Universality behind Basquin's law of fatigue

TL;DR

This paper reveals universal features in fatigue fracture across heterogeneous materials, showing that despite material differences, certain failure behaviors follow universal scaling laws and phase transition phenomena.

Contribution

It introduces a generic scaling form for deformation, links fatigue failure to a phase transition, and demonstrates universality in burst dynamics across different systems.

Findings

Fatigue failure exhibits universal power law burst distributions.

A phase transition occurs at the fatigue limit in the deformation process.

System-specific details are encapsulated in Basquin's exponent, enabling universal failure features.

Abstract

One of the most important scaling laws of time dependent fracture is Basquin's law of fatigue, namely, that the lifetime of the system increases as a power law with decreasing external load amplitude, $t_f\sim \sigma_0^{-\alpha}$, where the exponent $\alpha$ has a strong material dependence. We show that in spite of the broad scatter of the Basquin exponent $\alpha$, the fatigue fracture of heterogeneous materials exhibits intriguing universal features. Based on stochastic fracture models we propose a generic scaling form for the macroscopic deformation and show that at the fatigue limit the system undergoes a continuous phase transition when changing the external load. On the microlevel, the fatigue fracture proceeds in bursts characterized by universal power law distributions. We demonstrate that in a range of systems, including deformation of asphalt, a realistic model of deformation, and a fiber bundle model, the system dependent details are contained in Basquin's exponent for time to failure, and once this is taken into account, remaining features of failure are universal.