Statistical Models of Fracture
arXiv:cond-mat/0609650 · doi:10.1080/00018730300741518
Abstract
Disorder and long-range interactions are two of the key components that make material failure an interesting playfield for the application of statistical mechanics. The cornerstone in this respect has been lattice models of the fracture in which a network of elastic beams, bonds or electrical fuses with random failure thresholds are subject to an increasing external load. These models describe on a qualitative level the failure processes of real, brittle or quasi-brittle materials. This has been particularly important in solving the classical engineering problems of material strength: the size dependence of maximum stress and its sample to sample statistical fluctuations. At the same time, lattice models pose many new fundamental questions in statistical physics, such as the relation between fracture and phase transitions. Experimental results point out to the existence of an intriguing crackling noise in the acoustic emission and of self-affine fractals in the crack surface morphology. Recent advances in computer power have enabled considerable progress in the understanding of such models. Among these partly still controversial issues, are the scaling and size effects in material strength and accumulated damage, the statistics of avalanches or bursts of microfailures, and the morphology of the crack surface. Here we present an overview of the results obtained with lattice models for fracture, highlighting the relations with statistical physics theories and more conventional fracture mechanics approaches.
148 pages, 65 Figures
References in corpus (2)
Cited by in corpus (29)
- Crackling dynamics in material failure as the signature of a self-organized dynamic phase transition
- Exactly solvable model of avalanches dynamics for Barkhausen crackling noise
- Creep dynamics of elastic manifolds via exact transition pathways
- Thermal rounding of the depinning transition
- Driving-induced crossover: from classical criticality to self-organized criticality
- Role of disorder in the size-scaling of material strength
- Training-induced criticality in martensites
- Growing correlations and aging of an elastic line in a random potential
- Crack propagation through phase separated glasses: effect of the characteristic size of disorder
- Creep of a fracture line in paper peeling
- Morphology of two dimensional fracture surface
- Computer simulation of fatigue under diametrical compression
- Universality class of fiber bundles with strong heterogeneities
- Out-of-equilibrium relaxation of the Edwards-Wilkinson elastic line
- Subcritical crack growth: the microscopic origin of Paris's law
- Continuous Damage Fiber Bundle Model for Strongly Disordered Materials
- Universal non stationary dynamics at the depinning transition
- Discrepancy between sub-critical and fast rupture roughness: a cumulant analysis
- Slow crack growth : models and experiments
- Crack Roughness in the 2D Random Threshold Beam Model
- Aging dynamics of non-linear elastic interfaces: the Kardar-Parisi-Zhang equation
- Dynamics of k-core percolation
- Discrete Fracture Model with Anisotropic Load Sharing
- Energy dissipation statistics in the random fuse model
- Far-from-equilibrium state in a weakly dissipative model
- A thermodynamical fiber bundle model for the fracture of disordered materials
- Thermal Effects in the dynamics of disordered elastic systems
- Effect of Disorder and Notches on Crack Roughness
- Nucleation of interfacial shear cracks in thin films on disordered substrates