Some analytical results for the velocity of cracks propagating in nonlinear lattices

Guozden, T. M.; Jagla, E. A.

doi:10.1103/physreve.74.016106

Cited by 6 publications

(5 citation statements)

References 7 publications

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“…Much insight has been obtained by the use of lattice models with simple interaction laws, where the lattice constant provides a regularization length scale for the LEFM singularity [5,44,68,72,85,[112][113][114][115][116][117][118][119][120][121][122][123][124][125][126]. It is difficult, however, to directly relate these models to the failure of real non-crystalline solids, where a natural regularization scale is not obviously apparent and well-defined slip systems do not exist.…”

Section: Beyond Lefm: Regularization Of the Singularity And Dissipationmentioning

confidence: 99%

The dynamics of rapid fracture: instabilities, nonlinearities and length scales

2014

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Abstract. The failure of materials and interfaces is mediated by cracks, nearly singular dissipative structures that propagate at velocities approaching the speed of sound. Crack initiation and subsequent propagation -the dynamic process of fracture -couples a wide range of time and length scales. Crack dynamics challenge our understanding of the fundamental physics processes that take place in the extreme conditions within the nearly singular region where material failure occurs. Here, we first briefly review the classic approach to dynamic fracture, "Linear Elastic Fracture Mechanics" (LEFM), and discuss its successes and limitations. We show how, on the one hand, recent experiments performed on straight cracks propagating in soft brittle materials have quantitatively confirmed the predictions of this theory to an unprecedented degree. On the other hand, these experiments show how LEFM breaks down as the singular region at the tip of a crack is approached. This breakdown naturally leads to a new theoretical framework coined "Weakly Nonlinear Fracture Mechanics", where weak elastic nonlinearities are incorporated. The stronger singularity predicted by this theory gives rise to a new and intrinsic length scale, nl . These predictions are verified in detail through direct measurements. We then theoretically and experimentally review how the emergence of nl is linked to a new equation for crack motion, which predicts the existence of a high-speed oscillatory crack instability whose wave-length is determined by nl . We conclude by delineating outstanding challenges in the field.

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Section: Beyond Lefm: Regularization Of the Singularity And Dissipationmentioning

confidence: 99%

The dynamics of rapid fracture: instabilities, nonlinearities and length scales

2014

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“…This smooth behavior is a form of hyperelastic softening. Previous results obtained in a special model under Mode III conditions (Guozden and Jagla 2006) have shown unambiguously that softening of the springs at large deformations produces systematic reductions of the crack velocities.…”

Section: Hyperelastic Softeningmentioning

confidence: 81%

Supersonic cracks in lattice models

2009

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We have studied cracks traveling along weak interfaces. We model them using harmonic and anharmonic forces between particles in a lattice, both in tension (Mode I) and antiplane shear (Mode III). One of our main objects has been to determine when supersonic cracks traveling faster than the shear wave speed can occur. In contrast to subsonic cracks, the speed of supersonic cracks is best expressed as a function of strain, not stress intensity factor. Nevertheless, we find that supersonic cracks are more common than has previously been realized. They occur both in Mode I and Mode III, with or without anharmonic changes of interparticle forces prior to breaking, and with or without dissipation. The extent and shape of the supersonic branch of solutions depends strongly on details such as lattice geometry, force law anharmonicity, and amount of dissipation. Particle forces that stiffen prior to breaking lead to larger supersonic branches. Increasing dissipation also tends to promote the existence of supersonic states. We include a number of other results, including analytical expressions for crack speeds in the high-strain limit, and numerical results for the spatial extent of regions where particles interact anharmonically. Finally, we note a curious phenomenon, where for forces that weaken with increasing strain, cracks can slow down when one pulls on them harder.

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“…In this description, the system is continuous along the chains, although it remains essentially discrete in the perpendicular direction. This kind of continuous limit along a single spatial dimension is well defined (Guozden and Jagla, 2006), contrary to the case of a full continuous limit in which the transition from discrete to continuous is much more subtle. Given a distribution of plasticity l 0 (x) the previous equation can be solved.…”

Section: Details Of the Model And The Numerical Techniquementioning

confidence: 93%

“…Having in mind the cyclic loading fatigue crack advance problem, the possibility that we have been studying corresponds to spring lattice systems with plasticity in the springs. In fact, lattice spring models have been a very important benchmark where many predictions of fracture mechanics were tested, and also where effects that go beyond the reach of analytic treatments were obtained (Slepyan, 1981;Marder and Gross, 1995;Levine, 1999b, 2001;Guozden and Jagla, 2006). These studies have mainly focused on propagation in lattices with linear, non-linear elastic, or visco-elastic springs.…”

Section: Introductionmentioning

confidence: 99%

“…In absence of plasticity, this kind of "one-dimensional" geometry has been studied in detail in the context of dynamical fracture, and has proved to be useful as a simple benchmark for the more complex behavior that is observed in a more thorough two dimensional implementation (Langer, 1992;Bouchbinder and Lo, 2008). We have also used this model in a previous work (Guozden and Jagla, 2006) and obtained results in the dynamical propagation case. We now concentrate in this quasi one-dimensional model because in addition to the numerical implementation, it allows a detailed, mostly analytical description of the fatigue propagation mechanisms involved, and also because in this case, the germ of experimental features of fatigue crack growth is already observed.…”

Section: Introductionmentioning

confidence: 99%

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Fatigue crack propagation in a quasi-one-dimensional elasto-plastic model

Guozden

Jagla

2012

International Journal of Solids and Structures

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Fatigue crack advance induced by the application of cyclic quasistatic loads is investigated both numerically and analytically using a lattice spring model. The system has a quasi-one-dimensional geometry, and consists in two symmetrical chains that are pulled apart, thus breaking springs which connect them, and producing the advance of a crack. Quasistatic crack advance occurs as a consequence of the plasticity included in the springs which form the chains, and that implies a history dependent stress-strain curve for each spring. The continuous limit of the model allows a detailed analytical treatment that gives physical insight of the propagation mechanism. This simple model captures key features that cause well known phenomenology in fatigue crack propagation, in particular a Paris-like law of crack advance under cyclic loading, and the overload retardation effect.

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Some analytical results for the velocity of cracks propagating in nonlinear lattices

Cited by 6 publications

References 7 publications

The dynamics of rapid fracture: instabilities, nonlinearities and length scales

The dynamics of rapid fracture: instabilities, nonlinearities and length scales

Supersonic cracks in lattice models

Fatigue crack propagation in a quasi-one-dimensional elasto-plastic model

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