Subcritical fatigue in fuse networks

¹ Departamento de Física, Universidade Federal do Ceará - 60451-970 Fortaleza, Ceará, Brazil
² Instituto de Física, Universidade de São Paulo - 05314-970, São Paulo, Brazil
³ Computational Physics, IfB, ETH Zürich - Hönggerberg, CH-8093 Zürich, Switzerland

^(a) lucas@fisica.ufc.br
^(b) apvieira@if.usp.br
^(c) hans@ifb.baug.eth.ch
^(d) soares@fisica.ufc.br

Received: 7 August 2012
Accepted: 16 October 2012

Abstract

We obtain the Paris law of fatigue crack propagation in a fuse network model where the accumulated damage in each resistor increases with time as a power law of the local current amplitude. When a resistor reaches its fatigue threshold, it burns irreversibly. Over time, this drives cracks to grow until the system is fractured into two parts. We study the relation between the macroscopic exponent of the crack-growth rate —entering the phenomenological Paris law— and the microscopic damage accumulation exponent, γ, under the influence of disorder. The way the jumps of the growing crack, Δa, and the waiting time between successive breaks, Δt, depend on the type of material, via γ, are also investigated. We find that the averages of these quantities, and , scale as power laws of the crack length a, and , where is the average rupture time. Strikingly, our results show, for small values of γ, a decrease in the exponent of the Paris law in comparison with the homogeneous case, leading to an increase in the lifetime of breaking materials. For the particular case of γ = 0, when fatigue is exclusively ruled by disorder, an analytical treatment confirms the results obtained by simulation.