A mathematical model for deformation of bcc single crystals taking into consideration the twinning mechanism

The paper is concerned with modeling of the elastoviscoplastic deformation of bcc single crystals. Dislocation slip and twinning are mechanisms for plastic deformation. Due to the dislocation nature of twinning, it can be treated as slip. To solve the nonlinear programming problems, numerical algorithms are used. The procedures of identification and verification of the model parameters are described in detail. The evolution relationships of the critical shear stress and twinning allow us to obtain acceptable quantitative agreement between the simulation and experimental results. The implementation of the model is carried out using the developed numerical algorithms and programs. The results of simulations of the stress-strain state of α-iron and tantalum single-crystals in uniaxial loading are shown for different lattice orientations relative to the loading axis.