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

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.

arXiv comment4 pages with 1 figure

References in corpus (5)

• Tri-critical behavior in rupture induced by disorder
• Positive Feedback, Memory and the Predictability of Earthquakes
• The effect of disorder on the fracture nucleation process
• Failure time in the fiber-bundle model with thermal noise and disorder
• Elastic Theory Has Zero Radius of Convergence

Cited by in corpus (18)

• Andrade and Critical Time-to-Failure Laws in Fiber-Matrix Composites: Experiments and Model
• Magnitude-Dependent Omori Law: Empirical Study and Theory
• Brittle to Ductile Transition in a Fiber Bundle with Strong Heterogeneity
• Experimental study of the effect of disorder on subcritical crack growth dynamics
• Relaxation dynamics in strained fiber bundles
• Gravity-driven instabilities: interplay between state-and-velocity dependent frictional sliding and stress corrosion damage cracking
• The cooperative effect of load and disorder in thermally activated rupture of a two-dimensional random fuse network
• Ubiquitous power law scaling in nonlinear self-excited Hawkes processes
• Record statistics of bursts signals the onset of acceleration towards failure
• Super-Arrhenius dynamics for sub-critical crack growth in disordered brittle media
• Exact asymptotic solutions to nonlinear Hawkes processes: a systematic classification of the steady-state solutions
• Crack Localization and the Interplay between Stress Enhancement and Thermal Noise
• Creep-like behavior in athermal threshold dynamics: Effects of disorder and stress
• Micro-structure of damage in thermally activated fracture of Lennard-Jones systems
• Creep failure in a threshold activated dynamics: Role of temperature during a sub-critical loading
• Hidden jerk in universal creep and aftershocks
• Statistical Physics of Rupture in Heterogeneous Media
• Non-equilibrium statistical mechanics of non-equilibrium damage phenomena