Non-Linear Evolution of a Uniaxially Stressed Solid: A Route to Fracture?

Kassner, Klaus; Misbah, Chaouqi

doi:10.1209/0295-5075/28/4/005

Cited by 55 publications

(52 citation statements)

References 14 publications

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“…This result points to the fact that amplitude expansions are inadequate and, therefore, one has to perform a fully nonlinear analysis in order to describe the subsequent development of the instability. The numerical nonlinear analysis of the customary ATG instability [13,14] shows that even close to the instability threshold deep cracklike grooves form. These grooves, pointing into the solid, sharpen and accelerate as they deepen.…”

Section: (Received 13 August 1998)mentioning

confidence: 99%

Surface Instabilities in Cracks

Brener

Марченко

1998

Phys. Rev. Lett.

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The surface of a propagating crack is shown to be morphologically unstable because of the nonhydrostatic stresses near the surface (Asaro-Tiller-Grinfeld instability). We find that the energy of a wavy crack becomes smaller than the energy of a straight crack if the crack length is a few times larger than the Griffith length. The local dispersion relation is derived assuming that the instability develops via mass transport by surface diffusion. We also argue that the widely used condition of the vanishing of K II , the stress-intensity factor of the sliding mode, appears in a natural way in our description as an effective boundary condition at the tip of the crack. [S0031-9007(98) 07834-X]

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Section: (Received 13 August 1998)mentioning

confidence: 99%

Surface Instabilities in Cracks

Brener

Марченко

1998

Phys. Rev. Lett.

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“…[53,[114][115][116][117][118][119]). More accurate calculations involving the numerical solution of the mechanical equilibrium equations by Finite Element Method (FEM) have also been exploited [120,121]. All of these approaches, however, agree in the tendency to form cusp-like structures with rounded tops and sharp trenches, yielding the best tradeoff between strain relaxation and total surface area.…”

Section: Non-linear Effectsmentioning

confidence: 99%

Continuum modelling of semiconductor heteroepitaxy: an applied perspective

Bergamaschini

Salvalaglio

Backofen

et al. 2016

Advances in Physics: X

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Semiconductor heteroepitaxy involves a wealth of qualitatively different, competing phenomena. Examples include threedimensional island formation, injection of dislocations, mixing between film and substrate atoms. Their relative importance depends on the specific growth conditions, giving rise to a very complex scenario. The need for an optimal control over heteroepitaxial films and/or nanostructures is widespread: semiconductor epitaxy by molecular beam epitaxy or chemical vapour deposition is nowadays exploited also in industrial environments. Simulation models can be precious in limiting the parameter space to be sampled while aiming at films/nanostructures with the desired properties. In order to be appealing (and useful) to an applied audience, such models must yield predictions directly comparable with experimental data. This implies matching typical time scales and sizes, while offering a satisfactory description of the main physical driving forces. It is the aim of the present review to show that continuum models of semiconductor heteroepitaxy evolved significantly, providing a promising tool (even a working tool, in some cases) to comply with the above requirements. Several examples, spanning from the nanometre to the micron scale, are illustrated. Current limitations and future research directions are also discussed.

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“…The initial and late stage of the ATG instability has been modeled analytically, with sharp interface and phase field descriptions, see e.g. [92][93][94][95][96][97] and references therein; recently, also phase field models for surface diffusion reproduced the instability [98,99], and also phase field crystal investigations have been pre- Figure 7. Nonlinear evolution of the ATG instability, as obtained from phase field simulations.…”

Section: Models With Sharp Interface Limitmentioning

confidence: 99%

Phase field modeling of crack propagation

Spatschek¹,

Brener²

2011

Philosophical Magazine

150

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Fracture is a fundamental mechanism of materials failure. Propagating cracks can exhibit a rich dynamical behavior controlled by a subtle interplay between microscopic failure processes in the crack tip region and macroscopic elasticity. We review recent approaches to understand crack dynamics using the phase field method. This method, developed originally for phase transformations, has the well-known advantage of avoiding explicit front tracking by making material interfaces spatially diffuse. In a fracture context, this method is able to capture both the short-scale physics of failure and macroscopic linear elasticity within a self-consistent set of equations that can be simulated on experimentally relevant length and time scales. We discuss the relevance of different models, which stem from continuum field descriptions of brittle materials and crystals, to address questions concerning crack path selection and branching instabilities, as well as models that are based on mesoscale concepts for crack tip scale selection. Open questions which may be addressed using phase field models of fracture are summarized.

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Non-Linear Evolution of a Uniaxially Stressed Solid: A Route to Fracture?

Cited by 55 publications

References 14 publications

Surface Instabilities in Cracks

Surface Instabilities in Cracks

Continuum modelling of semiconductor heteroepitaxy: an applied perspective

Phase field modeling of crack propagation

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