Dislocation nucleation from a crack tip : an analysis based on the Peierls concept
TL;DR: In this paper, a periodic relation between shear stress and atomic shear displacement is assumed to hold along the most highly stressed slip plane emanating from a crack tip, which allows some small slip displacement to occur near the tip in response to small applied loading and, with increase in loading, the incipient dislocation configuration becomes unstable and leads to a fully formed dislocation which is driven away from the crack.
Abstract: Dislocation nucleation from a stressed crack tip is analyzed based on the Peierls concept. A periodic relation between shear stress and atomic shear displacement is assumed to hold along the most highly stressed slip plane emanating from a crack tip. This allows some small slip displacement to occur near the tip in response to small applied loading and, with increase in loading, the incipient dislocation configuration becomes unstable and leads to a fully formed dislocation which is driven away from the crack. An exact solution for the loading at that nucleation instability is developed via the J -integral for the case when the crack and slip planes coincide, and an approximate solution is given when they do not. Solutions are also given for emission of dissociated dislocations, especially partial dislocation pairs in fcc crystals. The level of applied stress intensity factors required for dislocation nucleation is shown to be proportional to √γ us , where γ us , the unstable stacking energy, is a new solid state parameter identified by the analysis. It is the maximum energy encountered in the block-like sliding along a slip plane, in the Burgers vector direction, of one half of a crystal relative to the other. Approximate estimates of γ us are summarized and the results are used to evaluate brittle vs ductile response in fcc and bcc metals in terms of the competition between dislocation nucleation and Griffith cleavage at a crack tip. The predictions seem compatible with known behavior and also show that in many cases solids which are predicted to first cleave under pure mode I loading should instead first emit dislocations when that loading includes very small amounts of mode II and III shear. The analysis in this paper also reveals a feature of the near-tip slip distribution corresponding to the saddle point energy configuration for cracks that are loaded below the nucleation threshold, as is of interest for thermal activation.
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TL;DR: In this article, a finite element methodology for the analysis of problems requiring the simultaneous resolution of continuum and atomistic length scales-and associated deformation processes-in a unified manner is presented.
Abstract: We develop a method which permits the analysis of problems requiring the simultaneous resolution of continuum and atomistic length scales-and associated deformation processes-in a unified manner. A finite element methodology furnishes a continuum statement of the problem of interest and provides the requisite multiple-scale analysis capability by adaptively refining the mesh near lattice defects and other highly energetic regions. The method differs from conventional finite element analyses in that interatomic interactions are incorporated into the model through a crystal calculation based on the local state of deformation. This procedure endows the model with crucial properties, such as slip invariance, which enable the emergence of dislocations and other lattice defects. We assess the accuracy of the theory in the atomistic limit by way of three examples: a stacking fault on the (111) plane, and edge dislocations residing on (111) and (100) planes of an aluminium single crystal. The method correctly predicts the splitting of the (111) edge dislocation into Shockley partials. The computed separation of these partials is consistent with results obtained by direct atomistic simulations. The method predicts no splitting of the Al Lomer dislocation, in keeping with observation and the results of direct atomistic simulation. In both cases, the core structures are found to be in good agreement with direct lattice statics calculations, which attests to the accuracy of the method at the atomistic scale.
1,487 citations
TL;DR: In this paper, a three-dimensional finite deformation cohesive element and a class of irreversible cohesive laws are proposed to track dynamic growing cracks in a drop-weight dynamic fracture test.
Abstract: SUMMARY We develop a three-dimensional nite-deformation cohesive element and a class of irreversible cohesive laws which enable the accurate and ecient tracking of dynamically growing cracks. The cohesive element governs the separation of the crack anks in accordance with an irreversible cohesive law, eventually leading to the formation of free surfaces, and is compatible with a conventional nite element discretization of the bulk material. The versatility and predictive ability of the method is demonstrated through the simulation of a drop-weight dynamic fracture test similar to those reported by Zehnder and Rosakis. 1 The ability of the method to approximate the experimentally observed crack-tip trajectory is particularly noteworthy. Copyright ? 1999 John Wiley & Sons, Ltd.
1,375 citations
Cites background from "Dislocation nucleation from a crack..."
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...In this simple case, the cohesive law (14) reduces to...
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TL;DR: In this paper, a methodology to determine the constitutive parameters for the simulation of progressive delamination is proposed, which accounts for the size of a cohesive finite element and the length of the cohesive zone to ensure the correct dissipation of energy.
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TL;DR: In this paper, a review of deformation twinning in nanocrystalline materials is presented, including deformation twins observed by molecular dynamics simulations and experiments, twinning mechanisms, factors affecting the twinning, analytical models on the nucleation and growth of deformations, interactions between twins and dislocations, and the effects of twins on mechanical and other properties.
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TL;DR: In this paper, the authors present a review of recent developments in the field of deformation behavior of high manganese face-centered cubic γ-Fe alloys, referred to as twinning-induced plasticity, or TWIP, steels.
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References
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Book•
01 Jan 1968
TL;DR: Dislocations in Isotropic Continua: Effects of Crystal Structure on Dislocations and Dislocation-Point-Defect Interactions at Finite temperatures.
Abstract: Dislocations in Isotropic Continua. Effects of Crystal Structure on Dislocations. Dislocation-Point-Defect Interactions at Finite Temperatures. Groups of Dislocations. Appendixes. Author and Subject Indexes.
10,220 citations
TL;DR: In this paper, an integral is exhibited which has the same value for all paths surrounding a class of notches in two-dimensional deformation fields of linear or non-linear elastic materials.
Abstract: : An integral is exhibited which has the same value for all paths surrounding a class of notches in two-dimensional deformation fields of linear or non-linear elastic materials. The integral may be evaluated almost by inspection for a few notch configurations. Also, for materials of the elastic- plastic type (treated through a deformation rather than incremental formulation) , with a linear response to small stresses followed by non-linear yielding, the integral may be evaluated in terms of Irwin's stress intensity factor when yielding occurs on a scale small in comparison to notch size. On the other hand, the integral may be expressed in terms of the concentrated deformation field in the vicinity of the notch tip. This implies that some information on strain concentrations is obtainable without recourse to detailed non-linear analyses. Such an approach is exploited here. Applications are made to: Approximate estimates of strain concentrations at smooth ended notch tips in elastic and elastic-plastic materials, A general solution for crack tip separation in the Barenblatt-Dugdale crack model, leading to a proof of the identity of the Griffith theory and Barenblatt cohesive theory for elastic brittle fracture and to the inclusion of strain hardening behavior in the Dugdale model for plane stress yielding, and An approximate perfectly plastic plane strain analysis, based on the slip line theory, of contained plastic deformation at a crack tip and of crack blunting.
7,468 citations
TL;DR: In this paper, the authors derived an expression for the total energy of a metal using the embedding energy from which they obtained several ground-state properties, such as the lattice constant, elastic constants, sublimation energy, and vacancy-formation energy.
Abstract: We develop the embedded-atom method [Phys. Rev. Lett. 50, 1285 (1983)], based on density-functional theory, as a new means of calculating ground-state properties of realistic metal systems. We derive an expression for the total energy of a metal using the embedding energy from which we obtain several ground-state properties, such as the lattice constant, elastic constants, sublimation energy, and vacancy-formation energy. We obtain the embedding energy and accompanying pair potentials semiempirically for Ni and Pd, and use these to treat several problems: surface energy and relaxation of the (100), (110), and (111) faces; properties of H in bulk metal (H migration, binding of H to vacancies, and lattice expansion in the hydride phase); binding site and adsorption energy of hydrogen on (100), (110), and (111) surfaces; and lastly, fracture of Ni and the effects of hydrogen on the fracture. We emphasize problems with hydrogen and with surfaces because none of these can be treated with pair potentials. The agreement with experiment, the applicability to practical problems, and the simplicity of the technique make it an effective tool for atomistic studies of defects in metals.
5,912 citations
"Dislocation nucleation from a crack..." refers methods in this paper
...…class of these, going beyond pair potentials and thus avoiding Cauchy symmetry of crystal moduli, have been formulated within the embedded-atom method (DAw and BASKES, 1984) and have found extensive applications to solid state phenomena, including interfacial structure and deformation and fracture....
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TL;DR: A consistent set of embedding functions and pair interactions for use with the embedded-atom method was determined empirically by fitting to the sublimation energy, equilibrium lattice constant, elastic constants, and vacancy-formation energies of the pure metals and the heats of solution of the binary alloys as discussed by the authors.
Abstract: A consistent set of embedding functions and pair interactions for use with the embedded-atom method [M.S. Daw and M. I. Baskes, Phys. Rev. B 29, 6443 (1984)] have been determined empirically to describe the fcc metals Cu, Ag, Au, Ni, Pd, and Pt as well as alloys containing these metals. The functions are determined empirically by fitting to the sublimation energy, equilibrium lattice constant, elastic constants, and vacancy-formation energies of the pure metals and the heats of solution of the binary alloys. The validity of the functions is tested by computing a wide range of properties: the formation volume and migration energy of vacancies, the formation energy, formation volume, and migration energy of divacancies and self-interstitials, the surface energy and geometries of the low-index surfaces of the pure metals, and the segregation energy of substitutional impurities to (100) surfaces.
3,734 citations
01 Jan 1985
TL;DR: In this article, the authors describe the behavior of grain boundaries in a two-dimensional model ordered alloy and the effects of elastic anisotropy on the anomalious yield behavior of cubic ordered alloys.
Abstract: This book contains over 50 selections. Some of the titles are: Order-disorder behavior of grain boundaries in a two-dimensional model ordered alloy; Dislocation reactions at grain boundaries in Ll/sub 2/ ordered alloys; Creep cavitation in a nickel aluminide; Effects of elastic anisotropy on the anomalious yield behavior of cubic ordered alloys; and Processing technology for nickel aluminides.
2,123 citations