Creep rupture of materials: insights from a fiber bundle model with relaxation

TL;DR

This paper introduces a fiber bundle model with relaxation to simulate creep rupture in materials, capturing all three creep stages and matching experimental observations of failure timing and event statistics.

Contribution

It adapts a seismic-inspired fiber bundle model to accurately reproduce creep rupture stages and failure timing in materials.

Findings

Model reproduces initial, steady, and tertiary creep regimes.

Time of minimum strain rate occurs at 60-65% of failure time.

Burst size distribution follows a -3/2 power law near failure.

Abstract

I adapted a model recently introduced in the context of seismic phenomena, to study creep rupture of materials. It consists of linear elastic fibers that interact in an equal load sharing scheme, complemented with a local viscoelastic relaxation mechanism. The model correctly describes the three stages of the creep process, namely an initial Andrade regime of creep relaxation, an intermediate regime of rather constant creep rate, and a tertiary regime of accelerated creep towards final failure of the sample. In the tertiary regime creep rate follows the experimentally observed one over time-to-failure dependence. The time of minimum strain rate is systematically observed to be about 60-65 % of the time to failure, in accordance with experimental observations. In addition, burst size statistics of breaking events display a -3/2 power law for events close to the time of failure, and a steeper decay for the all-time distribution. Statistics of interevent times shows a tendency of the events to cluster temporarily. This behavior should be observable in acoustic emission experiments.