The fractal nature of gliding dislocation lines

• Published in: Scripta metallurgica et materialia 1991-02, Vol.25 (2), p.355-360
• Main Authors: Sevillano, J.Gil, Bouchaud, E., Kubin, L.P.
• Format: Article
• Language: English
• ISSN: 0956-716X
• DOI: 10.1016/0956-716X(91)90192-4

The motion of a dislocation line gliding through a random planar array of point obstacles is a classical problem in dislocation theory. The observation of simulated shapes published in the literature strongly suggests that the gliding line has a fractal nature. In such conditions, the yield stress, which is essentially a percolation threshold at microscopic scale, may be associated with a fractal dimension of the microstructure. The measurement of the fractal dimension of simulated dislocation lines and on its dependence on the strength of the point obstacles are reported. These results are discussed by analogy with a few equivalent physical systems involving both percolation and a fractal structure. A possible extension to dislocation cell structures is suggested by measurements of the fractal dimension of the dislocation microstructure in heavily cold-rolled Cu. Three conclusions are drawn. A dislocation line gliding past an array of randomly distributed point obstacles has a fractal geometry with a dimension which depends on the obstacle strength and of maximum value 1.33. The spreading of glide on a slip plane is a particular case of invasion percolation. It seems possible to attribute a fractal dimension to two- or three-dimensional dislocation structures when they are not in equilibrium, and an Euclidean dimension at equilibrium or close to steady state. Graphs. 18 ref.--J.H.