From nucleation to percolation: the effect of system size when disorder and stress localization compete

Abstract

A phase diagram for a one-dimensional fiber bundle model is constructed with a continuous variation in two parameters guiding the dynamics of the model: strength of disorder and range of stress relaxation. When the range of stress relaxation is very low, the stress concentration plays a prominent role and the failure process is nucleating where a single crack propagates from a particular nucleus with a very high spatial correlation unless the disorder strength is high. On the other hand, a high range of stress relaxation represents the mean-field limit of the model where the failure events are random in space. At an intermediate disorder strength and stress release range, when these two parameters compete, the failure process shows avalanches and precursor activities. As the size of the bundle is increased, it favors a nucleating failure. In the thermodynamic limit, we only observe a nucleating failure unless either the disorder strength is extremely high or the stress release range is high enough so that the model is in the mean-field limit. A complex phase diagram on the plane of disorder strength, stress release range, and system size is presented showing different failure modes - (I) nucleation, (II) avalanche, and (III) percolation, depending on the spatial correlation observed during the failure process.

arXiv comment16 pages, 10 figures. arXiv admin note: substantial text overlap with arXiv:2107.09979

References in corpus (26)

• Statistical Models of Fracture
• Statistical similarity between the compression of a porous material and earthquakes
• First-Order Transition in the Breakdown of Disordered Media
• Quasi-static crack propagation in heterogeneous media
• From damage percolation to crack nucleation through finite size criticality
• Acoustic Emission from Paper Fracture
• Fracture model with variable range of interaction
• Origin of the Universal Roughness Exponent of Brittle Fracture Surfaces: Correlated Percolation in the Damage Zone
• Crack roughness and avalanche precursors in the random fuse model
• Fracturing highly disordered materials
• Fracture strength of disordered media: Universality, interactions and tail asymptotics
• Crack avalanches in the three dimensional random fuse model
• Crack propagation through phase separated glasses: effect of the characteristic size of disorder
• Modes of failures in disordered solids
• Nucleation versus percolation: Scaling criterion for failure in disordered solids
• Onset of Localization in Heterogeneous Interfacial Failure
• Spatial scaling in fracture propagation in dilute systems
• Size scaling of failure strength with fat-tailed disorder in a fiber bundle model
• Record statistics of bursts signals the onset of acceleration towards failure
• Predictability and Strength of a Heterogeneous System : The Role of System Size and Disorder
• Phase transitions and correlations in fracture processes where disorder and stress compete
• Role of spatial patterns in fracture of disordered multiphase materials
• System-size-dependent avalanche statistics in the limit of high disorder
• Size distribution of emitted energies in local load sharing fiber bundles
• Crack Localization and the Interplay between Stress Enhancement and Thermal Noise
• Correlation between avalanches and emitted energies during fracture with variable stress release range

Cited by in corpus (1)

• Correlation between avalanches and emitted energies during fracture with variable stress release range