Asymptotic expressions for the nearest and furthest dislocations in a pile-up against a grain boundary

Cameron Luke Hall (1)

1 OCCAM, Mathematical Institute

In 1965, Armstrong and Head (\textit{Acta Metall.}~13(7):759--764, 1965) explored the problem of a pile-up of screw dislocations against a grain boundary. They used numerical methods to determine the positions of the dislocations in the pile-up and they were able to fit approximate formulae for the locations of the first and last dislocations. These formulae were used to gain insights into the Hall-Petch relationship. More recently, Voskoboinikov \textit{et al.}~(\textit{Phil.~Mag.~Lett.}~87(9):669--676, 2007) used asymptotic techniques to study the equivalent problem of a pile-up of a large number of screw dislocations against a bimetallic interface. In this paper, we use the techniques developed by Voskoboinikov \textit{et al.}~to construct systematic asymptotic expressions for the formulae proposed by Armstrong and Head. The further extension of these techniques to more general pile-ups is also outlined. As a result of this work, we show that a pile-up against a grain boundary can become equivalent to a pile-up against a locked dislocation in the case where the mismatch across the boundary is small.

Mots clés: Physical Sciences

Cameron Luke Hall. Asymptotic expressions for the nearest and furthest dislocations in a pile-up against a grain boundary. Philosophical Magazine, 2010, 90 (29), pp.3879. ⟨10.1080/14786435.2010.499859⟩. ⟨hal-00608030⟩