Time dependent fracture under unloading in a fiber bundle model

TL;DR

This study models how heterogeneous materials fracture under unloading, revealing a phase transition between partial failure with infinite lifetime and finite-time failure, with implications for predicting catastrophic failure.

Contribution

It introduces a fiber bundle model capturing time-dependent fracture under unloading, identifying a phase transition and universal behaviors in burst activity.

Findings

Rapid unloading leads to partial failure with infinite lifetime.

Slow unloading causes finite-time macroscopic failure.

Burst activity follows universal power law decay and Omori law-like acceleration.

Abstract

We investigate the fracture of heterogeneous materials occurring under unloading from an initial load. Based on a fiber bundle model of time dependent fracture, we show that depending on the unloading rate the system has two phases: for rapid unloading the system suffers only partial failure and it has an infinite lifetime, while at slow unloading macroscopic failure occurs in a finite time. The transition between the two phases proved to be analogous to continuous phase transitions. Computer simulations revealed that during unloading the fracture proceeds in bursts of local breakings triggered by slowly accumulating damage. In both phases the time evolution starts with a relaxation of the bursting activity characterized by a universal power law decay of the burst rate. In the phase of finite lifetime the initial slowdown is followed by an acceleration towards macroscopic failure where the increasing rate of bursts obeys the (inverse) Omori law of earthquakes. We pointed out a strong correlation between the time where the event rate reaches a minimum value and of the lifetime of the system which allows for forecasting of the imminent catastrophic failure.