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Representation of Finite Cracks by Dislocation Pileups: An Application to Atomic Simulation of Fracture

Published online by Cambridge University Press:  10 February 2011

Vijay Shastry  and
Diana Farkas
Vijay Shastry
Affiliation:
Department of Materials Science and Engineering, Virginia Tech., Blacksburg VA 24061.
Diana Farkas
Affiliation:
Department of Materials Science and Engineering, Virginia Tech., Blacksburg VA 24061.
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Abstract

The elastic displacement field solution of a semi-infinite crack in an anisotropic body, calculated using a complex variable approach due to Sih and Liebowitz, is usually used by atomistic simulations of fracture. The corresponding expression for the displacement field of a finite crack is numerically cumbersome since it involves multiple square roots of complex numbers. In this study, displacement field of the crack is calculated by superposing the displacements of dislocations in an equivalent double pileup, equilibrated under mode I conditions. An advantage of this method is its extensibility to atomistic studies of more complex systems containing multiple cracks or interfaces. The pileup representation of the finite crack is demonstrated as being equivalent to its corresponding continuum description using the example of a double ended crack in α-Fe, loaded in mode I. In these examples, the interatomic interaction in α-Fe is described by an empirical embedded atom (EAM) potential.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 408: Symposium P – Materials Theory, Simulations, and Parallel Algorithms , 1995 , 217
Copyright
Copyright © Materials Research Society 1996

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