The Mathematical Institute, University of Oxford, Eprints Archive

On approaches to modelling lattice dislocations

Hall, C. L. and Markenscoff, X. (2011) On approaches to modelling lattice dislocations. Philosophical Magazine Letters . (Submitted)

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Abstract

By proposing a sinusoidal relationship between slip discontinuity and the associated mismatch force, Peierls and Nabarro famously developed a dislocation model that eliminates the stress singularity from the Volterra dislocation model. Recently, Lubarda and Markenscoff (Appl. Phys. Lett. 89:151923, 2006) developed a model in which the Burgers vector of the dislocation is applied over some finite distance, , described as the ‘core radius’. They found that the shear stress on the glide-plane predicted in the Lubarda-Markenscoff model is identical to that predicted by the Peierls-Nabarro model. In this paper, we investigate generalisations of both the Lubarda-Markenscoff and Peierls-Nabarro models, demonstrating that different distributions of infinitesimal dislocations in a generalised Lubarda-Markenscoff model can be associated with different expressions for the misalignment force in a generalised Peierls-Nabarro model. Our results indicate that the generalised Lubarda-Markenscoff framework is a versatile and useful method for modelling the core of a dislocation that neatly complements the well established Peierls-Nabarro framework.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1412
Deposited By:Peter Hudston
Deposited On:08 Nov 2011 09:49
Last Modified:09 Feb 2012 13:59

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