Transformation and misfit dislocations are used to describe the motion of glissile interfaces with one set of misfit dislocations in the framework of the Frank-Bilby equation. The sweep of these glissile interfaces brings about an invariant-plane-strain type shape deformation. Our approach explains the glissile motion of martensitic interfaces and small-angle symmetrical tilt grain boundaries. It is consistent with the phenomenological theory of martensite crystallography but more flexible.
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