Constrained glide and interaction of bowed-out screw dislocations in confined channels

Abstract

In the present work, a particular case of constrained dislocation glide that is typical of deformation in small volumes as, for example, in thin films was studied. The specific problem addressed concerns the glide and interaction of two unlike screw dislocations bowing out in constrained channels on parallel glide planes. The situation described corresponds not only to thin film deformation but also to the constrained glide of dislocations in the channels between the dislocation walls in persistent slip bands (PSBs) in fatigued metals. The main objective of the study was to determine the flow stress and to assess in an analytic approximation how the contributions of the dipolar interaction stress and of the bowing stress which both vary in space superimpose. It was argued that the dipolar interaction between the two dislocations is overcome by ‘bowing-out’ and not by separation of the aligned dislocation dipole ‘at constant shape’. A general conclusion of the numerical analysis is that, aside from one trivial irrelevant case, the resulting flow stress is never a simple linear sum of the Orowan bowing stress and the dipole passing stress. Rather, the flow stress is always governed by the stronger of the two interactions and is, typically, at most ca. 20% larger than either the Orowan stress or the dipole passing stress, depending on which of the two is larger. The numerical results are discussed briefly with respect to an idealized example of dislocation glide in thin films and in more detail with regard to dislocation glide in the channels of PSBs. In the latter case, the present results match nicely with the interpretation of the cyclic flow stress of PSBs in terms of the so-called composite model which considers explicitly the weighted contributions of the local flow stresses in the relatively soft channels and in the harder dislocation walls to the overall stress.

Acknowledgements

One of the authors (H.M.) wishes to express his appreciation to Professor Mick Brown of the Cavendish Laboratory at Cambridge University for enlightening discussions over many years on a variety of topics of plasticity. Sincere thanks are also due to Professor Carl Holste, Technische Universităt Dresden, and two unknown reviewers for helpful comments. The help of Dr Philip Eisenlohr in producing figure 11 is acknowledged gratefully.