Lattice imperfections studied by use of lattice Green’s functions

Thomson, Robb; Zhou, Shujia; Carlsson, Anders; Tewary, Vinod K.

doi:10.1103/physrevb.46.10613

Cited by 92 publications

(56 citation statements)

References 17 publications

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“…The interactions of atoms in the non-linear zone with atoms in the linear zone are also described by the Green's function, and are therefore linear. The Green's function can be calculated in a computationally efficient way 21 . The total energy of the system can then be described as the sum of the energy in the elastic far field (calculated from the Green's function) and in the non-linear interactions 22 .…”

Section: Simulation Methodsmentioning

confidence: 99%

Effects of crack tip geometry on dislocation emission and cleavage: A possible path to enhanced ductility

1997

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We present a systematic study of the effect of crack blunting on subsequent crack propagation and dislocation emission. We show that the stress intensity factor required to propagate the crack is increased as the crack is blunted by up to thirteen atomic layers, but only by a relatively modest amount for a crack with a sharp 60 • corner. The effect of the blunting is far less than would be expected from a smoothly blunted crack; the sharp corners preserve the stress concentration, reducing the effect of the blunting. However, for some material parameters blunting changes the preferred deformation mode from brittle cleavage to dislocation emission. In such materials, the absorption of preexisting dislocations by the crack tip can cause the crack tip to be locally arrested, causing a significant increase in the microscopic toughness of the crack tip. Continuum plasticity models have shown that even a moderate increase in the microscopic toughness can lead to an increase in the macroscopic fracture toughness of the material by several orders of magnitude. We thus propose an atomic-scale mechanism at the crack tip, that ultimately may lead to a high fracture toughness in some materials where a sharp crack would seem to be able to propagate in a brittle manner.When the crack is loaded in mode II, the load required to emit a dislocation is affected to a much higher degree by the blunting, in agreement with the estimates from continuum elasticity. In mode II the emission process is aided by a reduction of the free surface area during the emission process. This leads to emission at crack loadings which are lower than predicted from the continuum analysis of Rice.

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Section: Simulation Methodsmentioning

confidence: 99%

Effects of crack tip geometry on dislocation emission and cleavage: A possible path to enhanced ductility

1997

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“…Physical properties of defects are governed by their atomic structure which is reflected in their overall shape. The shape directly controls the strain field induced by defects [20]. The long-ranged interaction between defects is dominated by the strain field and hence the shape of the defects.…”

Section: Shape Based Classificationmentioning

confidence: 99%

Dynamic Classification of Defect Structures in Molecular Dynamics Simulation Data

Mehta¹,

Barr²,

Choy³

et al. 2005

Proceedings of the 2005 SIAM International Conference on Data Mining

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In this application paper we explore techniques to classify anomalous structures (defects) in data generated from Molecular Dynamics (MD) simulations of Silicon (Si) atom systems. These systems are studied to understand the processes behind the formation of various defects as they have a profound impact on the electrical and mechanical properties of Silicon. In our prior work [12,13,14] we presented techniques for defect detection. Here, we present a two-step dynamic classifier to classify the defects. The first step uses up to third-order shape moments to provide a smaller set of candidate defect classes. The second step assigns the correct class to the defect structure by considering the actual spatial positions of the individual atoms. The dynamic classifier is robust and scalable in the size of the atom systems. Each phase is immune to noise, which is characterized after a study of the simulation data. We also validate the proposed solutions by using a physical model and properties of lattices. We demonstrate the efficacy and correctness of our approach on several large datasets. Our approach is able to recognize previously seen defects and also identify new defects in real time.

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“…Tewary and colleagues [35,36] demonstrated the feasibility of representing lattice defects in reduced form using Green's function methods. In such a lower-order method, the defect core can be represented with semianalytical functions, thereby providing an initial estimate that can be used as an initial state in a more computationally intensive, larger-scale atomistic simulation.…”

Section: Introductionmentioning

confidence: 99%

Multiscale Modeling of Point and Line Defects in Cubic Lattices

Chung

Clayton

2007

Int J Mult Comp Eng

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY) March 2008 REPORT TYPE Reprint DATES COVERED (From SPONSOR/MONITOR'S ACRONYM(S) 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution is unlimited. SUPPLEMENTARY NOTESA reprint from the International Journal for Multiscale Computational Engineering, vol. 5, nos. 3 and 4, pp. 203-226, 2007. 14. ABSTRACT A multilength scale method based on asymptotic expansion homogenization (AEH) is developed to compute minimum energy configurations of ensembles of atoms at the fine length scale and the corresponding mechanical response of the material at the coarse length scale. This multiscale theory explicitly captures heterogeneity in microscopic atomic motion in crystalline materials, attributed, for example, to the presence of various point and line lattice defects. The formulation accounts for large deformations of nominally hyperelastic, monocrystalline solids. Unit cell calculations are performed to determine minimum energy configurations of ensembles of atoms of body-centered cubic tungsten in the presence of periodic arrays of vacancies and screw dislocations of line orientations [111] or [100]. Results of the theory and numerical implementation are verified versus molecular statics calculations based on conjugate gradient minimization (CGM) and are also compared with predictions from the local Cauchy-Born rule. For vacancy defects, the AEH method predicts the lowest system energy among the three methods, while computed energies are comparable between AEH and CGM for screw dislocations. Computed strain energies and defect energies (e.g., energies arising from local internal stresses and strains near defects) are used to construct and evaluate continuum energy functions for defective crystals parameterized via the vacancy density, the dislocation density tensor, and the generally incompatible lattice deformation gradient. For crystals with vacancies, a defect energy increasing linearly with vacancy density and applied elastic deformation is suggested, while for crystals with screw d...

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Lattice imperfections studied by use of lattice Green’s functions

Cited by 92 publications

References 17 publications

Effects of crack tip geometry on dislocation emission and cleavage: A possible path to enhanced ductility

Effects of crack tip geometry on dislocation emission and cleavage: A possible path to enhanced ductility

Dynamic Classification of Defect Structures in Molecular Dynamics Simulation Data

Multiscale Modeling of Point and Line Defects in Cubic Lattices

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