Instability dynamics of fracture: A computer simulation investigation

Abraham, Farid F.; Brodbeck, D.; Rafey, R. A.; Rudge, W. E.

doi:10.1103/physrevlett.73.272

Cited by 314 publications

(167 citation statements)

References 12 publications

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“…The atomistic simulations of Abraham et al [2,1] display dynamic crack instabilities reminiscent of the experimental results though at decidedly smaller length and time scales. The numerical studies of Xu and Needleman [95], employing networks of cohesive surface elements, are also successful in producing crack tip instabilities that qualitatively match the experimentally observed behavior.…”

Section: Theoretical Analysis Of Branchingmentioning

confidence: 95%

“…The normal direction may be written aŝ In three dimensions, the transformation tensor Q may be expanded as 22) where the local normal directionn and the two tangent directionst (1) andt (2) are defined using the parameterization of the surface with respect to ξ = [ξ η] T . At any point on the surface, two tangential, but not necessarily orthogonal, directions are defined by the columns of the surface jacobian…”

Section: Element Formulationmentioning

confidence: 99%

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Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods

Klein

Foulk

Chen

et al. 2001

Theoretical and Applied Fracture Mechanics

151

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Simulation of generalized fracture and fragmentation remains an ongoing challenge in computational fracture mechanics. There are difficulties associated not only with the formulation of physically-based models of material failure, but also with the numerical methods required to treat geometries that change in time. The issue of fracture criteria is addressed in this work through a cohesive view of material, meaning that a finite material strength and work to fracture are included in the material description. In this study, we present both surface and bulk cohesive formulations for modeling brittle fracture, detailing the derivation of the formulations, fitting relations, and providing a critical assessment of their capabilities in numerical simulations of fracture. Due to their inherent adaptivity and robustness under severe deformation, meshfree methods are especially well-suited to modeling fracture behavior. We describe the application of meshfree methods to both bulk and surface approaches to cohesive modeling. We present numerical examples highlighting the capabilities and shortcomings of the methods in order to identify which approaches are best-suited to modeling different types of fracture phenomena.

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Section: Theoretical Analysis Of Branchingmentioning

confidence: 95%

Section: Element Formulationmentioning

confidence: 99%

Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods

Klein

Foulk

Chen

et al. 2001

Theoretical and Applied Fracture Mechanics

151

View full text Add to dashboard Cite

show abstract

“…The effective sharpness of the blade depends upon the power with which it presses through material; press too hard, and it blunts, presenting enormous resistance to speeding up further. Both idealized calculations [3,4], as well as more realistic simulations [5,6] showed how this process could occur, as indicated on the right hand side of Fig. . Last fall, Sharon, Fineberg, and Gross [7] showed that cracks in Plexiglas develop branching structures, as shown on the right hand side of Fig. .…”

mentioning

confidence: 99%

Energetic developments in fracture

Marder

1996

Nature

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What drives physicists to study cracks? There is certainly some attraction in being able to tell the children one is getting paid to break things. There is also a perverse pleasure in learning the physical laws underlying irreversible change, decay, and destruction. A paper of Eran Sharon, Steven Gross, and Jay Fineberg, "Energy Dissipation in Dynamic Fracture" which appeared on 18 March in Physical Review Letters contains an answer to an old and deceptively simple question, "How fast do things break, and why?"The first scientific attempts to answer this question go back to research of Hubert Schardin and Wolfgang Struth in 1937[1], who used sparks to take photographs of cracks in less than one ten-millionth of a second. They concluded that "the maximum velocity of propagation of glass fractures is to be considered a physical constant," and they measured crack speeds that were approximately one quarter the speed of sound in many different glasses.Some time after these experiments came theories of crack motion, which firmly insisted that cracks should move at about twice the speed observed. The classic theory[2], developed by B. V. Kostrov, J. D. Eshelby, and L. B. Freund, left little room for uncertainty. Cracks leave two new surfaces behind them. The speed at which vibrations travel across a free surface is the Rayleigh wave speed, a speed governing the motion of sound when one raps one's knuckles on the top of a table, or the speed at which earthquakes travel on the surface of the earth. Cracks, said the theory, should move at this Rayleigh wave speed too -but it does not happen. In Plexiglas, for example, the Rayleigh wave speed is around 1000 metres per second, but cracks never exceed 600 metres per second. This descrepancy was widely acknowledged to 1

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“…3,4 The same phenomenology was observed in simulations, where departure from steady state propagation for cracks exceeding a threshold speed was observed, with zig-zag motion and formation of microstructures. 15 Molecular dynamics simulations of crystalline silicon showed that cracks can dissipate large amounts of energy, up to seven times the energy needed to create a smooth surface as estimated in the framework of the continuum theory, the suggestion being that this energy goes into lattice oscillations. 16 The idea that the energy available does not all go into fracture work is not new.…”

Section: Introductionmentioning

confidence: 99%

Relation between driving energy, crack shape, and speed in brittle dynamic fracture

Parisi

Ball

2005

Phys. Rev. B

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We report results on the interrelation between driving force, roughness exponent, branching and crack speed in a finite element model. We show that for low applied loadings the crack speed reaches the values measured in the experiments, and the crack surface roughness is compatible with logarithmic scaling. At higher loadings, the crack speed increases, and the crack roughness exponent approaches the value measured at short length scales in experiments. In the case of high anisotropy, the crack speed is fully compatible with the values measured in experiments on anisotropic materials, and we are able to interpret explicitly the results in terms of the efficiency function introduced by us in our previous work [A. Parisi and R. C. Ball, Phys. Rev. B 66(16) 165432 (2002)]. The mechanism which leads to the decrease of crack speed and the appearence of the logarithmic scaling is attempted branching, whilst power law roughness develops when branches succeed in growing to macroscopic size.

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Instability dynamics of fracture: A computer simulation investigation

Cited by 314 publications

References 12 publications

Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods

Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods

Energetic developments in fracture

Relation between driving energy, crack shape, and speed in brittle dynamic fracture

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