Scaling of brittle failure: strength versus toughness

Brochard, Laurent; Souguir, Sabri; Sab, Karam

doi:10.1007/s10704-018-0268-9

Cited by 6 publications

(13 citation statements)

References 44 publications

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“…Dynamics becomes essential to the evolution of the atomic systems, in particular for crack propagation (Marder and Gross, 1994). In a recent study by molecular simulation at finite temperatures, we show that, for mono-crystals, strength and toughness follow analogous scaling laws in temperature and loading rate, but differ regarding the scaling with system size (Brochard et al, 2018). The scaling in temperature and loading rate (inverse of loading time) has long been identified and is known as Zhurkov's law (Zhurkov, 1984), but the effect of system size has been disregarded so far.…”

Section: Introductionmentioning

confidence: 80%

“…Confronting those two materials, one can evaluate whether the physics of failure observed for simplistic systems (closest-neighbor pair interactions) holds for more complex realistic systems (many-body potential not limited to closest neighbors), which bring confidence to the physical interpretations. The toy model was previously investigated in the context of the scaling laws of strength and toughness mentioned in the introduction (Brochard et al, 2018). This fictitious material has a 2D crystalline structure of regular triangular lattice and the inter-atomic interactions are limited to pair interactions between nearest neighbors.…”

Section: Methodsmentioning

confidence: 99%

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Stress concentration and instabilities in the atomistic process of brittle failure initiation

2020

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A major challenge in the macroscopic modeling of brittle failure initiation is to reconcile stressdriven failure in absence of stress concentration and energy-driven failure under high stress concentration (crack). In this paper, we perform athermal molecular simulations to investigate the underlying physics behind stress-to energy-driven failures. In the athermal limit, the evolution of an atomic system is deterministic and is obtained by energy minimization. Failure is expected when the system suddenly bifurcates to a broken configuration which can be formally evaluated as an atomic instability characterized by a negative eigenvalue of the Hessian matrix. We applied this methodology to a 2D toy model and to pristine graphene. Both stress-and energy-driven failures are triggered by an instability at the atomic scale, but the two types of failure differ widely regarding the mechanisms of instability (eigenvectors) and their multiplicity (degeneracy). With respect to existing macroscopic theories of failure initiation, these results raise some issues. In particular,

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Section: Introductionmentioning

confidence: 80%

Section: Methodsmentioning

confidence: 99%

Stress concentration and instabilities in the atomistic process of brittle failure initiation

2020

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“…This points to a similar form of the energy barrier ∆E in function of the remote loading, irrespective of the stress concentration. This can be proven formally for the toy model, since atomic interactions are all linear (see demonstration in [10]). The energy barrier…”

Section: Failure Initiation At Finite Temperaturementioning

confidence: 88%

“…All simulations are performed with LAMMPS (http://lammps.sandia.gov, [8]). See [9][10][11] for more details regarding the set up of the molecular simulations.…”

Section: Simulation Methodsmentioning

confidence: 99%

“…The difference in scaling between graphene and the toy model is reminiscent of the atomic interactions. Numerical estimation of the transition path energy can be achieved for graphene, and leads to an energy barrier different from that of the toy model: ∆E ∝ 1 − Σ Σ 0 [10]. Interestingly, a majority of brittle materials exhibit a linear scaling of strength with temperature like graphene, which is known as Zhurkov's law [12].…”

Section: Failure Initiation At Finite Temperaturementioning

confidence: 99%

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Fundamentals of brittle failure at the atomic scale

Brochard

Souguir

Sab

2019

Proceedings of the 10th International Conference on Fracture Mechanics of Concrete and Concrete Structures

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In this work, we investigate the elementary processes of brittle failure initiation with molecular simulation techniques. Failure initiation theories aim at bridging the gap between energy-driven failure at high stress concentrations and stress-driven failure in absence of stress concentration, and thus capturing the transition at moderate stress concentrations and associated scale effects. We study graphene, which is one of the few materials with a sufficiently small characteristic length (ratio between toughness and strength) to be addressed by molecular simulations. We also consider a toy model that proves helpful for physical interpretations. Performing molecular simulations of precracked graphene, we found that its failure behavior can overcome both strength and toughness in situations of very high or low stress concentrations, respectively; which is consistent with one particular theory, namely Finite Fracture Mechanics (FFM), which considers failure initiation as the nucleation of a crack over a finite length. Details of the atomic mechanisms of failure are investigated in the athermal limit (0K). In this limit, failure initiates as an instability (negative eigenvalue of the Hessian matrix), irrespective of the stress concentration. However, the atomic mechanisms of failure and their degeneracy (eigenvector of the negative eigenvalue) strongly depend on stress concentration and points to the nucleation of a deformation band whose length decreases with stress concentration. This atomic description is quite similar to FFM theory. At finite temperature, failure is no more deterministic because of thermal agitation. An extensive study to characterize the effects of temperature, loading rate and system size leads to the formulation of a universal scaling law of strength and toughness which extends existing theory (Zhurkov) to size effects. Interestingly, the scalings of stress-driven failure (strength) and of energy-driven failure (toughness) differ only regarding the scaling in size, which relates to the effect of stress concentration on degeneracy identified in the athermal limit.

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