Journal ArticleDOI
Dislocation nucleation from a crack tip : an analysis based on the Peierls concept
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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.read more
Citations
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Generalized stacking fault energies for embedded atom FCC metals
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Multiscale friction mechanisms and hierarchical surfaces in nano- and bio-tribology
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References
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Book
Theory of Dislocations
John Price Hirth,Jens Lothe +1 more
TL;DR: Dislocations in Isotropic Continua: Effects of Crystal Structure on Dislocations and Dislocation-Point-Defect Interactions at Finite temperatures.
Journal ArticleDOI
A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks
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.
Journal ArticleDOI
Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals
Murray S. Daw,Michael I. Baskes +1 more
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.
Journal ArticleDOI
Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys.
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.
High-temperature ordered intermetallic alloys
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.