Andrade, Omori and Time-to-failure Laws from Thermal Noise in Material Rupture

TL;DR

This paper presents an analytical model explaining empirical laws in material rupture under thermal fluctuations, linking creep behavior, time-to-failure, and acoustic emissions through thermally activated processes.

Contribution

It introduces a simple rupture model with thermal noise that analytically reproduces key empirical observations and reveals a new re-entrant effect related to disorder.

Findings

Reproduces Andrade and Omori decay laws analytically.

Describes the critical time-to-failure behavior prior to rupture.

Identifies a re-entrant effect of lifetime depending on disorder amplitude.

Abstract

Using the simplest possible ingredients of a rupture model with thermal fluctuations, we provide an analytical theory of three ubiquitous empirical observations obtained in creep (constant applied stress) experiments: the initial Andrade-like and Omori-like $1/t$ decay of the rate of deformation and of fiber ruptures and the $1/(t_c-t)$ critical time-to-failure behavior of acoustic emissions just prior to the macroscopic rupture. The lifetime of the material is controlled by a thermally activated Arrhenius nucleation process, describing the cross-over between these two regimes. Our results give further credit to the idea proposed by Ciliberto et al. that the tiny thermal fluctuations may actually play an essential role in macroscopic deformation and rupture processes at room temperature. We discover a new re-entrant effect of the lifetime as a function of quenched disorder amplitude.