Self-consistent method applied to quasi-rate-independent polycrystals

Geometric and kinematic aspects of intragranular, as well as intergranular plastic deformation of polycrystals, are discussed. Elastic strain is covered by the effective field homogenization method inside a representative volume element (RVE). Evolution equation formed by tensor representation having incremental form is postulated to model inelastic metals. The rate dependence takes place by means of stress rate-dependent value of the initial yield stress. Extending concept of Zorawski [private commun., 1974] deformation geometry is based on constrained micro and free macro rotations in intermediate reference configuration. This has as a consequence that evolution equation for plastic spin of RVE is an outcome of evolution equation for plastic stretching. The macroscopic evolution equation is based on the Vakulenko's concept of thermodynamic time [Izv. AN SSSR Mekhanika Tverdogo Tela 1 69 (1970)]. Eshelby 4-tensor [Proc. R. Soc. A 241 376 (1957)] is determined numerically taking account of cubic anisotropy and the theory is applied to slightly disordered fcc polycrystals. For some characteristic-given stress histories (leading to low., medium and high strain rates) number of active slip systems for RVE with 125 grains are found and compared with the so-called J2-approach.