Mechanical twins, their development and growth

Mechanical or deformation twinning is first explained as a shearing mechanism and compared to crystallographic slip. Then twinning in several metals is discussed. A twin can be represented as a thin layer, bound by an upper and lower plane. The average width of a disk-shaped twin is either given by the average diameter of a microregion (grain) or is calculated in the case of twin nuclei. An energy balance is outlined in detail for the untwinned and twinned status of a representative volume element. The elastic strain energy due to the twinning shear eigenstrain is studied in detail both analytically and numerically. An energy criterion for the stability of equilibrium allows to formulate a twinning condition which yields a minimum thickness in the case of a deformation twin. In the case of a twin nucleus Onsagerʹs principle of maximum dissipation rate is engaged as a further criterion to find the dimensions of the twin nucleus. Comparisons with experimentally observed twins in TiAl intermetallics are reported finally. Further consequences of the study are listed, such as the estimation of the critical resolved shear stress for twinning.