By J. Friedel, R. Smoluchowski and N. Kurti (Auth.)
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Additional info for Dislocations
I), such a dislocation, where the axis of rotation is, along the dislocation line, has the lowest energy for a given rotation. As with the edge and screw dislocation, the rotation dislocation is assumed to be along the axis of a cylinder of matter of inner and outer radii ro and r\ respectively. With the cylindrical coordinates of Fig. 33 — ν(σ ΓΓ + σ 00 ) other aij = 0. Here, R = (μω)/2π(1 — v), and ω is the rotation of the dislocation. The stored energy is then, per unit length of dislocation, w = i W ^ v ) (*·-'»·> 4ro a ri* ( r i 2 _ ro2,y.
Vacancy loops in quenched graphite (after Amelinckx and Delavignette) (25,000 x ) . FIG. 39. Tetrahedra of stacking faults, bordered by imperfect dislocations, in gold quenched from 930°C and aged 1 hr at 100°C (after Silcox and Hirsch, 1959) (166,500 χ ) . FIG. 40. Helicoidal dislocations in quenched AlCu (after Thomas and Whelan, 1959) (29,000 χ ) . (a) (b) F I G . 41. Dislocations observed in silicon by X-rays in transmission (after L a n g , 1959). a. and b . correspond to two different Bragg reflections, and show dislocations of different slip systems.
It will apply to homogeneous elastic bodies, submitted to no external forces, and large enough to be treated as infinite. We follow Seeger's presentation (1961). 1. The tensor of dislocation density (Nye, 1953; Bilby, 1955; cf. Eshelby, 1956; Kröner, 1958; Bilby, 1960; deWit, 1960; Seeger, 1961) Let us define the internal stresses as those stresses that remain in an elastic body when all the externally applied stresses are removed. It is obvious that such stresses cannot arise if the displacements are continuous and can be differentiated everywhere in the body.