Continuous Distributions of Dislocations: Surface Dislocations and the Crystallography of Martensitic Transformations

Some results of the theory of plane surface dislocations required for the analysis of martensite crystallography are derived. In their subsequent application, the surface dislocation forming the boundary between the phases is assumed to correspond to one parallel array of like dislocations of arbitrary Burgers vector moving in an arbitrary plane, and the Burgers vector and plane are assumed given. It is also assumed that the relative pure lattice strain of the phases is quite general, and given. Using these data, the theory is applied to deduce the habit plane, shape deformation and orientation relationship occurring. The relative shape deformation is an invariant plane strain. The method enables the effect of different assumptions about the Burgers vector, plane of motion, and lattice pure strain to be easily examined. The method is compared with other treatments to which it is essentially equivalent. The use of the surface dislocation theory, however, simplifies some of the analysis. The relation of the method to analyses assuming a finely twinned product is also discussed.