Relations between twin and slip in parent lattice due to kinematic compatibility at interfaces

► Tangential continuity of the plastic distortion rate at twin/parent interface. ► Relations between a parent slip system and its transform by twinning shear. ► Admissible twin modes in hcp crystals whether slip is along 〈a〉 or 〈c+a〉. The relationships between a slip system in the parent lattice and its transform by twinning shear are considered in regards to tangential continuity conditions on the plastic distortion rate at twin/parent interface. These conditions are required at coherent interfaces like twin boundaries, which can be assigned zero surface-dislocation content. For two adjacent crystals undergoing single slip, relations between plastic slip rates, slip directions and glide planes are accordingly deduced. The fulfillment of these conditions is investigated in hexagonal lattices at the onset of twinning in a single slip deforming parent crystal. It is found that combinations of slip system and twin variant verifying the tangential continuity of the plastic distortion rate always exist. In all cases, the Burgers vector belongs to the interface. Certain twin modes are only admissible when slip occurs along an 〈a〉 direction of the hexagonal lattice, and some others only with a 〈c+a〉 slip. These predictions are in agreement with EBSD orientation measurements in commercially pure Ti sheets after plane strain compression.