The stress-fields around groups of dislocations in face-centred cubic metals

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Abstract
The various components of the stress-fields of piled-up groups of screw and edge dislocations are calculated by replacing the array of discrete dislocations by a continuous distribution. The stress-fields are resolved onto each of the eleven secondary systems of the face-centred cubic lattice; by mapping out the stress-fields, it is shown that secondary slip can occur in the localized region at the head of the pile-up. This secondary slip modifies the stress-field of the pile-up and gives rise to dislocation tangles containing a high density of forest dislocations. The amount of secondary slip depends on the sum of the resolved applied stress on each secondary system and the resolved stress from the pile-up, so that the amount of secondary slip is orientation dependent. In addition, latent hardening of the secondary systems, such as occurs in alloy crystals, can be taken into account and it is shown that secondary slip near a pile-up is inhibited by latent hardening. The calculations are discussed in terms of theories of work-hardening.