Fractures in heterogeneous two-dimensional systems (original) (raw)
Related papers
Molecular dynamic study of fracture in 2D disordered elastic Lennard-Jones solids
Zeitschrift f�r Physik B Condensed Matter, 1986
The time-dependent deformation of a solid under stress is studied by molecular dynamics in a continuum, starting with atoms randomly distributed on a triangular lattice. The stress needed for fracture seems to vanish and the time to complete fracture seems to diverge at the percolation threshold, whereas the elastic modulus vanishes at a different concentration.
The European Physical Journal B, 2005
This article reports results concerning the fracture of a 2d triangular lattice of atoms linked by springs. The lattice is submitted to controlled strain tests and the influence of both porosity and temperature on failure is investigated. The porosity is found on one hand to decrease the stiffness of the material but on the other hand it increases the deformation sustained prior to failure. Temperature is shown to control the ductility due to the presence of cavities that grow and merge. The rough surfaces resulting from the propagation of the crack exhibit self-affine properties with a roughness exponent ζ = 0.59 ± 0.07 over a range of length scales which increases with temperature. Large cavities also have rough walls which are found to be fractal with a dimension, D, which evolves with the distance from the crack tip. For large distances, D is found to be close to 1.5, and close to 1.0 for cavities just before their coalescence with the main crack.
International Journal of Fracture, 2015
Any fracture process ultimately involves the rupture of atomic bonds. Processes at the atomic scale therefore critically influence the toughness and overall fracture behavior of materials. Atomistic simulation methods including large-scale molecular dynamics simulations with classical potentials, density functional theory calculations and advanced concurrent multiscale methods have led to new insights e.g. on the role of bond trapping, dynamic effects, crackmicrostructure interactions and chemical aspects on the fracture toughness and crack propagation patterns in
Fracture precursors in disordered systems
Europhysics Letters (EPL), 2004
A two-dimensional lattice model with bond disorder is used to investigate the fracture behaviour under stress-controlled conditions. Although the cumulative energy of precursors does not diverge at the critical point, its derivative with respect to the control parameter (reduced stress) exhibits a singular behaviour. Our results are nevertheless compatible with previous experimental findings, if one restricts the comparison to the (limited) range accessible in the experiment. A power-law avalanche distribution is also found with an exponent close to the experimental values. PACS numbers: 46.50.+a, 62.20.Mk, 05.70.Ln Fractures are very complex phenomena which involve a wide range of spatial and sometimes temporal scales. Accordingly, the development of a general theory is quite an ambitious goal, since it is not even clear whether a continuous coarse-grained description makes sense; additionally, for the very same reason, realistic simulations are almost unfeasible. However, such difficulties have not prevented making progress on several aspects of fracture dynamics such as propagation velocity, roughness, or the failure time under a constant stress [1, 2, 3]. In this paper we are interested in studying the development of the socalled precursors, microcracks preceding the macroscopic fracture in a brittle disordered environment. Some recent experiments suggest that we are in the presence of a critical phenomenon, although the accuracy is not yet high enough not only to discuss its universality properties, but also to assess the order of the transition.
Role of lattice discreteness on brittle fracture: Atomistic simulations versus analytical models
Physical Review B, 2006
By means of thorough atomistic simulations an energy-based theory, named quantized fracture mechanics, is commented and validated. This approach modifies continuum linear elastic fracture mechanics by introducing the hypothesis of discrete crack propagation, taking into account the discreteness of the crystal lattice. We investigate at an atomistic level the crack energy resistance for a matrix of silicon carbide with an isolated crack, and the effect on the stress at the crack tip due to a second phase particle. In both cases our results show that, while atomistic simulations provide the most basic level of understanding of mechanical behavior in nanostructured brittle materials, quantized fracture mechanics is able to effectively incorporate the main latticerelated feature, thus enlarging the realm of continuum modeling.
Dissipative dynamic fracture of disordered systems
Physical Review E, 1995
Breakdown of two-dimensional disordered systems is studied with a time-dependent network model. The dependence of fracture process on the local relaxation of the force field is included within the framework of Maxwellian viscoelasticity. The dynamics and characteristics of crack formation and propagation are shown to depend on disorder and relative time scales of dissipation and loading. Brittle behavior is encountered in the adiabatic limit of slow straining. At finite strain rates, the development of damage shows ductile behavior with increasing dissipation. Nucleation of cracks in various dynamical situations is discussed.
A molecular dynamics investigation of rapid fracture mechanics
Journal of the Mechanics and Physics of Solids, 1997
for two-dimensional notched solids under tension using million atom systems. Brittle material and ductile material are modeled through the choice of interatomic potential functions which are Lennard-Jones and embedded-atom potentials, respectively. Numerical calculations are carried out on the IBN SP parallel computer and molecular dynamics is implemented using a spatialdecomposition algorithm. Many recent laboratory findings occur in our simulation experiments. A detailed comparison between laboratory and computer experiments is presented, and microscopic processes are identified. For rapid brittle fracture, the dynamic instability of the crack growth is observed as the crack velocity approaches one-third of the Rayleigh wave speed. At higher crack velocity, the crack either follows a wavy path or branches and the anisotropy due to the large deformation at the crack tip plays the governing role in determining the crack path. Limited comparison of rapid brittle fracture process with the rapid ductile fracture process is made. 0 1997 Elsevier Science Ltd.
Fracture surfaces of heterogeneous materials: A 2D solvable model
Europhysics Letters (EPL), 2007
Using an elastostatic description of crack growth based on the Griffith criterion and the principle of local symmetry, we present a stochastic model describing the propagation of a crack tip in a 2D heterogeneous brittle material. The model ensures the stability of straight cracks and allows for the study of the roughening of fracture surfaces. When neglecting the effect of the nonsingular stress, the problem becomes exactly solvable and yields analytic predictions for the power spectrum of the paths. This result suggests an alternative to the conventional power law analysis often used in the analysis of experimental data.