Abstract
The three most important deformation systems in metals and alloys are (i) slip, (ii) twinning and (iii) transformation to product phases labelled martensite by the motion of an invariant interface. The physical and geometric criteria for slip and twin-ning to occur now appear to be well established and satisfied by the majority of observations. The situation regarding martensitic transformations is less satisfactory, however, and an increasing amount of evidence over recent years suggested the inadequacy of the standard theories first published over fifteen years ago. Recent detailed evidence for iron alloys, especially, indicated realistic ways to extend these theories and the major part of the thesis introduces a resulting generalized, essentially geometric treatment of martensite crystallography which is applied in detail to transformations in iron and titanium alloys. The transformation phenomena of deformation twinning and martensite are closely related but no single theory encompassing both has been published. An elegant general theory is therefore presented, which covers both types of transformation as degenerate cases. In addition, a further degeneracy enables the examination of strain-related lattices to be conducted for the first time. The martensite degeneracy is identical to the previous generalized theory and its inherent algebraic sophistication complements in a very satisfactory manner the geometrical emphasis of the former treatment. The occurrence of single and multiple homogeneous invariant plane strains and the use of matrix algebra to describe them, is common to the plane plastic strain deformation of crystals treated and discussed as the final topic. Although susceptible to an approach similar to that involved in the other transformation phenomena, a homogeneous plastic strain approach is adopted for preference and the permissible crystal orientations for multiple slip obtained. The results are directly applicable to the plastic bending of crystals.