Twinning modes in lattices

Abstract

Deformation twinning is an important contributory factor in the plastic deformation of crystalline materials. The macroscopic shape deformation associated with deformation twinning is a simple shear, and in this paper the generalized theory of twinning shears developed in an earlier paper (Bevis & Crocker 1968), is applied to specific lattices and the resulting twinning modes described. Examples of all seven different classes of twinning mode, five of which do not satisfy the classical orientation relations of deformation twinning are first examined for the special case of cubic lattices. Relations between modes in the seven crystal systems which arise from variants of the unit correspondence matrix are then investigated. These modes are all conventional in character, but, when this procedure is repeated for a more complex correspondence matrix, most of the resulting modes are non-conventional, having four irrational twinning elements. The orientation relations associated with several of these modes are discussed in detail. Although the modes presented have been chosen specifically to illustrate pertinent features of the theory, many of them are shown to be the operative deformation twinning modes in metals and other crystalline materials. Finally the physical significance of the component correspondence and rotation matrices, into which a twinning shear is formally resolved in the theory, is discussed and extensions of the analysis, which enable transformation shears in lattices to be studied, are briefly considered.