{false(t_f-tfalse)}^{-\beta }$ where t f is the failure time, C is a scaling parameter, and β is the critical exponent.…”

“…Analyzing the precursors to failure has been a long-standing problem and has been widely accepted as a significant way to predict material failure [5,11,12,13,14,15,16]. Voight [12,13] proposed a materials failure law to describe the accelerating precursory immediately prior to failure.…”

“…Voight [12,13] proposed a materials failure law to describe the accelerating precursory immediately prior to failure. The Materials Failure Forecasting Method (FFM) [5,14,15,16,17,18], which is based on the accelerating precursors, has been proposed for the prediction of natural disasters such as volcanic eruptions, earthquakes and landslides.…”