Phase transitions and correlations in fracture processes where disorder and stress compete

Abstract

We study the effect of the competition between disorder and stress enhancement in fracture processes using the local load sharing fiber bundle model, a model that hovers on the border between analytical tractability and numerical accessibility. We implement a disorder distribution with one adjustable parameter. The model undergoes a localization transition as a function of this parameter. We identify an order parameter for this transition and find that the system is in the localized phase over a finite range of values of the parameter bounded by a transition to the non-localized phase on both sides. The transition is first order at the lower transition and second order at the upper transition. The critical exponents characterizing the second order transition are close to those characterizing the percolation transition. We determine the spatiotemporal correlation function in the localized phase. It is characterized by two power laws as in invasion percolation. We find exponents that are consistent with the values found in that problem.

arXiv comment8 pages, 5 figures

References in corpus (8)

• Failure Processes in Elastic Fiber Bundles
• Tri-critical behavior in rupture induced by disorder
• Burst avalanches in solvable models of fibrous materials
• From damage percolation to crack nucleation through finite size criticality
• Fracturing highly disordered materials
• Onset of Localization in Heterogeneous Interfacial Failure
• The Local load sharing fiber bundle model in higher dimensions
• Verification of a dynamic scaling for the pair correlation function during the slow drainage of a porous medium

Cited by in corpus (7)

• Thermal effects on fracture and brittle-to-ductile transition
• 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
• Failure process of fiber bundles with random misalignment
• From nucleation to percolation: the effect of system size when disorder and stress localization compete
• From nucleation to percolation: the effect of system size and system disorder