Validity of linear elasticity in the crack-tip region of ideal brittle solids

Singh, Gaurav; Kermode, James R.; Vita, Alessandro De; Zimmerman, Robert W.

doi:10.1007/s10704-014-9958-0

Cited by 19 publications

(13 citation statements)

References 34 publications

(39 reference statements)

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“…This conclusion is relevant and further confirms what is found by other researchers [40] : the crack-tip region in a molecular system can be described by linear elastic fracture mechanics, at least in the case of static crack and ideal brittle material containing no other defects. This conclusion is relevant and further confirms what is found by other researchers [40] : the crack-tip region in a molecular system can be described by linear elastic fracture mechanics, at least in the case of static crack and ideal brittle material containing no other defects.…”

Section: Discussionsupporting

confidence: 91%

On the Crack‐Tip Region Stress Field in Molecular Systems: The Case of Ideal Brittle Fracture

Gallo

2019

Advcd Theory and Sims

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Continuum-based fracture mechanics breaks down at the nanoscale where the discrete nature of atoms cannot be neglected. Intriguingly, this work shows that the concept of stress intensity factor is still valid if the atoms are modeled. Molecular statistics simulations are conducted on single-edge cracked samples of ideal brittle silicon, varying the size until few nanometers. The local virial stress, derived as the functional derivative of the free energy of a molecular system with respect to the deformation tensor, is used as a measure of the mechanical stress at the atomic level. Then, stress intensity factor at failure is evaluated. The results show that regardless of the size, the atomistic stress field varies according to the classical 1/r 0.5 relation, and discrete stress intensity factors can be derived for all the geometries. Continuum values, in contrast, fail to describe the fracture when the length of the singular stress field is smaller than 4-5 times the fracture process zone. Thus, this work shows that the stress intensity factor from atomic stress may be useful to describe the fracture criterion at extremely small dimensions, provided that virial stress is accepted as a representation of mechanical stress at the atomic level.

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Section: Discussionsupporting

confidence: 91%

On the Crack‐Tip Region Stress Field in Molecular Systems: The Case of Ideal Brittle Fracture

Gallo

2019

Advcd Theory and Sims

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“…However, explaining complex, material-specific dynamical phenomena requires a new level of accuracy from atomistic simulations, going beyond the generic features that arise from the discretization of the material lattice (Marder 2004). The strong coupling between lengthscales inherent to fracture means that accurate modelling often requires non-uniform approaches that couple the long-range stress concentration, which can be captured very well by classical interatomic potentials (Singh et al 2014), with local crack-tip chemistry, which must be modelled with more accurate techniques, typically with quantum mechanical precision (Abraham et al 1998b;Bernstein and Hess 2003;Kermode et al 2008). For a detailed review of these "hybrid" multiscale simulations methods for materials problems see Bernstein et al (2009).…”

Section: Dynamical Effects-instabilities Defects and Perturbationsmentioning

confidence: 99%

Atomistic aspects of fracture

2015

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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, crack-microstructure interactions and chemical aspects on the fracture toughness and crack propagation patterns in metals and ceramics. This review focuses on atomistic aspects of fracture in crystalline materials where significant advances have been achieved over the last ten years and provides an outlook on future perspectives for atomistic modelling of fracture

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“…8 The first condition is met when the fracture process zone is smaller than the K-dominated zone (the region with a significant gradient in the stress), which is the case in brittle materials. 9,10 A crucial point to consider in practical applications within a finite element method (FEM) implementation is that CZ-based numerical techniques require cracks to propagate along the element boundaries. Therefore, an inherent nonvanishing amount of mesh dependency arises, which can become dominant for three-dimensional simulations in a homogeneous material.…”

Section: Introductionmentioning

confidence: 99%