The role of slip and twinning in the deformation behaviour of polysynthetically twinned crystals of TiAl: A micromechanical model

An energy approach to the formation of twins in TiAl

“…As a direct consequence of Eq. [16] and the assumed uniformity of C ijkl , we obtain [17] in which ⌬⌺ ij is associated with the external load drop which can also be observed experimentally, e.g., as reported for zinc crystals by Bell and Cahn [25] and Mügschl and Stüwe. [26] The stress state after the twin formation consists of three contributions: [18] A direct consequence of Eq.…”

“…Marketz et al [15,16,18] and Schlögl and Fischer [17] have presented the most advanced formulation of twinning applied to both polysynthetically twinned single crystals and polycrystalline ␥(TiAl)-based alloys with a neargamma microstructure. They consider four twin systems (1/6 Ͻ 11 ]{111}) as a unilateral slip and a given amount of shear (␥ t ϭ /2) with the volume fraction of the twin system as an internal variable.…”

“…If external displacements are assumed to be momentarily fixed, then twinning leads to a sudden drop in the macroscopic resolved shear stress, , according to Eq. [17], by the amount [30] One may compare the change in energy (Eq. [24]) with that used in the literature as the starting relation for a twinning condition (e.g., the extensive review by Christian and Mahajan, [3] Section 4.1).…”

Thermomechanical modelling of polysynthetically twinned TiAl crystals

“…In some previously reported models, the Hall-Petch relation Equation (1) is considered by precalculating the critical resolved shear stresses τ Y 0 (λ L , λ D ) as a temperatureindependent input for the simulations [26,28,29]. This approach is suitable for a homogeneous temperature field, but not sufficient in a fully coupled thermomechanical analysis.…”

“…Other authors model the micromechanical deformation in the lamellar compound as detailed as possible by developing representative volume elements (RVEs) of a single lamellar colony, e.g. [23][24][25][26][27][28][29].…”